INTEGRATION OF CORE AND WIRELINE DATA FOR THE

Akademia Górniczo-Hutnicza im. Stanisława Staszica
Wydział Geologii, Geofizyki i Ochrony Środowiska
Katedra Geofizyki
AGH University of Science and Technology
Faculty of Geology, Geophysics and Environment Protection
Department of Geophysics
ROZPRAWA DOKTORSKA
DISSERTATION
KOMPLEKSOWA CHARAKTERYSTYKA WŁASNOŚCI
ZBIORNIKOWYCH DLA MODELOWANIA PRZEPŁYWU
MEDIÓW W ZŁOŻU GAZU ZIEMNEGO Z
W ZAPADLISKU PRZEDKARPACKIM
INTEGRATED RESERVOIR CHARACTERIZATION FOR
FLUID FLOW MODELING OF THE Z GAS DEPOSIT
AT THE CARPATHIAN FOREDEEP
M.Sc. MAN HA QUANG
Hanoi University of Mining and Geology, Vietnam
Promotor/Supervisor: PROF. DR HAB. INŻ. JADWIGA JARZYNA
KRAKÓW, 2011
ABSTRACT
The purpose of this study was to use many statistical and geostatistical methods to integrate
data of various scales: starting from microscopic scale (core plugs) through mesoscopic scale
(logs) to megascopic (seismic) for improved reservoir characterization and reservoir modeling
in order to generate a reliable geological model which was then used for dynamic simulation.
This case study was performed for the Z gas reservoir depositional environment, of very
complicated deltaic facies distribution which belongs to a group of the Miocene gas reservoirs
in the northern-eastern part of the Carpathian Foredeep of Poland.
The Hydraulic Flow Unit (HU) method was used to subdivide the reservoir into hydraulic
flow units on the basis of conventional core data and conventional statistical methods. Two
statistical approaches, namely Alternating Conditional Expectation (ACE) and Linear
Multiple Regression (LMR) were applied to predict HU_log from core and log data. Since
there is no rock type (RT) descriptive data available in the study area, unsupervised K means
clustering was used for RT classification based on log data.
Building static geological model both deterministic and stochastic geostatistical methods
including Unsupervised Neural Network (UNN), Sequential Indicator Simulation (SIS), and
Sequence Gaussian Simulation (SGS) were used to integrate 2D seismic and log data to
perform static model. The innovative approach of the methodology developed and
demonstrated in this study was building the pseudo 3D seismic cube from all available 2D
seismic lines which were used as conditional data for hydraulic flow unit modeling. In order
to verify the static geological model, history matching was performed constrained by the
hydraulic flow unit distribution in the reservoir.
The study has shown that even without 3D seismic and with limited well log control, the new
hydraulic flow unit method can be used successfully to integrate reservoir data from different
domains and from a wide range of scales. The resulting robust 3D property model can be
validated by history matching. This methodology can be usefully extended to the upper part of
the study area or other hydrocarbon reservoirs in Poland where dense networks of 2D seismic
data are commonly available.
i
SUMMARY IN POLISH
Geologiczna, petrofizyczna i geofizyczna charakterystyka złoża węglowodorów jest cennym
źródłem informacji dla zrozumienia procesów zachodzących w formacji skalnej podczas
eksploatacji. Przedstawienie wzajemnych relacji między porowatością efektywną i
przepuszczalnością oraz zaileniem z uwzględnienie facjalnych zmian w trójwymiarowym
ośrodku skalnym jest znakomitym ułatwieniem analizy procesów przepływu mediów w złożu.
Szybki rozwój metod matematycznych i technik informatycznych oraz specjalistycznego
oprogramowania stosowanego w modelowniach geofizycznych i geologicznych oraz inżynierii
złożowej znacznie ułatwił parametryzację i opis procesów geologicznych niezbędnych przy
poszukiwaniu i eksploatacji złóż węglowodorów. Wymusił także konieczność przedstawienia w
postaci wzorów związków pomiędzy opisywanymi wielkościami. Do tego celu bardzo
przydatne okazały się procedury geostatystyczne oraz sieci neuronowe pozwalające powiązać
koncepcje geologiczne ze ścisłą, liczbową charakterystyką procesów.
W pracy przedstawiono charakterystykę petrofizyczną i geofizyczną wybranego złoża gazu w
zapadlisku przedkarpackim oraz zaproponowano podejście geostatystyczne do modelowania
facji sejsmicznych oraz modelowania procesu przepływu mediów w złożu gazu w przypadku
ograniczonej liczby danych. Celem pracy było połączenie danych geologiczno-geofizycznych
pochodzących z różnych źródeł: punktowych wyników badań laboratoryjnych (skala mikro),
jednowymiarowych danych geofizyki otworowej (skala mili) oraz sejsmiki 2D (skala makro)
dla udokładnienia opisu złoża gazu oraz dla utworzenia poprawnego statycznego,
trójwymiarowego modelu złoża w celu wykonania modelowania przepływu. Końcowym
efektem pracy było sprawdzenie wyników symulacji przepływów z danymi otworowymi
uzyskanymi podczas produkcji.
Wykorzystane procedury wymagały spełnienia następujących warunków:

dostępność danych i oprogramowania oraz efektywność finansowa,

możliwość obliczenia wskaźników Flow Zone Index, FZI, oraz podziału obszaru złoża
na jednostki hydrauliczne, HU,

dysponowanie danymi sejsmicznymi 2D (jeśli byłyby dostępne dane sejsmiczne 3D
wyniki będą dokładniejsze),
ii

dostęp do danych umożliwiających poprawne skalowanie modeli statycznych i
dynamicznych od poziomu mikro do skali makro,

sprawdzenie
poprawności
wyników
na
podstawie
historycznych
danych
eksploatacyjnych.
Kolejne kroki wykonane w pracy są przedstawione na diagramie (Fig. 1.1). Diagram ten może
być podstawą organizacji podobnych prac przy spełnieniu warunków wymienionych powyżej.
Praca doktorska składa się z 7. rozdziałów.
Pierwszy rozdział stanowi wprowadzenie do tematu konstrukcji statycznego i dynamicznego
modelu ośrodka skalnego w warunkach ograniczonej dostępności danych. Zawiera również
krótki opis treści pozostałych rozdziałów.
W rozdziale 2. przedstawiono zarys budowy geologicznej złoża gazu ziemnego Z w
zapadlisku przedkarpackim. Złoże należy do typowych wielowarstwowych nagromadzeń
gazu ziemnego w utworach sarmatu w północno-wschodniej części zapadliska. Do prac
modelowych wybrano fragment cienkowarstwowej formacji piaskowcowo-mułowcowoiłowcowej,
powstały w warunkach
sedymentacji
deltowej.
Zwrócono uwagę na
skomplikowany charakter utworów zbiornikowych i pokazano, że cechy obserwowane na
anomaliach geofizyki otworowej oraz widoczne na przekrojach sejsmicznych (amplitud oraz
innych atrybutów) wskazują na określone warunki sedymentacji.
W rozdziale 3. przedstawiono koncepcję konstrukcji jednostek o jednakowych zdolnościach
do przepływu (Hydraulic Units, HU) na podstawie parametru Flow Zone Index, FZI,
wyznaczonego tylko na podstawie porowatości i przepuszczalności. FZI oraz HU zostały
wyznaczone na podstawie wyników badań laboratoryjnych dostępnych w 10. otworach na
złożu gazu Z (560 analiz).
W rozdziale 4. omówiono wyniki połączenia danych laboratoryjnych i profilowań geofizyki
otworowej w celu utworzenia jednowymiarowych modeli zmian HU w profilach otworów. W
tym celu zastosowano regresję wielowymiarową, Linear Multiple Regression, LMR, oraz
metodę Alternating Conditional Expectation, ACE. Nie dysponowano geologicznym opisem
facji w interwałach, z których pobrano rdzenie, zatem zastosowano statystyczną metodę K
mean do wydzielenia charakterystycznych warstw w badanej formacji, czyli wyznaczenia
Rock Types. Uzyskane wyniki podziału mioceńskiej formacji cienkowarstwowej na 6 typów
iii
skalnych (litofacji), RT, okazały się spójne z wynikami uzyskanymi wcześniej na drodze
wykorzystania ACE do przeniesienia rozkładu HU na pełne profile geologiczne w badanych
otworach.
W rozdziale 5 opisano sposób wyznaczenia statycznego, trójwymiarowego modelu ośrodka
skalnego na bazie wcześniejszych wyników oraz 25 profili sejsmicznych 2D. Do połączenia
wyników profilowań geofizyki otworowej i danych sejsmicznych wykorzystano metody
deterministyczne, Unsupervised Neural Network, UNN, oraz geostatystyczne, Sequential
Indicator Simulation, SIS, i Sequence Gaussian Simulation, SGS. Zastosowano innowacyjne
przejście od danych sejsmicznych 2D do modelu trójwymiarowego (Pseudo 3D Seismic
Cube). Następnie wykorzystano trójwymiarowy rozkład facji sejsmicznych w połączeniu z
litofacjami, RT, wyznaczonymi wcześniej na podstawie geofizyki otworowej do utworzenia
trójwymiarowego modelu jednostek przepływu, HU. W celu udokładnienia informacji
pozyskiwanej na podstawie danych o zróżnicowanej pionowej rozdzielczości podczas
tworzenia trójwymiarowego modelu statycznego wprowadzono dodatkowo więzy oparte na
wielkości stosunku Net to Gross. Ostatecznym sprawdzianem poprawności przygotowanego
modelu było porównanie wartości współczynnika przepuszczalności wyznaczonego w
jednostkach jednakowego przepływu w modelu, K_HU i wartości przepuszczalności
wyznaczonych na podstawie danych laboratoryjnych i geofizyki otworowej, K_log.
W
rozdziale
6
przeprowadzono
modelowanie
przepływu
gazu
na
podstawie
trójwymiarowego modelu opracowanego w rozdziale 5. Jako weryfikację poprawności
modelowania zastosowano historyczne dane produkcyjne w 3. otworach na badanym obszarze
złoża Z. Zastosowanie jednostek jednakowego przepływu okazało się skuteczne pod wieloma
względami - i: uzyskano bardzo dobre korelacje między porowatością i przepuszczalnością w
jednostkach HU, ii: dzięki użyciu HU możliwe było zredukowanie obliczeń w programie
Eclipse do jedynie tych jednostek, które miały wysoki współczynnik FZI, czyli dużą
porowatość i przepuszczalność oraz wysoki stosunek NTG, iii: funkcja kompakcji była
dobrze dopasowana do modelu porowatości w każdej jednostce HU.
W rozdziale 7 podsumowano wykonane prace oraz podkreślono innowacyjne aspekty
modelowania statycznego – tworzenia trójwymiarowego ośrodka geologicznego z podziałem
na jednostki HU oraz dynamicznego dla obliczenia przepływu mediów. Zwrócono uwagę na
celowość proponowanego połączenia danych laboratoryjnych i geofizyki otworowej poprzez
iv
wyliczanie parametrów FZI oraz HU. Włączenie do obliczeń jednostek litologicznych (Rock
Types) wyznaczonych na podstawie geofizyki otworowej stanowi dodatkowy element
skalowania danych i przejścia od wartości punktowych do ciągłej informacji wzdłuż osi
otworu. Włączenie danych sejsmicznych 2D, dzięki wykorzystaniu metod geostatystycznych i
deterministycznych do konstrukcji facji sejsmicznych, pozwoliło na utworzenie statycznego
modelu trójwymiarowego (Pseudo 3D Seismic Cube). Obliczenie porowatości i
przepuszczalności w trójwymiarowym modelu statycznym zostało dodatkowo uzupełnione
informacją na temat Net to Gross. Wyniki modelowania przepływów zostały zweryfikowane
na podstawie danych historycznych.
Ocena niepewności uzyskanych wyników jest najtrudniejszym do wykonania elementem
przedstawionego schematu postępowania, zalecanego do wykorzystania w obszarach, gdzie
do dyspozycji pozostaje ograniczona liczba danych geofizycznych i geologicznych.
Stosowanie metod statystycznych i geostatystycznych powoduje konieczność wykorzystania
dużej ilości danych laboratoryjnych dla uzyskania wiarogodnych wartości średnich i odchyleń
standardowych porowatości i przepuszczalności. Stosowanie procedur statystycznych w
modelowniach skutkuje brakiem powtarzalności przy powtarzaniu obliczeń, a nie
uwzględnienie szczegółowych informacji o elementach tektonicznych w badanym obszarze z
powodu
niepełnych
danych
geologicznych
powoduje
ograniczenie
wiarogodności
ostatecznych wyników modelowani. Ograniczenie wiarogodności predykcji zachowania złoża
w przyszłości wynika z braku historycznych danych z długiego okresu produkcji złoża.
Zatem, ograniczona wiarogodność uzyskanych wyników wynika z ograniczeń zastosowanych
metod i dostępu do danych.
v
ACKNOWLEDGMENTS
I would like to take this opportunity to thank all the family and friends who have helped and
inspired me during my doctoral study!
I would like to express my sincere thanks to Prof. dr Jadwiga Jarzyna, who patiently
supervised the progress of my work and it is for her patient supervision, useful advice and
discussions that led to the completion of this project. Many thanks also go to Prof. Le Hai An
for his helpful counsels and arguments.
I owe my deepest gratitude to the Rector of AGH University of Science and Technology,
Cracow, Poland for granting me the scholarship and also Hanoi University of Mining and
Geology for their support to my accomplishing this study. I am grateful to Prof. Jacek
Matyszkiewicz, the Dean of the Faculty of Geology Geophysics and Environmental
Protection AGH UST, Cracow, Poland.
My special thanks to the Polish Oil and Gas Company Ltd., Warsaw, Poland for the
permission to use the data. Petrel®, Eclipse®, Interactive Petrophysics® were used thanks to
the university’s grant donation by Schlumberger to AGH UST. STATISTICA software was
used thanks to AGH UST, Cracow, Poland license.
I am also grateful to dr Jerzy Ziętek and his family, Ms. Maria Cicha and all of staff in
Geophysics Department for helping me to adopt myself into Polish life style and other official
matter. Without their helps this project would not have been completed.
Thanks also go to Mr. Graham Dryden from Subsurface Consultants & Associates, Houston,
USA for help with the English corrections and also helpful discussions.
A special thanks to many of the students at AGH University. In particular, thanks to Wojciech
Machowski, Michał Michna, Paulina Krakowska for the friendship we have developed. Also
thank to all my Vietnamese friends in Cracow for their invaluable support and consideration
during my stay here.
I would like to thank my dear parents, parents-in-law and my brothers, sisters for their
encouragement and support during the last 4 years when I was absent from home. Finally, I
am deeply indebted to my dear wife Thu and daughter Minh Hằng for their love and their
encouragement to my course-choosing and study.
vi
DEDICATION
This thesis is dedicated to my Grandparents, my Parents, my Parents-in-law,
my wife Thu and my daughter Minh Hằng
vii
TABLE OF CONTENTS
ABSTRACT…………………………………………………………………………………….i
SUMMARY IN POLISH……………………………………………………………………....ii
ACKNOWLEDGMENTS……………………………………………………………….........vi
DEDICATION…………………………………………………………………………...….. vii
Chapter 1……………………………………………………………………………………...1
INTRODUCTION
Chapter 2
GEOLOGICAL SETTING
2.1 Introduction to the geology and tectonic framework of the study area…………………….5
2.2 Lithology and sedimentological environment…………………………….………………10
2.3 Core Analysis……………………………………………………………………………..13
2.4 Relationship between reservoir parameters and sedimentary environment………………17
2.5 Organization of succession, its division and correlation diagram……………...………...20
2.6 Conclusions……………………………………………………………………….………28
Chapter 3
HYDRAULIC FLOW UNIT
3.1 Concept of Hydraulic Flow Unit……………………………….…………………………29
3.2 Hydraulic Flow Unit classification technique…………………………………………….35
3.2.1 Histogram……………………………………………………………….….…..36
3.2.2 Probability plot………………………………………………………….……...38
3.2.3 Ward's algorithm approach…………………………………………….…….....39
3.3 Critical review on determining HU in the Lower Miocene reservoir of Z gas field……..40
3.3.1 Preliminary outcomes…………………………………..………………...…….40
3.3.2 Global Hydraulic Elements………………….…………………………..……..41
3.4 Conclusions……………………………………………………………………………….46
viii
Chapter 4
CORE – LOG INTEGRATION
4.1 Core - log depth matching…………………………………………...……………………47
4.2 Hydraulic flow unit prediction…………………………………………………….……...50
4.2.1 Methodology……………………………………………………………..…......50
4.2.2 Flow Zone Indicator prediction………………………………………….……..52
4.2.2.1 Linear Multiple Regression (LMR)…………………………….…….52
4.2.2.2 Alternating Conditional Expectations algorithm (ACE)…….….…….56
4.2.2.3 Comparison of LMR and ACE algorithm…………………….………59
4.2.3 Hydraulic Flow Unit Prediction (HU_log) from FZI_pre_ACE……..….……..60
4.2.4. Validation of results………………………………………..………………..…63
4.3 Rock types classification………………………………………………………..…….…..66
4.3.1 K means clustering background ………………………………………..……….66
4.3.2 Applying K means for the data group 3 (G3: Z-76, Z-81, Z-82)……….………69
4.4 Relationship between Hydraulic Flow Unit (HU) and Rock Types (RT)……...…………69
4.5 Conclusions…………………………………………………………………………….…77
Chapter 5
STATIC MODELING
5.1 Reservoir modeling overview………………………………………………….…………79
5.1.1 Reservoir modeling workflow……………………………………….………...…79
5.1.2 Deltaic facies and spatial relationship………………………………..…….…….80
5.1.3 Geostatistical methods overview…………….…………………..….………...….83
5.2 Structure modeling……………………………………………………………….……….86
5.2.1 Miss-tie correction for 2D seismic survey…………………………..……….…...87
5.2.2 Horizons picking and 3D grid…………………………………….….………......87
ix
5.3 Rock Type and Hydraulic Flow Unit Modeling…………….……………..……………..91
5.3.1 Convert 2D seismic to pseudo 3D seismic……………………….…….……...…93
5.3.2 Rock Type modeling constrained by seismic facies model…………………..….96
5.3.2.1 Seismic facies extraction volume…………………………………….96
5.3.2.2 Seismic facies classification………………………….……………...100
5.3.2.3 Rock Type modeling………………………………..………..……...104
5.3.3 Hydraulic Flow Unit modeling constrained by Rock Type model..….……...….107
5.4 Properties modeling constrained by HU model………………………………..………..112
5.4.1 Porosity and permeability modeling……………………………….…………....112
5.4.2 Water saturation and Net to Gross modeling………………………………...….116
5.5 Conclusions……………………………………………………………………….……..120
Chapter 6
HISTORY MATCHING UNDER HYDRAULIC FLOW UNIT CONTROL
6.1. History matching under Hydraulic Flow Unit control………………………………….123
6.1.1 History Matching Overview……………………………………..……….……..123
6.1.2 History matching under Hydraulic Flow Unit control………………….…..…..125
6.2. Upscaling...…………………….……………………………………………...…….….129
6.3. Reservoir initial condition………………………………………………………………134
6.4 History matching and discussions……………………………………………………….137
6.4.1 Results…………………………………………………………………..………137
6.4.2 Discussion……………………………………………………………..………..138
6.5 Conclusions……………………………………………………………………………...143
Chapter 7
CONCLUSIONS AND RECOMMENDATIONS
7.1 Conclusions…………………………………………………………………………...…144
7.2 Recommendations……………………………………………………………………….147
x
REFERENCES.......................................................................................................................151
LIST OF FIGURES AND TABLES………………………………………………….....…..158
LIST OF ABBREVIATIONS…………………………………………….…………...…….168
APPENDIX A…………………………………………………………………….…………169
xi
Chapter 1
INTRODUCTION
In the upstream petroleum industry, reservoir characterization and description plays an
important role giving geologists and geophysicist a more accurate and detailed
understanding of the subsurface reservoirs. Understanding key reservoir properties such as
porosity, permeability, their relationship as well as their spatial distribution by having
precise and realistic reservoir model, assists petroleum engineers in improving the
characterization of the reservoir, and to enhance the development and performance of the
reservoir throughout its life.
In recent years, with the robust development of the mathematics and computer science such as
modeling, geostatistics, and neural networks, geological ideas have become easier to realize
and be verified, especially with the advanced tools available through specialized software in
the petroleum industry like Schlumberger Petrel and Eclipse. The need to bring the latest
developments to the petroleum industry has led to one of the major motivations of this study.
This thesis looks at various aspects of reservoir characterization and modeling where the
geological and geophysical data available is rather limited. The aim of this thesis is to
integrate G&G data from diverse disciplines; from core plugs through wireline logs to
seismic. To this aim we develop suitable methodologies for improved reservoir
characterization and reservoir modeling with rather limited data (mainly 2D seismic available)
in order to generate a reliable geological model which was then used for dynamic simulation.
On top of that, this study has successfully verified a recently emerged Hydraulic Flow Unit
approach in various scales from micro scale of the core plug to mega scale of the seismic
within a constraint of dynamic data through history matching processes.
The methodologies developed in this study were designed to be:

reliabile and cost-effective,

applicable to rocktyping by mean of hydraulic flow unit in reservoir characterization,

applicable to dealing with limited data availability, especially where no 3D seismic
data available,
1

