Lithofacies and Petrophysical Properties of Mesaverde Tight

Transcription

Lithofacies and
Petrophysical Properties
of Mesaverde Tight-Gas
Sandstones in Western
U.S. Basins:
a short course
Alan P. Byrnes
formerly Kansas Geological Surveynow Chesapeake Energy
Robert M. Cluff
John C. Webb
Daniel A. Krygowski
Stefani D. Whittaker
The Discovery Group, Inc
2009 AAPG Annual Convention
Short course #1
6 June 2009, Denver, Colorado
Cluff: Introduction and Overview
Lithofacies and Petrophysical
Properties of Mesaverde TightTight-Gas
Sandstones in Western U.S. Basins:
a short course
Alan P. Byrnes
formerly Kansas Geological Survey
Survey-now Chesapeake Energy
Robert M. Cluff
John C. Webb
Daniel A. Krygowski
Stefani D. Whittaker
The Discovery Group, Inc
2009 AAPG Annual Convention
Short course #1
AAPG ACE 2009: Denver Colorado
1
Denver, Colorado
Short course agenda
8:00-8:30
8:008:30--10:00
8:30
Project overview, Bob Cluff
Lithofacies and geology of the
Mesaverde Group, John Webb
10:0010
10:00
00-10:15
10 15 b
break
eak
10:1510:15-noon
Porosity & permeability of Mesaverde
tight gas sands, Alan Byrnes
noon--1:00p lunch
noon
1:00--2:30
1:00
Pc, resistivity, and relative
perm of Mesaverde, Alan Byrnes
2:30--2:45
2:30
break
2:452:45-4:15
Log evaluation of the Mesaverde,
Mesaverde Dan
Krygowski, Stefani Whittaker,
& Bob Cluff
4:15--4:30
4:15
discussion, Q&A period
AAPG ACE Short Course 1: 06.06.2009
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Project title:
Analysis of Critical Permeability,
Capillary and Electrical Properties for
Mesaverde Tight Gas Sandstones
from Western U.S. Basins
US DOE # DE-FC26-05NT42660
website: http://www.kgs.ku.edu/mesaverde
3
Project overview
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¾
Project proposal submitted on 21 March 2005 in
response to DOE solicitation DEDE-PS26
PS26--04NT42720
DOE award DEDE-FC26
FC26--05NT42660 in October 2005
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for $411K DOE funds/$103K industry coco-share
Discovery Group inin-kind contribution of manpower and
facilities
2 ½ year study with nono-cost extension
Alan P. Byrnes, Principal Investigator
University of Kansas Center for Research was the
umbrella contracting organization
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Kansas Geological Survey and The Discovery Group, cocoparticipating research contractors
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Team Members
University of Kansas
Kansas--Kansas Geological Survey
Alan P. Byrnes (Principal Investigator)
Support Team Members:
John Victorine, Ken Stalder, Daniel S. Osburn,
Andrew Knoderer, Owen Metheny, Troy
Hommertzheim, Joshua P. Byrnes
The Discovery Group, Inc.
Robert M. Cluff (co(co-Principal Investigator)
John C. Webb, Daniel A. Krygowski, Stefani Whittaker
5
Future Gas Supply
Lower 48 unconventional gas sources will meet nearly 50% of US demand
(Caruso, EIA, 2008)
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Future Gas Supply
While tight gas sandstones represent over half of unconventional supply
(Caruso, EIA, 2008)
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Annual Gas Production (Tcf)
Production Projected to Increase from Rocky
Mountain Region
Date
(US EIA, 2004)
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Natural Gas Type
Lower 48 Technically Recoverable Resources
Tcf
(US EIA, 2004)
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PGC Rocky Mountain Gas Resources
Kmv
Shallow Resources (0(0-15,000 ft)
Deep Resources (15,000(15,000-30,000 ft)
Total Traditional Resources
Coalbed Gas Resources
Total Recoverable Resources
99,167 Bcf
24,429 Bcf
123,596 Bcf
63,273 Bcf
186,869 Bcf
Data source: Potential Gas Committee (2003)
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Why pick the Mesaverde?
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Tight gas sandstones (TGS) represent
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72% (342 TCF) of the projected unconventional gas
resource (474 TCF).
Rocky Mountain TGS are 70% of the total TGS resource
base (241 Tcf; USEIA
USEIA, 2004)
and the Mesaverde Group represents the main gas
productive sandstone unit in the Rocky Mtn. TGS basins
and the largest shallow (<15,000 ft) target.
Understanding of reservoir properties and accurate
tools for formation evaluation are needed for:
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assessment of the regional gas resource
projection
j ti off ffuture
t
gas supply
l
exploration programs
optimizing development programs
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Project objectives
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The project provides petrophysical tools that
address fundamental questions concerning
z
z
z
z
z
z
gas flow,
flow critical gas saturation
saturation, Sgc=f
Sgc=
Sgc f (lithofacies,
(lithofacies
Pc, architecture)
capillary pressure, Pc=f
Pc=f (P), Pc=f
Pc=f (lithofacies, k, φ,
architecture)
electrical properties, m* & n*
facies and upscaling issues
wireline log interpretation algorithms
providing a webweb-accessible database of advanced
rock properties.
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Specific research objectives
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explore nature of critical gas saturation, capillary
pressure, and electrical properties of Mesaverde
tight gas sandstones
h
how
d
do th
these vary with
ith porosity,
it permeability,
bilit and
d
lithofacies?
better understanding of minimum gas saturation
required for gas flow
improve log calculations through better corrections
for conductive solids/surface effects
address the lack of adequate public domain
databases covering petrophysics of tight gas
sandstones
z
lots of proprietary data out there, numerous publications
with partial datasets, but nothing integrated to work with
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Tasks
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¾
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Task 1. Research Management Plan
Task 2. Technology Status Assessment
Task 3. Acquire Data and Materials
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Task 4. Measure Rock Properties
p
z
z
z
z
z
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¾
z
z
Subtask 6
6.1.
1 Compare log and core properties
Subtask 6.2. Evaluate results and determine loglog-analysis algorithm inputs
Task 7. Simulate ScaleScale-dependence of Relative Permeability
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Subtask 5.1. Compile published and measured data into Oracle database
Subtask 5.2. Modify existing webweb-based software to provide GUI data access
Task 6. Analyze WirelineWireline-log Signature and Analysis Algorithms
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Subtask 4.1. Measure basic properties (k, φ, GD) and select advanced population
Subtask 4.4. Measure critical gas saturation
Subtask 4.3. Measure inin-situ and routine capillary pressure
Subtask 4.4. Measure electrical properties
Subtask 4.5. Measure geologic and petrologic properties
Subtask 4.6. Perform standard logs analysis
Task 5. Build Database and WebWeb-based Rock Catalog
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Subtask 3.1. Compile published advanced properties data
Subtask 3.2. Compile representative lithofacies core and logs from major basins
Subtask 3.3. Acquire logs from sample wells and digitize
Subtask 7.1. Construct basic bedform architecture models
Subtask 7.2. Perform numerical simulation of flow for basic bedform architecture
Task 8. Technology Transfer
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Research strategy
¾
compile all available published advanced
rock properties (Pc, FRF, Krg,
compressibility, etc.)
¾ collect 300+ core plug samples from 20 to
25 wells across 5 major basins
¾ sample full range of rock types, porosity and
permeability found in Mesaverde throughout
the Rockies
z
Kmv is widespread, lots of core available,
representative example for most TGS problems
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Sampling
¾
¾
¾
¾
44 wells in 6
basins
described
7000 ft core
(digital)
2200 core
samples
120
120--400
advanced
properties
ti
samples
Powder
River
Wind River
Wyoming
Green River
N
Washakie
Utah
Colorado
Uinta
Piceance
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Number of wells by basin
Number of W
Wells
12
10
Industry-contribution
USGS Core Library
8
6
4
2
Wind Riverr
Washakie
(Sand
Wash)
Washakie
Uinta
Powder
River
Piceance
Green
n
River
0
Basin
17
Core Plugs by Basin
Number of Core
e Plugs
700
600
500
400
300
200
100
Powderr
River
Wind R iverr
Piceance
e
Uinta
a
Washakie
e
Greater
Green Riverr
0
Basin
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Sampling by depth
0.20
0.18
0 16
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0 02
0.02
0.00
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
Fraction
Depth Histogram
Depth (ft)
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All
Green River
Piceance
Powder River
Sand Wash
Uintah
Wind River
Washakie
40
35
30
25
20
15
10
5
10-100
100-1,000
1-10
0.1-1
0.01-0.1
0.001-0.01
0.0001-0.001
0
1E-5 - 1E-4
¾
Petrophysical property
distributions are generally
normal or loglog-normal
SubS b-distributions
Sub
di t ib ti
=f
(basin, lithofacies,
marine/non--marine, etc.)