applicable and reliable in upscaling from micro to mega scale in the framework of
geological reservoir modeling constrained by dynamic data.
The workflow, which while by no means universally applicable, illustrates a practical
approach to handling sparse data in a deltaic environment gas reservoir. The workflow was
used throughout the course of this study, and is summarized in figure 1.1.
Core, Logs
2D Seismic
Production
Qg, BHP,
PVT,…
FZI_core
FZI_log
K-mean
Clustering
Pseudo 3D
Seismic
HFU_core
HFU_log
RT_log
3D
Seismic
Structure
Facies
3D Rock Type
Modeling
3D HFU
Modeling
Dynamic
Modeling
History
Matching
3D Properties
Modeling (PHI, K)
Fig. 1.1 The main workflow in this study for integration of static and dynamic models
The rest of the thesis consists of 6 further chapters.
Chapter 2 reviews the geological setting, including geology, tectonic framework, lithology
and sedimentological environment of the Z gas deposit belonging to a group of Miocene gas
reservoirs in the northern part of the Carpathian Foredeep of. This chapter also addresses the
relationship between reservoir parameters and deltaic sedimentary environment due to the
complexity of the structure of the Miocene (Sarmatian) succession in study area.
2
Chapter 3 introduces the concept of the hydraulic flow unit (HU) and applies this
approach to determine HU throughout the field based on conventional core data and
conventional statistical methods. The results show that using all available 570 core plugs
from the study area resulted in a reliable model of 6HUs. These were consequently used
for the reservoir simulation.
Chapter 4 discusses the application of two statistical approaches, namely Alternating
Conditional Expectation (ACE) and Linear Multiple Regression (LMR), which were applied
to predict hydraulic flow units (HU_log) from cores and logs. Since there is no rock type (RT)
descriptive data available in the study area, unsupervised K means clustering was used for
facies classification based on log data. The results demonstrate that statistical methods are
useful, flexible, and effective, and that they delivered acceptable results. Unsupervised K
means clustering is effective for classifying six rock types. The ACE method is good for
predicting FZI from core and log.
Chapter 5 proposes an appropriate approach in building static geological modeling for the
reservoir in study area. Both deterministic and stochastic geostatistical methods including
Unsupervised Neural Network (UNN), Sequential Indicator Simulation (SIS), and Sequence
Gaussian Simulation (SGS) were used to integrate 2D seismic and log data to perform static
modeling. The innovative approach of the methodology developed and demonstrated in this
chapter was building the pseudo 3D seismic cube from all available 2D seismic survey for use
as conditional data for hydraulic flow unit modeling. The derived results show clearly that
there is a good correlation between permeability log (K_log) and 3D permeability model
(K_HU) was and also confirm the advantage of applying the HU approach in this study. Due
to lack of SCAL data for reservoir rock parameters, the 3D NTG model was calculated
directly from 3D HU and it again showed the advantages of HU methods.
In Chapter 6, in order to verify the static geological model built in chapter 5, history
matching was performed constrained by the hydraulic flow unit distribution in the reservoir.
Some recent accomplishments in jointly integrating static and dynamic information into a
reservoir flow simulation model and history matching were reviewed. History matching was
tested by manually adjusting a few reservoir model parameters through a trial-and-error
procedure. Manual history matching was performed by running the simulator over the static
3D reservoir model for the historical production period, and then the results were compared
3
with known field performance. The history matching results of three cases from 3 wells (Z74,
Z75 and Z76) showed good results for gas flow rate for a few years production. As the study
evolved, it became abundantly clear that when comparing the results of the traditional method
(two stages) to the HU method (four stages), there are three distinct advantages of the HU
approach: (i) at each HU we have very good correlation between porosity and permeability
that is good for classification of cells in fluid flow for Eclipse simulation, (ii) from 6HUs
distribution we can easy control NTG model for Eclipse simulation cutting off HU1 with
lower PHI and K while reducing number of cells in the 3D grid to increase CPU processing
speed, and (iii) the rock compaction function can respond to the porosity model (PHI) and
each hydraulic flow unit.
Chapter 7 summaries all of the innovative aspects of the thesis, the conclusions from various
studies in the thesis and gives some recommendations and suggestions for future work that
might benefit the reservoir in the study area.
4
Chapter 2
GEOLOGICAL SETTING
2.1 Introduction to the geology and tectonic framework of the study area
The multi-pay gas field, Z-L, is located in the north-eastern part of the Polish Carpathian
Foredeep (Fig. 2.1). The Carpathian Foredeep is a peripheral molasse sedimentary basin
which has been being overthrust in a northerly direction. The most hydrocarbon prospective
sedimentary section is Miocene age (Karnkowski, 1999). The Miocene sediments can be up
to 3500 m thick in the south part of the Carpathian Foredeep and are thinner in the northern
part (Fig. 2.2).
Fig. 2.1 General overview of the Carpathians and Carpathian Foredeep (Oszczypko, et al., 2006)
Two main geological components are important in the Carpathian Foredeep: first – the
structural Precambrian - Palaezoic unit – constituting the base for the Neogene sediments,
whilst in the Z-L region the unit is comprised of Proterozoic rock. The second structural unit
is formed by the autochtonous Miocene formation including Lower Badenian, Middle
Badenian and Upper Badenian and Lower Sarmatian and Quaternary sediments.
5
Fig. 2.2 Schematic map showing the submarine deposits diversity in the eastern part of the
Carpathian Foredeep (Myśliwiec, 2004)
The Precambrian basement is made of fyllitic Table 2.1 Top of the Precambrian in
shales. The rocks are ductile, with common study area
cracks and fissures, most of which are filled with
Well
Depth [m]
clay minerals or calcite. Also present are thin
Z2
1283
laminae of hard sandstone. In the study area the
Z24
1223
top of the Precambrian was observed in four
Z72
1237
wells as follows in Table 2.1.
Z75
1097
In the Z72 well, the Precambrian formation consists of mudstones of low or moderate
cohesion, fissured and cracked, and moderately to poorly lithified. These beds dip at 45o. In
the Z74 well, the Precambrian rocks comprise mudstones and sandy-mudstones having a
6
wackestone texture. In the D2 well the Precambrian rocks comprise massive mudstones and
claystones. The mudstones sporadically include thin layers of fine-grained sandstone lenses,
and more rarely continuous laminae. Sandstones textures include subarkose or arkose arenites,
and rarely wackestones. The dense network of fissures, fractures and cracks range from closed
to partially-open and are filled with quartz, chlorite and kaolinite. In the Z77 well the
Precambrian rocks comprise claystones and mudstones. The Precambrian formation was also
found in the Ch.D. 1, 2 and 3 wells and in the G.D. 1 and 3 wells.
Generally, the Precambrian succession is covered by the autochtonous Miocene sediments,
but in the southern part of the central element of the Z gas field, in the cores in the Z76 well,
weathered fragile mudstones, claystones and fine grained quartzite sandstones with carbonateclay cement, and calcite cement are found. Organic matter is also present. There is no
paleontological documentation, although by way of analogy with other formations in the
Carpathian Foredeep it was assumed that the sediments are of Paleogene age. In the most
wells in the Carpathian Foredeep the basement is covered by the Badenian and Sarmatian
sediments. To the south of the Z-L gas field there is a zone without the Lower and Middle
Badenian sediments, the so called Rzeszów Iceland. Its northern border coincides with the
southern edge of the central element of the Z-L gas field.
The Miocene formations of the Carpathian Foredeep have many years been divided into the
Lower Badenian sub-evaporitic series, Middle Badenian evaporites, and the Upper Badenian
and Sarmatian supra-evaporitic formations. Newer and more precise stratigraphic studies
slightly modify the age determined for the above-mentioned principal series of sediments
occurring within the Z-L bed. The former divisions are still used, however, because evaporites
are the most important reflecting horizon identified in seismic sections in the foredeep
(Myśliwiec, 2004, 2006a).
The gas field Z-L consists of three components: the eastern component, central component
and western component (Fig. 2.3). To the south there is another gas field, G.D., and to the east
there is the Ch.D. gas field. The studied gas field Z-L and the surrounding fields are formed
on the uplifts of the older base of the Miocene succession (Myśliwiec, 2004, 2006a).
7
Fig. 2.3 Location of Z
gas-field with cored
and logged wells;
tectonic
elements
marked in red (after
Myśliwiec, 2006b and
Myśliwiec et al., 2004)
Lower Badenian
This formation comprises grey-green shales deposited in the outer shelf environment and
green glauconite sandstones from the shallow shelf environment. It has not been thoroughly
explored, because most of the wells were drilled only to the bottom of the Sarmatian.
Sandstones are average in terms of sorting and hardness, but they are fractured. However they
are not important as a reservoir because they are generally of insufficient thickness (Dziadzio
2000). In the Z74 well, the Lower Badenian (Baranów beds) were penetrated from 1199 to
1204 m, in the Z72 well: 1228 to 1237 m, and in the Z77 well: 1215 to 1220 m. According to
core descriptions from the Z72 well, the Baranów beds comprise clay shales and mediumgrained sandstones, medium-sorted, with only slightly rounded grains.
Middle Badenian
In the eastern and southern part of the central element of the Z gas field, the Middle Badenian
comprises anhydrite with clays, salts and calcites, including also epigenetic calcite (Mysliwiec
2004). The anhydrite is about 10 – 25 m thick. In the west central element, the Middle
Badenian comprises hard and massive limestones, with mudstone intercalations. The rocks are
10-15 m thick and are deformed. This evaporite series was formed during the shallowing of
marine environment in which the reservoir rocks were being deposited, and this resulted in its
partial isolation (Oszczypko, 1999). The evaporites in the eastern part of the foredeep are
called the Krzyżanowice formations (Table 2.2) Their age, determined on the basis of
nanoplankton, was established as the top of the Upper Badenian (Olszewska, 1999), thus
8
these formations are not as old as previously thought (Middle Badenian). The thickness of the
evaporites fluctuates around ten meters or so.
Upper Badenian - Lower Sarmatian
The sedimentation associated with the Upper Badenian and Sarmatian subsidence formed
thick shaly-sandy layers, overlaying evaporites or, whenever the latter are absent, lying
directly on the substrate rocks. There are many divisions concerning these formations, but
they are most often called the Machów formations (Table 2.2). In the area of the Z gas field,
these sediments consist of hard shales rarely laminated with fine-grained sandstones and
mudstones. The sediments dip at from 5 to 30o and their thickness increases to the south.
Separating the formations of the Upper Badenian from the Lower Sarmatian is difficult and
usually made on the basis of increased sand content in the Sarmatian formations. In the places
where the Middle Badenian is absent, the Upper Badenian is deposited directly on the
Precambrian basement. The thickness of the Upper Badenian sediments in the central element
of the Z gas field varies from 10-40 m (Z82). The greatest thickness is where the Middle
Badenian is absent.
Sarmatian
The most important and thickest deposits of the autochtonous Miocene are the Sarmatian
sandstones and shales, which are about 1100 m thick in the area of the Z gas field. The
Sarmatian formations are most prospective in the study area because of significant
accumulations of bitumens in the Z-L, G.D., and Ch.D. gas fields. The origin of the
geobodies, was based on sedimentological investigation of cores and dipmeter interpretation
(Documentation of wells: Z75, 79 and 84).
Sedimentary environment studies of the Sarmatian, as well as the studies of the geometry and
the lithology and facies of the geobodies enable us to recognize relationships between the
lithofacies and gas reservoir rocks of Miocene age. These studies also show that the Miocene
sediments form stacks of layers, which vary from very thin (several centimeters thick) up to
10 meters thick. These studies also indicate that these particular sandy bodies are comparable
to those of other Miocene gas deposits. These studies have also contributed to our knowledge
about horizontal and vertical variation in lithology and reservoir properties, and allow us to
predict which sand bodies are likely to be the best gas prone reservoir rocks.
9
Table 2.2 Stratigraphy of the Miocene formation (Rögl, 1996; Martini, 1971)
2.2 Lithology and sedimentological environment
A characteristic feature of the Miocene deposits in the Carpathian Foredeep is the
considerable diversification of facies. Facies changes related to the differentiation of a
sedimentation environment are distinctly visible in the Sarmatian rocks. The depositional
environment strongly influences the reservoir parameters of rocks (Dziadzio et al., 1997). In
terms of their lithology, petrography and particularly facies characteristics, the Miocene
reservoir rocks are extremely diversified. It occurs so often that each region, bed or even a
well or single gas-bearing horizon, have their own specific characteristics. For this reason it
is very difficult to systematize the data relevant to them. However, it is possible to classify
them into several such types which, although of different age, lithology and origin, are - at
the same time – of major economic importance (Myśliwiec, 2004; Myśliwiec, 2006a;
Matyasik et al., 2007).
In the Carpathian Foredeep, four main litho-facies have been identified. These are, starting
from the deepest sediments:
1. A complex of turbidite sediments of the lowest Sarmatian, 450-500 m thick. It comprises
sandstones of submarine fans and heteroliths of sandstone-mudstone-claystone from the
basin plain. This sequence is organized as about 50 m cyclothems. A characteristic feature
is the presence of a thin or very thin laminae. Some of these laminae are over one meter
thick. Sandstone sequences do not cover very large areas and on their edges, they grade
into mudstones. Heteroliths are good reservoir rocks; their porosity exceeds 20% and
10
permeability reaches 500 mD (Myśliwiec, 2006a; Dziadzio, 2000). These rocks appear to
have been developed on the slopes of vast prograding accumulation levees typical of the
distal parts of submarine complex. This type of prograding or accreting submarine fan
complex, with thin laminae suggests that the environment of deposition was distal from
the source, where hydrodynamic energy was almost exhausted.
2. A transitional sediment complex about 220 m thick. It comprises sandstone laminae fining
upwards into sandstone-mudstones. In the upper part of the complex, sandstones prevail
over fine-grained sediments. The complex is a result of progradation of a deltaic
depositional system and is transitional between turbidites and deltaic sediments.
3. A complex of deltaic sediments is the most diverse in terms of a sedimentation
environment and facies. Its most important feature is a vertical cycling. The 300 m thick
complex comprises several parasequences (cyclothems) each 20-30 m thick. The
parasequences have a complicated structure, but in each, one can observe sets of laminae
of coarse grained sandstones with the thickness of each set of laminae increasing towards
the top of the parasequence. Parasequences start with sediments of prograding
accumulation levees (piles or bars). Inside of these sediments one can select parts of
various sedimentation environments: delta slope, estuary levees (piles/bars) and deltaic
plain. Sandstones in parasequences occur in the form of several meters thick packets
bordered by underlying heteroliths of similar thickness. In the region of the Z gas field,
not all cyclothems underwent typical or complete development, particularly in the middle
and upper part of the deltaic sediment complex. Deltaic sediments are built in a zone
where the river and the sea meet.They include a considerable amount of organic matter.
This fact together with prograding deltas, is important from a hydrocarbon prospecting
point of view because:
1) organic matter can be converted into hydrocarbons, which means the Sarmatian
deltaic deposits are mature source rock for hydrocarbons and
2) the maximum flooding surfaces (MFS) indicated by the muddy-shaly upper
limits of the parasequences form hydrocarbon seals for the reservoirs below. In
fact deltaic sediments, especially those built in estuary ostiary levees (piles/bars),
are good reservoir rocks. The sandstones have porosities ranging from 15-32 %
and permeabilities of around 900 mD (Myśliwiec, 2006a, Śmist, 2003).
11
4. A complex of shallow shelf, littoral sediments represents the final stage of sedimentation
in the Carpathian Foredeep. Deposits are poorly sorted and include fine grained lithofacies and muddy-shaly litho-facies. There is great vertical and horizontal variation in
facies, which makes it difficult to recognize, classify and correlate them. Despite these
litho-facial complexities, these sediments include gas accumulations in the shallow
horizon (nr I) of Z gas field, representing sediments of a near shore coastal environment
and open shelf and in the horizon nr II, as sediments from sandy barriers delimiting
lagoons (Myśliwiec, 2004).
The sandstones of the Sarmatian deltaic formations, and particularly the sandstones occurring
in heterolithic or clayey formations, are characterized by low textural and mineral maturity.
This first feature means that there is a relatively high content of a clayey-shaly matrix in the
cement, and low rounded detritus. The second feature shows as a varied petrographic
composition with minerals of platy crystal habit, plagioclases and various rock fragments. The
deltaic sandstones of the Sarmatian usually contain large quantities of dispersed calcium
carbonate, thus they are sometimes called marly sandstones. The total calcium carbonate
content is increased also by the mud derived from from erosion of limestone rock, which,
together with shale, forms cement. The grain matrix of sandstones is typically fine- to
medium-grained with an admixture of silty-shaly material. Using the typical classification of
lithoclasts, the deltaic sandstones include lithic and sublithic wackes, quartz-mica wackes, and
– when better-sorted – sublithic arenites. The dominant mineral components include quartz
and fragments of other rocks (limestones, dolomites, radiolarites, quartzites, quartz-muscovite
shales, inter alia), as well as plagioclases, micas, calcium feldspars, glauconite, and
carbonized plant detritus. Also present are bioclasts – foraminifera, fragments of bryozoans,
and bivalves. The cement is made of shaly material, limestone mud, and terrigenous silt.
Incidentally, crystalline calcite and dolomitic cements occur, filling single pores.
On the basis of geological and geophysical studies it may be stated that the trap for natural gas
in the Z gas deposit, which consists of a number of gas-bearing horizons, is of a structuralstratigraphic type. It is an anticline formed above an uplift of substrate rocks. In some
horizons, the factors creating the trap also include lithological changes and more precisely,
changes in facies together with local variations in porosity and permeability.
12
In the Z gas deposit several types of gas-water contact were identified depending on the facies
and lithology of the reservoir rocks (Geological Documentation of the Z-L gas field, 2007). In
terms of different positions of separation surfaces between parts saturated with natural gas and
those saturated with formation water, in the horizons where edge water occurs, the deposit is
partly a thinly bedded sheet-deposit, whereas it is partly a more massive deposit in those
horizons where bottom water occurs. In the sandstone horizons, and particularly these
occurring in the upper parts of deltaic prograding accumulation levees, sealed by shaly
sediments of the basin bottom, or those in sand-filled canals of the upper undersea fans,
seismic profiling shows a visible gas-water boundary.
The reservoir drive mechanism in these types of sediments is either edge drive in the case of
thin laminated reservoirs, or bottom water in the case of thick and massive sandstone
reservoirs When the gas is accumulated in heterolithic sediments of the delta plain or in
deposits in the bays of a shallow shelf/near-shore coastal environment zone each thin
sandstone or shale layer may have has its own individual gas-water contact.
2.3 Core Analysis
Results of porosity and permeability obtained by laboratory measurements on cores are
presented on the examples from 3 wells: Z75, Z84 and Z78. Core samples in other wells from
the Z gas field provided similar results. Porosity distribution was measured using an Auto
Pore 9320 mercury porosimeter. A scanning electronic microscope, SEM, and Roentgen
microanalyser were used to examine the pore structure. Information was also obtained on
cement type and distribution.
Porosity in Z75 ranged commonly from 23 to 28 percent with rare samples having a range of
16-20 percent. The grain diameters fall within the 0.032 – 2 mm range, with the dominant
fraction in the range of 0.033 – 0.125 mm (Fig 2.4). The average diameter of a pore throats is
high and ranges from 0,2 to 2 μm. Over 50% of throat diameters exceed 1 μm. Polished
sections impregnated with blue resin and images from the scanning microscope illustrate the
nature of porous space perfectly (Fig 2.5). The porosity of this sample is 20.85%. The grain
material is loosely packed and the proportion of diagenetic cement is low. Envelopes of
quartzite cement and aggregations of clay materials are seen on scanning microscope images
along with single quartzite crystals (Fig 2.6). Porosity is distinctly macropore in character.
Pores with a diameter greater than 1 μm total some 80 to 95 percent, which means they
13
possess good filtration abilities. The SEM showed that there is not much cement among the
mineral components. It was also shown that porosity is inter granular or inter crystalline and
pores are in communication, not isolated, suggesting high permeability. There is also a minor
secondary porosity related to pores and micropores in grains of feldspar and plagioclases and
in the lithoclasts. In some cases porosity exceeded 30 percent with permeability higher than 1
Darcy. These excellent reservoir characteristics were observed in well sorted sediment
deposited in a high energy sedimentary environment, typically in the channel axes at the head
of the delta or in distributary channels.
Number of data (%)
45
40
35
30
25
20
Fig.2.4 The result of grain size
15
analysis of powdered sandstone
10
taken at 677m, the depth of the
5
0
0.031
Z75 well
0.063
0.125
0.25
0.5
1
2
Grain size (mm)
Fig. 2.5 Photomicrographs of a polished section impregnated with blue resin, from a
sample obtained at a depth of 855.20m in well Z75; crossed nicoles (left – magnification
14X, right – 120X) (Documentation of wells: Z75, 79 and 84)
14
Fig. 2.6 Scanning microscope
photomicrographs of a polished section from
a sample obtained at a depth of 855.20m in
well Z75; magnification 600X
(Documentation of wells: Z75, 79 and 84)
Samples in the Z84 well were highly diversified. Many of them, taken from the shallower part
of the borehole, were too soft and shaly to make measurements. Only samples from the depth
section of 720-729 m enabled regular measurements. Porosity in that section ranged from 24
to 25 percent and permeability in some samples was higher than 1 Darcy. Most of the samples
revealed permeability of 100-500 mD. However, a few samples with a high porosity of 20
percent - show permeability lower than 2 mD. SEM investigations showed that rocks are
porous and permeable, and that there is a small amount of carbonate-shaly matrix cement.
SEM investigation showed conclusively that even when there was intergranular and
intercrystal porosity with clear interpore communication, the presence of significant amounts
of matrix cementation, degraded porosity and permeability so that these rocks were probably
not capable of producing hydrocarbons.
In the Z78 well, the reservoir parameters were also very diversified. In the upper part, from
528-537 m, the rock displayed high porosity (almost 30 percent) and high permeability (more
than 100 Darcy). In other sections there are also good reservoir parameters except for 717-726
m, where extensive cementation lowers the porosity to 5-6 percent. Average porosity is equal
to 23-26 percent and permeability about 100 mD. Similar to previous wells, porosity values of
about 20 percent with permeability close to zero, were observed. Such samples are common
in the lowest part of the Sarmatian.
Geological core descriptions were also used for lithofacies calibration (Mastalerz et al., 2004).
The short descriptions of the cores in two selected depth sections in the Z76 well are
presented as example:
15
691-700 m
Lithology: the upper part of the section comprises thinly bedded heteroliths of mudstones and
sandstones, whilst the lower section exhibits a higher proportion of sandstone heteroliths.
Also observed were the frequent synsedimentological deformations, mostly in one directional
slope of diagonal laminae, rarely bimodal, there are frequently observed small nodules. In the
lower part of the section, the normal sorting of grains is observed, and in some parts frequent
bioturbacies have been detected. In addition lithoclasts are occasionally deposited in waves.
In other areas nodular concretions are present.
Facies: The environment of deposition is characterized by traction currents with a
considerable amount of suspension; suspension currents, high movement of deposits in an
area with a soft nonconsolidated bottom, a lower share of hemipelagic suspension deposition;
probably sporadic influence of wave action and tidal currents; this sedimentation being typical
of submarine deltaic slope.
Other: Dip is generally horizontal or slightly inclined (0-5o); transportation is generally from
one direction, in parts bimodal; the cores from that interval were correlated with logs in the
depth section 689 – 698.5 m.
700-709 m
Lithology: the upper part of the section is mostly heterolithic with mudstones and sandstones,
of various lamina thickness; the dip direction in the sandstones is primarily in one direction, ,
rarely bimodal; frequent small nodules are visible, current ripple marks are deformed
synsedimentologically; in thicker sets a normal grain size distribution is present, and not the
frequent modifications due to wave activity; in the middle part of the interval sandstone clasts
become more common; laminae are thicker and grains are coarser; in the lower part poorly
sorted material occurs, and coarse and medium-coarse sandstones with few mudstone laminae
are observed.
Facies: the upper part of this section is similar to the previous one (691-700 m). In the lower
part there is observed influence of weak suspension currents and traction currents. A
considerable result of traction currents is also observed in the upper part.
16
Other: horizontal lamination or minor dips (0-5o), transportation from one direction - of
structural dip, is rarely bimodal. The cores from the interval were correlated with logs in the
depth section 698.5 – 707.5 m.
2.4 Relationship between reservoir parameters and sedimentary environment
The discussion presented below is based on data from the Z75, Z78, Z79 and Z84 wells
selected as the typicall wells of the Z gas field. The best reservoir rocks were deposited in
turbidite fans. They are thinly laminated, the laminae are equal in thickness and are parallel.
Grain size is generally fine. Fining upwards sequences are common. The thickest laminae
occur in coarse grained poorly sorted sandy lenses. They are formed in zones of migrating
channels in the upper submarine fan. In the middle fan and between channels, sediments are
more fine grained and their characteristics are more akin to typical turbidites. Turbidites in the
Z gas field exhibit high porosity (up to 20 percent) and permeability (up to 500 mD). In the
discussed wells sediments from the submarine fan turbidites do not contain any gas
accumulations.
Proximally the turbidites are replaced by a series of deltaic sediments. This transition occurs
gradually, over a long distance. The transition zone is typified by laminae of fining upwards
cycles typical of turbidites diminishing as they are replaced by sandy-muddy packets with a
characteristic increase in grain size. Turbidites have low values of GR and rather low NPHI,
whilst the occurrence of sandstones predominates over shales. An example is presented from
the depth section of 925 – 1025 m in the Z84 well (Fig 2.7a).
Deltaic sediments are where the richest gas accumulations are found. Thirteen of the
seventeen gas horizons identified in the Z gas field are located in deltaic facies. They are
cyclic and it is the reason why the Sarmatian gas deposits are found in stacked reservoirs.
Changes in grain size and their sorting are related to cycles in parasequences. At the
beginning of the parasequence, grain size increases except for in the top laminae where the
grain size decreases. A similar pattern in terms of thickness of the laminae can also be seen.
The frequent erosion of bars is typical of deltaic sediments caused by changes in the direction
of the channel axes supplying the sedimentary material. The erosion cuts are filled with sands.
From a hydrocarbon prospecting point of view there is an important stable geometrical shape
of the deltaic sediments. It is related to a decrease in the energy of the sedimentation
environment from stream outlets to the open sea. The shape of the deltaic area also depends
17
on the mutual relationship between energy of sources, i.e. current flow in river, sea wave
energy and tides. The fusion of the river environment with a considerable inflow of clastic
material and the sea environment enables accumulation in the same place, of large amounts of
organic matter, sandy material and shaly components.
A typical parasequence consists of claystone forming the basis for levee (bar), overlying this
are heteroliths Heterolithic bedding is defined as a closely interbedded deposit of sand and
mud, generated in environments where current flow varies considerably. The three main types
of heterolithic bedding are called flaser, wavy, and lenticular. Flaser bedding is characterized
by cross-laminated sands with thin mud drapes over foresets. Wavy bedding consists of
rippled sands with continuous mud drapes over the ripples. Lenticular bedding consists of
isolated lenses and ripples of sand set in a mud matrix. Heterolithic sediments can be
deposited in storm-wave influenced shallow marine environments, river floodplains, tidal
flats, or delta front settings where fluctuating currents or sediment supply permit the
deposition of both sand and mud.
At the beginning of the sedimentation process the heteroliths form as a result of prograding of
the bar slope. During the parasequence development phase, the genesis of heteroliths is
connected with the channel fill. The top of the parasequence is built up of sandstones from the
prograding head of the accumulation levee. The sequence terminates with the deposition of
pelagic shales. These represent the maximum flooding surface which coincides with the
beginning of the next parasequence. This pattern of deltaic sediments is well illustrated by
pairs of GR and NPHI and electric logs (depth sections of 550-690 in the Z75 well) (Fig.
2.7b). In the study area the deltaic sediments are not homogeneous. A typical parasequence is
observed in the Z75 well in the eastern part of the central element of the Z gas field.
Boundaries between parasequences are distinct and relatively easy to discriminate. A similar
picture is observed in the Z84 well. Moving to the west, the distinct picture of the
parasequences is not observed. The same problem appears in the Z79 well, where
distinguishing the boundaries is difficult.
Sediments of the shallow shelf form the top of the Sarmatian succession. Their genesis is
associated with the last stage of sedimentation in the Carpathian Foredeep, in which they
filled the remaining free sedimentation space. They are not vertically organized, and are not
well sorted, but they are composed of fine-grained sediments, mainly claystone and mudstone.
18
They are not prospective for hydrocarbons. However, despite this, four of the highest
horizons in the Z gas field are composed of those layers, and are located in heteroliths and
mudstones intercalated with very fine-grain sandstones. GR and NPHI track each other
closely which is interpreted to mean that these sediments are shaly, as evidenced by the high
neutron porosity (high NPHI is observed in shaly formations due to water bound in clay
minerals or in small micropores). The depth section of 410-500 m in the Z79 well presents a
typical littoral deposit (Fig. 2.7c).
RMS amplitude map and GR log for each well from top (~400m) to bottom (~900m) in the
study area are presented in the figure 2.8.
Shallow marine shelf
Fluvial system/Open sea ?
Baries
Coarsening
Upward
Fining
Upward
(b)
Shallow marine shelf
Deltaic
(a)
(c)
Fig. 2.7 Well logs (GR and NPHI) showing vertical facies distribution;
a) an example of turbidities from the depth section of 925 – 1025 m in the Z84 well; low
value of GR and rather low NPHI, sandstones dominate over shales,
b) a typical parasequence coarsening upward in deltaic sediments in the Z75 well,
c) sediments of shallow shelf form the top of the Sarmatian succession (GR and NPHI
are very close to one another), sediments are shaly and have high neutron porosity
19
Fig.2.8. RMS amplitude map and GR log for each well shows deltaic facies distribution in the
study area
2.5 Organization of succession, its division and correlation diagram
Several analyses of sedimentological and structural conditions for the Z gas field area were
provided on the basis of well log data (including dipmeter measurements and interpretation).
The type example for sedimentological and structural analysis of the Miocene sediments in
the Z75 and the Z76 wells is presented on the basis of dipmeter SED (Halliburton)
measurements and interpretation (Mastalerz et al., 2004).
Organization of a series and its structural-textural characteristics shows that in the profile we
find series of sequences (cyclothems), mostly of a prograding character at the beginning and
retrograding character in the next stage. In the Sarmatian sediments one can distinguish a few
dozen sedimentary sequences with a hierarchic organization with varying character (part of
them there are parasequences or sequences of a higher order in a sequential stratigraphical
sense). Single sequences run from several to more than a hundred meters in thickness (mainly
depending on their rank). A considerable part of the sequences show an almost symmetric
20
structure: in the lower parts there is a visible general increase in the sandy character at higher
elevations (it is connected with the gradual increase in the average thickness of the sandy
laminae), however shallower sandstones are gradually fine grained, and laminae, especially
the sandy ones, become thinner and thinner.
Considerably rarer are sequences that are distinctly asymmetric (i.e. almost solely increase in
grain size or almost solely decrease of grain size up to the top of sequences). Most of the
sequences of a higher order are complex, i.e. they have internal subsequences of higher frequency.
Generally speaking, for an accuratecorrelation of sediments in two geological profiles from
the, it is important to distinguish marker correlation horizons with a characteristic structure.
However in the case of the Z76 and the Z75 wells it was impossible due to their belonging to
different structural units and the considerable distance between them. Additionally, the Z76
well and the Z75 well penetrate two sedimentary accumulations related to different
depositional systems (as seen on well logs, especially on the arrow plot of the dipmeter)
(Mastalerz et al., 2004). In the basin influenced by differential synsedimentary tectonics (as
seen in the Miocene succession in the Carpathian Foredeep), a correlation of horizons
between separate depositional systems is very difficult.
A basic step of differentiation of a sedimentary series, due to genetic sequence stratigraphy
criterions, is to find maximum flood surfaces (MFS). These are associated with periods of
relative increase in water depth of the basin in which the tempo of growth of accommodation
space was not compensated by an accumulation of sediments. These surfaces are connected to
phases of maximum range of successive transgressions and are boundaries of genetic
sequences. Such surfaces are of fundamental significance due to the chronostratigraphy of
horizons in sedimentary series of transitional and shallow shelf types of environment. Parts of
them can be connected with episodes of intensive subsidence in the parts of the basin or in the
whole basin or with eustatic episodes.
Then come the surfaces of the maximum range of progradation, named by some of the
scientists as transgression surfaces, which may be treated as helpful horizons of
chronostratigraphic significance. Their identification on well logs is more difficult and needs
experience and a Dipmeter may be helpful here. Identification of these surfaces is
indispensable for more detailed differentiation of the sedimentary series into tract systems in
genetic sequences.
21
The basis of a more detailed differentiation may be identification of boundary surfaces for
depositional sequences, i.e. distinct erosion surfaces (erosion in sub-areal conditions) or their
correspondents from more distant parts of the basin. In this stage it is important to show
regressive surfaces of submarine erosion and transgressive erosion surfaces (connected with
retrogradation of the shoreline).
In Table 2.3 there are important horizons which can be treated as candidates of correlation
horizons of various rank. Table 3 and 4 present sketches of divisions in the Sarmatian series
of the Z region into stratigraphic sequences (also semi-genetic). This division may form the
basis of a general prognosis for the place and geometry of sandy lithosomes.
An overview of sequence stratigraphy results in the study area based on 2D seismic data are
shown in figure 2.9. In figure 2.10 a comparison of the results of well log correlation (the
cross section correlation: Z81 - Z76 - Z82 based on GR and NPHI) and the cross section
based on seismic facies classification (Chapter 5) is presented and showed facies distribution
various from well to well.
In Table 2.3 there are important horizons which can be treated as candidates of correlation
horizons. Table 2.4 and 2.5 present sketches of divisions in the Sarmatian series of the Z
region into stratigraphic sequences (also semi-genetic). This division may form the basis of a
general prognosis for the areal extent and geometry of sandy lithosomes.
On the basis of presented data we can say that the main factor controlling sedimentation and
the means of filling a basin was local tectonic subsidence. The analyzed series consists of
various rank sequences. Each sequence of the main scale is several dozen meters thick and
comprises a few sub-ranked sequences of a lower scale, which frequently reveal a complete
inner structure and almost symmetrical character. The degree of development of the
sequences of lower rank is diverse in different areas, and as such, the correlation of inner parts
of sequences can be difficult. In each of the basal sequences, there are several candidates for
maximum flooding surfaces, MFS, maximum progradation surfaces, MPS, or erosion
surfaces, which may be treated as surface boundaries. This means also that the development
of sequences of higher rank (lower scale) was not only controlled by tectonics, or eustatics,
but also authocycling (parasequencies). It is worth remembering that sequences of higher rank
can range on average from a few meters to several tens of meters in thickness. Differentiation
of such sequences and describing their character and variability is crucial for a credible
22
prognosis of the extent and geometry of single reservoir lithosomes. In addition, the inner
geometry of such sequences cannot be followed by routine seismic methods.
(a)
(b)
Upper delta
Delta lobe
SB
MFS
SB
MFS
SB
Fault ?
MFS
SB
(c)
(d)
MFS: Maximum Flooding
Surface
SB : Sequence Boundary
Fig. 2.9 Overview sequence stratigraphy in the study area based on 2D seismic data
a) seismic facies classification based on seismic attributes (Chapter 5),
b) balancing section a)
c) some basic sequence stratigraphy interpretation,
d) successive progradation of delta lobes deposits an offlap succession with a
clinoform geometry (after Frazier 1974)
23
24
Fig. 2.10 Comparison of the result of well log correlation;
a) cross section correlation Z-81 – Z76 - Z-82 based on GR and NPHI, (after Mastalerz, et al., 2004)
b) cross section basic on seismic facies classification (Chapter 5)
Table 2.3 Important correlation horizons (event markers) distinguished in the Z75 and Z76
wells in the selected depth section according to its geological core description (after
Mastalerz, et al., 2004)
Depth Depth
Horizon
Well logging features
Comments
Z75
Z76
the lowest
rank MFS
481
490 ?
distinct maximum on
GR
top of fundamental sandy
sequence SG9, close to
depicted seismic horizon
boundary not distinct in the
MFS_SG8/9 538
(525
distinct maximum on
Z76 well (at the top a
?)/534
GR
relatively fine-grained
sequence is visible)
distinct maximum on
MFS_SG7/8 612
623-638 GR and dramatic
change of plots in Z76
boundary not distinct in Z76,
probable tectonic discontinuity
distinct maximum on
MFS_SG6/7 696
699
GR and minimum on
close to described seismic
resistivity, insignificant
horizon
extremes in other curves
MFS_SG5/6 737
733
distinct maximum on
probably boundary of lower
GR
rank
not very distinct boundary in
MFS_SG4/5 777
776
distinct maximum on
GR
the Z75 well. Close to
described seismic horizon
(probably boundary of lower
rank)
distinct maximum in
MFS_SG3/4 863
850
GR and extremes in
other logs
MFS of
lower rank
distinct maximum in
908
897
GR and extremes in
other logs
close to depicted seismic
horizon
25
Table 2.4 Genetic sequences, SG, and other stratigraphic intervals distinguished in the
Miocene succession in the Z75 well (after Mastalerz, et al., 2004)
Depth Depth Seque
Paleo
Lithology, lamination
from
to
nce
slope
463
538
SG9_
Z75
Complex sequence (two distinguished sandy intervals)
with almost symmetrical structure. Various lamination,
mostly of medium thickness and up to thick laminae
WSW
(ENE)
Complex sequence of a complicated structure and with
a significant part comprised of relatively fine grained
538
612
SG8_
material – mostly heterolithic and sandy-shaly with
Z75
thinly laminated sandstones. Sandstones are mainly in
NNW
lower and middle part, mostly with middle and low
thickness laminae
Sequence of complicated structure and great litho –
612
696
SG7_
Z75
facial variability; from thinly laminated mudstones
including nodules and ferrous cements (in top and in
bottom about 605 m) to various in facies sandstones
NNWSSE
(thickly laminated are rare)
696
737
SG6_
Z75
Sequence with distinct tendency of increasing average
SSE
size of grains to the top and distinct boundaries in parts
(signifi
of fine-grained sediments. Sandstones of variable
cant
characteristics with a relatively large amount of thickly
dispers
laminated ones
ion)
Sequence of a complex structure (probably two
737
777
SG5_
Z75
equivalent sequences) and various lithofacial
characteristics: from thinly-bedded mudstones to
thickly bedded sandstones. At the depth of 768 m –a
distinct zone MFS of ferrous cement
variabl
e
SSESW?
Complex sequence with almost symmetric structure.
777
863
SG4_
Domination of sandstones (including a distinct part of
ESE-
Z75
thick and very thickly laminated) about fine-grained
SE
sediments
26
Table 2.5 Genetic sequences and other stratigraphic intervals distinguished in the Miocene
succession in the Z76 well (after Mastalerz, et al., 2004)
Depth Depth Seque
Paleoslope
Lithology, lamination
nce
from
to
/transport
Complex sequence with domination of fine grained
(465)
(525)
SG9_
sediments, various in facies; only in the middle part
491
534
Z76
is there a packet 10 m thick dominated by thin
bedded sandstones
Sequence of a very complicated structure: several
thick intervals of largely sandstone (various
(525)
623-
SG8_
lamination, mostly middle and thin-bedded). Upper
534
638
Z76
sandstones have much better marked progradation
segments, and a relatively large proportion of fine-
SW-NE
(significant
dispersion)
grained sediments
Complex sequence with an almost symmetric
623638
699
SG7_
Z76
vertical structure; several thicker intervals with a
NE ?
larger share of sandstones (mostly middle-size
(significant
lamination, only in the lower part are they thicker);
dispersion)
generally dominated by fine-grained sediments
699
733
SG6_
Z76
Relatively homogeneous, slightly asymmetric
sequence with hard progradation segment;
NNE
sandstones, only thin and middle laminated
Complex sequence with two thicker intervals with
733
776
SG5_
Z76
a domination of sandstones of variable lamination
(in the lower part there is a larger share of thick
laminae), in the upper part fine-grained sediments
NE (great
dispersion)
dominate.
Complex interval (at least two thick sequences)
776
850
SG4_
Z76
with a large share of sandstones of variable
lamination, increasing up to very thick in the
central part (815-830 m), distinct domination of
NNE to
NNW
fine-grained sediments (MFS zone)
SG – genetic sequences
27
2.6 Conclusions
The sources of the presented data were geological information, core descriptions, results of
laboratory measurements of porosity, permeability, volume of carbonates, mineralogical
information, well logging data, and especially dipmeter interpretation and parts of seismic
structural interpretation. We do not have a complete data set from all wells in the discussed Z
gas field, but on the basis of those which we gathered, we have attempted to build the
geological (sedimentological and depositional) framework of the study area. After studying
all of the geological information we are aware of the complexity of the structure of the
Miocene (Sarmatian) succession.
To realize the goals presented in the Ph.D. dissertation, we decided to use all lab data
available in all wells and select a consistent group of data from the depth section between 500
and 900 m, comprising the deltaic sedimentation environment. After this we selected other
geological and depositional data according to the depth section limit and according to the area
surrounding the wells. We intentionally limited the amount of data to make them more
coherent and uniform.
Petrel® software (Schlumberger) provides us on the one hand, with very good mathematical
and computer science tools which make it easier to develop a static geological model on the
basis of presented data. On the other hand the model has many limitations and constraints,
with some simplification forced by automation of the method.
28
Chapter 3
HYDRAULIC FLOW UNIT
Petrophysical parameters including porosity, permeability and water saturation are
compulsory input to modeling and simulation of any hydrocarbon reservoir. Among them,
porosity and permeability are the most important features controlling productivity of reservoir
that can be assessed by its flow properties through a factor named Flow Zone Indicator (FZI).
This chapter introduces the concept of hydraulic unit, HU on the basic of FZI and its
application to the Z gas field. The HU throughout the field is determined based on
conventional core data and conventional statistic methods such as histogram, probability plot
and cluster analysis.
This chapter introduces the concept of hydraulic unit (HU) and its relationship to the Flow
Zone Indicator (FZI) as it applies to the Z gas field. The Fluid Zone Indicator incorporates
numerous petrophysical parameters critical for modeling and simulation of a hydrocarbon
reservoir, including porosity and permeability. The Hydraulic Flow Units at Z field are
determined from conventional core data analysis and conventional statistical approach.
3.1 Concept of Hydraulic Flow Unit
The hydraulic flow unit concept provides a method for classifying rock types and predicting
their flow properties based on geological parameters and the physics of flow at the pore scale.
This concept is significant because it helps unify several theories relating to reservoir rocks
and the fluids they contain. Amaefule et al. (1993) suggested that the hydraulic quality of a
rock is controlled by its pore geometry. In contrast, other authors have proposed various
definitions of hydraulic flow units based on depositional and diagenetic processes. More
recently, the concept of the HU has become an important tool in describing a reservoir in term
of its flow zones.
Bear (1972) defined the hydraulic (pore geometrical) unit as the representative elementary
volume of the total reservoir rock within which the geological and petrophysical properties
are the same. Hear et al. (1984) defined a flow unit as a reservoir zone that is laterally and
vertically continuous and has similar permeability, porosity, and bedding characteristics.
Gunter et al. (1997) defined a flow unit as a stratigraphically continuous interval of similar
29
reservoir process that honors the geological framework and maintains the characteristics of
the rock types.
The focus on detail in one or more aspects of the reservoir flow modeling process can obscure
the fundamental reservoir concept in a model study. One way to integrate available data
within the context of a “big picture” is to apply the flow unit concept.
The concept of hydraulic flow unit was introduced by Ebanks (1987) who defined a HU as a
mappable portion of a reservoir within which the geological and petrophysical properties that
affect the fluid flow are internally consistent and predictably different from the properties of
other reservoir volumes. He described the flow units as the following:
1. a specific volume of a reservoir; it is composed of one or more reservoir-quality
lithology and any none-reservoir-quality rock types within that same volume, as well
as the fluids they contain,
2. a correlative and mappable unit at the interwell scale,
3. a recognizable section on wireline logs,
4. a unit being in communication with other flow units. However, flow units based on
lithostratigraphic characteristics are not always in pressure communication (Fig. 3.1).
Fig. 3.1 Various parameters used in defining geologic flow units (Ebanks et al., 1992); four
flow units are defined on the basis of lithofacies, pore types, porosity, and
permeability crossplots, capillary pressure measurements, and gamma-ray log
response (after Ebanks et al. (1992)
30
Understanding flow unit concept in reservoir is very important for reservoir modeling and
simulation. Permeability is one of the key parameters influencing reservoir flow properties.
Ideally, permeability is measured directly from core analysis or repeated formation test
equipment. However, in the absence of direct measurements of permeability, more indirect
measurement methods must be used. Several models have been developed to reveal the
relationship between porosity and permeability. These are primarily based on empirical and
theoretical techniques, most of which employ simple regression analysis. Table 3.1 shows a
chronological summary of the models. In reality, permeability not only depends on porosity
but also on other factors such as pore space geometry, grain size distribution, specific surface
area, tortuosity, fluid saturation and others. The most common equation used to calculate
permeability is the Kozeny-Carman equation (3.1) (Kozeny, 1927; Carman, 1937). This
approach suffers from two parameters which are either unknown or difficult to calculate:
special surface (Sgr) and tortuosity ().
e
1
K 
2
2 2 S gr
(1   e ) 2
3
(3.1)
Where:
K: permeability (m2),
e: effective porosity (fraction),
: tortuosity,
Sgr : specific surface area per unit grain.
In equation 3.1, factor 2 accounts for the assumption that pores are cylindrical with circular
cross-sections. In 1993 Amaefule et. al. generalized this equation to include the pore shape
(Fs) parameter as follows:
K
1
2
Fs 2 S gr
e
(1   e ) 2
3
(3.2)
The term (Fs or Kozeny constant, usually has a value between 5 and 100 in most reservoir
rock. The term (FsSgr) is a function of geological characteristics of porous media and varies
with changes in pore geometry. The determination and discrimination of the (FsSgr) group is
the main point of the HU classification technique. Equations 3.1 and 3.2 are only partially
successful in predicting permeability from porosity. In reality, most pores are not circular
cylinders and so equation 3.1 has limited applicability. Some parameters such as , Sgr, and Fs
31
are not readily available and so equation 3.2 is also difficult to apply. Amaefule et al. (1993)
addressed the variability of Kozeny’s constant by dividing Eq. 3.2 by effective porosity (e)
and taking the square root of both sides resulted in:

K
1

 e  Fs SVgr
 
e

 (1   e )




(3.3)
Where K is in m2 and if permeability is presented in millidarcy then the following parameter
can be defined:
RQI (m) = Reservoir Quality Index
RQI ( m)   10 2
K
K
 0.0314
e
e
(3.4)
z is defined as the pore volume to grain volume ratio:
z 
e
1 e
(3.5)
FZI (m), designated as the Flow Zone Indicator, is given by:
FZI 
1
Fs  S gr

RQI
z
(3.6)
Substituting these variables into equation 3.3 and taking the logarithm of both sides resulted in:
log RQI  log  z  log FZI
(3.7)
RQI vs. z can be plotted on a log-log plot as a straight line with the slope equal to one if FZI is
constant for all core samples. Representation of data on a log-log graph is more useful because
unit slope lines can be distinguished easily. Data samples with similar but not identical FZI
values are located around a single unit-slope straight line with a mean FZI value. Samples with
significantly different FZI lie on other parallel unit-slope lines. Each line represents a HU with
an associated mean FZI value. The mean FZI value is the intercept of a unit slope line with the
coordinate z = 1. The scatter of data about the straight lines is owing to measurement errors in
core data analysis and minor fluctuations around main geological controls on pore throat
characteristics of rock samples.
The basis of HU classification is to identify groups of data that form the unit-slope straight
lines on a log-log plot of RQI versus z. The permeability of a sample point is then calculated
32
from a pertinent HU using the mean FZI value and the corresponding sample porosity using
the following equation:
e
K  1014.24( FZI )
(1   e )2
3
2
(3.8)
In this equation, the FZI must be correlated to wireline log responses for known core
permeability and porosity data. As a first step, the FZI is classified using some sort of cluster
analysis, such as a histogram analysis, probability plot or other. Then the FZI must be
predicted in wells where only logs are available. This will be discussed in more detail on the
next section.
Table 3.1 Permeability correlations developed on the basis of pore and grain properties
(modified after Babdagli and Al-Slmin, 2004)
Model
Equation
KozenyCarman
(1937)
Archie
(1942)
Krumbein
and
k
f 
Variables
3
2
g
1   
2
r 2 eff
k
8F
k  0.760D2g exp( 1.31D)
Berg
(1970)
Effective pore radius, eff, and
formation factor, F.
Geometric mean grain diameter, Dg
diameter, D.
(1943)
(1968)
, shape factor, and porosity, .
and standard deviation of grain
Monk
Timur
Specific surface area, f, tortuosity,
0.136 4.4
k
2
Sw
k  80.8 5.1D2  1.385 j
Irreducible water saturation, Sw, and
porosity, .
Median grain diameter, D, and
sorting term,  , porosity, .
33
Van
Baaren
k  10Dd2  3.64  mC  3.64
(1979)
For clean formation and
Domain grain size, D, and sorting
index, C, porosity,.
Irreducible water saturation, total
and
100 (1  Swt) 
k

Swt

Denoo
For clayey material
(1981)
100 2e (  Vwt)  2
k

Vwt

Swanson
Maximum capillary pressure and
(1981)
S 
k  a b 
 Pc  max
Herron
f 3 exp(  Mf )
Mineral composition feldspar
Coates
(1987)
2
e
e
k
(1990)
Coates
(1991)
2.08
k  10  0.1 T 2.15
m
2
 FFI 
 BVI 
3
k  1,014FZI 
1   2
2
Amaefule
et al.
(1993)
Ohen et
al. (1995)
FZI 
1
F  g
k  1,014( FZI )2

water saturation, volume of bound
water, bulk irreducible water, and
total immovable water
content, and textural maturity of
sediments
k  106.59 Vp / S 
2.56 m
k  10  / Qv 2.11
 
k 
C 
porosity, effective porosity, bound
saturation percent
(1   )2
m
Sen et al.
2
RQI
z
3
1   2
Volume (Vp) to the surface (S)
ratio, exchange cation molarity
(Qv), and proton NMR decay
constant (T1)
FFI = free flow index and BVI =
Bulk volume irreducible water
Flow-zone indicator (FZI),
Reservoir quality index (RQI)
Kozeny constants (shape factor,
tortuosity, and specific surface area)
Flow-zone indicator (FZI),
Reservoir quality index (RQI), and
34
 b1  NMRSWR  
FZI  

1  aNMRSWR  1
1/ C
k  1,014FZI 
2
3
1   2
Altunbay
NMR measured water saturation
Flow zone indicator (FZI),
FZI  a  bR1  cRxo  fR1Rxo  gRGR 
(Resistivity, gamma ray, GR, grain
(1997)
hRGD  jRxoGD  iGRGD  mR2 
density, GD)
Quintero
k  Cpf 4.6 T
et al.
et al.
nR 2xo  pGR2  rGD2
4
2
2m
(1999)
pf  10i 2 widlk _ 1 /  2 widlh _ m
Haro
b 1
 log R  RW 
a m
(2004)
Width of T2 distribution at a
specific depth interval (T2 width)
and of the T2 distribution in a mudsupported facies
a
 m log k 
n log Swf 
Water saturation, Swf formation
resistivity, Rt, formation water
resistivity, Rw, cementation factor,
m, and saturation component, n.
3.2 Hydraulic Flow Unit classification technique
A reservoir can be modeled by subdividing its volume into several HUs. Recall that a HU is a
continuous part of the reservoir that has similar flow properties as characterized by geological
and petrophysical properties. Several flow unit identification techniques are proposed in the
literature. Some of the more prominent techniques are based on identification of rock type and
illustration of the results on the Winland porosity – permeability crossplot (R35) (Kolodziej,
1980) and on the modified Lorenz plot (Gunter, et al., 1997).
After calculating pore-throat related parameters of RQI and FZI from core data, HU’s can be
discriminated based on FZI values. Although each HU should be associated with one FZI
value, in reality a HU typically exhibits a distribution for each FZI around its true mean. This
is most commonly caused by random measurement errors in core analysis. When multiple HU
groups exist, the overall FZI distribution function is an upper position of the individual
35
distribution functions around their mean FZI. Identification of each mean FZI, or the
corresponding HU, can be achieved by decomposition of the overall FZI distribution into its
constituting elements. This desuperposition problem can be solved using cluster analysis
techniques (Abbaszadeh, et al., 1995).
In this section, we apply the following statistical analysis: histogram, probability plot, Ward’s
algorithm, and Global Hydraulic Elements (GHE) for HU classification based on core data.
3.2.1 Histogram
Because FZI distribution is a superposition of multiple log-normal distributions, a histogram
of FZI (with the log scale in the x-axis) should show “n” number of normal distributions for
“n” number of HU’s. When clusters are distinctly separated, the histogram clearly delineates
each HU and provides their corresponding FZI values. This is the easiest and simplest
approach. However, it is often difficult to separate the overlapped individual distributions
from a histogram plot. Therefore, this method is not suitable for most field applications
because the transition zones between HU’s often clouds the judgment on their identity
(Abbaszadeh, et al., 1995).
To explore this method, the experimental FZI was calculated from the core data by Eq. 3.6.
The distribution of the log(FZI) is shown in Fig. 3.2 which is similar with log(K). Each of the
peaks in the log(FZI) distribution should represent a group or cluster with Gaussian
distribution, since log(K) have normal distributions. However, the group classification is not
apparent since there is a strong overlapping.
36
Phi (dec)
K
Multi-w ell Interval histogram
Multi-w ell Interval histogram
60
60
50
Number of points
40
Number of Points
Number of Points
50
40
30
30
20
20
10
10
(a)
(b)
0
0.
570 points plotted out of 82307
Curv e
Well
Depths
Mean

(%)
Std Dev
0
0.01
0.35
0.1
1.
570 points plotted out of 82307
Curv e
Well
10.
100.
D_2
680.85M - 938.9M
0.23732
0.03449
K
D_2
680.85M - 938.9M
1.7518 histogram
0.9244
Multi-w
ell Interval
Phi
Z_72
253.1M - 967.35M
0.24891
0.02485
K
Z_72
253.1M - 967.35M
2.0065
0.6968
Phi
Z_74
675.4M - 1071.6M
0.22928
0.03607
K
Z_74
675.4M - 1071.6M
1.4271
0.9059
Phi
Z_75
509.05M - 951.3M
0.26502
0.03111
K
Z_75
509.05M - 951.3M
2.5008
0.6602
Phi
Z_76
501.1M - 1155.85M
0.25385
0.04303
K
Z_76
501.1M - 1155.85M
2.0756
0.9935
Phi
Z_77
708.15M - 1091.95M
0.2298
0.02228
50
K
Z_77
708.15M - 1091.95M
2.1262
0.6398
Phi
Z_78
528.4M - 1092.55M
0.24706
0.03442
K
Z_78
528.4M - 1092.55M
1.7368
0.9079
Phi
Z_79
642.3M - 798.65M
0.24743
0.05572
K
Z_79
642.3M - 798.65M
2.0597
1.126
Phi
Z_81
741.1M - 1018.1M
0.259
0.0288
K
Z_81
741.1M - 1018.1M
2.5588
0.5286
Phi
Z_82
646.05M - 837.35M
0.27038
0.02245
K
Z_82
646.05M - 837.35M
2.5332
0.647
Phi
Z_84
650.1M - 726.8M
0.22261
0.05854
K
Z_84
650.1M - 726.8M
1.4053
1.305
0.24845
0.03691
2.0781
0.8945
40
All Zones
5
4
Gaussian fit for each group
Number of Points
All Zones
10000.
Std Dev
Phi
Gaussian fit for all data
1000.
logK (mD)
FZI
Mean
Depths
30
3
20
2
6
10
1
(c)
0
0.05
0.1
570 points plotted out of 82307
Curv e
Well
0.2
0.5
Depths
1.
2.
logFZIMean
5.
10.
Std Dev
FZI
D_2
680.85M - 938.9M
0.19939
0.3551
FZI
Z_72
253.1M - 967.35M
0.28482
0.2933
FZI
Z_74
675.4M - 1071.6M
0.06734
0.3252
FZI
Z_75
509.05M - 951.3M
0.48351
0.2635
Fig. 3.2 Histogram of porosity (a), permeability (b), FZI (c) for 570 core data
measurements
FZI
Z_76
501.1M - 1155.85M
0.31387
0.3568
FZI
Z_77
708.15M - 1091.95M
0.40795
0.2564
FZI
Z_78
528.4M - 1092.55M
0.15977
0.3477
FZI
Z_79
642.3M - 798.65M
0.33969
0.3322
FZI
Z_81
741.1M - 1018.1M
0.53128
0.1866
FZI
Z_82
646.05M - 837.35M
0.4808
0.2734
FZI
Z_84
650.1M - 726.8M
0.09748
0.4714
0.32805
0.3394
All Zones
37
3.2.2 Probability plot
The probability plot, or cumulative distribution function, is the integral of the histogram
(probability density function) and it is smoother than the histogram. The scatter in data is
reduced on this plot and the identification of clusters becomes easier. A normal probability
plot has a specially arranged coordinate system where each normal distribution forms a
distinct straight line. Hence, the number of straight lines and the FZI limiting boundary for
each HU can be obtained from the probability plot of logFZI.
This exactly corresponds to a linear least-squares regression of data where the slope of the
regression line is equal to unity. This method is more useful than histogram method because it
is easier to identify straight lines visually, although the superposition effects may shift or
distort the straight lines to some degree.
In the figure 3.3, six distinct straight lines were recognized. Therefore, we decided to group
the core plug data into six clusters, corresponding to six appropriate HUs.
Normal Probability Plot
6
0.999
0.997
0.99
4
0.98
5
0.95
0.90
Probability
0.75
3
0.50
2
0.25
0.10
1
0.05
0.02
0.01
0.003
0.001
-1
-0.8
-0.6
-0.4
-0.2
0
Data
0.2
0.4
0.6
0.8
Log(FZI)
Fig. 3.3 Normal probability plot of log(FZI) with division into 6 homogeneous groups of HUs
with constant FZI
38
3.2.3 Ward’s algorithm approach
Ward’s algorithm is an analytical technique in hierarchical cluster analysis. In this method,
the distance between data points (FZI values) is calculated, initially treating each sample data
as a cluster. Next, the two clusters that are closest in distance are merged and the distance of
new cluster from other clusters is computed. The process of distance calculation and emerging
of clusters is continued until all available data points are emerged or until the required number
of clusters is attained.
One of the advantages of the Ward’s algorithm over the others is its special treatment of the
cluster variances. Clusters are formed so as to minimize the increase in the within-cluster
sums of squares of deviations from their mean. The distance between two clusters causes an
increase in the sum of squares if the two clusters were emerged. Therefore, each cluster tends
to attain a minimum spread around its mean value while having maximum separation from the
other clusters. This is exactly what is expected from a HU (Abbaszadeh et al., 1995).
Therefore this method for hierarchical clustering was selected for use in this study.
The six clusters are provided as input to Ward’s algorithm based on the probability plot (Fig.
3.3) and as such provide a good means to determine an appropriate number of HU’s for a data
set. The results of the clustering are presented in Fig. 3.4. The three black dashed lines and a
red line shows the possible cutoffs for the proposed divisions into 3, 4, 8, and 6 groups,
respectively. We then decided to use six groups (the continuous red line in Fig. 3.4) that are
consistent with the results from probability plot in the previous section.
39
Fig. 3.4 Clustering of the FZI – HU data set into six groups, according to the Ward method
3.3 Critical review on determining HU in the Lower Miocene reservoir of Z gas field
3.3.1 Preliminary outcomes
The cluster analysis presented in section 3.2 resulted in six clusters. Care was taken to
assign each original core plug data set (K & ) the same number as its associated HU. In
this way, the HU of each core plug could be identified and plotted on the permeability porosity plot (Fig. 3.5)
Because mean FZI values are not calculated from the histogram, the probability plots or
Ward’s HU classification algorithm, a plot of z vs. RQI for each HU was constructed (Fig.
3.6). The unit slope lines were drawn for each HU through their data clusters according to the
mean value of FZI calculated for each HU at the intercept with z = 1. The mean FZI values
were then used to construct the porosity - permeability relationship within each HU using
Equation 3.8. Figure 3.7 shows the porosity-permeability crossplot combined with the HUs
40
for all core data. The curves represent the porosity – permeability relationship based on
Equation 3.6 using the mean value of FZI for each hydraulic unit.
Simple statistics of permeability, porosity and FZI show that the uniform separate groups are
unambiguously described by the mean value of FZI (Table 3.2). For these six defined groups
of data, each with homogeneous HUs of constant reservoir parameters, we calculated the
equations relating FZI to the permeability and porosity using core data. Finally, the
permeability that was calculated on the basis of Equation 3.8 with mean values of FZI for
each HUs was highly correlated to the core origin permeability (Table 3.2, Fig. 3.8) (Ha
Quang and Jarzyna, 2008 a, b).
Table 3.2 Simple statistics of permeability, porosity, FZI and the determination coefficients
(R2) for the permeability, calculated from the FZI_mean and from the core in 6 HUs.
HUs
min
mean
max
min
mean
max
min
mean
max
R2
(k_FZI_mean
vs. k_core)
K (mD)
Nr. of data
in HU
PHI (%)
FZI
HU1
28
0.02
0.72
2.82
0.07
0.16
0.233
0.095
0.283
0.400
0.728
HU2
58
0.17
9.15
24.33
0.078
0.21
0.251
0.466
0.734
0.971
0.888
HU3
89
9.78
50.75
120.04
0.15
0.24
0.292
0.997
1.379
1.687
0.645
HU4
117
40.470
144.72
358.55
0.203
0.257
0.315
1.733
2.10
2.563
0.743
HU5
214
79.79
445.77
1461.7
0.189
0.26
0.32
2.587
3.51
4.512
0.603
HU6
64
430.07
1458.96
3631.1
0.229
0.27
0.306
4.555
5.85
8.833
0.411
All
0.97
3.3.2 Global Hydraulic Elements
Corbett et al. 2003 proposed the rapid and more straightforward approach to plot the porosity
and permeability data on the pre-determined global hydraulic elements (GHE) template (Fig.
3.9) which is constructed on the basis of eq. 3.8. A systematic series of a priori FZI values
was arbitrarily chosen to define 10 porosity-permeability elements. Only ten were chosen in
order to split the wide range of porosity and permeability parameter space into a manageable
number of GHEs (Table 3.3).
Table 3.3 Global hydraulic elements (GHE) template parameters
GHE1
GHE2
GHE3 GHE4 GHE5 GHE6 GHE7 GHE8 GHE9 GHE10
0.0938
0.1875
0.375
0.75
1.5
3
6
12
24
48
41
The series of FZI values (0.0938 – 48) corresponds respectively to the lower boundary of
Global Hydraulic Elements (1-10). This allows any core plug to be rapidly classified in terms
of GHEs merely by plotting its porosity and permeability values on the template. There is no
need to calculate FZI values. The GHE approach also permits selection of representative
samples even when core data availability is limited.
The core porosity and permeability data from Z gas field was projected on the appropriate
GHE template constructed for each HU (Fig. 3.9). It was observed that the study fit the
processing model exactly as predicted: In each HU / GHE pair, the close relationship between
permeability and porosity was established and those equations were used to calculate K from
Φ. Fig. 3.10 shows the relationship between permeability from the core data and permeability
calculated from the means of FZIs in GHE. When Φ is available from the comprehensive
interpretation of logs, we can construct a continuous log, as k=f(depth) (Jarzyna and Ha
Quang, 2009).
The GHE results gave approximately the same number of GHEs as the HUs. It was therefore
useful to compare the previous conventional approach (Fig. 3.7) with the GHE approach (Fig.
3.9) to show that GHEs are a useful concept, and the number of arbitrary GHEs on the
template is probably about right. In the future, GHEs appear to provide an easy, rapid way of
classifying core data (An, 2004).
42
10000
1000
100
K [mD]
HU6
10
HU5
HU4
1
HU3
HU2
0.1
HU1
0.01
0.1
0.05
0.2
0.15
0.3
0.25
0.35
PHi [fraction]
Fig. 3.5 Porosity-permeability crossplot, the hydraulic unit classification of all the core data
10
RQI
1
HFU6
0.1
HFU5
HFU4
HFU3
HFU2
HFU1
0.01
0.01
0.1
PhiZ
z
1
Fig. 3.6 z vs. RQI crossplot of all the hydraulic units. The mean FZI values for each
hydraulic unit are given by the intercept of the straight lines at z =1
43
10000
1000
K [mD]
100
10
HU1
HU2
HU3
HU4
HU5
HU6
1
0.1
0.01
0.05
0.1
0.15
0.2
0.25
0.3
0.35
PHI [fraction]
Fig. 3.7 Dispersion plot of PHI_core vs. K, and the six HUs defined in the area of core origin data
10000
1000
y = 1.33x0.95
K_pre [mD]
100
2
R = 0.97
10
HU1
HU2
1
HU3
HU4
0.1
HU5
HU6
0.01
0.01
0.1
1
10
100
1000
10000
K_core [mD]
Fig. 3.8 Dispersion plot and correlation line between the core origin permeability vs. the
permeability calculated from the mean values of FZI for H
44
Fig. 3.9 Permeability vs. porosity data on the background of 7 GHE
Fig. 3.10 Permeability, K_GHE, calculated on the basis of relationship RQI vs. Φz for 7 GHE
and core origin permeability, K_core
45
3.4 Conclusions
The hydraulic flow unit technique has been developed and applied to identify the reservoir
characteristics. This technique has a wide variety of practical field applications to both cored
and uncored intervals/wells. In the study area, 6 HUs were identified based on 570 core plugs
data by applying conventional cluster analysis techniques: these included histogram,
probability plot and Ward’s algorithm. The calculated permeability using the 6 HUs
classification shows very good result. The determination coefficient R2 between the calculated
permeability and the actual permeability measured on core plugs was 0.97 (Fig. 3.8), indicates
nearly perfect correlation.
Using GHE, the reservoir can be divided into 7 distinct GHEs. The calculated permeability
using this method resulted in a correlation coefficient of 0.96 (Fig. 3.11), which is slightly
smaller than that of when applying 6HUs. However this method, is very useful for a reservoir
with limited core plugs data. In fact using this method means we can reduce the amount of
core data taken from the reservoir limited datasets and still provide with acceptably accurate
results. Because of the slight increase in correlation coefficient from the HU method over the
GHE method, and because of the reservoir complexity at Z gas field, the following was
decided:
1) all 570 core plugs from the study area would be used,
2) the HU technique would be used with,
3) a model of 6HUs, therefore, is being used for the reservoir simulation that will be
discussed in more detail in Chapter 6.
To summarize the methodology: The HU technique first identifies the prevailing HU’s in a
reservoir using core data and various cluster analysis techniques. A linear multiple regression
(LMR) and alternating conditional expectation (ACE) statistical method is then used to infer
HU and permeability prediction at logged wells will be discussed in the next chapter.
46
Chapter 4
CORE – LOG INTEGRATION
In this chapter, we will apply two statistical approaches: Alternating Conditional Expectation
(ACE) and Line Multiple Regression (LMR) to predict six hydraulic flow units (HU_log)
from core and log integration. There is no rock types (RT) descriptive data in the study area
so unsupervised clustering method such as K means clustering will be used for facies
prediction based on log data. The results of the Rock Type (RT) prediction and Hydraulic
Units from log (HU_log) will be also compared and presented in this chapter. Before applying
the statistical techniques, it is very important that core and log should be depth matched.
4.1 Core - log depth matching
Core - log data
Core and well log data from wells in the Z gas field (Z72, Z74, Z75, Z76, Z77, Z78, Z79,
Z81, Z82, Z84, and D2) in the NE Polish part of the Carpathian Foredeep were available (Fig.
4.1). Laboratory core measurements included effective porosity, (Φe) and absolute
permeability, (K), were taken from various depths in the selected wells. The study dataset
included 570 core samples from 11 wells. All primary statistical analyses, i.e., basic statistics,
histograms, and FZI calculations, were performed on the full data set. After core-depth
matching and min-max standardization of the data, 396 core samples from 10 wells were
retained for analyses. We omitted the D2 well to verify our correlations with blind tests. The
interval 253.10 – 1154 m was cored. Most of samples were obtained in deltaic sandy-muddyshaly deltaic facies. A small number of samples (12) came from turbidites at depths below
1000 m. Three samples were taken from a littoral facies at a depth between 253.10-272.00 m.
The primary focus was on 313 samples taken from deltaic sediments at a depth section
between 400 - 900 m. The Z gas deposit consists of several gas areas (Fig.2.3). Sediments are
of the same age (Sarmatian) and generally come from the same sedimentation environment
(deltaic). Because of local variation in sediment type, and the presence of faulting, the data
was further subdivided. Lab data were combined with eight logs from eleven wells. These
logs included spontaneous potential (SP), natural gamma ray intensity (GR), resistivity log
EN16 (short normal) and EN64 (long normal) and EL14 (short lateral) and EL28 (long
lateral), neutron porosity (NPHI), and transit time interval (DT). In a few wells, the bulk
47
density (RHOB) was also available however, this log was used only to assist in the
recognition of lithology and saturation. Z gas field logs represented various vintages, and
from different log manufacturers. To prevent this non-standardization from introducing
artifacts in the log analysis results, the number of logs used was further reduced to a selected
uniform group.
Core – log depth matching
Core and log depth matching is an important problem to address. In many cases, data was
selected from the continuously cored section, to achieve good correlation between the
laboratory measured values and the values measured from field logs. This approach is
illustrated in well Z76 (Fig. 4.1), by matching the depth sections with the porosity from the
core (PHI_core) and the neutron porosity (NPHI) from the log. Additionally, the gamma ray
(GR) log was used to obtain information about the shaliness of rocks, to help establish a shift
of the discreet lab data along the continuous log. It was decided to shift the core data along the
depth scale, since samples cut from the cores for lab measurements are very small compared
with the space covered by log. Consideration was given to the fact that the Sarmatian
formation is thinly laminated and that logging results can be influenced not only by the beds
penetrated directly by the well bore or core barrel, but also from lateral variation in beds a
short distance away from the well bore not sampled by the core barrel.
Correlation coefficients (R) calculated for the log estimated NPHI and the core data PHI_core
provide a measure of the success of the depth matching. Additionally, the constant slope of
regression lines in selected depth sections with depth matching was used independently to
control the established correspondence between the NPHI and the PHI_core. A study of depth
matching reveled that after depth matching, the correlation coefficient increased from 0.11 to
0.87, Fig. 4.1). Therefore, depth matching was performed on all wells used in the study.
48
922
922
922
924
924
922
926
Depth [m]
Depth [m]
924
926
924
926
926
928
928
928
NPHI
PHI_core
930
NPHI
PHI_core
928
930
930
0.1
0.2
0.3
0.4
0.1
0.2
0.3
0.4
NPHI
PHI_core
0.1
0.2
0.3
0.4
0.1
0.2
0.3
0.4
930
NPHI
PHI_core
Fig. 4.1 Two approaches to depth matching between the core and log data in well Z76.
Crosses – lab porosity – PHI_core, sampled irregularly; continuous curves with
triangles – NPHI, sampled regularly, 0.25 m. The two horizontal scales of porosity
and two vertical scales of depth relate to the matched data sets
49
4.2 Hydraulic Flow Unit Prediction
4.2.1 Methodology
In this section, the goal was to prepare petrophysical data for modeling media flow in the pore
space domain. The rock formations were divided into homogeneous hydraulic units based
upon parameters measured from laboratory tests and log analysis (Fig. 4.2). At the beginning
of two branches of the flow chart (the left hand side is based entirely on core data, and the
right hand side is based on core and log data) there was a calculation of Flow Zone Indicator
(FZI) in cored sections of the wells. Next, is a section to include log data in the relationships
that determine the HUs continuously in a full geological profile, using linear multiple
regression (LMR) and alternating conditional expectation (ACE) algorithm. Finally, these
methods were extended into the uncored parts of the wells, including log analysis. The first
part of the analysis was to establish a training stage, using core results from ten wells. The
subsequent prediction stage was performed in the eleventh well.
The quantities under consideration were the effective porosity from the core, the permeability
from the core, the Flow Zone Indicator (FZI), and the Hydraulic Unit (HU). FZI is a
mathematically obtained parameter which characterizes media flow in a rock formation better
than simple porosity and permeability. Hydraulic Unit (HU) is derived from FZI. HU and FZI
have well defined physical interpretations, and they are obtained by simple mathematical
transformation of the well known Cozeny-Carman equation. In the second branch of the flow
chart (Fig. 4.2), we included well log data.
The process starts with simple statistics, histograms, and a linear two-dimensional regression
applied to the core data. The statistical approach also includes an Linear Multiple Regression
(LMR) to establish the relationship between the core and log data, and a more sophisticated
method of data processing, such as the Alternating Conditional Expectation (ACE) algorithm,
to improve that statistical relationship. While dividing the FZI data set into uniform hydraulic
units, we applied a clustering method and calculated a probability function to confirm the
division of the data set. A correlation coefficient (R) and determination coefficient (R2)
provided measures of reliability for the determined relationships between the FZI and the HU
obtained from core data and estimated from log. The following decision chart (Fig. 4.2) shows
how to apply the selected statistical methods:
50
Fig. 4.2 Flow chart for two procedures applied to obtain uniform HUs in the study data
51
4.2.2 Flow Zone Indicator prediction
4.2.2.1 Linear Multiple Regression (LMR)
An LMR is an efficient statistical procedure for determining the linear relationship between a
dependent variable and several independent variables. In the multivariate case, a regression
function is easy to compute but is difficult to visualize in a two-dimensional space. To solve
this problem, an equation is needed to illustrate the relationship between the dependent
variable, Y=ln(FZI), and the independent variables, Xi, i=1,2, ..., p. This equation shows the p
logs measuring p various parameters X1, ..., Xp, b0, b1….bp predictors:
Y=b0+b1*X1+b2*X2+...+bp*Xp
(4.1)
Typically, equation 4.1 is accompanied by a table showing the regression coefficients from
the contribution of each independent variable (i.e., p-log) to the dependent variable.
Controlling and selecting the proper number and type of variables, such as the number and
type of log and other factors, result in sufficient information to describe the dependent
variable.
LMR assumes that the relationship between the independent variable and each dependent
variable is linear. However, that assumption is rarely satisfied in this study: All twodimensional dispersion plots of Y vs. Xi, and linear regression equations Y=a+bi*Xi, were
analyzed in a full correlation matrix. Dispersion plots of the natural logarithm of FZI vs. the
GR and NPHI, and histograms of the GR and NPHI are presented in Fig. 4.3. Also tested was
the normality of all independent variables to explain the departures from the Gaussian curve
due to the geological/geophysical nature of the data and the available accuracy of the
measurement (laboratory and log).
52
60
40
Mean
StDev
N
Mean
StDev
N
40
30
20
60.59
11.74
327
30
Frequency
Frequency
50
31.97
4.296
327
20
10
10
15
20
25
30
NPHI
35
40
0
45
2
2
1
1
lnFZI
lnFZI
0
0
-1
30
40
50
60
GR
70
80
90
50
60
GR
70
80
90
0
-1
-2
15
20
25
30
NPHI
35
40
45
-2
30
40
Fig. 4.3 Dispersion plots of ln(FZI) vs. GR and ln(FZI) vs. NPHI, and histograms of GR and
NPHI; Gaussian distributions included in histograms
The goal was to construct an efficient function to determine ln(FZI) from the available log or
combinations of log. The selected final regression equation was a compromise between the
expected high quality of the result (e.g., high accuracy of the calculation of the dependent
variable) and the number of available logs. The accuracy of ln(FZI) was determined from
selected sets of independent variables, and was based on the correlation coefficient between
ln(FZI) calculated from core data and from multiple regression.
Linear multiple regression (LMR) - raw and standardized data
The starting point for this task was to select all of the data from 10 wells in the deltaic
sedimentation environment section after core-log depth matching (313 samples). After
calculating the ranking correlations between ln(FZI) and selected log, the best correlation
coefficient was observed between ln(FZI) and an apparent resistivity from a short normal
device, R_E16N, equal to -0.353. In other words, no simple correlations exist to predict FZI
from log data (Table 4.1).
Next, an LMR was applied to raw log data, in order to learn more about the relationship
between several independent variables (log data) and a dependent variable (ln(FZI_core)), and
to establish which log combinations provide the best equation for predicting the dependent
53
variable. The correlation coefficients (R) between ln(FZI) and selected groups of log are
presented in Table 4.2. The results showed that the correlations were not high enough to
predict ln(FZI) on the basis of raw data from eight different logs.
Four groups of wells were selected based on the distance between the wells and tectonic
events dividing the study area: G1(Z72-Z74-Z77), G2(Z75-Z84), G3 (Z76-Z81-Z82), and
G4(Z78-Z79). Clustering the data was also justified by the facies development of the Ż gas
field. All of the data belong to the deltaic facies. Sandy - muddy-shaly thinly bedded rocks are
very complex in lithology, and in the deltaic environment of sedimentation, there are tidal,
near shore, lagoon, and mixed facies. By basing the grouping on geology (Fig. 2.3), and
following the core description, the selected clusters should be be self-consistent (Mysliwiec,
2006a; Matyasik et al., 2007). After applying the LMR prediction of ln(FZI_log) for each
group, the correlation coefficients R calculated from the raw data for each group increased,
with the best result being R = 0.78 for G4.
Table 4.1 Correlation coefficient (R) between ln(FZI) and log
Log
SP
DT
GR
NPHI
E16N
E64N
EL14
EL28
R
-0.198
0.069
-0.171
0.252
-0.353
-0.221
-0.141
-0.019
Table 4.2 Correlation coefficients (R) between ln(FZI) and groups of log with raw data
Log
R
E16N, SP
0.334
E16N, SP, DT
0.380
E16N, SP, DT,GR
0.383
E16N, SP, DT,GR, NPHI
0.439
E16N, SP, DT,GR, NPHI, E64N
0.440
E16N, SP, DT,GR, NPHI, E64N, EL14
0.445
E16N, SP, DT,GR, NPHI, E64N, EL14, EL28
0.446
Equation (4.2) shows the position of selected variables in the raw data regression from eight
log for group G3 (Z76-Z81-Z82).
54
Ln(FZI_G3) = -1.51296 + 0.020277*SP - 0.01482*DT - 0.01101*GR + 0.202763*NPHI 0.02721*E16N + 0.027615*E64N - 0.02083*EL14 + 0.189517*EL28
(4.2)
To improve the multiple regression between ln(FZI_core) and the log data, we introduced
min-max standardization and added extra variables as combinations of log (Table 43).
The min-max standardization was done according to the following Equation (4.3):
Vst = (Vx – Vmin)/(Vmax-Vmin)
(4.3)
where Vx: the current value of the variable,
Vmin, Vmax: the minimum and maximum values of the variable in the study section.
The min-max standardization transformed the raw log data into the range [0 – 1], so that after
the transformation 16 data points were lost for each variable. To reduce the number of lost
data from the 14 variables, we standardized all of the data from 10 wells before dividing them
into four groups.
Table 4.3 Selected independent variables used in a linear multiple regression
Logs
(raw data)
SP
[mV]
DT
GR
NPHI
[μs/m] [API] [dec.]
Logs
(max-min)
standardization
SP_st
DT_st
Combinations
of log
A1=
EL14_st
/EL28_st
EN16
[omm]
GR_st NPHI_st EN16_st
A2=
A3=DT_st
|EN16_st /GR_st
EN64_st |
EN64
[omm]
EL14
[omm]
EL28
[omm]
EN64_st
EL14_st
EL28_st
A4=DT_st A5=DT_st A6=GR_st
/NPHI_st /SP_st
/NPHI_st
We obtained better results during the training and testing processes after the min-max
standardization than we did using raw data. Equation (4.4) presents the result obtained for the
group G3 (Z76-Z81-Z82), with the standardized data from eight log_st, and six additional
variables A, which are combinations of standardized log (Table 4.3).
ln(FZI_G3) =
1.525422
0.77622*NPHI_st
+
-
0.63514*SP_st
2.363566*E16N_st
–
+
1.919128*DT_st
1.48731*E64N_st
–
-
0.90813*GR_st
-
0.98887*EL14_st
+
2.37722*EL28_st + 0.562993*A1 + 0.598027*A2 + 0.012519*A3_st – 2.00357*A4 –
0.02804*A5 + 0.230311*A6
(4.4)
Clustering the data, using a standardization procedure, and adding additional variables
improved the results of the estimation of ln(FZI) on the basis of log (Table 4.4). However, the
correlation coefficients were still not very high, so it was decided to see if the ACE algorithm
would provide a better estimation of ln(FZI).
55
Table 4.4 Correlation coefficients (R) between ln(FZI_core) and the results of LMR and ACE.
LMR
ACE
Number of
8 log
8 log +6 A
8 log +6 A
Groups
Wells
normalized
standardized
samples
raw data
standardized data
data
G1
Z72-Z74-Z-77
89
0.627
0.762
0.899
G2
Z75-Z84
103
0.735
0.838
0.906
G3
Z76-Z-81-Z82
76
0.627
0.747
0.889
G4
Z78-Z79
45
0.783
0.884
0.982
All data (10 wells)
313
0.446
0.507
0.643
4.2.2.2 Alternating Conditional Expectations algorithm (ACE)
An LMR provides a good result when there are functional relationships between the
independent and dependent variables. However, in this case a basic LMR led to
unsatisfactory, unstable results, since there was a complex relationship between the
permeability, the porosity, and additional unparameterized factors, such as the specific surface
or radii of pores. Also, the relationship between the log and the permeability of the FZI was
poorly defined. The non-linear regression technique ACE was considered as an efficient
variable selection method for reducing the subset of significant predictors for a considered
dependent variable response (Breiman and Friedman, 1985).
A very general and computationally efficient nonparametric regression algorithm, ACE, was
applied following similar works in petrophysics (for instance Xue et al., 1996). The ACE
algorithm estimates the transformations of variables used in a multiple regression, without a
prior assumption of a functional relationship between the dependent and independent
variables. An optimal transformation minimizes the variance of the linear relationship
between the transformed variable and primary variable, both dependent and independent.
Using ACE, arbitrary measurable mean-zero transformations were defined. These yielded a
maximum correlation between the primary variables and their transformations in the
transformed space. There should be minimal error that is unexplained by a regression of the
transformed dependent variable and the sum of the transformed independent variables. Also
defined was a correlation coefficient between the transformed dependent variable and the sum
of transformed independent variables. The coefficient should be maximal. The power of the
56
method lies in its ease of use and its ability to identify and correct for outliers; these outliers
should be removed from a constructed relationship without subjective assumptions.
Although ACE provided a fully automated approach to estimating optimal transformations, it
was decide to also examine using heuristic reasoning based on the experience gained from the
data analysis. In fact, the ACE algorithm permitted incorporating a presumed functional form
in the model. However, it should be emphasized that the success of the ACE algorithm, like
any other regression method, is dependent on the quality of the data and the underlying
association between the dependent and independent variables.
An optimal relationship between a transformed response variable FZI_tr, and a sum of
transformed independent variables (log_tr)s, was derived by minimizing the variance of a
linear relationship between them. We estimated the optimal function, f, between the
transformed FZI_tr and the transformed log using equation (4.5), below. Finally, we predicted
FZI through the reverse transformation, F-1 (4.6).
FZI _ tr  f ( log i _ tr )
(4.5)
i
FZI  F 1 ( f ( log i _ tr ))
(4.6)
i
FZI_tr is an ACE transformed FZI, and logi_tr is an ACE transformed logi.
Alternating Conditional Expectations (ACE) algorithm
The ACE algorithm was applied to find a better correlation between ln(FZI_core) vs.
ln(FZI_log). Based on the experience of other authors (Xue et al., 1996) who performed a
permeability determination from log data, a selection was made of the best transforms of
the dependent variable (ln(FZI)) and the independent variables (logs and A1 -A6
combinations of log, Tab. 4.3). Several approaches were investigated and allowing
selection of a group of independent predicting factors in the transformed space (Fig. 4.4).
Parameters were excluded when the correlation coefficient between the primary and
transformed values was too low (Fig. 4.4b).
57
Using the ACE algorithm, it was possible to calculate a correlation between the transformed
natural logarithm of FZI, ln(FZI_tr), and a sum of selected transformed independent variables.
Equation (4.7) presents this relationship.
ln FZI _ tr  f ( (log i _ tr  Ai _ tr ))
(4.7)
i
0.6
0.6
0.4
0.4
0.2
A2_Tr
EL14_n_Tr
0.2
0
-0.2
0
-0.4
-0.2
-0.6
3
y = 0.0579x - 0.3226x - 1.9846x + 0.7047
R2 = 0.9986
-0.8
y = 19.888x3 + 0.304x2 + 0.5583x - 0.1217
R2 = 0.4616
2
-0.4
-1
-0.6
0
0.2
0.4
0.6
0.8
0
0.05
0.1
0.15
EL14_n
Fig. 4.4a Optimal transformation of EL14
0.25
0.3
Fig. 4.4b Optimal transformation of A2
3
3
3
2
y = 0.0444x - 0.3812x + 2.6381x - 2.5387
R2 = 0.995
2
y = 1.10x
R2 = 0.81
2
1
1
LnFZI_tr
LnFZI_tr
0.2
A2
0
-1
0
-1
-2
-2
-3
-3
-4
-4
-0.5
0
0.5
1
1.5
2
2.5
LnFZI
Fig. 4.4c Optimal transformation of ln(FZI)
-4
-3
-2
-1
0
1
2
∑(log_tr)
Fig. 4.4d Dispersion plot and correlation
for FZI_tr vs.  (log i _ tr  Ai _ tr )
i
The GRACE program (Xue et al., 1996) based on the ACE algorithm was used to generate an
optimal correlation between a dependent variable ln(FZI_tr) and multiple independent
variables
 (log _
i
tr
 Ai _ tr ) . This is accomplished through non-parametric transformations of
i
the dependent and independent variables. Non-parametric implies that no functional form is
assumed between the dependent and independent variables, so that the transformations are
derived solely based on the data set. The final correlation is determined by plotting the
transformed dependent variable against the sum of the transformed independent variables.
Ln(FZI_tr) obtained using the ACE algorithm showed a higher correlation with ln(FZI_core)
than the results from LMR (Table 4.4).
58
4.2.2.3 Comparison of LMR and ACE algorithm
Results from the LMR (ln(FZI_pre_LMR)) and the ACE algorithm (ln(FZI_pre_ACE)) were
compared. The correlation coefficient between ln(FZI_core) and ln(FZI_pre_LMR) was
calculated as well as the correlation coefficient between ln(FZI_core) and ln(FZI_pre_ACE)
(Table 4.4). The regression was calculated for data from well Z76 and for data from group
G3. In both cases ln(FZI_pre_ACE) vs. ln(FZI_core) resulted in the higher determination
coefficients (Fig. 4.5). The dispersion of data on the plain of ln(FZI_core) vs. ln(FZI_pre) was
caused by errors of regression and diversity of the lithology, resulting in an imprecise HU
classification in the data set.
At the end of the ln(FZI) and FZI estimation procedure (flow chart in Fig. 4.2), it was decided
to use the ACE algorithm to obtain a continuous curve of FZI _log vs. depth. The two curves
presented in Fig. 4.6.b have greater similarity compared with similar curves in Fig. 4.6a,
especially in the section between points 24 and 38. This reinforced the decision to use the
ACE algorithm to estimate ln(FZI), and to calculate permeability (K) along the entire well
2.5
2.5
2
2
lnFZI_pre (LMR)
lnFZI_pre (LMR)
profile, starting with the uncored section.
1.5
1
0.5
1.5
1
0.5
2
R = 0.6603
2
R = 0.5102
0
0
-0.5
-0.5
-0.5
0
0.5
1
1.5
2
2.5
-0.5
0
0.5
lnFZI_core
Fig. 4.5a Comparison of ln(FZI_core) to
ln(FZI_pre_LMR) for group G3
1.5
2
2.5
Fig. 4.5b Comparison of ln(FZI_core) to
ln(FZI_pre_LMR) for well Z76
2.5
2
2
1.5
lnFZI_pre (ACE)
lnFZI_pre (ACE)
1
lnFZI_core
1.5
1
0.5
1
R2 = 0.7559
0.5
R2 = 0.7651
0
0
-0.5
-0.5
0
0.5
1
lnFZI_core
1.5
2
2.5
-0.5
-0.5
0
0.5
1
1.5
2
2.5
lnFZI_core
Fig. 4.5c Comparison of ln(FZI_core) to Fig. 4.5d Comparison of ln(FZI_core) to
ln(FZI_pre_ACE) for group G3
ln(FZI_pre_ACE) for well Z76
59
2.5
lnFZI_core
lnFZI_pre(LRM)
2
1.5
1
0.5
Z_76
0
Z_81
Z_82
(a)
-0.5
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
2.5
lnFZI_core
2
lnFZI_pre(ACE)
1.5
1
0.5
Z_76
0
Z_81
Z_82
(b)
-0.5
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
Fig. 4.6 Results of FZI_core and FZI_pre (predicted from log) for two approaches in the
selected section of well Z76; a) LMR; b) ACE; consecutive numbers of data in the
depth section are on the horizontal axis
4.2.3 Hydraulic Flow Unit Prediction (HU_log) from FZI_pre_ACE
Table 4.4 presents examples of the prediction results, i.e., FZI and HU in well Z76, based on
core data (FZI_core and 6 HU_core) and log data using ACE (FZI_pre_ACE and 6
HU_pre_ACE). In general, strong similarity of the results can be seen, but there are a few
depth points at which there is no agreement between the two solutions. The training data was
not uniform due to a number of HUs in the selected ranges. For instance, with only 10 data
points in HU1 after depth matching, there was insufficient representation of the low media
flow parts of the formation in the training data set. Therefore, it was decided to exclude data
with GR greater than 75 API in the continuous geological profile (in well Z76 for example).
This effectively excluded pure shales from the testing data set. Two solutions were examined
for predicting hydraulic units from log using the ACE solution for group G3 in a continuous
geological profile for well Z76 (Fig. 4.7). Plots were prepared in Schlumberger Petrel®
60
software. Fig. 4.7 shows the GR (left hand side of the figures) and hydraulic units HU
(colored bands on the right hand side). The left contour of the GR shows true natural gamma
intensity. The colors mark the completion of the GR curve to the right edge. The GR and HUs
estimated for the full data set are seen in Fig. 4.7a. A solution excluding pure shales
(GR>75API) is is shown in Fig. 4.7b. The included histogram of the GR (Fig. 4.7) shows that
part of the geological profile in well Z76 consisted of pure shales. There is a distinct visual
similarity between the GR anomalies and the log predicted HUs for the sandier part of the
reservoir in well Z76. In other words, visual inspection suggests that low GR anomalies
correlate with high HUs for parts of the reservoir
Z_76_logfavorable to fluid flow in the pore space.
GR (API)
Interval : 200. : 1000.
100
160
140
80
100
60
80
40
60
Cumulative Frequency
Number of Points
120
40
20
20
0
0
75 API
25.
3201 points plotted out of 3201
Curv e
Well
GR
All Zones
Z_76_log
100.
Depths
Mean
Std Dev
200.M - 1000.M
65.585
13.08
65.585
13.08
Fig. 4.7a Prediction results for FZI_pre Fig. 4.7b Prediction results for FZI_pre for well
for well Z76, by applying the ACE Z76, by applying the ACE solution for group G3
solution for group G3 for the full excluding pure shales; left colored field – GR
geological profile; left colored field – anomaly, right colored steps – log predicted HU;
GR anomaly, right colored steps – log bimodal histogram of GR in well Z76 to show
predicted HU.
how to exclude pure shales
61
Table 4.5 Comparison of results obtained in well Z76; FZI_core – calculated on the basis of
porosity and permeability from cores, HU_core – six hydraulic units determined according to
FZI_core, FZI_pre - calculated on the basis of log and using ACE algorithm, HU_pre – 6HUs
determined according to FZI_log
Depth (m)
FZI_core
700.25
1.745
701.25
FZI_pre
HU_core
HU_pre
K_core (mD)
K_pre(mD)
1.954
4
4
127.3
184.30
4.478
3.627
5
5
1288.94
791.58
704.50
1.302
1.460
3
3
43.71
49.08
704.75
2.154
1.938
4
4
155.39
147.66
705.00
4.119
2.884
5
5
690.26
501.07
705.25
3.534
4.342
5
5
706.85
697.26
705.75
1.570
1.404
3
3
71.52
55.23
706.50
0.722
0.713
2
2
9.4
9.61
709.50
8.607
4.999
6
6
3312.29
1529.93
709.75
2.563
4.174
4
5
293.7
550.77
711.00
2.831
3.406
5
5
419.98
645.27
711.25
3.291
2.933
5
5
440.49
501.07
924.00
3.033
2.318
5
4
379.29
181.82
924.25
1.929
2.775
4
5
126.38
418.39
925.00
3.572
2.548
5
4
471.37
162.89
925.75
1.082
1.285
3
3
22.9
37.21
928.25
2.370
2.459
4
4
228.51
179.36
928.50
2.525
2.753
4
5
190.48
367.85
928.75
2.625
2.886
5
5
172.38
308.15
929.00
3.757
3.529
5
5
452.87
395.29
929.25
2.779
3.943
5
5
318.43
507.94
929.50
3.698
4.459
5
5
619.67
558.19
930.25
4.149
2.899
5
5
529.29
378.64
62
Values of the permeability from cores (k_core) and the permeability predicted using the ACE
algorithm from log (k_pre) in well Z76 are presented in table 4.5. Two dispersion plots
illustrate the variability of k_core vs. k_pre for group G3 (Fig. 4.8a) and for well Z76
(Fig.4.8b). The determination coefficients are high enough to confirm the correctness of the
proposed approach.
The gamma ray intensity and the HU in three wells (Z81-Z76-Z82) on 2D seismic profile are
presented in Fig. 4.9 on the background of the seismic section. The Hydraulic Units correlate
with the seismic horizons. Fig. 4.9 illustrates the 2D section of a continuous static model for
fluid flow in a reservoir.
4.2.4 Validation of results
The proposed estimation of FZI and HU based on core data and well log was tested in well
D2. The predicted values of FZI_pre_ACE were compared with the core origin FZI in well
D2 at two cored depth sections (679-687 and 930-940) (Fig. 4.10a). Solutions from the ACE
algorithm were used from group G1 to predict FZI. The predicted FZI ranged between 0.1 –
10 were similar to FZI determined from the core data. The validation results were positive,
despite a few observed discrepancies. These differences were due to the large inhomogeneity
of the reservoir as confirmed by the geological core description. Similar results are presented
in Fig. 4.10b for permeability (K).
K_pre(ACE) of Group 3
K_pre(ACE) of Z_76
10000
10000
y = 0.8802x 1.0138
R2 = 0.8049
y = 0.9253x 1.0096
R2 = 0.8303
1000
K_core
K_core
1000
100
10
100
10
1
1
1
10
100
1000
10000
1
K_pre(ACE)
10
100
1000
10000
K_pre(ACE)
Fig. 4.8a Dispersion plot and correlation Fig. 4.8b Dispersion plot and correlation
line between K_core and K_pre(ACE) for
line between K_core and K_pre(ACE) for
the G3 group
the Z76 well
63
64
Fig. 4.9 GR (left hand side) and HU (right hand side) presented in wells Z81-76-82 in group G3 on the background of 2D seismic
section; HU color scale is the same as in Fig. 13
LnFZI
1
10
750
930
751
931
752
932
753
933
754
755
10
934
935
756
936
757
937
758
938
FZI_pre
FZI_pre
759
LnFZI
1
0.1
Depth (m)
Depth (m)
0.1
939
FZI_core
FZI_core
940
760
Fig. 4.10a Comparison of FZI_pre_ACE (line) and FZI_core (points) in well D2
K [mD]
1
10
K [mD]
100
1000
1
930
752
932
754
934
Depth [m]
756
936
758
938
K_core
1000
K_core
K_pre
760
100
Depth [m]
750
10
K_pre
940
Fig. 4.10b Comparison of K_pre_ACE (line) and K_core (points) in well D2
65
4.3 Rock types classification
Lithofacies classification is a purely geological grouping of reservoir rocks, which have
similar texture, grain size, sorting etc. Each lithofacies indicates a certain depositional
environment with a distribution trend and dimension. Petrophysical groups are classified by
porosity, permeability, capillary pressure and pore throat size distribution. A Rock Type
combines both these classifications by linking petrophysical properties and lithofacies as
part of the reservoir rock type definition (Varavur, et al. 2005). Rushing, et al. 2008
developed a workflow process that identifies and compares three different rock types:
depositional, petrographic and hydraulic. Each rock type represents different physical and
chemical processes affecting rock properties during the depositional and paragenetic cycles.
A summary of rock type definition, data source, and evaluation methodology for selected
reservoir description and characterization studies of sandstone reservoirs is presented in
Table 4.6. Inspection of the compiled references shows that most of the technical literature
addressing rock-typing studies does include some or most of the aspects suggested by
Archie's definition.
Rock type identification is used in well correlation and is also important in 3D facies
modeling of the reservoir. In this study, modeling of an HU should be constrained by rock
type model to better understand of the geological basis of each hydraulic flow unit. Due to
lack of availability of core facies description in this section, the focus will be on prediction of
the rock type using unsupervised clustering, or K means clustering for classification of similar
rock types (Ha Quang, 2011).
4.3.1 K means clustering background
Cluster analysis encompasses a number of different classification algorithms that can be used
to organize observed data into meaningful groups. Today, in reservoir characterization and
interpretation workflows, the application of clustering techniques is becoming more popular,
especially for automatic core, log and seismic facies determination and classification.
Unsupervised clustering methods presently available for manipulating core, log and seismic data
with good results for predicting reservoir characterization include: Model-based Cluster Analysis
(MCA) (Sang, et al., 2002), Self Organizing Map (SOM) (Skalinski et al., 2005), Unsupervised
Neural Network (UNN) and K means clustering (Antelo, et al., 2001).
66
Table 4.6 Summary of selected rock types studies and definitions for sandstone reservoirs
(Rushing, et al. 2008)
Formation/
Location
Rock Type
Definitions
Davies, et al.
[1991]
Travis Peak
sands, East
Texas Salt Basin
No specific
definitions
Porras, et al.
[1999]
Santa Barbara and
Pirital Field sands,
Eastern Venezuela
Basin
Lithofacies,
petrofacies
Davies, et al.
[1999]
Wilmington Field
Pliocene-Age
sands
No specific
definitions
Boada, et al.
[2001]
Santa Rosa
Field, Eastern
Venezuela Basin
Lithofacies,
petrofacies
Leal, et al.
[2001]
Block IX sands,
Lake Maracaibo
Basin, Venezuela
Lithofacies,
petrofacies
Reference
Madariage,
et al. 2001]
Porras, et al.
[2001]
Solo, et al.
[2001]
Sandstone/
C4 & C5 sands,
Lagunillas Field,
Lake Maracaibo
Basin, Venezuela
Tertiary &
Cretaceous sands,
Santa Barbara
Field, Eastern
Venezuela Basin
K1sands,Suria
& ReformaLibertad Fields,
Apiay-Ariari
Basin, Columbia
Lithofacies,
petrofacies
Data Sources Evaluation Methodologies
 Depositional environments, sand body geometry, dimensions
from core descriptions
 Texture, composition, lithology from microscopic imaging
 No Quantitative porosity-permeability ranges, provided qualitative
indicators
 Physical core descriptions of both large-scale & small-scale features
microscopic imaging of texture, composition, lithology, diagenesis
 Core-based measurement of porosity, permeability; dominant pore throat
diameter from mercury-injection capillary pressure data
 Depositional environments, sand body geometry, dimensions from
core descriptions
 Texture, composition, lithology from microscopic imaging
 No quantitative porosity-permeability ranges ;provided qualitative
indicators
 Physical core descriptions of both large-scale & small-scale features;
microscopic imaging of texture, composition, lithology, diagenesis
 Core-based measurement of porosity, permeability; dominant pore
throat diameter from mercury-injection capillary pressure data
 Physical core descriptions of both large-scale & small-scale features;
microscopic imaging of texture, composition, lithology, diagenesis
 Core-based measurement of porosity, permeability; dominant pore throat
diameter from mercury-injection capillary pressure data
 Physical core descriptions of both large-scale & small-scale features;
microscopic imaging of texture, composition, lithology, diagenesis
 Core-based measurement of porosity, permeability, electrical
properties; dominant pore throat diameter from mercury-injection
capillary pressure data
No specific
definitions
 Physical core descriptions of both large-scale & small-scale features;
microscopic imaging of texture, composition, lithology, diagenesis
 Core-based measurement of porosity, permeability; dominant pore throat
diameter from mercury-injection capillary pressure data
No specific
definitions
 Core-based measurement of porosity, permeability; dominant pore throat
diameter from mercury-injection capillary pressure data
 Used fuzzy logic to predict rock types in uncored wells
Marquez, et
al.
[2001]
LL-04 sands,Tia
Juana Field, Lake
Maracaibo Basin,
Venezuela
Lithofacies,
petrofacies
 Identification of stratigraphic units and lithofacies from log analysis
 Physical core descriptions of small-scale features; microscopic
imaging of texture, composition, lithology
 Core-based measurement of porosity, permeability; up scaled
permeability using NMR log measurements
Ali-Nandalal
& Gunter
[2003]
Pleistocene-age
sands, Mahogany
Field, Columbus
Basin, Venezuela
Geological
facies,
Petrophysic
al rock
types
 Facies identified using core- and log-based analyses of primary
sedimentary structures
 Core-based measurement of porosity, permeability and electrical
properties
Shushufindi
Field sands,
Oriente Basin,
Ecuador
Geological
facies
El Furrial Field
sands, Venezuela
Geological
facies,
Petrophysic
al rock
types
Napo formation
sands, Oriente
Basin Ecuador
Petrophysical
rock type
Formation
unknown, location
unknown
Geological
facies,
Petrophysic
al rock
types
Ohen, et al.
[2004]
Acosta, et al.
[2005]
Guo, et al.
[2005]
Shenawn, et
al.
[2007]
 Facies identified using core- and log-based analyses of stratigraphy,
structure, depositional environment
 Core-based measurement of porosity, permeability and water
saturation
 Facies identified using core- and log-based analyses of stratigraphy,
structure, depositional environment
 Core-based measurement of porosity, permeability and water
saturation; pore characteristics from mercury-injection capillary
pressure data
 Core-based measurement of porosity, permeability and water
saturation; pore characteristics from mercury-injection capillary
pressure data
 Facies identified using log-based definitions of shale content,
lithology (density log)
 Core-based measurement of porosity, permeability and water
saturation; pore mercury-injection capillary pressure data
67
In this study, K means clustering is used for rock type classification because the method is
very effective when large quantities of data are available.
Macqueen (1967) developed the K means clustering algorithm. This algorithm assign a
specific number of centers, k, to represent the clustering of N points (k<N). These points are
iteratively adjusted so that each point is assigned to one cluster, and the centroid of each
cluster is the mean of its assigned points. In general, the K means technique will produce
exactly K different clusters of the greatest possible distinction. The main idea behind the K
means algorithm is the minimization of an objective function usually taken up as a function
of the deviations between all patterns from their respective cluster centers. The
minimization of such an objective function is found using an iterative scheme, which starts
with an arbitrary chosen initial cluster membership. Further iterations refine the clustering
result (Michael, 1999).
The algorithm is summarized as follows (Fig. 4.11):
1. Consider each cluster consisting of a set of M samples that are similar to each other:
x1, x2 , x3 , . . . , xm,
2. Choose a set of clusters [y1 , y2 , y3 , . . . , yk],
3. Assign the M samples to the cluster, using the minimum Euclidean distance rule,
4. Compute a new cluster so as to minimize the cost function,
5. If any cluster changes, return to step three; otherwise stop,
6. End.
Before applying K means clustering it should be noted that some limitations of data
distributions occurred such as variation in size, differing densities and non-globular shapes.
They key in overcoming this limitation is to use many clusters (find parts of clusters and then
apply a merge strategy) (Fig.4.12).
Two stages are applied for overcoming the K means limitation noted above. Firstly, the data
are divided up into manageable data clusters. The number of clusters should be enough to
cover all the different data ranges seen on the log. 15 to 20 clusters appears to be a reasonable
number for most data sets. The second step, which is more manual, is to take these 15 to 20
68
clusters and group them into a manageable number of geological facies. This may involve
reducing the data to 4 or 5 clusters (IP-3.5 manual, 2009).
4.3.2 Applying K means for the data group 3 (G3: Z76, Z81, Z82)
This process mirrors the approach taken in section 4.2 in which 6 HUs were predicted.
Grouped wells (G1, G2, G3, G4) were used to predict the rock types in the study area. After
testing six logs provided good response for the rock types selected for the K means clustering:
GR, DT, NPHI, EN16 and EN64. For testing, data was selected from top horizon 1 (H1) to
top horizon 2 (H2) (~ 500 to ~800 m). The matrix crossplots and histograms for each log
exhibit a simple normal distribution, which in case of K means clustering will simplify
classification of rock types (Fig. 4.13).
Firstly, to overcome K means limitations and cover all of clusters, the data was divided into
14 clusters. The 14 “clusters mean” and standard deviation of logs after applying the K means
method are presented in table 4.7.
Based on the cluster grouping dendrogram (Fig. 4.14a) we can select the number of clusters.
Alternatively the cluster randomness plot (Fig. 14.14b) indicates the number of clusters that
can be selected in the study area. Finally, it was decided to reduce 14 clusters to 6 clusters to
correspond to 6 rock types (6RTs) in the reservoir.
Crossplots of 5 logs against 6RTs in the well Z76 are presented in figure 4.15. In figure 4.15a
(GR/DT) and 4.15b (GR/NPHI) with GR < 70 the separation between two main groups (RT5,
RT6, RT7) and (RT8, RT9, RT10) can be clearly seen. The RT5 can be seen in figure 4.15b
with GR <70 and 0.26 < NPHI < 0.42. Separation between RT8 and RT9 is indistinct. RT6
and RT7 can be seen in the crossplot GR/EN16 and GR/EN64 where GR < 70 and EN64 > 3
for RT4 (Fig. 4.15c, d). The results of the rock type selection and GR in wells of group 3 are
presented in figure 4.16.
4.4 Relationship between Hydraulic Flow Unit (HU) and Rock Types (RT)
To understand the underlying geology controlings petrophysical properties for different rock
types, Svirsky, et al. 2004, investigated available results of sieve analysis, thin sections and other
special core analyses giving grain size, sorting, pore geometry and mineralogy. This geological
and physical background provides vital links between micro-characteristics of the pore space and
commonly available log data, which are used for HU prediction in uncored wells.
69
Rock types can be used to link depositional facies and wireline log response. Mikes al et.
(2006) presented ideas for the relationship and upscaling between static models (geological
models, reservoir models) to dynamic models (flow unit models). Schematic relationships are
presented in figure 4.17:

Standard facies models can serve as a template for reservoir models,

Flow unit and facies are key elements of the reservoir and geological model,
respectively,

Reservoir models can be represented by a small number of units, whilst preserving all
levels of heterogeneity, the spatial distribution of facies/flow units and their hydraulic
flow properties,

All elements (facies) and boundaries for a specific depositional environment are
universal, whilst facies geometries are specific.
The transformation of facies into flow units and hence the geological model into a reservoir
model is not simple task. The value of this approach is that the reservoir model preserves the
spatial distribution of facies. It is especially this spatial distribution that controls flow on a
regional scale. This makes the method an efficient tool to quickly model fluid flow through a
reservoir, enabling routine modeling and sensitivity analysis (Mikes al et., 2006) .
Hydraulic units are related to geological facies (rock types) distributions but do not
necessarily coincide with facies boundaries (Abbaszadeh, al et., 1995). Comparison between
rock types (RTs) and hydraulic flow units (HUs) is presented in table 4.8. In figure 4.16 GR,
6HUs and 6RTs of the group 3 is presented to show that the best rock type properties of RT5
response to HU5 and HU6.
70
Start
Number of
cluster K
Centroid
Distance objects
to centroids
N
No object
move
group?
Y
End
Grouping based on
minimum distance
Figure 4.11 The workflow of the K mean clustering
3 Groups
10 Groups
3 Groups
10 Groups
2 Groups
10 Groups
Fig.4.12 The limitations and overcomes limitations of the K mean clustering (after
Tan, al et, 2004)
71
400
350
Frequency
300
250
Z76
200
150
100
50
0
20
40
60
80
GR (API)
100
Z81
120
700
440
420
600
400
500
Frequency
DT (US/M)
380
360
340
320
Z82
400
300
200
300
100
260
40
60
80
GR (API)
100
0
250
120
0.5
0.5
0.45
0.45
0.4
0.4
0.35
0.35
NPHI (NPHI)
NPHI (NPHI)
20
0.3
0.25
300
350
DT (US/M)
400
450
700
600
Frequency
280
0.3
500
400
300
0.25
200
0.2
0.2
0.15
0.15
100
0
40
60
80
GR (API)
100
120
250
300
350
DT (US/M)
400
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
NPHI (NPHI)
450
8
7
7
7
600
6
6
6
500
5
4
3
2
5
4
3
2
Frequency
8
EN16 (OHMM)
8
EN16 (OHMM)
EN16 (OHMM)
20
5
4
400
300
3
200
2
100
1
1
1
0
40
60
80
GR (API)
100
120
250
300
350
DT (US/M)
400
450
2
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
NPHI (NPHI)
4
EN16 (OHMM)
6
8
8
8
7
7
7
7
400
6
6
6
6
350
4
3
5
4
3
5
4
3
450
Frequency
5
EN64 (OHMM)
8
EN64 (OHMM)
8
EN64 (OHMM)
EN64 (OHMM)
20
5
4
300
250
200
3
150
100
2
2
2
2
1
1
1
1
50
0
20
40
60
80
GR (API)
100
120
250
300
350
DT (US/M)
400
450
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
NPHI (NPHI)
2
4
EN16 (OHMM)
6
8
2
4
EN64 (OHMM)
6
8
Figure 4.13 The matrix crossplots of 5 logs (GR, DT, NPHI, EN16 and EN64) and
histograms for each curves show data distribution of group 3 (Z76, Z81, Z82)
before applying K means clustering
72
Table 4.7 The statistics of the group 3 (Z-76, Z-81, Z-82) for 14 clusters after applying K
means clustering
Cluster Groups Randomness
20
19.5
Lever cut off to select
six Grouping
clustersDendrogram
Cluster
19
18.5
Randomness Ratio (Low more Random)
18
27
26
25
24
23
22
21
20
19
18
17
16
10
17
16.5
16
15.5
15
14.5
14
13.5
13
12.5
12
11.5
11
10.5
15
13
17.5
2
9
14
12
7
6
11
8
5
1
4
3
10
9.5
Number of Cluster Groups : 6
Clustering Method : Maximum distance between all objects in clusters
2
3
4
5
6
7
8
9
10
11
12
13
14
Number of Clusters
(a)
(b)
Figure 4.14 Applying K mean clustering for the group 3:
(a) The cluster grouping dendrogram shows 4 clusters with diffident 4 colors
respond
(b) The cluster groups randomness
73
Z-values: 6RTs
0.2
96
0.25
104
0.3
112
DT
0.35
NPHI
120
0.4
128
0.45
136
0.5
144
Z-values: 6RTs
(b)
0.15
88
(a)
30
40
50
60
70
80
90
30
100
40
50
60
GR
RT5
RT6
RT7
RT8
RT9
90
100
Z-values: 6RTs
7.2
9
80
RT10
Z-values: 6RTs
F7
F10
F8
F9
F6
F5
1
1.6
2
2.4
3
3.2
4
EN16
5
4
EN64
4.8
6
5.6
7
6.4
8
70
GR
0
0.8
(c)
40
50
60
70
GR
80
90
100
(d)
40
50
60
70
80
90
100
GR
Figure 4.15 The cross plots of data in well Z-76 shows 6 rock types (6 clusters)
a) GR/DT,
b) GR/NPHI,
c) GR/EN64, d) GR/EN16
74
Figure 4.16 Comparison between 6 rock types (6RTs) and 6 hydraulic flow unit (6HUs)
75
Figure 4.17 Relationship between geological model, reservoir model and flow unit model
(after Mikes D., al et. 2006)
1. Geological model and assignment of its elements
2. Reservoir model and assignment of its elements
3. Micro simulation model, consisting of numerical flow simulation on all flow cell
models of the reservoir, yielding effective one- and two-phase permeabilities, and
capillary pressures
4. Macro simulation model, consisting of numerical flow simulation on the entire
reservoir, yielding production history
76
Table 4.8 Comparison between hydraulic flow units (HUs) and rock types (RTs) in the study
Data
Hydraulic Flow Units
Cores, logs
Driver
FZI_core (K and Phi)
Classification/
Prediction
Number
Probability plot, Ward’s
cluster, ACE and cutoff of GR
6HUs
Characterizations
Similar fluid flow zone in the
reservoirs
Rock Types
Logs
Log properties: shape, value of
parameter
K means clustering
6RTs
Lithologies facies, depositional
environments facies
(Reservoir and non-reservoir flows)
4.5 Conclusions
Effective methods were proposed to calculate the Flow Zone Indicator, FZI, as a continuous
function of depth using well log data, and to determine hydraulic units in a reservoir. These
definitions of the homogeneous parts of a formation will form the basis for media flow
modeling. The study started from core data, since they are relatively easily measured and
available, and since they are frequently proposed to reservoir engineers as the only data
available to determine permeability. Our goal was to show that the correct combination of
well log and core data will provide reservoir engineers with a tool for determining FZI and
permeability in a continuous geological profile.
Statistical methods that combine core and log data provide an effective and multidimensional
tool for reservoir engineers to construct a static model of a reservoir that agrees well with
reality. Correctness of statistical data should be taken into account in the defined range of
accuracy. The range of accuracy obtained in the study is acceptable, for the given precision of
the laboratory measurements and logging measurements. The choice of alternating conditional
expectations algorithm (ACE) instead of linear multiple regression (LMR) was based on the
assumption that petrophysical parameters belong to a group of fuzzy data. The relationships
between the individual factors are known and we can describe them, yet it is very difficult to
parameterize most of these relationships. When applying ACE heuristic reasoning was included
for the relationships between real parameters, but a “blind” statistical tool was used to determine
the optimal transformation of data, treating the data as values without geological meaning.
77
The method proposed for obtaining core origin FZI, for determining a continuous log of FZI
on the basis of well log in full geological profile, and for determining homogeneous hydraulic
units in a reservoir rock in the study area was tested and validated. Since permeability is an
extremely important reservoir parameter for reservoir engineering, the solutions for modeling
this parameter described in literature and tested by various authors are of great interest. From
a practical point of view, it is very important to develop an effective method for precisely
dividing the Sarmatian reservoir into HUs. The permeability predicted from logs in uncored
sections of individual wells was correct and could be used in a modeling stage.
Statistical methods turned out to be useful, flexible, and effective, and they provide the
interpreter with tools that deliver acceptable results. Unsupervised K means clustering is
effective for classifying six rock types. The ACE method is good for predicting FZI from core
and log. The results obtained in this chapter were used to create a static model of the reservoir
for media flow modeling in the next chapter.
78
Chapter 5
STATIC MODELING
In chapter 3, using core and well log data we divided the reservoir into six HUs (Tab. 3.2, Fig.
3.7). Integrating both types of data, the FZI_log was predicted using the Alternating
Conditional Expectations (ACE) algorithm and then six HU_logs were generated (Fig. 4.5).
Six rock type logs (6RTs) were classified using K-mean clustering (Fig. 4.25) in Chapter 4.
In this chapter, 2D seismic data and log data were integrated for static modeling by applying
geostatistical methods as Sequential Indicator Simulation (SIS) for rock type and hydraulic
flow unit modeling and Sequence Gaussian Simulation (SGS) for reservoir properties (PHI,
Sw) modeling. This chapter is divided into three parts:
1. A discussion of the basic theory of reservoir modeling, spatial relationships and
geostatistical (SIS, SGS) methods.
2. Creating a 3D structure model with four horizons, derivation of Rock Type and
hydraulic flow unit models.
3. Generation of property models (PHI, K, Sw and Net to Gross, NTG) constrained
by the HU model.
5.1 Reservoir modeling overview
5.1.1 Reservoir modeling workflow
Three dimensional reservoir modeling is a broad field of expertise in which geostatistics is
one of several key components. The aim of 3D modeling is to provide one or more alternative
3D numerical models to represent those geological, geophysical, and reservoir engineering
aspects of the subsurface that help achieve the study goal. These numerical models are used to
estimate key reservoir parameters such as original oil in place (OOIP), to predict production
performance, and to provide uncertainty statements when needed (Caers, 2005).
Generally, we can divide reservoir modeling into two main parts: static modeling and
dynamic modeling. There are four steps to reflect the different scales of heterogeneity
modeling:
1. to build the structural framework of the reservoir,
2. to model the facies architecture and the distribution of the different facies types,
79
3. to describe the petrophysical properties,
4. to generate a homogeneous model which can be upscaled model for application to
fluid flow simulations.
In this study, the main modeling workflow is shown in figure 1.1. To create the fluid flow
simulation (Chapter 6) we modeled the Hydraulic Flow Units that constrain the rock type
model. In the next step, the property model (porosity) was constrained by HU model.
5.1.2 Deltaic facies and spatial relationships
It was particularly difficult to generate an accurate 3D distribution of hydraulic flow units
(HU) using only geostatistical methods and data only from 7 wells. To improve the HU
model, we constrained it by the facies model. The facies model provided additional spatial
classification of porosity and permeability, which are the two main parameters influencing
FZI. Some basic concepts of deltaic facies and spatial relationship are introduced below.
Deltaic facies:
As discussed in Chapter 2, the depositional environment in the study area is mainly influenced
by deltaic processes. The deltaic lobes have a distinct morphology which reflects the dynamic
fluvial and marine processes controlled by variations in climate and paleogeography. This
explains why the facies distribution is very complex in the deltaic environment.
An example of a deltaic model is shown in figure 5.1a. The overall geometry of a
distributary channel deposit is of a low sinuosity sand body elongated parallel to the channel
axis. Mud plugs accumulated at the end of flood stages locally compartmentalize the
reservoir sands. Sand thicknesses decrease rapidly away from the channel axis. Parallel to
the distributary channel, the sand thickness decreases over a distance of 5 km from a
maximum of 5 m at the fluvial channel mouth, to 25 cm within coalescent braid bar deposits
on the delta front (Lang et al., 2000).
Variogram and spatial relationships:
In figure 5.1b we can easy see that distance of the point C (unknown point) is closer to point
B than point A but the value of parameter in that point (for example PHI) of point C should be
closer to point A than point B because both of points C and A belong to the channel. It is
clearly explained:
80
-
how an unknown point relates to a known point with the facies constrain,
-
how properties modeling is strongly influenced by facies models.
The variogram is the most commonly used measure of spatial correlation for cell based facies
and property modeling. Various discussions on variogram and variogram modeling are
available in the literature (Clayton, 2002). A variogram is a description of the variation in a
property, based on the principle that two points close together are more likely to have similar
values than points far from each other (Fig. 5.2 a, b).
The concepts of variogram parameters and the variogram ellipsoid around a grid cell are
shown in figure 5.3b and 5.3b. The variogram is defined as the expected value, 2(h).
Experimentally, the semivariogram is one half of the variogram that for lag distance h is
defined as the average squared difference of values separated approximately by h (Eq. 5.1).
(5.1)
Where:
h
: lag vector representing separation between two spatial locations,
N(h)
: the number of pairs for lag h,
u
: vector of spatial coordinates,
z(u)
: variable under consideration as a function of spatial location,
z(u+h) : lagged version of variable under consideration.
81
(a)
CHANEL
Nearest known value
data point
B
Unknown point
? C
A
(b)
Fig. 5.1 Deltaic facies model and special relationships control by facies distribution
a) reservoir heterogeneity and longitudinal facies variation developed within the eastwest distributary channel of the Neales Delta (modified from Lang et al., 2000)
b) how unknown point relates to a known point (Gocad Manual, 2009)
82
Because geological data is usually anisotropic (at least between the vertical and horizontal
directions), variograms can be calculated in several different directions. These are commonly
created with the major and minor axes in the XY plane and in the vertical direction. However
the major axes may not necessarily follow geological layers.
Major direction: The major axis or direction defines the direction where the sample points
have the strongest correlation. The angle of this major direction can be changed interactively
by editing the direction in the search cone. The angle is specified as the clockwise angle from
north (in degrees) for the main search direction.
Minor direction: The minor search direction is perpendicular to the major direction.
Vertical direction: The program searches for sample pairs vertically using the vertical search
distance. Orientation is not used when calculating a vertical sample variogram.
In the study area, due to the irregular distribution of wells it was difficult to generate a good
horizontal variogram model (Fig. 5.2c). In the vertical direction we have a better variogram
model with the range about 10 m (Fig. 5.2d).
Normally, the range of a variogram could be different in different directions and often vary
vertically, therefore in this study we used the same variogram parameters model for all
stochastic models (Tab. 5.1).
Table 5.1 The grid parameters used for stochastic variogram models
Type
of function in
variogram
Exponential
Vertical
Range
Minor
Major
Azimuth
Nugget
10
4000
5000
0
0.01
5.1.3 Geostatistical methods overview
Traditional reservoir modeling techniques use variogram and two-point statistics to represent
geological phenomena that have complex geometrical configurations. The use of multipoint
statistics improved the modeling techniques in recent years, reducing the limitations. The
Multiple Point Statistics (MPS) module in Petrel® 2009 for facies modeling release
reintroduced multipoint geostatistics, providing a new method to model complex geological
features and connectivity.
83
However, in this study, with lack of geological information to create a training image for MPS
modeling process, we used two methods that are still the most popular and flexible techniques
for geostatistical applications - Sequential Gaussian Simulation (SGS) for continuous
variables like porosity and Sequential Indicator Simulation (SIS) for categorical variables like
rock type and HU. Some main points for SIS and SGS are reviewed below.
Sequential modeling is a general approach to conditional stochastic simulations. Gaussian
random models are used in statistics and simulations due to their analytical simplicity.
Gaussian models are theoretically consistent models. The Gaussian approach is also related to
maximum entropy and correspondingly to the maximum disorder in the data. It is not the best
choice when spatial correlations between extremes are of special interest. In that case we can
use another nonparametric model like indicator based simulations.
(a)
(b)
(c)
(d)
Fig. 5.2 Variogram modeling
a) concepts of variogram parameters,
b) variogram ellipsoid around a grid cell. The values of cells outside the ellipsoid are
independent of the value of the current cell (Roxar Manual, 2009),
c) horizontal variogram of porosity modeling (7 wells),
d) vertical variogram of porosity modeling (7 wells).
84
Sequential Gaussian Simulation (SGS)
The basic idea of Sequential Gaussian Simulation (SGS) is similar to kriging. Recall that
kriging gives us an estimate of both the mean and standard deviation of the variable at each
grid node, meaning that a variable at each grid node can be represented as a random variable
following a normal (Gaussian) distribution. Rather than to choose the mean as the estimate at
each node, SGS chooses a random deviate from this normal distribution, selected according to
an uniform random number representing the probability level. So, the basic steps in the SGS
process are:

generate a random path through the grid nodes,

visit the first node along the path and use kriging to estimate a mean and standard
deviation for the variable at that node based on surrounding data values,

select a value of random deviate from the corresponding normal distribution and set
the variable value at that node to that number,

visit each successive node in the random path and repeat the process, including
previously simulated nodes as data values in the kriging process.
A random path is used to avoid artifacts induced by walking through the grid in a regular
fashion. We include previously simulated grid nodes as “data” in order to preserve the proper
covariance structure between the simulated values (Bohling, 2005).
Sequential Gaussian simulation generates a set of equally probable realisations of a 3D
porosity field. Each simulated realisations also different share the same global distributions
and spatial correlation. The differences between realisations characterise the variability and
uncertainty in the model.
Sequential Indicator Simulation (SIS):
The sequential indicator simulation (SIS) includes all data available within a neighborhood,
including the original data and all previously simulated values. The objective is to generate a
joint realization of the random variables at the unsampled locations. The sequential simulation
approach requires simulation of a prior distribution at each unsampled location.
The SIS method is similar to Sequential Gaussian Simulation (SGS), expecting that indicator
kriging is used to build up a discrete cumulative density function (CDF) for the individual
85
categories at each case and the node is assigned a category selected at random from this
discrete CDF. Very briefly, an indicator representation for a categorical variable such as
facies would be formulated as:
1
i (u ; k )  
0
(5.2)
where: 1, when facies k present at uα,
0, otherwise,
and we have one indicator variable for each of the K different facies. We can then use kriging
(based on indicator semivariograms) to produce a set of facies membership probabilities at
each grid point, build up a cumulative distribution function (CDF) from the probabilities, and
select a facies as random from the CDF (Bohling, 2005). Sequential Indicator Simulation
results are realisations of facies distributions. A set of equally probable realisations can be
post processed to obtain statistical inference used directly in further simulation steps as
independent realisations.
5.2 Structure modeling
Structure modeling is the first step in the reservoir modeling workflow (Fig. 1.1). In the
Petrel® system structure modeling is subdivide into three main steps (Petrel® Manual, 2009):

Fault modeling: defining the faults in the geological model which form the basis for
generating the 3D grid.

Pillar Gridding: generating the grid representation as the base of all models.

Making Horizons: building the zones in the reservoir model and then creating the
layers in the zones.
In this study, we have a 2D seismic survey with 25 lines which were recorded in 2002 (Fig.
5.3a). As the first stage in processing the miss-tie between all lines was corrected.
86
5.2.1 Miss-tie correction for 2D seismic survey
A simple, but effective algorithm based upon weighting value assignments using a variance
criterion was used. It assumed miss-tie values to be random variables. The algorithm satisfies
the following requirements:

after correction the miss-ties should be reduced to a minimum after the error
adjustment,

the method should be applicable to any survey configuration.
There should be a way to define a weighting factor to good lines (reference lines) in
comparison to lines showing data of poor quality (Petrel® Manual, 2009). An example of the
result before and after correction the miss-tie between two lines is presented in figure 5.3b.
5.2.2 Horizons picking and creating the 3D grid
Horizon picking
In this study we only focused on picking the Miocene horizons in the lower part of borehole
profiles and also ignored some small faults that were mentioned in some geological setting
documents (Chapter 2).
After the miss-tie correction, four horizons - H1, H2, H3 and H4 were mapped on the basis of
the phase of maximum amplitude on 25 seismic lines corresponding to well markers (well
tops ) Top_7, Top_12, Top_15 and Top_17 (Fig. 5.4a) (Gas Field Z-L, Report, 2005). 4
surfaces that were created by gridding corresponding to 4 horizons are presented in figure
5.4b. We can see that 7 wells (Z75, Z76, Z78, Z79, Z81, Z82 and Z84) are located at the
central part of the study area, where there is a structural high, coinciding with good reservoir
potential for the gas flow (Table 6.1 in Chapter 6). Another group of 3 wells (Z72, Z72, Z77)
is located in the eastern part of the study area.
Creating the 3D grid
The next step of structure modeling is to create 3D grid blocks within the reservoir base
volume of 4 horizons. The volume of reservoir is divided into 3 zones: Zone1, Zone2 and
Zone3 between each horizon (H1-H4). Initially, in order to capture all of the reservoir
property down to fine level, a very fine model was created with the grid block size being 50m
87
x 50m in the X and Y direction. In the vertical direction - Z, we used grid size about 1 meter
as the layer scale. So, the reservoir was divided into 189 layers. This grid method led to a grid
that was 170x168x198 in size containing 8934354 grid blocks in total. Since it was assumed
that reservoir contains no important faults, the gridding process was simplified and any faults
were not included. Basic parameters of the 3D grid are shown in Table 5.2.
At the final step, on the basis of the check-shot data of 7 wells in the central part the study
area the model were converted from time (ms) to depth (m) (Fig. 5.4b). In order to keep better
correlation between seismic and log data and also focus on the central part where better
reservoir is potential in the next step 7 wells were used for rock type and properties modeling.
Table 5.2 The 3D grid parameters
Zone
Average thickness (m)
Number of layers
Number of cells
Zone1 (H1-H2)
58
54
2436642
Zone2 (H2-H3)
55
44
1985412
Zone3 (H3-H4)
100
100
4512300
Total
213
198
8934354
88
(a)
Before
After
(b)
Fig. 5.3 2D seismic data in the study area
a) 25 lines 2D seismic survey and 10 wells location
b) the miss-tie correction for the 2D seismic survey
89
H1
H2
H3
H4
(a)
H1
H2
H3
H4
(b)
Fig. 5.4 Horizon picking
a) four horizons interpreted basically on 25 lines of 2D seismic and the well-tops of
main interpreted horizons: H1(Top_7), H2(Top_12), H3(Top_15) and H4(Top_17),
b) the 3D structure mode in the study area; four surfaces were created from 4 horizons
H1, H2, H2 and H4 and 10 well locations
90
5.3 Rock Type (RT) and Hydraulic Flow Unit (HU) modeling
Several new methods are presented in the literature discussing use of 3D seismic data to
improve facies modeling. But only a few papers discuss using 2D seismic with facies
modeling. Shuguang, et al. (1999) presented conditional 3D simulation of lithofacies with 2D
seismic data using a new methodology and the corresponding GSLIB-type program to
integrate 2D average information, such as vertically averaged lithofacies proportions, into
estimation/simulation of 3D lithofacies distributions. Seismic information, available in 2D, is
used in the cokriging of the 2D average lithofacies proportions. Results showed that even with
limited well data, the input vertical lithofacies proportions (which carry the seismic
information) is honored quasi-exactly. Three steps were taken:

co-located cokriging is used to incorporate 2D seismic information into the estimation
of vertical lithofacies proportions,

indicator kriging is used to derive the facies conditional probabilities at each of the 3D
simulation grid node; this 3D indicator kriging uses the hard well data and the
previously estimated vertical proportions,

p-field simulation algorithm is used to draw simulated lithofacies indicators from the
previously obtained distributions.
In this study, facies modeling on the basis of 7 wells lead us to unexpected results so in this
part we also integrated log information from 7 wells and seismic data from 25 lines of 2D
seismic to improve the facies modeling. The results of facies modeling are used to constrain
HU modeling and 3D property modeling. The main steps used in this study are shown in the
workflow below (Fig. 5.5) (Ha Quang and Jarzyna, 2010).
91
Fig. 5.5 The workflow for reservoir modeling in this study
92
HU_MODEL
2D SEISMICS
SGS: Sequence Gaussian Simulation
SIS: Sequence Indicator Simulation
UNN: Unsupervised Neural Network
ACE: Alternating Conditional Expectation
K.C.A: Kozeny-Carman equation modified by Amaefule
PHI_MODEL
SGS
SIS
PHI_log
SIS
RT_MODEL
Facies_UNN
UNN
Attributes
PSEUDO 3D SEISMICS
Mis-tie Correction
Horizon Picking
Surfaces mapping
Up scaling
Amplitude to 3D Grid
Amplitude Modeling
SGS
AMPLITUDE MODEL
ACE
ECLIPSE
K_MODEL
HU_log
GR_cutoff
FZI_log
Upscaling
K.C.A
RT_log
K-mean
A_logs
LOGS
FZI_mean
HU_core
Ward’s
FZI_core
CORES
5.3.1 Conversion of 2D seismic to pseudo 3D seismic
Nowadays, 3D seismic is the most common and effective method for reservoir structure
interpretation (horizons and faults) and properties prediction (porosity, permeability, fluid
saturation). Rapid improvement of the strong hardware and software in the petroleum industry
allowed us to visualize and extract 3D objects (geobody) directly from 3D seismic and
improve reservoir understanding, detect anomalies, and define facies model.
In the study area the 2D seismic survey has a density of 25 lines (Fig. 5.3a) and this dense
grid can be leveraged to overcome some of the limitations of 2D seismic data. At the first step
of modeling we converted the 2D survey to a pseudo 3D seismic cube using the Sequence
Gaussian Simulation (SGS). The main steps for converting the 2D seismic survey to a pseudo
3D seismic cube are shown in the workflow (Fig. 5.5, left column).
The volume of the 3D seismic cube was limited to the reservoir interval study - between top
of horizon H1 and bottom of horizon H4 (Fig. 5.6a).
The 2D seismic profiles were upscaled into the 3D grid (Fig. 5.6b, 5.7a) using the
2DSeis2Seis3D plug-in of Petrel® (SLB, plug-in, 2008). Then, SGS geostatistical technique
was applied to interpolate all data in three directions. The result is named the pseudo 3D
seismic cube and the amplitude model is shown in figure 5.6c.
The amplitudes in both the pseudo 3D seismic and the 2D seismic were compared for
validation purposes. The results are shown in figure 5.7. This indicates clearly that the pseudo
3D seismic is well matched to the 2D seismic. This pseudo 3D seismic will be useful for
extracting attributes and geobodies for seismic stratigraphic classification in the next sections.
93
H1
H4
(a)
(b)
(c)
Fig. 5.6 Convertion from 2D seismic to pseudo 3D seismic cube using SGS
a) 2D seismic survey - top and bottom of the reservoir,
b) 2D seismic profiles - uplscaled to 3D grid,
c) pseudo 3D seismic cube after applying the SGS method.
94
The block average
of 2D seismic
(a)
2D seismic
Pseudo 3D seismic
(b)
Fig. 5.7 Pseudo 3D seismic cube
a) the block average data of 2D seismic after upscaling into 3D grid,
b) comparison between 2D seismic profiles and the pseudo 3D seismic cube.
95
5.3.2 Rock Type modeling constrained by seismic facies model
First we modeled Rock Type because the outcome of this modeling narrowed the range of
possible porosity and permeability models and because the Hydraulic Flow Unit properties
can vary significantly between each rock type. Three methods for the 3D rock type modeling
are applied in this study responding to the workflow in figure 5.5:
1. seismic facies extraction volume,
2. seismic facies classification using Unsupervised Neural Network (UNN) –
deterministic statistic method,
3. Rock Type modeling using Sequential Indicator Simulation (SIS) - stochastic method.
Applying K mean clustering method to the RT well log data allows us to derive 6 classes, as
summarized in section 4.3.
5.3.2.1 Seismic facies extraction volume
Seismic surveys typically provide exhaustive coverage of the reservoir volume, but unlike
wells, seismic provides only indirect information on reservoir properties and at a much
coarser scale and resolution. The scale of observation can usually be estimated, typically on
the order of 10 to 100 ft in the vertical and 100 to 1000 ft in the horizontal, depending on the
reservoir depth. The difference between the seismic data scale and the scale at which
geocellular models are built can be one order of magnitude or more in the vertical dimension.
Such a difference is of critical importance when simulating fluid flow: this is why a
geocellular model is needed.
Seismic facies and seismic attributes
Seismic facies analysis is an example of other than structural information derived from
seismic. Seismic facies analysis is an useful tool for reservoir characterization. A seismic
facies unit can be defined as a sedimentary unit which is different from adjacent units in its
seismic characteristics. Parameters that should be taken into consideration in the seismic
facies analysis are as follows: reflection amplitude, dominant reflection frequency,
reflection polarity, interval velocity, reflection continuity, reflection configuration,
abundance of reflections, geometry of seismic facies unit, and relationship with other units
(Roksandić, 2006).
96
Interpretation of seismic facies data may be either direct or indirect. The purpose of the direct
interpretation is to find out geological causes responsible for the seismic signature of a
seismic facies unit. So, the direct interpretation may be aimed at predicting lithology, fluid
content, porosity, relative age, overpressure shales, type of stratification, geometry of the
geological body corresponding to the seismic facies unit and its geological setting. The
indirect interpretation is intended to reach some conclusions on depositional processes and
environments, sediment transport direction, and some aspects of geological evolution
(transgression, regression, subsidence, uplift, erosion) (Roksandić, 2006).
Seismic attributes and their applications as geological indicators for reservoir interpretation
are presented in Table 5.3. Generally, frequency attributes relate to bed thickness, wave
scattering, and absorption. Time attributes relate to structure and amplitude attributes relate to
stratigraphy (Chopra, et al., 2005). In this study, several seismic attributes were extracted
from the pseudo 3D seismic volume (Fig. 5.11).
Table 5.3 Seismic attributes corresponding to reservoir characterizations (Chopra, et al., 2005)
Volume Attributes
Bedding
Continuity
Lithology,
Porosity
Structure
Thickness
Envelope
Instantaneous
Phase
Instantaneous
Frequency
Average Weighted
Frequency
Semblance
Waveform Difference
Spectral Decomposition
Simple Difference
Relative Acoustic
Impedance
Sweetness
97
Seismic facies extraction volume
We were able to interactively blend multiple seismic volumes, isolate areas of interest, and
then extract what is visualized into a 3D object called a geobody. As the geobody was
extracted, the interpreter assigned a geological template to the geobody, assigning the
geobody to a geological class providing the body with instant geological meaning. Geobodies
could be included directly in the 3D geological model, bridging the gap between geophysics
and geology (Petrel® Manual 2009).
The histogram of the “amplitude envelope” attribute reveals the distribution of the geobodies
inside the volume. This is achieved by visual inspection and interactive filtering of the
rendered volume (Fig. 5.8a, b). The resulting geobody representing the deltaic environment in
the study area is shown in figure 5.8c. We can observe the geobody/facies is close to the
concept of the deltaic environment outlined in chapter 2. The main direction of channel
system in this interval from northwest to southeast with one delta lobe being very clearly
imaged in the west part.
In figure 5.8c we show that the G3 group of wells (Z76, Z81, Z82) and G4 group of wells
(Z78, Z79) were drilled in the west part of the study area in an area having a very complex
facies distribution. Wells of G2 group (Z75, Z84) were drilled in the channel system (middle
part) and wells of G1 group (Z72, Z74, Z77) were drilled in the east part of the study area
where there is the delta lobe facies. The well Z72 is at the extreme edge of the delta lobe.
Due to low vertical resolution of the pseudo 3D seismic the result achieved using this
methodology provided a simple picture of the facies distribution in the study area. We could
not clearly differentiate the facies distribution in the west part of the study area. In addition
the distribution of the six rock types (chapter 4) was sub optimal. In order to improve
discrimination within the facies model we apply Unsupervised Neural Network (UNN) for
seismic facies classification.
98
Data filter
(a)
(b)
Delta plain
Channel system
Delta lobe
Fault (?)
(c)
Fig. 5.8 Channel system and delta lobe (geobody) facies from pseudo 3D seismic extraction
a) envelope histogram before filtering,
b) envelope histogram after filtering,
c) model of deltaic environment in the study area.
99
5.3.2.2 Seismic facies classification
Artificial Neural Network (ANN) is becoming more popular as a tool utilized in the field of
reservoir characterization. The neural network techniques are applied for well log and seismic
facies classification and characterization of reservoir properties. For seismic facies analysis
Unsupervised Neural Network (UNN) is most commonly used. This technique does not
require prior knowledge of object to be classified and is based on pattern recognition and a
self-organization program which decides how to separate some attributes into classes. The
neural network program then classifies the data, based on the amplitude and shape
characteristics of the attributes that are input.
Supervised Neural Networks (SNN) are applied for classification of facies and for predicting
reservoir properties (porosity, permeability) from the combination of various samples based
on seismic attributes including acoustic impedance and well log data. In this approach well
points are considered as training points and the statistical methods are used to derive the
relationships between the attributes and well log data. Carrillat and Valles (2005) have
showed clearly eight steps for seismic facies classification workflow (Fig. 5.9):
1. generation of the seismic texture attribute cubes,
2. running a classification in an unsupervised mode (A) and inspection of the results,
3. running a supervised classification with user-defined selection of training points (B),
and examination of these points in N-dimensional space to ensure adequate clustering
and minimal overlap between the training points,
4. evaluation of the supervised classification output, using (i) checking the result in 3D
and comparing the results against the seismic/attribute cubes used and, (ii) the
uncertainty analysis of the classification with probability cubes,
5. the removal/incorporation of training points/seismic attribute cubes prior to making a
revised classification,
6. final tuning of the neural network parameters,
7. visualization and interpretation of the data and the analysis of facies associations and
structures in 3D space,
100
8. finally, the calibration of the results against well data allows establishing a
deterministic link between seismic facies and lithology.
In this study, due to the paucity of wells for training data and limitations in the quality of the
pseudo 3D seismic we did not observed a good correlation between seismic attributes and log
data. Therefore we applied the Unsupervised Neural Network method for seismic facies
classification to improve the results from this area of investigation. UNN technology is shown
in figure 5.10 where we input the seismic attributes for UNN processing, the output result
being the facies classes.
In order to reduce noise in the seismic data and also to focus on the reservoir interval
(between H1 and H4), all of the attributes were sampled into the 3D grid. After testing UNN
with several seismic attributes we identified four attributes that correlated well with facies:
these are Amplitude (raw data), Relative acoustic impedance, Envelope, and Sweetness (Fig.
5.11). There are different attributes here and in Fig. 5.11.
Fig. 5.9 The workflow for seismic facies classification using ANN method (Carrillat and
Valles, 2005)
101
Attributes input
UNN processing
Facies classes
Fig. 5.10 Application of the Unsupervised Neural Network technology for seismic facies
classification
Relative acoustic impendence
Sweetness
Envelope
Root mean square (RMS)
Fig. 5.11 Seismic attributes generated from pseudo 3D seismic amplitude for UNN processing
102
Because we used the UNN method for the facies classification, the main consideration in
choosing the number of classes/facies was focused to balance the level of real geological units
with the statistical outcomes. Ideally, each chosen facies should be geologically significant
and yet we need to have enough data to allow reliable inference of the required statistics for
reservoir modeling. In practice, it is difficult to support more than four different facies from
the data. The facies must have clearly different petrophysical properties or spatial features that
make them easy to model. There is no benefit to separate the data according to facies that do
not lead to distinguishable flow properties (Clayton, 2002).
Now, we met the same problem discussed in section 4.4 - to overcome limitation of
unsupervised clustering method - unknown number of classes for the primary input. The same
problem in the K-mean clustering method had been discussed when we derived HU from well
log data. At the first step we divided the data into 10 classes/facies for UNN processing to
recognize a maximum number of classes/facies in the data. The names and percentage (%) of
data of each facies are shown in figure 5.12a and the 3D model result named 10Facies_UNN
is displayed in figure 5.13a.
In the next step, on the basis of the histogram of 10 facies (Fig. 5.12a) we decided to reduce
the number of facies to 6 facies (Fig. 5.12b) to secure correspondence with 6 Rock Types
from log data. In this case, in a very simple way we could combine the first four facies (0 + 1
+ 2 + 3) with smaller percentage (%) into the facies 4 and keep the same next five facies with
higher percentage (%). Figures 5.12c, d, e, f showed the crossplots between two seismic
attributes corresponding with the colors of 10 and 6 facies.
At the final step, in order to reduce the influence of noise in the pseudo 3D seismic data we
smoothed the 6Facies_UNN model. The 6Facies_UNN model after smoothing is displayed in
figure 5.13b. This result showed clearly the delta lobe and the channels system that was
similar to the geobody facies model in figure 5.8. But this model shows more details for each
facies distribution, both laterally and vertically. A comparison between 10Facies_UNN model
and 6Faceis_UNN model in cross sections cut through 3 wells (Z81 – Z76 – Z82) from upper
to lower part is also presented in figure 5.13.
103
5.3.2.3 Rock Type modeling
Seismic data are often ideal for constraining numerical facies models of object based or
training image based algorithms. The large scale information provided by seismic correlates
better with large scale facies variations (proportions) than with fine scale petrophysical
properties. Directly constraining porosity model to seismic is difficult because porosity
measurements from cores or well logs often show a low collocated correlation with the
seismic data. Before applying a geostatistical algorithm for constraining facies models to
seismic, a calibration of the information content of seismic on facies presence is obtained.
From the 3D seismic data, for calibration purposes, one retains only seismic observations
made along the well paths that contain logs or have been cored. Next, one estimates the
probabilistic relationship between facies presence and seismic data from the pair of seismic
and well data (Caers, 2005).
Seismic waves respond to large scale geological events within the reservoir. Geological events
can be seen directly from seismic attributes. The result outcome using seismic extraction
volume and seismic facies classification in this study has proved high usefulness for rock type
modeling. The 6Facies_UNN (Fig. 5.13b) showed very good distribution close to our
understanding of deltaic depositional environment. However, it was built automatically and
only on the base of pseudo 3D seismic data. Manual interpretation may improve this model.
In figure 5.13b we observe the lateral facies distribution which we assume as good for
horizontal (X and Y directions) scale because of the relatively high density of the 2D seismic
data. In figure 5.14a, however, we need to consider that for the vertical (Z direction) scale the
resolution is not sufficient due to complex geological structure of the thin interbedded sandyshaly layers in the study area. We can easily recognize that if the thickness of facies is smaller
than seismic vertical resolution (~10 – 20 m) that facies cannot be displayed in the facies model.
Figures 5.14 shows the comparison between seismic based 6Facies_UNN and the 6RT_log
results. In the vertical direction the seismic facies have a low resolution on the order of 10’s
of meters. Conversely the log based Rock Type facies results has a very high resolution on the
order of 1 meter or so. For this reason, to improve the 3D Rock Type model in vertical Z
direction, after the seismic facies classification step, we applied the stochastic method Sequential Indicator Simulation (SIS) for Rock Type modeling (the workflow in Fig. 5.5).
104
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 5.12 Reduction from 10Facies_UNN to 6Facies_UNN on the basis of the facies histogram
a) 10Facies_UNN histogram,
b) 6Facies_UNN histogram,
c) Crossplot of Amplitude & Relative acoustic impedance for 10Facies_UNN,
d) Crossplot Amplitude & Relative acoustic impedance for 6Facies_UNN,
e) Envelope & Relative acoustic impedance for 10Facies_UNN,
f) Envelope & Relative acoustic impedance for 6Facies_UNN.
105
(a)
Delta plain
Delta lobe
Mouth bar
(b)
Fig. 5.13 3D Facies classification using UNN method
a) 3D 10Facies_UNN and cross section
b) 3D 6Facies_UNN and cross section
106
The SIS is a kriging-based stochastic method mentioned in section 5.1.3. Application of that
method to the rock type distribution provided a result which honored at the well data at each
well location. In order to improve in horizontal resolution caused by uneven spatial distribution
of wells the 6Facies_UNN is used for rock type conditioning in this step. The resulting model
6RT_SIS is shown in Fig. 5.16a. The cross section in the figure 5.14b shows a good match
between the 6RT_SIS model and the 6RT_log model. For the purpose of comparison in three
dimensions the 6Facies_UNN model was filtered to display only facies F8 which imaged delta
lobe distribution very clearly. In addition, the 6RT_SIS model was filtered to display 3 rock
types (RT7, RT8, RT9). This showed more detail in the Rock Type distribution and while
honoring the log data at the respective well locations (Fig. 5.15). The 4 rock type maps
responding to 4 surfaces (H1, H2, H3 and H4) show that rock type distribution varies with
depth as shown in figure 5.17.
5.3.3 Hydraulic Flow Unit modeling constrained by Rock Type model
Six hydraulic flow units (6HUs) have been defined in the study area (Chapter 4) and upscaled
into the 3D grid as facies data. Once again, the Sequence Indicator Simulation (SIS) method
was applied for 3D HFU modeling. In order to control distribution of HU, the 6RT_SIS is
used for constraining the HU model. The resulting model 6HU_SIS is shown in Figure 5.16b.
A comparison between 6RT_SIS and 6HU_SIS in 3D window is shown in figure 5.16. On the
different surfaces (H1, H2, H3 and H4) in figure 5.17 we can see that edges of the rock type
and hydraulic flow units do not match exactly but the overall depositional trend is similar.
The trend of rock type 10 (RT10/shale) is close that of to HU1 and the trend of the good
reservoir units (HU6, HU5) are close to the trend of facies RT7, RT8.
107
108
(d)
(b)
Matching with RT_log
Not Matching with RT_log
Fig. 5.14 Comparison 6Facies_UNN and 6RT_SIS;
a) 6Facies_UNN and 6RT_log,
b) 6Facies_UNN histogram,
c) 6RT_SIS and 6RT_log,
d) 6RT_SIS (blue) and 6TR_log (green) histogram.
(c)
(a)
(a)
(b)
Fig. 5.15 Comparison between seismic facies classification (6Facies_UNN) and 3D rock type
model (6RT_SIS)
a) 6Facies_UNN model filtered to display only faceis F8_UNN showing clearly delta
lobe distribution in the study area,
b) 6RT_SIS model filtered to display 3 Rock Types (RT7, RT8, RT9) showing in more
details rock type distribution and honoring wells location.
109
(a)
(b)
Fig. 5.16 Comparison between the 6RT_SIS and 6HU_SIS
a) 3D 6RT_SIS,
b) 3D 6HU_SIS
110
6RT_SIS
6HU_SIS
(H1)
(H2)
(H3)
(H4)
Fig. 5.17 Comparison of 6RT_SIS and 6HU_SIS in 4 horizons: H1, H2, H3 and H4
111
5.4 Property modeling constrained by HU model
The final step of static modeling is property modeling (Fig. 5.5). As discussed in section
5.1.3, Sequence Gaussian Simulation (SGS) is commonly used in property modeling. In this
study, 3D porosity (3D PHI) models are generated corresponding to the six hydraulic flow
units model (6HU_SIS) using the SGS method.
Due to very complex variation of permeability in the reservoir model we should first model
porosity and then permeability. Generally, permeability modeling will be done using SGS and
co-kriging with the porosity model. In this project with advantages of applying the hydraulic
flow unit method we can directly calculate the 3D permeability model from the 3D porosity
model using Kozeny- Carman equation 3.8 in Chapter 3 (Ha Quang and Jarzyna, 2011a,b).
5.4.1 Porosity and permeability modeling
a) Porosity modeling without any conditions or constraints
Porosity was calculated on the basis of logs from 7 wells and then upscaled into the 3D grid.
The SGS method was applied to interpolate porosity into the 3D model, without any
conditions or constraints so the result was strongly influenced by variogram parameters.
b) Porosity modeling constrained by 3D Hydraulic Flow Unit model (PHI_HU)
Following the workflow in this study (Fig. 5.5), the final porosity model was constrained by
the 3D Hydraulic Flow Unit model using the SGS method and the same variogram parameters
(Table 5.1). 3D porosity model (PHI_HU) is shown in figure 5.18a where porosity
distribution responds to 6 HUs, high porosity values correlate with HU6s, HU5s and HU4s
and low porosity with HU1s, HU2s and HU3s.
c) Permeability calculation using Kozeny-Carman equation (K_HU)
In the 3D model we also applied equation 3.8 to calculate permeability model (K_HU) on the
basis of 3D 6HU_SIS (Fig. 5.16b), 3D PHI_HU (Fig. 5.18a) and FZI_mean (Table 3.2). The
result is shown in figure 5.18b and distributions of PHI_HU and K_HU are presented in figure
5.19. The cross plot of 3D PHI_HU vs. 3D K_HU shows very clearly the relationship between
K and PHI corresponding to each HU (Fig. 5.20). The picture in this figure can be compared
with the plot in figure 3.7 (Chapter 3). There is observed correlation between permeability from
logs (K_log) and permeability calculated for 3D model (Fig. 5.21). We can see that
permeability of HU1 is slightly smaller than K_log but in other HUs the correlation is excellent.
112
(a)
(b)
Fig. 5.18 Comparison between 3D PHI_HU model and the 3D K_HU model
a) porosity model constrained by HU model (PHI_HU)
b) permeability model calculated from the porosity model using Kozeny-Carman
equation (K_HU)
113
Porosity
Permeability
(H1)
(H2)
(H3)
(H4)
Fig. 5.19 Comparison between PHI_HU model and the K_HU model; results presented on
various surfaces
114
Fig. 5.20 Cross plot of 3D PHI_HU versus 3D K_HU; shown very clear relationship between
K and PHI responding to each HU
Fig. 5.21 Cross plot between permeability from logs (K_log) and permeability calculated for
3D_K_HU model from the mean values of FZI for HU
115
5.4.2 Water saturation and Net to Gross modeling
a) Water saturation modeling
An improved technique for modeling the initial reservoir hydrocarbon saturation is presented.
In contrast to the Leverett J- function approach (5.3), this methodology (hereby termed flowunit-derived initial oil saturation or FUSOI) determines the distribution of the initial oil
saturation from a measure of the mean hydraulic radius, referred to the flow zone indicator
(FZI). In the FUSOI approach, capillary pressure parameters (Pc), irreducible water saturation
(Swir), pore-entry pressure (Pd), and pore-size distribution index (, derived from the Brooks
and Corey (1966) model (Eq. 5.4), are correlated to the FZI. Subsequent applications of these
parameters then permit the computation of improved hydrocarbon saturations as functions of
FZI and height above the free water level (FWL). This technique has been successfully
applied in the Mississippian Aux Vases Sandstone reservoirs of the Illinois Basin (USA)
(Udegbunam & Amaefule, 1996).
Amaefule (1995) showed that the Leverett J function should only be used to correlate
capillary pressure data for samples from the same flow unit (Fig. 5.22). The Pc and Sw data are
very satisfactorily matched by Brooks and Corey’s equation and the best correlations of Swir,
 and Pd are shown as equation 5.5, 5.6 and 5.7 (Udegbunam & Amaefule, 1996).
However, in this particular gas reservoir, due to lack of data for reservoir rock properties and
uncertainty about the free water level (FWL), in order to correlate Sw to the hydraulic flow
units, one again, we used the SGS method for water saturation modeling and constrained it by
the 6HU_SIS model. The Sw model was shown in figure 5.23 made it easy to calculate gas
saturation model (Sg) by equation 5.8.
 
 









116



Sg = 1 – Sw

(5.8)
Where: J(Sw) = Leverett J function (dimensionless),
Sw = water saturation for a given capillary pressure,
Swir = irreducible water saturation,
Pc = capillary pressure at any height above the free water level,
Pd = pore-entry pressure,
pore-size distribution index,
 = contact angle,
 = interfacial tension.
Fig. 5.22 Typical capillary pressure curves for different flow units fitted with the Brooks and
Corey’s equation (Udegbunam & Amaefule, 1996)
117
Fig. 5.23 Water saturation model constrained by Hydraulic Flow Unit model (6HU_SIS)
b) The 3D Net to Gross model (NTG)
The principal use of cut-offs is to delineate net pay, which can be broadly described as the
summation of those depth intervals through which hydrocarbons are (economically)
producible. In the context of integrated reservoir studies, net pay has an important role to play
both directly and through a net-to-gross pay ratio. Net pay demarcates those intervals that are
the focus of the reservoir study. It defines an effective flow thickness that is pertinent to the
identification of flow units, that identifies target intervals for well completions and
stimulation programs, and that is needed to estimate permeability through the analysis of well
test data. The net to-gross pay ratio is input directly to volumetric computations of
hydrocarbons in place and then to "static" estimates of reserves. It is a key indicator of
hydrocarbon connectivity, and it contributes to the initializing of a reservoir simulator and
then to "dynamic" estimates of reserves. Unfortunately, there is no universal definition of net
pay nor is there general agreement on how it should be delineated. For this reason, net pay has
been incorporated within integrated reservoir studies in many different ways that have not
always been fit for purpose. In particular, there is no generally accepted method for
118
quantifying net pay cut-offs, without which net pay cannot be delineated (Worthington and
Cosentino, 2003).
Normally, in sandstone reservoir we can use Vsh, Sw, PHI and K from logs data for reservoir
cut-off values. In this study with some advantages of applying HU method we directly
calculated 3D NTG model on the basis of 3D HU model. Histograms of 6HUs and NTG
models are presented in figure 5.24 and parameters used to calculate 3D NTG (Fig. 5.25) are
shown in table 5.4.
Table 5.4 The values cut-off reservoir basic on 6 HUs
6HUs
Cutoff value
for 3D NTG
HU1
HU2
HU3
HU4
HU5
HU6
0
0.4
0.5
0.7
0.8
1
6HUs Histogram
Net to gross histogram
Fig. 5.24 Comparison between 6HUs histogram and Net to Gross (NTG) histogram
119
Fig. 5.25 Net to gross model based on 3D HU model
5.5 Conclusions
In this chapter one of possible methodologies for incorporating 2D seismic information
and well logs in stochastic simulations of rock type modeling was presented. A main point
in this approach is the ability to simulate the 3D rock type at a fine scale while accounting
for larger scale 2D seismic derived information and then constrain to 3D HU modeling in
the study area.
Geostatistical modeling using the Sequence Indicator Simulation (SIS) and the Sequence
Gaussian Simulation (SGS) methods were used in this study for rock type modeling.
Specially, with high density distribution of 2D seismic data, the stochastic method (SGS) was
a good choice to convert the 2D seismic survey into pseudo 3D seismic cube.
The geobodies that were extracted from the pseudo 3D seismic show a simple picture of
deltaic facies distribution and the channel systems prograding from northwest to southeast.
Applying this solution, the results mainly depended on the density of 2D seismic lines and
also quality of seismic data.
120
Seismic traces contain information about facies changes and contrasts. Cluster analysis
was the approach that had potential to classify seismic trace shapes into meaningful facies.
In this study the Unsupervised Neural Network (UNN) was used to classify the pseudo 3D
seismic attributes into six facies (6Facies_UNN). In order to improve result seismic
attributes were resampled into the 3D grid before clustering and the final facies model
also needed to be smoothed.
Applying deterministic-statistic (seismic extraction volume, UNN) and stochastic (SIS)
methods and then combining them we improved Rock Type modeling. The result (6RT_SIS)
showed better rock type distribution in lateral (X, Y) and vertical (Z) directions and then the
model was used to constrain the hydraulic flow unit modeling. Comparing the rock type
model and HU model we observed that although the borders did not match the trends of HU
were similar to the rock type distribution. It means that the 3D HU model was not only
dependent on reservoir properties (K, PHI) but also was controlled by paleostratigraphy
(facies or rock type).
The porosity model was constrained by the 6HU_SIS model obtained using SGS method. The
PHI_HU model showed porosity distribution corresponding to 6HUs, with higher porosity
value in HU6, HU5 and HU4 and lower porosity in HU1, HU2 and HU3. The 3D
permeability model (K_HU) was calculated using Kozeny-Carman equation on the basis of
3D PHI_HU and FZI_mean of each HU. In each HU a good correlation between permeability
log (K_log) and 3D permeability model (K_HU) was clearly visible which confirmed the
advantage of applying the HU method in this study.
Due to lack of SCAL data for reservoir rock parameters the 3D NTG model was calculated
directly from 3D HU and it again showed the advantages of HU methods. The static models
created in this chapter will be upscaled for reservoir simulation in the next chapter.
121
Chapter 6
HISTORY MATCHING UNDER HYDRAULIC FLOW UNIT CONTROL
Static modeling presented in the previous chapters provides an effective method to
characterize reservoirs using cores, logs, and seismic data. However, they do not account
for the dynamic data such as pressure, and oil and gas production, which are an important
goal of the petroleum industry. Engineering decisions cannot be based on static models
that do not match historical production data. Historical production data provide a direct
observation of the ultimate modeling goal: reservoir flow performance. Any method for
integrating production data into 3D static models will call upon a reservoir simulator or
dynamic modeling.
Theoretically, an integration of additional data into reservoir model should lead to a more
realistic model with reduced uncertainty range. In reality however, flow simulation requires
the knowledge of many additional reservoir parameters that sometimes simply are not
available. In such situations flow simulation becomes closer to an art rather than an
engineering science.
In this chapter, the static models in Chapter 5 need to be constrained to dynamic data obtained
from historical production data. To achieve this, we used the ECLIPSE® 100 software for
history matching. The workflow used was as follows:

up scaling of the Petrel® geological model to a reservoir model for input to Eclipse®,

specifying the reservoir initial condition,

running the model to extract reservoir performance data on history matching control
by HU model,

discussion.
Due to lack of initial condition data in the reservoir interval we used some default parameters
in Petrel® software for simulation case such as relative permeability (Kg, Kw). Before
discussing history matching under HU control, some main points of history matching will first
be reviewed.
122
6.1. History matching under Hydraulic Flow Unit control
6.1.1 History Matching Overview
Ideally, reservoir models should match the observed dynamic behavior of the reservoir within
some accepted tolerance. To check the model's consistency with dynamic data, flow
simulation is required. However, flow simulation is CPU-demanding and is only rarely
applied directly to the high-resolution geocellular model. Some form of upscaling, also
termed model coarsening, is required to reduce the number of grid cells and make flow
simulation feasible. Even if upscaling were not required, the geocellular model built solely
from well-log and seismic data rarely matches the production data. The process of
adjusting/perturbing an initial reservoir model to match production data is commonly known
as history matching. The history matching step is iterative, whereby the initial model is
perturbed many times, either manually or automatically, to achieve a satisfactory history
match (Caers, 2005).
The purpose of history matching is not just to match historical results to current results, but
rather to produce models that can be used to forecast reservoir performance within some
accepted tolerance. The goal is to produce reservoir models that have an improved prediction
power over models that do not match history. It is the combination of all data matching,
including production data plus a correct geological model that makes a good reservoir model.
Because there is no objective measure to gauge the degree by which a model will predict
future performance accurately, the best one can be done is to build reservoir models that
match all relevant reservoir data, including production data, and reflect as realistically as
possible the subsurface heterogeneity.
History matching, therefore, should never be an isolated task left to the sole ability of the
reservoir engineer. Instead, production data should be considered as one additional, important
piece of information in model building. One should take care in integrating this information
jointly with all other relevant data. History matching is called for at various stages of the
reservoir modeling task depending on the amount of production data available. In general,
there are two main stages:
123
Stage 1: Adjusting Large/Field-Scale Structural Elements
At this stage, one is merely interested in determining the large-scale "plumbing" of the reservoir
correctly. Usually, this involves adjusting the following elements of a reservoir model:

position and transmissibility of the main faults,

depth and strength of the fluid contacts (water/oil/gas),

overall reservoir pore volume,

fluid properties [pressure/volume/temperature (PVT)] and rock compressibility,

for all compartments: average permeability, porosity, and saturations,

relative permeability curves.
These properties are often adjusted manually or interactively. Automatic procedures are rarely
applied at this stage.
Stage 2: Adjusting Local Reservoir Properties
Stage 1 may provide a good overall field match (total production, rates, and pressure), but it
may not provide a satisfactory local, well-by-well match. This would involve the following
adjustments:

variable transmissibilities along the fault surfaces,

local facies proportions and their spatial distribution, including relative permeability
curves per facies,

porosity and permeability distributions within facies.
Before any history matching exercise, whether manual or automatic, a sensitivity study
investigating which component (global or local) of the reservoir model has greatest influence
on production data is required. Regardless of the efficiency of any particular history matching
method, if one does not perturb the components ranked as most sensitive to production data, a
history match may never be achieved. Such a study may also expose the shortcomings of the
initial geocellular model. For example, if an inappropriate variogram based approach for
modeling permeability is used in a strongly channeled reservoir, then regardless of how much
one perturbs that variogram, a history match may never be achieved. Sensitivity can be
evaluated from sound engineering expertise and insight into the particular situation at hand;
that in sight can be confirmed by means of experimental design-type studies.
124
6. 1.2. History matching under Hydraulic Flow Unit control
Traditional method:
Normally, a two stage approach is used to produce consistent petrophysical properties, i.e.,
porosity and permeability, with the underlying geological description. This goal is achieved
through two independent processes, which are later combined to produce the final result by a
filtering process. The first process is the simulation of geological description. The second
process is the simulation of porosity. The permeability description can be obtained through
correlation between porosity and logarithm of permeability once the final porosity description
is produced. To combine the results of these two processes, i.e., geological and porosity
simulations, a filtering process is applied. The filtered porosity at a grid block is obtained by
first examining the type of geological unit at that location and then selecting the porosity
value from the corresponding realization. Once the filtered porosity is known, the
permeability value at that location can be determined using the suitable correlation. This
approach has produced consistent result, between the petrophysical properties and the
underlying geological description (Kelkar al el., 1997) (Figure 6.1).
Fig. 6.1 Schematic diagram of two stages approach (Kelkar al el., 1997)
History matching under Hydraulic Flow Unit control:
Figure 6.2 shows in more detail the four main stages used to integrate from geophysical to
geological data into static models. Note that for each HU we have good correlation between
porosity and permeability (Fig. 6.3). The final results will be upscaled and input to Eclipse® for
125
126
Fourth stage
Fig. 6.2 The four main stages to integrate geophysical and geological data into reservoir modeling with
HU method in the study (modified from Kelkar al el., 1997)
Third stage
KHU6
HU6
HU6
RT10
F10
Second stage
KHU5
HU5
HU5
RT9
F9
First stage
KHU4
HU4
HU4
RT8
F8
KHU3
HU3
RT7
F7
HU3
KHU2
&K
Correlation
HU2
Filtering by
SGS method
HU2
Filtered
Permeability
RT6
Filtered
porosity
F6
1 2 3 4 5 6
Porosity simulation
for each HU
KHU1
HUs
HU1
HU1 HU2 HU3 HU4 HU5 HU6
HU simulation
for each Rock type
HU1
Geological
simulation
RT5
RT5 RT6 RT7 RT8 RT9 RT10
Rock type
simulation
F5
Geophysical
simulation
flow simulation. The workflow of history matching is controlled by hydraulic flow unit
method displayed in figure 6.4. The procedure workflow is as follows:
1. data input: static model (PHI, K, NTG), PVT data, and initial reservoir condition, and
historical production data,
2. flow simulation using program ECLIPSE® 100,
3. history matching criteria, which either require some adjustment of the model parameters,
4. model adjustment includes: change of size grid upscaling, relative permeability
function(s), Net to Gross cut off,
5. Production forecast for gas volume production.
(b)
10000
1000
K [mD]
100
10
HU1
HU2
HU3
HU4
HU5
HU6
1
0.1
0.01
0.05
0.1
0.15
0.2
0.25
0.3
(c)
0.35
PHI [fraction]
(a)
Fig. 6.3 Hydraulic Flow Unit control
a) Cross plot K vs. PHI responding to 6HUs (core data),
b) 6HUs section of 3 wells (Z81, Z76 and Z82),
c) Permeability section of 3 wells (Z81, Z76 and Z82).
127
core
Logs
Seis.
HU
PHI
Production
& PVT data
NTG
K
ECLIPSE
Adjust Model
HISTORY
MATCHING
No
Yes
Production Forecast
Fig. 6.4 The workflow of history matching under Hydraulic Flow Unit control (modified from
Mikhail, 1997)
128
6.2. Upscaling
Many reservoir flow simulators cannot directly and effectively handle the size of grids used in
geological models. Such models can easily contain as many as 10 million cells, whereas
single CPU simulations will only run in reasonable time with models of the order of 100,000
cells. Furthermore, grids used in geological models are often unsuitable for simulation due to
geometric problems such as inside-out cells. Upscaling is the process of creating a coarser
(lower resolution) grid based on the geological grid which is more appropriate for simulation.
While this necessitates the omission of much of the geological models fine detail, the result is
intended to preserve representative simulation behavior. In Petrel®, upscaling is split into two
steps (Petrel® 2010, Manual):

Scale up Structure: define the new layering scheme (numbers and shapes of layers) of
the simulation grid,

Scale up Properties: populate grid properties, such as porosity and permeability, based
on those in the fine grid.
Scale up Structure:
Table 6.1 shows the parameters of scale up grid structure. The number of cells must
therefore be reduced by up scaling structure. In this study, we tested many grids and a
bigger grid with bock sizes of 300x300x99 gave better results and also increased the speed
of simulation in Eclipse®.
Table 6.1 Upscaling structure models for Eclipse® simulation
Models
Grid parameters
Grid size
Total cells
Fine scale
50x50x189
267x169x198
8934354
Model 1
100x100x189
133x84x198
2212056
Model 2
200x200x99
66x42x99
274428
Model 3
300x300x99
44x28x99
121968
129
Scale up Properties:
Properties from one grid can be transferred to another grid of a different resolution or
orientation using the Scale up properties process. This is usually done in the context of
building a simulation model from a geological model, where the simulation model has been
coarsened and reoriented for flow simulation. Some quantities, such as porosity and water
saturation are easy to upscale, because they may be averaged arithmetically.
Averaging can be based on volume or on number of cells. Volume-weighted averaging will
weight source property values by the volume contributed by the fine cell, whereas cell count
averaging will give equal weight to all source cells involved in the average (regardless of
variations in their volumes). Cell count averaging is not available when using the all
intersecting cells sampling method because a fine grid cell will contribute to multiple coarse
grid cells when using this sampling method, so volume-weighting must be used to ensure its
overall contribution respects fine grid volumes (Petrel® 2010, Manual). In figures 6.7 a, b, c, d
there are shown 3D_HU and 3D_PHI upscalings into grid 300x300x99 (Model3 – Table 6.1).
However, the 3D permeability model (3D_K) is much more difficult to upscale. There are
many papers discussing how to make an optimal upscaled permeability model for reservoir
simulation. In this study, due to complex HU distribution, we used the Flow Based Tensor
Upscaling method for upscaling permeability with some of the input parameters shown in
figure 6.5. A comparison between fine scale and the result after downscaling of permeability
is show in figures 6.6 and 6.7.
130
Fig. 6.5 The Process Dialog for Flow-Based Tensor Upscaling
Flow-based upscaling involves performing a numerical pressure simulation on the block of
fine cells coinciding with each coarse cell to determine a representative coarse cell
permeability. The process will calculate I, J, and K or X, Y, and Z permeabilities from input
as permeability in the I, J and K directions, net-to-gross and porosity. If the Output full tensor
permeabilities option is used, then off-diagonal terms in the permeability tensor (in the IJ, IK
and JK directions) will also be calculated. It is assumed that the system is symmetrical, i.e. IJ
= JI. Tensor upscaling methods always include a fine grid cell in its entirety (or not at all) in
the calculation of each coarse grid cell value. As such, small intersections can cause more
cells than expected to be incorporated, particularly when using the all intersecting cells
sampling method. When doing tensor upscaling between closely aligned grids, always use the
cells with center inside target cell or Zone-mapped layers sampling methods to avoid
unexpected "grazing" intersections (Petrel® 2010, Manual).
131
(1)
(2)
(3)
(4)
(5)
Fig. 6.6 Comparison of scale of permeability in well Z76
(1) Log scale, (2) Log upscaled in 189 layers (static model scale),
(3) Ki, (4) Kj, (5) Kk - permeability downscaled in 99 layers by Flow Based Tensor
Upscaling method (dynamic scale).
132
Static models
Dynamic models
(a) HU (50x50x198)
(b) HU (300x300x99)
(c) PHI (50x50x198)
(d) PHI (300x300x99)
(e) K (50x50x198)
(f) K (300x300x99)
Fig. 6.7 Comparison of static scale results (a, c, e) and dynamic scale results (b, d, f)
133
6.3 Reservoir initial condition
The conditions in the reservoir that the simulator used to calculate the pressure and phase
saturations in every grid block during initialization should be defined. Each fluid region in the
reservoir may contain a number of different, unconnected initial condition regions. For each
region we must specify a reference depth and corresponding pressure, gas-oil contact depth
and water contact depth that depending on which phases in the reservoir.
Make fluid model:
Fluid models are used by the simulator to define how physical properties of the fluid such as
density and viscosity vary with pressure and temperature. Fluid models may also define how
the initial conditions in the simulator are to be calculated, by specifying the fluid contacts,
pressure, and compositional variation with depth.
In the reservoir study, due to lack of initial condition data we can take the average value of
initial pressure and temperature measured in some wells from Table 6.2 - Pi = 60 bar and Ti =
35oC and also unclearly information for a gas-water contact (GWC); so we assumed that it is
below 900m (almost below reservoir section). The gas components taken from the report
(Geological documentation of Z-L gas field) are shown in Table 6.3.
Table 6.2 Pressure and temperature measurement results (Geological documentation of Z-L
gas field)
Wells
Z74A
Z74A
Z74A
Z74A
Z74A
Z74A
Z74A
Z74A
Z75
Z75
Z76
Z76
Z76
Z76
Z76
Z76
Z76
Z76
Z82
Z82
Depth [m]
650
552.5
873.5
734
783.5
765.5
734
783.5
778.5
617.5
739.5
702.5
686
646.5
612.5
593
560
563
549.5
487
Pressure [bar]
62.8
54.6
89.2
76.3
82
79.9
46.7
51.3
76.9
61.2
70.3
67.9
64.9
61.1
56.5
55.2
52.6
35.7
51.7
37.7
Temperature [oC]
33.65
34.75
34.85
32.85
30.85
30.05
-
134
Table 6.3 Gas components (Geological documentation of Z-L gas field)
Components
CH4
C2H6
C3+
C02
N2
3
H2S[mg ]
He[%]
[%]
96.98
0.109
0.015
0.000
2.896
0.000
0.000
Making rock physics functions:
Petrel® software includes some functions of saturation or pressure used in simulation that
represent the physical parameters of fluids and rocks, or interaction between rocks and fluids.
Saturation functions are in tables showing relative permeability and capillary pressure versus
saturation. These tables are used to calculate:

the initial saturation for each phase in each cell,

the initial transition zone saturation of each phase,

fluid mobility to solve the flow equations.
Unfortunately, without lab data for the relative permeability and capillary pressure curves data
we had to use default values for saturation function. Figure 6.8 shows gas and water relative
permeability in sand and shaly-sand (Petrel® 2010, Manual).
Fig. 6.8 Gas (Kg) and water (Kw) relative permeability curves in sand and shaly-sand reservoir
(Petrel® 2010, Manual)
135
Rock compaction functions are in tables showing pore volume multipliers versus pressure,
or a single rock compressibility value used by the simulator to calculate the p ore volume
change. Creating rock compaction functions also creates a transmission multiplier versus
pressure curves. Figure 6.9 shows parameters of rock compaction function where we also
used porosity and HU model. In this case, we assume that all cells with the similar
properties (PHI) form a region of the grid, and a separate rock compaction function is
created for each hydraulic flow unit.
Fig. 6.9 Rock compaction function responding with porosity model and each hydraulic
flow unit
136
6.4 History matching and discussions
Historical production data (observed data)
In this study for history matching simulation only 3 wells (Z74A and Z75 and Z76) which
have gas flow production between H1 and H4 horizon were used. The perforation intervals
and time starting produce and status of each well are presented in Table 6.4.
Table 6.4 Perforation intervals and time starting produce and status of Z74A, Z75, and Z76 wells
Perforation (m)
Time starting produce
Status
Top
Bottom
Thickness
[DD/MM/YYYY]
(10/01/2010)
Z74Ad
781
786
5
09/01/2006
production
Z74Ag
723
744
21
09/01/2006
shut-in
Z75d
656
660
4
06/01/2009
shut-in
Z75g
541
571
30
06/01/2009
shut-in
Z76
560
566
6
12/01/2008
production
Wells
“g” means upper completion,
“d” means lower completion
The observed historical gas flow rate and bottom hole pressure (BHP) data are shown in
figure 6.9 and Table 6.5 (Appendix A). In order to show more clearly advantages of applying
HU method for reservoir simulation we also run Eclipse® with static models by using
traditional method.
6.4.1 Results
Traditional method with two stages (Fig. 6.1):
Following the work flow in figure 6.1 means that we only use facies model constrains to
property models (K, PHI) and then make up scaling of the data and input them into Eclipse®
for history matching. The results of history matching simulation in the form of gas flow rate
and bottom hole pressure, BHP, are displayed in figure 6.11.
HU method with four stage (Fig. 6.2):
After testing history matching for several various grid sizes (table 6.1), NTG models, and
some functions of back-oil fluid model (PVT) we decided to run the simulation with main
parameters as follows:
1. grid: 3D grid size (300x300x99) with: Ki, Kj, Kk, PHI_HU and NTG,
137
2. functions: Back-oil fluid model (PVT) controlled by hydraulic flow units model,
3. strategies: Development strategy from 09/01/2006 to 1/10/2010 with two option of
production control mode: Reservoir volume and Gas control.
The result of the first case simulation with reservoir volume control is shown in figure 6.12
and the results of the second case with gas control are presented in figure 6.13. In both cases
of simulation for 3 wells we see that the gas flow rate production was well matched with
historical production data (Figs 6.12a, 6.13a) and the BHP simulation is higher than observed
data. Only in the Z74Ag well at lower part of perforations the results of simulation are closed
to observed data (Figs 6.12b and 6.13b).
6.4.2 Discussion
Comparison of simulation results between traditional method and applying HU method in
figures 6.11 and 6.12 shows that HU method give better results than traditional method.
Especially BHP results in HU method are close to observed data even in this case parameters
as relative permeability (Kg, Kw) and rock compression were used as default ones. We also
considered the following reasons as influencing the history matching results:

from 3 wells used as input to Eclipse® simulation only two wells - Z75 and Z76 were
included to static modeling (Chapter 5); the Z74A well (close to well Z74) was
excluded so we can use this well for validation of static model in history matching,

in the reservoir interval, due to very thin and interbedded shaly - sandy layers we
observe high water saturation from well log data, somewhere over 80%, and the gas
water contact (GWC) was also unclear, so we decided exclude water saturation model
in Eclipse® simulation.
138
(a)
(b)
Fig. 6.10 Historical production data for 3 wells: Z74A, Z75 and Z76
a) Gas Flowrate,
b) Bottom Hole Pressure (BHP)
139
(a) Gas Flowrate
(b) Bottom Hole Pressure
Fig. 6.11 History matching results (line colors) and observed data (dot points) of traditional
method
140
(a) Gas Flowrate
(b) Bottom Hole Pressure
Fig. 6.12 History matching results (line colors) and observed data (dot points) by HU method
with reservoir volume control
141
(a) Gas Flow rate
(b) Bottom Hole Pressure
Fig. 6.13 History matching results (line colors) and observed data (dot points) by HU method
with gas control
142
6.5 Conclusions
The static models (Chapter 5) were upscaled and simulated using flow simulator Eclipse®.
History matching was performed by manually adjusting a few reservoir model parameters
through a trial-and-error procedure. Manual history matching run the simulation model for the
historical production period and then compared the results with known field performance.
After the comparison was made, history matching results of three cases from 3 wells (Z74,
Z75 and Z76) showed good results for gas flow rate for a few years production.
Comparison of the results between the traditional method (two stages) and HU method (four
stages) showed some distinct advantages of the HU method:

at each HU we have very good correlation between porosity and permeability that is good
for classification of cells in fluid flow for Eclipse® simulation,

from 6HUs distribution we can easy control NTG model for Eclipse® simulation cutting
off HU1 with lower PHI and K and also reducing number of cells in 3D grid and
increasing CPU processing,

rock compaction function can respond to porosity model (PHI) and each hydraulic
flow unit.
143
Chapter 7
CONCLUSIONS AND RECOMMENDATIONS
The main area of concentration for this study is integrating multiple datasets including
wireline logs, core data, production data, and other geological and geophysical data for
building static 3D reservoir property models. In particular, the concept of using hydraulic
flow units was explored in an attempt to simplify and improve the quality of the 3D static
model of a gas reservoir. To test this concept, the Eclipse simulation engine was run against
the 3D reservoir model. The results of these simulations was compared to actual reservoir
performance by history matching. The case study presented shows the methods used to
integrate data from various scales; from microscopic (core plugs) through mesoscopic (logs)
to megascopic (seismic). Because a 3D seismic survey was not available, a pseudo 3D cube
was created from a dense grid of 2D lines. Stochastic and deterministic geostatistical methods
were combined using Petrel software to generate static models which were then were used
for upscaling to the Eclipse simulation engine.
7.1 Conclusions
The case study presented was performed in the Z gas deposit belonging to a group of Miocene
gas reservoirs in the northern part of the Carpathian Foredeep of Poland. The Z gas field
reservoir depositional environment was deltaic. The water depth was shallow nearshore
marine and the sediments were laid down in an area where tidal influences resulted in a very
complicated facies distribution. The reservoir is thus comprised of interbeded sandy- shaly
layers which not only vary in thickness, but also in lateral extent. Despite the challenges
presented by this complex environment of deposition, a range of geophysical, geological, and
geostatistical modeling and reservoir simulation techniques was used to reach the following
conclusions:
Hydraulic flow unit classification using core data:
1. The hydraulic flow unit technique has been developed by oil industry researchers and
as such is routinely applied to the problem of identifying reservoir characteristics. This
technique has a wide variety of practical field applications to both cored and uncored
intervals/wells. In this study, the data from 570 core plugs (PHI_core and K_core)
from ten wells was classified into six Hydraulic Flow Units (6HUs) by applying
144
conventional cluster analysis techniques including histogram, probability plot and
Ward’s algorithm.
Hydraulic flow unit prediction using core and log data:
2. Statistical methods turned out to be useful, flexible, and effective, because they
provide the interpreter with tools that deliver acceptable results. Two methods were
tested. These were Linear Multiple Regression (LMR) and Alternating Conditional
Expectations (ACE). Both methods were used to solve the problem of integrating core
and log data to calculate the Flow Zone Indicator (FZI.) The FZI was in turn used to
divide the reservoir in each well into Hydraulic Flow Units (HUs). The applicability of
the two methods was tested by comparing the correlation coefficient of both sets of
theoretical transformations against the actual reservoir parameters. This revealed that
the optimal ACE transformations of dependent (FZI) and independent (logs) values
improved the correlation of the FZI from core and well log data and the results were
superior to those obtained by the LMR algorithm.
Rock type classification using log data:
3. Without core facies descriptions, the six Rock Types (RT) were classified by K mean
clustering method. After applying techniques to overcome the limitations of this
method, the resulting classification was used as background to control the distribution
of the HUs.
Hydraulic flow unit modeling using well log and 2D seismic data:
4. In recent years the Multiple Point Statistics (MPS) included in Petrel has shown its
ability to improve geostatistical modeling techniques. However, in this study the
traditional technique using variogram and two-point statistics such as Sequence
Indicator Simulation (SIS) and the Sequence Gaussian Simulation (SGS) methods
was applied to build a geostatistical model with good results. In particular, a pseudo
3D seismic cube was created from a high density grid of 25 lines of 2D seismic data
using SGS high speech computers and the powerful Petrel seismic interpretation
software simplified the extraction of geobodies from the pseudo 3D seismic cube.
This accelerated the process of mapping the deltaic facies revealed a channel system
145
flowing from northwest to southeast, with general progradation of the delta front to
the southeast.
5. Unsupervised Neural Network (UNN) was used to classify the pseudo 3D seismic
attributes (RMS, Envelope, and Sweetness) into six seismic facies (6Facies_UNN).
Rock type modeling using stochastic methods (SIS) helped to overcome the limitation
of the seismic scale by combining well log (6RTs) with seismic facies
(6Facies_UNN).
6. Six hydraulic flow units were modeled using the SIS method constrained by the six
rock types model. This was helpful in controlling the HUs distribution in three
dimensions. This was very significant because of the paucity of well control in the
study area. Since the method incorporated the facies distribution extracted from the
pseudo 3D cube it meant that the 3D HU model outcome was now not only dependent
on petrophysical properties (K, PHI) but also was controlled by paleostratigraphy.
7. To reduce uncertainty in the applied geostatistical methods, and to maximize the many
advantages of applying the hydraulic flow unit technique, the 3D permeability model
was directly calculated from the 3D porosity model constrained by HU model (using
Kozeny-Carman equation). The results show excellent correlation between the
permeability as measured from log data and calculated 3D permeability. As a bonus,
the 6HUs distribution enabled us to easily generate a net to gross ratio (NTG) model
by using cutoff value for each HU.
A comparison of deterministic (6Facies_UNN) and stochastic methods (6RT_SIS) shows
clearly that the stochastic method gives high resolution results (log scale) which are
honored at the well location. Because the stochastic method uses a random number
generator to generate equiprobable results away from well control, it is an appropriate
method for improving the abstract concept of reserves and overall probability of reservoir
characterization. Deterministic methods are more accurate but cannot predict reservoir
character away from well control. Both methods have their uses. The stochastic method is
an effective predictor for statistical estimation of the reservoir character away from well
control, however one should be aware of its limitations. In particular the stochastic
approach should not be used to predict the actual reservoir characteristics when
considering where to locate a new well.
146
History matching controlled by HU model:
8. The final statistic models (K, PHI and NTG) were upscaled and then input to Eclipse
for simulation and history matching. With the HU method controlling the static
models, even with lack of reservoir engineering parameters and initial condition data,
the results showed a good match for gas flow rate and slightly higher bottom hole
pressure (BHP). By comparing history match results with and without HU control we
can clearly see that some advantages: for example because the HU’s encapsulate a set
of reservoir parameters into discrete package, it is very easy to test the effect of
different NTG models and rock compaction factors on each individual HU.
7.2 Recommendations
The study workflow shows the advantages and disadvantages of the integrated reservoir
analysis approach to combining cores, logs and 2D seismic data for geological modeling
which can then be applied to production history matching via Eclipse simulation. However,
in order to get better results in static and dynamic modeling using the HU method, the points
listed below should be considered:
Core data:
1. Core plug porosity and permeability data (K_core, PHI_core) are parameters critically
necessary for calculating the FZI that is key to the HU method in the study. However,
after core depth matching by using PHI_core and Neutron porosity log (NPHI or PHI) we
found that about 30% of core data was unusable because it could not be reliably depth
registered. Since core data, very expensive to acquire, is essential to the task at hand, and
must be depth matched to be used effectively, we recommend that at a minimum both
Gamma ray log (GR_log) and Gamma ray core (GR_core) should always be run. In
addition the FMI log should be run across the reservoir, as this gives an excellent false
color image of the borehole for direct comparison to the recovered core.
2. No core facies descriptions were available. Even with the advantages of K mean
clustering for rock types classification, it is still only an unsupervised learning method
without a training data set. Due to complex facies distribution in deltaic environment
core facies description is very useful to validate the results. Therefore we recommend
to preserve core facies description with the other core material.
147
3. The HU approach in this project was used to perform a complex reservoir
characterization. However, due to lack of SCAL data some important parameters such
as water saturation, relative permeability, capillary pressure and others were excluded,
and therefore we had to use default values in the Eclipse simulation. We strongly
recommend that SCAL data be available to improve Eclipse results.
Log data:
4. The log data was sampled at 0.25m/point. This coarse sample interval introduced
several problems:
a. The resolution is incapable of resolving the fine detail in the very thin sand
shale layers in the study ,
b. It is too coarse also for core and log depth matching,
c. For a static 3D reservoir geology model, we should start with the highest
resolution logs possible. They can always be upscaled later to a coarser sample
interval suitable for a dynamic reservoir model.
5. A log sampling interval of 0.10m/point or less (as used in the Dipmeter) is
recommended. If the available LAS files are not sampled appropriately, then they can
be resampled at a higher resolution.
Seismic data:
6. Misties in amplitude, time and phase are a common problem with 2D seismic surveys,
especially when derived from different sources or if of different vintages. Petrel
software is able to correct misties, but we still recommend correcting 2D seismic
misties by using a professional seismic processing software that is designed
specifically for that task.
7. In the presented case study the high density of 2D seismic lines enabled the
conversion of 2D seismic to the pseudo 3D seismic cube. This technique is a very
helpful step to enable 3D seismic facies classification. The results can be used as a
conditional model for HU. The presented work flow can be applied to the upper part
of the study area (in the Z gas field) or other reservoirs in Poland where dense
148
networks of 2D seismic data commonly available. Of course, ideally one would want
to use a 3D survey, if available.
8. Time to depth conversion in this study based on the check shots from only 7 wells
provides a result of limited credibility.
Statistical methods:
9. Several statistical methods were used for HU classification and prediction based on
core and log data including Histogram, Probability plot, Ward’s clustering, LMR,
ACE (chapter 3 and 4). Other methods such as Principal Component Analysis (PCA),
Discriminant Analysis (DA), and Supervised Neural Network (SNN) might improve
the results of the study but are beyond the scope of this investigation.
10. 6HUs classification used in the study gave good correlation between porosity and
permeability in each HU. However, it is recommended to apply the GHE method as
quick look analysis tool, to reduce the number of cores in the new wells is
recommended.
Geostatistical methods:
11. Traditional geostatistic methods based on variogram analysis for trend detection
produced static 3D reservoir property models when combined with well log and 2D
seismic data. However, the newly developed Multiple Point Statistic (MPS) module in
Petrel might improve stochastic facies modeling, especially in very large and
complex deltaic environments.
Uncertainty analysis:
12. Stochastic models are based on statistical results from multiple applications of random
numbers (variogram models and conditional distributions). No two runs will produce
the same result, therefore we need to quantify our confidence in the results by using
uncertainty analysis for both static and dynamic modeling.
13. Because of the limitation of the 2D seismic grid, we were not able to reliably include
faults in our seismic interpretation. Therefore faults were excluded from the static 3D
property model. If fault barriers are present in reality, but not mapped, that might
introduce some mismatches in the history matching phase of the project. Since the
pseudo 3D cube is based on the 2D data, it cannot be used like a regular 3D cube to
149
map the faults in more detail. Similarly, using the pseudo 3D cube for detailed horizon
picking and inversion would probably not be effective. Generally speaking, a 3D
survey over a producing field would cost less than a dry hole, Therefore we
recommend to shoot a 3D survey over any producing field which has the upside
potential to justify the cost of such a survey.
150
REFERENCES
1. Abbaszadeh, M., Fujii, H., and Fujimoto, F., Permeability Prediction by Hydraulic
Flow Units - Theory and Applications, Paper SPE 30158 presented at the 1995 SPE
Petrovietnam Conference, Hochiminh, Vietnam, 1–3 March.
2. Amaefule, J. O., Altunbay, M., Tiab, D., Kersey, D. G., and Keelan, D. K., 1993,
Enhanced reservoir description: using core and log data to identify hydraulic (flow) units
and predict permeability in uncored intervals/wells, Paper SPE 26436, 205 – 220.
3. Amaefule, J.O., 1995, A Flow Unit Approach on Integrated Reservoirs, in World
Expo 1995. Sterling Publications, London, pp. 25–31.
4. An L. H., Innovative neural network approaches for petrophysical parameter
reduction, PhD. Thesis, 2004. Heriot-Watt University Institute of Petroleum
Engineering, UK.
5. Antelo R., Aguirre O., Andina S.A. (Repsol YPF), 2001, Permeability calculations
from clustering electrofacies technique for the petrophysical evaluation in La Peña
and Tundy oil fields, Paper SPE 69400.
6. Archie G.E., 1942, The Electrical Resistivity Log as an Aid in Determining Some
Reservoir Characteristics, Published in Petroleum Transactions, AIME, Volume 146,
1942, Paper SPE 942054 p. 54-62.
7. Babadagli T., Al-Salmi S., 2004, A Review of Permeability - Prediction Methods for
Carbonate Reservoirs Using Well-Log Data, Paper SPE 87824.
8. Bear, J., 1972, Dynamics of Fluids in Porous Media, Elsevier, New York, 1972.
9. Bohling, 2005, Stochastic simulation and reservoir modeling workflow: C&PE 940,
http://people.ku.edu/~gbohling/cpe940/Simulation.pdf.
10. Breiman, L. and Friedman, J. H., 1985, Estimating Optimal Transformations for
Multiple Regression and Correlation, Journal of the American Statistical Association
(September), p. 580 -598.
11. Brooks R.H. and Corey A.T., 1966, Hydraulic Properties of Porous Media.
Hydrology Papers, Colorado State University. Ft. Collins, No.3, March.
151
12. Caers J., 2005, Petroleum geostatistics: SPE - An interdisciplinary approach to topic
in Petroleum engineering and Geosciences.
13. Carman P.C., 1937, Fluid Flow through Granular Beds, Trans. Inst. Chem. Eng.
Vol.15, 1937, pp. 150-167.
14. Carrillat A. and Valles B., 2005, From 3D Seismic Facies to Reservoir Simulation: An
Example From the Grane Field, Mathematical Methods and Modeling in Hydrocarbon
Exploration and Production (Iske A. & Randen T., eds), Springer, 2005, VOL 7, p.
301-338.
15. Chopra S., Marfurt K. J., 2005. Seismic attributes – A historical perspective,
Geophysics vol. 70 (5), p. 3SO-28SO.
16. Clayton V. Deutsch, 2002, Geostatistical reservoir modeling, Oxford University press,
2002, p. 32-152.
17. Corbett P.W.M. and
Potter D.K., 2004 - Petrotyping: a basemap and atlas for
navigating through permeability and porosity data for reservoir comparison and
permeability prediction: Paper prepared for presentation at the international
symposium of the Society of Core Analysts held in Abu Dhabi, UAE, 5-9 October,
2004, p. 1-12.
18. Corbett P.W.M., Ellabard Y., Mohhammed K., 2003, Global Hydraulic ElementsElementary Petrophysics for Reduced Reservoir Modeling. EAGE 65th Conference
and Exhibition. Stavanger. F-26.
19. Documentation of wells: Z75, 79 and 84, Archive of POGC Warsaw, Department in
Sanok, Biuro in Jasło (in Polish).
20. Dziadzio P., 2000, Sekwencje depozycyjne w utworach badenu i sarmatu w SE części
zapadliska przedkarpackiego. Przegląd Geologiczny, v. 48, 1124 – 1138 (in Polish).
21. Dziadzio P., Liszka B., Maksym A., Staryszak G., 1997, Środowisko sedymentacji
utworów miocenu autochtonicznego w brzeżnej strefie Karpat a interpretacja
geologiczno-złożowa w obszarze Husów-Albigowa-Krasne. Nafta-Gaz, v.9, 40074014. (in Polish).
22. Ebanks W. J., 1987. Flow unit concept - integrated approach for engineering projects.
Abstract presented June 8, during the roundtable sessions at the 1987 American
Association of Petroleum Geologists Annual Convention.
152
23. Ebanks, W.J. Jr., Scheiling, M.H., Atkinson, C.D., 1992. Flow units for reservoir
characterization. In: D. Morton-Thompson, A.M. Woods (Eds.), Development
Geology Referrence Manual, Amer. Assoc. Petrol. Geol. Methods in Exploration
Series No. 10, p. 282-284.
24. Frazier, D. E., 1974, Depositional episodes: their relationship to the Quaternary
stratigraphic framework in the northwestern portion of the Gulf basin. Austin, Bureau
of Economic Geology, Geological Circular 71-1. The University of Texas at Austin.
25. Geological Documentation of the Z-L gas field by Bosak B., 2007. Appendix no 5,
2007, Archive of POGC Warsaw, Department in Sanok, Biuro in Jasło (in Polish).
26. Gocad 2009 Manual, Pradigm modeling Software.
27. Gunter, G.W., Finneran, J.M., Hartmann, D.J., Miller, J.D., 1997, Early
Determination of Reservoir Flow Units Using an Integrated Petrophysical Method,
paper SPE 38679 prepared for presentation at the 1997 SPE Annual Technical
Conference and Exhibition held in San Antonio, Texas, 5-8 October, 1997.
28. Ha Quang M. and Jarzyna J., 2008a, Dane petrofizyczne w jednostkach o jednakowych
własnościach hydraulicznych do modelowania przepływów w złożu gazu w zapadlisku
przedkarpackim, Pierwszy Polski Kongres Geologiczny, 26-28 czerwca, Kraków, p.
72-73.
29. Ha Quang M. and Jarzyna J., 2008b, Preliminary analysis of petrophysical parameters
of the Miocene sandy-shaly formation in the Carpathian foredeep as an introduction
to Eclipse® (Schlumberger) modeling, Prace INiG, 2008 nr 150 wyd. konf.
Geopetrol2008, p. 209-214 (in English).
30. Ha Quang M. and Jarzyna J., 2010, Application of artificial neural networks for
properties modeling using well logs and 2D seismics in the Carpathian Foredeep gas
field. Prace INiG; 2010 nr 170, wyd. konf. Geopetrol2010, p. 209-212 (in English).
31. Ha Quang M. and Jarzyna J., 2011a, Hydraulic Flow Unit classification for geological
modeling of the shaly-sandy reservoir using core, log and 2D seismic data, an
example of the Miocene formation. Workshop, held 26 - 30 June 2011 in Auberge
Saint Antoine, Quebec City, Canada.
153
32. Ha Quang M. and Jarzyna J., 2011b, Integrating of Core and Logs and 2D Seismic
Data to Improve 3D Hydraulic Flow Unit Modeling. Proceedings of the 73rd EAGE
Conference & Exhibition incorporating SPE EUROPEC 2011 in Vienna, Austria.
33. Ha Quang M., 2011, Deltaic Facies Classification Using Log data, International
conference of young geologists HERĽANY 2011.
34. Hear C. L., Ebanks W. J., Tye R. S. and Ranganatha V., 1984, Geological Factors
Influencing Reservoir Performance of the Hartzog Draw Field, Wyoming. Journal of
Petroleum Tech., August 1984, p. 1335-1344.
35. IP-3.5 Manual, Interactive Petrophysics Software, 2009.
36. Jarzyna J. and Ha Quang M., 2010, Classification of rock formation on the basis of
hydraulic features for porous media mobility evaluation, Klasyfikacja formacji
skalnych na podstawie ich zdolności hydraulicznych dla oceny możliwości ruchu
mediów w przestrzeni porowej. Jubileuszowa konferencja prof. Wacława M. Zuberka
Geofizyka w Geologii i Górnictwie, Sosnowiec-Zawiercie, 15-17 września 2010 r.
37. Jarzyna J. and Ha Quang M., 2009, Podział skały zbiornikowej na jednostki o
jednakowych właściwościach hydraulicznych w celu dokładniejszego wyznaczania
przepuszczalności podczas modelowania przepływów w złożu gazu, Przegląd
Geologiczny, v.57, nr.11, 996-1003 (in Polish, Abstract in English).
38. Karnkowski P., 1999, Oil and Gas Deposits in Poland. Geosynoptics Society
“GEOS”, Cracow, Poland.
39. Kelkar B. G., Gamble R. F., Kerr. D. R., Thompson L. G., Shenoi S., 1997,
Application of artificial intelligence to reservoir characterization, An interdisciplinary
approach, Final report, The University of Tulsa.
40. Kozeny, J., 1927, Uber Kapillare Letung des Wassers im Boden, Sitzungsberichte:
Royal Academy of Science, Vienna, Proc. Class I (1927) v. 136, p. 271-306.
41. Lang S.C., Kassan J., Benson J.M., Grasso C.A., 2000, Applications of modern and
ancient geological analogues in characterization of fluvial and fluvial-lacustrine
deltaic reservoirs in the cooper basin: APPEA Journal, 2000, p. 392-416.
http://www.appea.com.au/publications/appea-journal.html.
154
42. MacQueen J. B., 1967, Some methods for classification and analysis of multivariate
observations, Proceedings of the 5th Berkeley Symposium on Mathematical Statistics
and Probability, 1, p. 281–297.
43. Martini E., 1971, Standard Tertiary and Quaternary Calcareous Rannoplankton
Zonation. Proceedings of the II Planktonic Conference, Roma, 1870, 2, p. 739-785.
44. Mastalerz K., Aleksandrowski P. (Pracownia Geologiczna Explora), współpraca: P.
Pasek, M. Stadtműller (Geofizyka Kraków sp. z o.o.), Wrocław-Kraków, 2004,
Analiza sedymentologiczna i strukturalna osadów miocenu w otworach Z75 i Z76 na
podstawie danych z pomiarów upadomierza sześcioramiennego SED (Halliburton),
Sedimentological and structural analysis of the Miocene sediments in wells Z75 and
Z76 on the basis of dipmeter measurements SED (Halliburton), Archive of Geofizyka
Kraków sp. z o.o. (in Polish).
45. Matyasik I., Mysliwiec M., Lesniak G., Such P., 2007, Relationship between
Hydrocarbon Generation and Reservoir Development in the Carpathian Foreland,
Chapter 22 - Frontiers in Earth Science: Thrust Belt and Foreland Basin From Fault
Kinetics to Hydrocarbon System, Springer.
46. Michael K. Ng, 1999, A note on constrained k-means algorithms, Pattern Recognition
33 (2000), p. 515-519.
47. Mikes D., Barzandji O.H.M., Bruining J., Geel C.R., 2006, Upscaling of small-scale
heterogeneities to flow units for reservoir modeling, Marine and Petroleum Geology
23 (2006), p. 931–942.
48. Mikhail Y. T., 1997, Integrated reservoir description for boonsville (Texas) field
using 3-d seismic, well and production data, Master thesis, University of Tulsa, 1997.
49. Morrison D.F, 1990, Multivariate statistical methods. PWN, Warsaw, Poland, p. 590.
50. Myśliwiec M., 2004, Mioceńskie skały zbiornikowe zapadliska przedkarpackiego. The
Miocene Reservoir Rocks of the Carpathian Foredeep. Przegląd Geologiczny, v. 52,
581-592 (in Polish, Abstract in English).
51. Myśliwiec M., 2006a, Typy mioceńskich skał zbiornikowych złoża gazu ziemnego
Żołynia-Leżajsk, a objętościowe metody szacowania zasobów. Types of the Miocene
reservoir rocks (Żołynia-Leżajsk gas field) and the methods of the gas reserves
estimation, Nafta-Gaz, v. 62, no 4, p. 139-150 (in Polish, Abstract in English).
155
52. Myśliwiec M., 2006b – Żołynia – Leżajsk – stare złoża, nowe zasoby. Nafta-Gaz, v.
62, nr 3, p. 97-105. (in Polish, Abstract in English).
53. Myśliwiec M., Madej K., Bys I., 2004, The Miocene gas fields discovered in the
Rzeszów area, Carpathian Foredeep, on the base of the Direct Hydrocarbon
Indicators, Przegląd Geologiczny, v. 52, no 7, p. 501–506 (in Polish, Abstract in
English).
54. Olszewska B., 1999, Biostratygrafia neogenu zapadliska przedkarpackiego w świetle
nowych
badań
mikropaleontologicznych.
Prace
Państwowego
Instytutu
Geologicznego, 168, p. 9-28 (in Polish, Abstract in English).
55. Oszczypko N., 1999, Przebieg mioceńskiej subsydencji w polskiej strefie zapadliska
przedkarpackiego. Prace Państwowego Instytutu Geologicznego, 168, p. 209-213 (in
Polish, Abstract in English).
56. Oszczypko N., Krzywiec P., Popadyuk I., Peryt T., 2006, Carpathian Foredeep Basin
(Poland and Ukraine); Its Sedimentary, structural and Geodynamic Evolution. In:
Golonka J. and Picha F. (Eds.), The Carpathians and their Foreland: Geology and
Hydrocarbon resources. AAPG Memoir, 84, p. 293 – 350.
57. Oszczypko, 1999, From remmant oceanic basin to collision-related foreland basin - a
tentative history of the Outler Carpathians. Geol. Carpathica, 50 (special issue).
58. Petrel® 2009 and 2010 Manual, Schlumberger Software.
59. Rögl F., 1996, Stratigraphic Correlation of Paratethys Oligocene and Miocene. Mitt
Ges Geol Bergbaust ud Öster, p. 65-73.
60. Roksandić M., 2006, Seismic facies analysis concepts: Gephysical Processing Vol.26,
p. 382-398.
61. Roxar Manual, RMS modeling software, 2009.
62. Rushing J.A., Newsham K.E., Blasingame T.A., 2008, Rock Typing - Keys to
Understanding Productivity in Tight Gas Sands, Paper SPE 114164.
63. Sang H. L., Arun K, and Akhil D. G., SPE, 2002, Electrofacies characterization and
permeability predictions in complex reservoirs, Paper SPE 78662.
64. Shuguang M., Journel A.G., 1999, Conditional 3D simulation of lithofacies with 2D
seismic data, Computer & Geosciences 25, p. 845-862.
156
65. Skalinski M., Gottlib-Zeh S., Moss B., 2005, Defining and Predicting Rock Types in
Carbonates-an Integrated Approach using Core and Log Data in Tengiz Field,
SPWLA 46th Annual Logging Symposium.
66. SLB, Plug-in, 2008, Petrel plus-in upscaling 2D seismic into 3D grid,
http://slb.ru/sis/plugins/Petrel2008.Plugins.2DSeis2Seis3D.zip.
67. Śmist P., 2003 – Zmiany w litologiczno-facjalnym wykształceniu osadów miocenu w
rejonie Żołynia-Chałupki Dębniańskie-Grodzisko Dolne. Raport Przedsiębiorstwa
Usług Laboratoryjnych i Geologicznych Sp. z o.o., Oddział w Jaśle, Archive of POGC
Warsaw, Department in Sanok, Biuro in Jasło (in Polish).
68. Svirsky D., Ryazanov A., Pankov M., Corbett P.W.N., Posysoyev A., 2004, Hydraulic
Flow Units Resolve Reservoir Description Challenges in the Siberian Oil Fields.
Paper SPE 87056, p. 1-15.
69. Tan, Steinbach, Kumar, 2004, Introduction to Data Mining, Steven F. Ashby Center
for Applied Scientific Computing Month DD, 1997 (Internet presentation, only:
http://www.gersteinlab.org/courses/545/07-spr/slides/DM_cluster-tan.ppt).
70. Udegbunam, E. and Amaefule J.O., 1996, An Improved Technique for Modeling Initial
Reservoir Hydrocarbon Saturation Distributions: Applications in Illinois (USA) Aux
V. Oil reservoirs, JPT, V. 21.
71. Varavur S., Shebl H., Salman S.M., Shibasaki T., and Dabbouk C., 2005, Reservoir
Rock Typing in a Giant Carbonate, Paper SPE 93477.
72. Worthington, P.F. & Cosentino L. 2003. The role of cut-off in integrated reservoir
studies, Paper SPE 84387.
73. Xue G., Datta-Gupta A., Valko P., and Balsingame T., 1996, Optimal Transformations
for Multiple Regression: Application to Permeability Estimation from Well Logs, SPE
35412 presented at the Improved Oil Recovery Symposium, Tulsa, Ok, 21 April 1996.
157
LIST OF FIGURES AND TABLES
FIGURE
Page
Chapter1
1.1
The main workflow in this study for integration of static and dynamic
2
models
Chapter2
2.1
General overview of the Carpathians and Carpathian Foredeep
5
(Oszczypko, 2006)
2.2
Schematic map showing the submarine deposits diversity in the eastern
6
part of the Carpathian Foredeep (Myśliwiec, 2004a)
2.3
Location of Z gas-field with cored and logged wells; tectonic elements
8
marked in red (after Myśliwiec, 2006b and Myśliwiec et al 2004
2.4
The result of grain size analysis of powdered sandstone taken at 677m,
14
the depth of the Z75 well
2.5
Photomicrographs of a polished section impregnated with blue resin,
14
from a sample obtained at a depth of 855.20m in well Z75; crossed
nicoles (left – magnification 14X, right – 120X) (Documentation of
well Z75)
2.6
Scanning microscope photomicrographs of a polished section from a
15
sample obtained at a depth of 855.20m in well Z75; magnification
600X (Documentation of well Z75)
2.7
Well logs (GR and NPHI) showing vertical facies distribution;
19
a) an example of turbidities from the depth section of 925 – 1025
m in the Z84 well; low value of GR and rather low NPHI,
sandstones dominate over shales,
b) a typical parasequence coarsening upward in deltaic sediments
in the Z75 well,
c) sediments of shallow shelf form the top of the Sarmatian
succession (GR and NPHI are very close to one another),
sediments are shaly and have high neutron porosity
2.8
RMS amplitude map and GR log for each well shows deltaic facies
20
158
distribution in the study area
2.9
Overview sequence stratigraphy in the study area based on 2D seismic
23
data
a) seismic facies classification based on seismic attributes
(Chapter 5),
b) balancing section a)
c) some basic sequence stratigraphy interpretation,
d) successive progradation of delta lobes deposits an offlap
succession with a clinoform geometry (after Frazier 1974)
2.10
Comparison of the result of well log correlation;
24
a) cross section correlation Z-81 – Z76 - Z-82 based on GR and
NPHI (after Mastalerz, et al., 2004),
b) cross section basic on seismic facies classification (Chapter 5)
Chapter3
3.1
Various parameters used in defining geologic flow units (Ebanks et al.,
30
1992); four flow units are defined on the basis of lithofacies, pore
types, porosity, and permeability crossplots, capillary pressure
measurements, and gamma-ray log response (after Ebanks et al. (1992)
3.2
Histogram of porosity (a), permeability (b), FZI (c) for 570 core data
37
measurements
3.3
Normal probability plot of log(FZI) with division into 6 homogeneous
38
groups of HUs with constant FZI
3.4
Clustering of the FZI – HU data set into six groups, according to the
40
Ward method
3.5
Porosity-permeability crossplot, the hydraulic unit classification of all
43
the core data
3.6
z vs. RQI crossplot of all the hydraulic units. The mean FZI values for
43
each hydraulic unit are given by the intercept of the straight lines at z
=1
3.7
Dispersion plot of PHI_core vs. K, and the six HUs defined in the area
44
of core origin data
159
3.8
Dispersion plot and correlation line between the core origin
44
permeability vs. the permeability calculated from the mean values of
FZI for HU
3.9
Permeability vs. porosity data on the background of 7 GHE
45
3.10
Permeability, K_GHE, calculated on the basis of relationship RQI vs.
45
Φz for 7 GHE and core origin permeability, K_core
Chapter4
4.1
Two approaches to depth matching between the core and log data in
49
well Z76. Crosses – lab porosity – PHI_core, sampled irregularly;
continuous curves with triangles – NPHI, sampled regularly, 0.25 m.
The two horizontal scales of porosity and two vertical scales of depth
relate to the matched data sets
4.2
Flow chart for two procedures applied to obtain uniform HUs in the
51
study data
4.3
Dispersion plots of ln(FZI) vs. GR and ln(FZI) vs. NPHI, and
53
histograms of GR and NPHI; Gaussian distributions included in
histograms
4.4
a) Optimal transformation of EL14
58
b) Optimal transformation of A2
c) Optimal transformation of ln(FZI)
a) d) Dispersion plot and correlation for FZI_tr vs.
 (log _
i
tr
 Ai _ tr )
i
4.5
a) Comparison of ln(FZI_core) to ln(FZI_pre_LMR) for group G3
59
b) Comparison of ln(FZI_core) to ln(FZI_pre_LMR) for well Z76
c) Comparison of ln(FZI_core) to ln(FZI_pre_ACE) for group G3
d) Comparison of ln(FZI_core) to ln(FZI_pre_ACE) for well Z76
4.6
Results of FZI_core and FZI_pre (predicted from log) for two
60
approaches in the selected section of well Z76; a) LMR; b) ACE;
consecutive numbers of data in the depth section are on the horizontal
axis
4.7
a) Prediction results for FZI_pre for well Z76, by applying the ACE
61
solution for group G3 for the full geological profile; left colored
160
field – GR anomaly, right colored steps – log predicted HU
b) Prediction results for FZI_pre for well Z76, by applying the ACE
solution for group G3 excluding pure shales; left colored field – GR
anomaly, right colored steps – log predicted HU; bimodal
histogram of GR in well Z76 to show how to exclude pure shales
4.8
a) Dispersion plot and correlation line between K_core and
63
K_pre(ACE) for the G3 group
b) Dispersion plot and correlation line between K_core and
K_pre(ACE) for the Z76 well
4.9
GR (left hand side) and HU (right hand side) presented in wells Z81-
64
76-82 in group G3 on the background of 2D seismic section; HU color
scale is the same as in Fig. 13
4.10
a) Comparison of FZI_pre_ACE (line) and FZI_core (points) in well
65
D2
b) Comparison of K_pre_ACE (line) and K_core (points) in well D2
4.11
The workflow of the K mean clustering
71
4.12
The limitations and overcomes limitations of the K mean clustering
71
(after Tan, al et, 2004)
4.13
The matrix crossplots of 5 logs (GR, DT, NPHI, EN16 and EN64) and
72
histograms for each curves show data distribution of group 3 (Z76, Z81,
Z82) before applying K means clustering
4.14
Applying K mean clustering for the group 3:
73
(a) The cluster grouping dendrogram shows 4 clusters with diffident 4
colors respond
(b) The cluster groups randomness
4.15
The cross plots of data in well Z-76 shows 6 rock types (6 clusters)
a) GR/DT,
4.16
b) GR/NPHI,
74
c) GR/EN64, d) GR/EN16
Comparison between 6 rock types (6RTs) and 6 hydraulic flow unit
75
(6HUs)
4.17
Relationship between geological model, reservoir model and flow unit
76
model (modified from D. Mikes al et. 2006)
1. Geological model and assignment of its elements
161
2. Reservoir model and assignment of its elements
3. Micro simulation model, consisting of numerical flow simulation
on all flow cell models of the reservoir, yielding effective oneand two-phase permeabilities, and capillary pressures
4. Macro simulation model, consisting of numerical flow simulation
on the entire reservoir, yielding production history
Chapter 5
5.1
Deltaic facies model and special relationships control by facies
82
distribution
a) reservoir heterogeneity and longitudinal facies variation developed
within the east-west distributary channel of the Neales Delta
(modified from Lang et al., 2000),
b) how unknown point relates to a known point (Gocad Manual, 2009)
5.2
Variogram modeling
84
a) concepts of variogram parameters,
b) variogram ellipsoid around a grid cell. The values of cells outside the
ellipsoid are independent of the value of the current cell (Roxar
Manual, 2009),
c) horizontal variogram of porosity modeling (7 wells),
d) vertical variogram of porosity modeling (7 wells).
5.3
2D seismic data in the study area;
89
a) 25 lines 2D seismic survey and 10 wells location,
b) the miss-tie correction for the 2D seismic survey
5.4
Horizon picking
90
a) four horizons interpreted basically on 25 lines of 2D seismic and
the well-tops of main interpreted horizons: H1 (Top_7), H2
(Top_12), H3 (Top_15) and H4 (Top_17),
b) the 3D structure mode in the study area; four surfaces were created
from 4 horizons H1, H2, H2 and H4 and 10 well locations
5.5
The workflow for reservoir modeling in this study
92
5.6
Convertion from 2D seismic to pseudo 3D seismic cube using SGS;
94
a) 2D seismic survey - top and bottom of the reservoir,
162
b) 2D seismic profiles - uplscaled to 3D grid,
c) pseudo 3D seismic cube after applying the SGS method
5.7
Pseudo 3D seismic cube
95
a) the block average data of 2D seismic after upscaling into 3D grid;
b) comparison between 2D seismic profiles and the pseudo 3D seismic
cube
5.8
Channel system and delta lobe (geobody) facies from pseudo 3D seismic
99
extraction;
a) envelope histogram before filtering,
b) envelope histogram after filtering,
c) model of deltaic environment in the study area
5.9
The workflow for seismic facies classification using ANN method 101
(Carrillat and Valles, 2005)
5.10
Application of the Unsupervised Neural Network technology for seismic 102
facies classification
5.11
Seismic attributes generated from pseudo 3D seismic amplitude for UNN
102
5.12
Reduction from 10Facies_UNN to 6Facies_UNN on the basis of the 105
facies histogram;
a) 10Facies_UNN histogram,
b) 6Facies_UNN histogram,
c) Crossplot of Amplitude & Relative acoustic impedance for
10Facies_UNN,
d) Crossplot
Amplitude
&
Relative
acoustic
impedance
for
6Facies_UNN,
e) Envelope & Relative acoustic impedance for 10Facies_UNN,
f) Envelope & Relative acoustic impedance for 6Facies_UNN
5.13
3D Facies classification using UNN method
106
a) 3D 10Facies_UNN and cross section,
b) 3D 6Facies_UNN and cross section
5.14
Comparison 6Facies_UNN and 6RT_SIS;
108
a) 6Facies_UNN and 6RT_log, b) 6Facies_UNN histogram,
a) c) 6RT_SIS and 6RT_log, d) 6RT_SIS (blue) and 6TR_log (green)
163
histogram
5.15
Comparison between seismic facies classification (6Facies_UNN) and 109
3D rock type model (6RT_SIS)
a) 6Facies_UNN model filtered to display only faceis F8_UNN showing
clearly delta lobe distribution in the study area,
b) 6RT_SIS model filtered to display 3 Rock Types (RT7, RT8, RT9)
showing in more details rock type distribution and honoring wells
location
5.16
Comparison between the 6RT_SIS and 6HU_SIS
110
a) 3D 6RT_SIS
b) 3D 6HU_SIS
5.17
Comparison of 6RT_SIS and 6HU_SIS in 4 horizons: H1, H2, H3 and H4 111
5.18
Comparison between 3D PHI_HU model and the 3D K_HU model;
113
a) porosity model constrained by HU model,
b) permeability model calculated from the porosity model using KozenyCarman equation
5.19
Comparison between PHI_HU model and the K_HU model; results 114
presented on various surfaces
5.20
Cross plot of 3D PHI_HU versus 3D K_HU; shown very clear 115
relationship between K and PHI responding to each HU
5.21
Cross plot between permeability from logs (K_log) and permeability 115
calculated for 3D_K_HU model from the mean values of FZI for HU
5.22
Typical capillary pressure curves for different flow units fitted with the 117
Brooks and Corey’s equation (Udegbunam & Amaefule, 1996)
5.23
Water saturation model constrained by Hydraulic Flow Unit model 118
(6HU_SIS)
5.24
Comparison between 6HUs histogram and Net to Gross (NTG) histogram
119
5.25
Net to gross model based on 3D HU model
120
Chapter 6
6.1
Schematic diagram of two stages approach (Kelkar al el., 1997)
125
6.2
The four main stages to integrate geophysical and geological data into
126
reservoir modeling with HU method in the study (modified from Kelkar
164
al el., 1997)
6.3
Hydraulic Flow Unit control
128
a) Cross plot K vs. PHI responding to 6HUs (core data),
b) 6HUs section of 3 wells (Z81, Z76 and Z82),
c) Permeability section of 3 wells (Z81, Z76 and Z82)
6.4
The workflow of history matching under Hydraulic Flow Unit control
129
(modified from Mikhail, 1997)
6.5
The Process Dialog for Flow-Based Tensor Upscaling
131
6.6
Comparison of scale of permeability in well Z76
132
6.7
(1) Log scale; (2) Log upscaled in 189 layers (static model scale);
(3) Ki, (4) Kj, (5) Kk - permeability downscaled in 99 layers by Flow
Based Tensor Upscaling method (dynamic scale)
Comparison of static scale results (a, c, e) and dynamic scale results (b,
133
d, f)
6.8
Gas (Kg) and water (Kw) relative permeability curves in sand and shaly-
135
sand reservoir (Petrel 2010, Manual)
6.9
Rock compaction function responding with porosity model and each
136
hydraulic flow unit
6.10
Historical production data for 3 wells: Z74A, Z75 and Z76
139
a) Gas Flowrate,
b) Bottom Hole Pressure (BHP)
6.11
History matching results (line colors) and observed data (dot points) of
140
traditional method
6.12
History matching results (line colors) and observed data (dot points) by
141
HU method with reservoir volume control
6.13
History matching results (line colors) and observed data (dot points) by
142
HU method with gas control
TABLE
Page
Chapter 2
2.1
Top of the Precambrian in study area
6
2.2
Stratigraphy of the Miocene formation (Rögl, 1996; Martini, 1971)
10
165
2.3
2.4
Important correlation horizons (event markers) distinguished in the
Z75 and Z76 wells in the selected depth section according to its
geological core description (after Mastalerz, et al., 2004)
Genetic sequences, SG, and other stratigraphic intervals
25
26
distinguished in the Miocene succession in the Z75 well (after
Mastalerz, et al., 2004)
2.5
Genetic sequences and other stratigraphic intervals distinguished in
27
the Miocene succession in the Z76 well (after Mastalerz, et al., 2004)
Chapter 3
3.1
Permeability correlations developed on the basis of pore and grain
33
properties (modified after Babdagli and Al-Slmin, 2004)
3.2
Simple statistics of permeability, porosity, FZI and the determination
41
coefficients (R2) for the permeability, calculated from the FZI_mean
and from the core in 6 HUs.
3.3
Global hydraulic elements (GHE) template parameters
41
Chapter4
4.1
Correlation coefficient R between ln(FZI) and log
54
4.2
Correlation coefficients between ln(FZI) and groups of log with raw
54
data
4.3
Selected independent variables used in a linear multiple regression
55
4.4
Correlation coefficients (R) between ln(FZI_core) and the results of
56
LMR and ACE.
4.5
Comparison of results obtained in well Z76; FZI_core – calculated on
62
the basis of porosity and permeability from cores, HU_core – six
hydraulic units determined according to FZI_core, FZI_pre calculated on the basis of log and using ACE algorithm, HU_pre –
6HUs determined according to FZI_log
4.6
Summary of selected rock types studies and definitions for sandstone
67
reservoirs (Rushing, et al. 2008)
4.7
The statistics of the group 3 (Z-76, Z-81, Z-82) for 14 clusters after
73
applying K means clustering
4.8
Comparison between hydraulic flow units (HUs) and rock types
77
(RTs) in the study
166
Chapter 5
5.1
The grid parameters used for stochastic variogram models
83
5.2
The 3D grid parameters
88
5.3
Seismic attributes corresponding to reservoir characterizations
97
(Chopra, et al., 2005)
5.4
The values cut-off reservoir basic on 6 HUs
119
Chapter 6
6.1
Upscaling structure models for Eclipse simulation
129
6.2
Pressure and temperature measurement results (Documentation of Z-
134
L gas field)
6.3
Gas components (Documentation of Z-L gas field)
135
6.4
Perforation intervals and time starting produce and status of Z74A,
137
Z75, and Z76 wells
6.5
Historical production data for history matching simulation (Appendix A)
157
167
LIST OF ABBREVIATIONS
ACE:
Alternating Conditional Expectation
ANN:
Artificial Neural Network
BHP:
Bottom Hole Pressure
BVI:
Bulk Volume Irreducible Water
CDF:
Cumulative Density Function
DA:
Discriminant Analysis
FWL:
Free Water Level
FZI:
Flow Zone Indicator
GHE:
Global Hydraulic Elements
GSLIB
Geostatistical Software Library
GWC:
Gas Water Contact
HU:
Hydraulic Flow Unit
LMR:
Linear Multiple Regression
MCA:
Model Based Cluster
MFS:
Maximum Flooding Surfaces
MPS:
Multiple Point Statistics
NTG:
Net To Gross
OOIP:
Original Oil In Place
PCA:
Principal Component Analysis
PVT:
Back Oil Fluid Model
RHOB:
The Bulk Density
RMS:
Root Mean Square
RQI:
Reservoir Quality Index
RT:
Rock Types
SCAL:
Special Core Analysis
SEM:
Scanning Electronic Microscope
SGS:
Sequence Gaussian Simulation
SIS:
Sequential Indicator Simulation
SNN:
Supervised Neural Networks
SOM:
Self Organizing Map
UNN:
Unsupervised Neuron Network
168
APPENDIX A
Table 6.5 Historical production data for history matching simulation
Wells
[-]
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ad
Z-74ag
Top Bottom
[m]
[m]
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
781
786
723
744
Qg
Presure
[103nm3]
[MPa]
162.125
6.69
1529.181
6.34
1534.069
5.96
1639.6
5.72
1700.605
5.54
1495.481
5.16
1680.524
4.9
1599.296
4.64
1627.63
4.38
1563.286
4.08
1626.239
3.79
1455.28
3.63
1482.482
3.46
1405.91
3.43
976.21
3.65
1315.673
3.41
1214.373
3.36
1065.866
3.34
1107.32
3.23
1065.642
3.2
1062.075
3.14
996.39
3.09
979.864
3.19
933.339
3.02
564.734
4
663.921
3.91
657.605
3.86
683.731
3.6
649.732
4.16
608.734
3.88
606.785
3.83
489.339
3.75
411.331
3.75
340.133
3.83
234.236
3.75
263.551
3.88
219.418
3.76
239.911
3.76
211.77
2.62
19.704
0
128.039
6.69
Qw
[Kg]
0
375
780
855
1250
775
1160
1120
1080
670
1360
1315
746
827
620
1669
1089
898
971
400
1244
919
870
813
300
491
621
12599
19141
33013
84965
123775
186410
211521
199335
243467
251921
320876
329643
34201
0
Days
Time
[-]
[DD/MM/YYYY]
4
9/1/2006
31
10/1/2006
30
11/1/2006
31
12/1/2006
31
1/1/2007
28
2/1/2007
31
3/1/2007
30
4/1/2007
31
5/1/2007
30
6/1/2007
31
7/1/2007
31
8/1/2007
30
9/1/2007
31
10/1/2007
23
11/1/2007
31
12/1/2007
31
1/1/2008
29
2/1/2008
31
3/1/2008
30
4/1/2008
31
5/1/2008
30
6/1/2008
31
7/1/2008
31
8/1/2008
20
9/1/2008
31
10/1/2008
30
11/1/2008
31
12/1/2008
31
1/1/2009
28
2/1/2009
31
3/1/2009
30
4/1/2009
31
5/1/2009
30
6/1/2009
31
7/1/2009
31
8/1/2009
30
9/1/2009
31
10/1/2009
30
11/1/2009
4
12/1/2009
4
9/1/2006
169
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-74ag
Z-75d
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
723
656
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
744
660
1304.111
1275.55
1393.805
1410.978
1221.825
1352.397
1253.835
1209.746
1066.111
1128.999
1023.15
1044.447
1088.593
967.846
970.746
913.511
811.253
847.597
772.387
743.64
681.573
643.237
584.338
348.396
501.288
480.42
479.007
456.16
356.743
308.649
298.301
204.283
153.998
19.16
126.179
93.125
10.014
26.119
95.244
91.73
96.753
44.589
91.561
107.224
99.716
444.235
6.32
6.08
5.84
5.62
5.6
5.38
5.22
5.2
5.07
4.84
4.87
3.84
4.46
4.39
4.32
4.25
4.1
4
3.97
3.88
3.79
3.81
3.66
3.81
3.76
3.73
3.73
3.6
3.71
3.74
3.71
3.74
3.95
4.95
4.03
4.56
4.58
4.09
4.11
4.16
4.2
4.2
4.3
4.34
4.34
5.4
724
1372
1515
4130
4755
7710
8170
9440
9400
11720
13414
19543
23561
19620
23270
23838
23243
27793
27840
30789
32920
40529
41524
28260
40790
56205
62144
68746
60454
67405
85567
67199
53358
28417
115768
59950
7770
47480
75820
86560
62610
29040
82616
78020
75935
0
31
30
31
31
28
31
30
31
30
31
31
30
31
30
31
31
29
31
30
31
30
31
31
20
31
30
31
31
28
31
30
31
30
6
30
24
3
9
31
30
31
15
31
31
30
15
10/1/2006
11/1/2006
12/1/2006
1/1/2007
2/1/2007
3/1/2007
4/1/2007
5/1/2007
6/1/2007
7/1/2007
8/1/2007
9/1/2007
10/1/2007
11/1/2007
12/1/2007
1/1/2008
2/1/2008
3/1/2008
4/1/2008
5/1/2008
6/1/2008
7/1/2008
8/1/2008
9/1/2008
10/1/2008
11/1/2008
12/1/2008
1/1/2009
2/1/2009
3/1/2009
4/1/2009
5/1/2009
6/1/2009
10/1/2009
11/1/2009
12/1/2009
1/1/2010
2/1/2010
3/1/2010
4/1/2010
5/1/2010
6/1/2010
7/1/2010
8/1/2010
9/1/2010
6/1/2009
170
Z-75d
Z-75d
Z-75d
Z-75d
Z-75d
Z-75d
Z-75d
Z-75d
Z-75d
Z-75d
Z-75g
Z-75g
Z-75g
Z-75g
Z-75g
Z-75g
Z-75g
Z-75g
Z-75g
Z-75g
Z-75g
Z-75g
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
Z-76
656
656
656
656
656
656
656
656
656
656
541
541
541
541
541
541
541
541
541
541
541
541
560
560
560
560
560
560
560
560
560
560
560
560
560
560
560
560
560
560
560
560
560
660
660
660
660
660
660
660
660
660
660
571
571
571
571
571
571
571
571
571
571
571
571
566
566
566
566
566
566
566
566
566
566
566
566
566
566
566
566
566
566
566
566
566
938.399
899.973
854.949
548.64
316.657
370.409
278.502
221.221
283.789
37.726
525.425
1059.605
954.162
888.097
813.133
667.383
595.539
482.994
387.384
382.991
338.968
369.476
138.05
501.928
413.863
400.916
360.82
166.391
242.555
279.552
271.229
196.072
125.213
41.673
43.634
36.54
33.652
40.812
36.233
14.136
69.266
47.836
43.042
5.37
4.56
4.56
2.99
2.94
2.99
2.99
2.99
2.99
2.99
3
4.42
3.96
3.96
3.61
3.56
3.61
3.61
3.61
3.61
3.61
3.61
4.69
4.37
4.24
4.24
3.75
3.75
3.65
3.53
3.53
3.53
3.37
3.33
3.37
3.37
3.37
3.37
3.37
3.37
3.37
3.37
3.37
0
1235
932
2846
29187
50009
53988
58642
92049
15544
0
0
1380
2372
4747
4290
5489
4234
3891
4117
3970
4454
70
10
500
33
0
280
1091
3558
3703
2824
6301
5179
5014
5528
4480
4503
2323
1278
7822
9501
9349
31
31
30
31
30
31
31
28
31
6
15
31
31
30
31
30
31
31
28
31
30
31
9
31
28
31
30
24
30
31
31
25
31
30
31
31
28
31
22
6
31
31
30
7/1/2009
8/1/2009
9/1/2009
10/1/2009
11/1/2009
12/1/2009
1/1/2010
2/1/2010
3/1/2010
4/1/2010
6/1/2009
7/1/2009
8/1/2009
9/1/2009
10/1/2009
11/1/2009
12/1/2009
1/1/2010
2/1/2010
3/1/2010
4/1/2010
5/1/2010
12/1/2008
1/1/2009
2/1/2009
3/1/2009
4/1/2009
5/1/2009
6/1/2009
7/1/2009
8/1/2009
9/1/2009
10/1/2009
11/1/2009
12/1/2009
1/1/2010
2/1/2010
3/1/2010
4/1/2010
6/1/2010
7/1/2010
8/1/2010
9/1/2010
Note: Z74 and Z74A are the different wells, and both are dual-completed, equipped with
packers and two tubing strings;
“g” means upper completion;
“d” means lower completion (or horizon)
171