marine/non
45
1E-6 - 1E-5
¾
50
1E-7 - 1E-6
Property
distributions
Percent of Population (%)
P
Green River
Piceance
Powder River
Uintah
Wind River
Washakie
Sand Wash
50
40
30
20
10
0
40
Percent of Popu
ulation (%)
All
Green River
Piceance
Powder River
Sand Wash
Uintah
Wind River
Washakie
35
30
25
20
15
10
5
Grain Density (g/cc)
22-24
20-22
18-20
16-18
2.722.74
14-16
2.702.72
12-14
2.682.70
10-12
2.662.68
8-10
2.642.66
6-8
2.622.64
4-6
2.602.62
2-4
0
2.582.60
0-2
Percent of Bas
sin Population
In situ Klinkenberg Permeability (mD)
45
60
In situ Porosity (%)
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Core description
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rock typing at 0.5 ft
frequency
q
y to match
log data resolution
lithology, color, grain
size, sed structures
sample locations
important cements
d
depositional
iti
l
environments
21
Digital core description
¾
To provide lithologic input to
equations and predict
lithology from logs used 5
digit system
z
z
z
z
z
¾
¾
1 basic type (Ss, Ls, coal)
2 grain size/sorting/texture
3 consolidation
4 sedimentary structure
5 cement mineralogy
P
Property
t continuum
ti
- nott
mnemonic or substitution
cipher
Similar to system used in
our 1994 and subsequent
studies
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Petrography
¾
40X
¾
¾
~150 advanced
properties smpls were
petrographically
characterized
representative photos at
several magnifications
point counts
Williams PA 424, 6148.8’
15276
9.9%
2.66 g/cc Ka=0.0237 mD
100X
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Core analysis program
¾
¾
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Geologic description of cores and rock types
(Webb)
Wire--line log analysis of all project wells over Kmv
Wire
(Krygowski and Whittaker)
Collect plugs for basic properties (minimum 300
samples, we actually collected ~2200) (Byrnes)
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z
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routine porosity and permeability
porosity and permeability at reservoir stress
grain density
Select a subsub-set of 120120-400 samples for advanced
core analyses (Byrnes)
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“Routine” core analysis
¾
Routine porosity and permeability
¾ In
In--situ porosity and permeability
¾ Pore
P
volume
l
compressibility
ibilit (113 smpls)
l )
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¾
200
200--4000 psi NCS
determined new equations for
z
z
z
Klinkenberg correction
stress dependent porosity
stress
t
dependent
d
d t permeability
bilit
25
Prior work
In
n situ Klinkenberg Perrmeability
(md)
100
10
Council Grove
Mesaverde/Frontier
1
0.1
0.01
0.001
0.0001
0.00001
0.001
0.01
0.1
1
10
Routine Air Permeability (md)
100
logkik = 0.0588 (logkair)3 –0.187 (logkair)2 +1.154 logkair - 0.159
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SCAL work
¾
¾
routine and in situ mercury capillary pressure
investigate Pc as function of lithology, φ, K
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¾
investigate stress sensitivity of Pc
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¾
sample span range of basins, K, lithology
most MICP curves are run under lab conditions
we expect Pc to be confining stress sensitive
120 “high
“high--low” pairs of plugs run using highly similar plugs
selected from φ-K data
look at relationship between initial saturation and
residual gas saturation (“scanning curves”)
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only published data are for conventional rocks
ran mercury curves for this project
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Mesaverde, Frontier capillary
pressure vs. permeability
10 md
~Heightt above Free Waterr (ft)
350
1 md
0.1 md
300
0.01 md
0.001 md
250
200
150
100
50
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Water Saturation (fraction)
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Pc hysteresis
4
¾
¾
Non-wetting residual
Nonsaturation to
imbibition Snwr = f
(Snwi)
this was a “freebie”
added to the project
plan
Drainage-Imbibition
Cycles
5
3
2
1
Midale Dol
φ = 23%
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(after Larson & Morrow, 1981)
SCAL work
¾
routine and in situ mercury capillary
pressure
¾ drainage critical gas saturation
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Why is Sgc important?
Gas Relative Permeability
1
P = 1.7
Sgc = f (kik)
0.1
P = f (kik)
Sgc = 10%
0.01
0.001
0.0001
0.00001
0
10
20
30
40
50
60
70
80
90
100
Water Saturation
¾
2 alternative views of what happens at high
Sw, which is correct?
31
Saturation at capillary equilibrium for
breakthrough pressure (Hg experiment)
Saturation at Breakthrough in Pc
Equilibrium (%)
60
50
40
30
20
10
0
0
10
20
30
40
50
60
Critical Saturation at Breakthrough (%)
proof of concept dataset, 2005
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SCAL work
¾
routine and in situ mercury capillary
pressure
¾ drainage critical gas saturation
¾ cementation and saturation exponents
¾ cation exchange capacity using multimulti-salinity
method
33
When F and φ are plotted loglog-log
m= 2
1000
m= 3
but not this!
F
100
m= 1
10
We’ve seen this before,
1
0.01
0.1
log F = -m log φ
φ
1
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Products
¾
web-based database with output as XLS files,
webgraphical output, reports and presentations
z
z
z
¾
¾
¾
organized by data type and by area, well
htt //
http://www.kgs.ku.edu/mesaverde/
k k d /
d /
http://www.discovery--group.com/projects_doe.htm
http://www.discovery
methods for improved log calculations
industry talks, short courses, & forthcoming
publications
so here we go..........
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Webb: Lithofacies and Reservoir Quality
Influence of Lithofacies and Diagenesis
on Reservoir Quality of the Mesaverde
Group, Piceance Basin, Colorado
John Webb
Disco er Gro
Discovery
Group,
p Den
Denver,
er CO
AAPG Short Course no. 1, Denver, CO
June 6, 2009
1
Denver, Colorado
Outline
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¾
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¾
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¾
¾
¾
¾
Data collection procedures and methods
Di it l rock
Digital
k classification
l
ifi ti system
t
Thin section preparation and petrography
Example from the Piceance basin
Paleogeography and depositional environments
Lithofacies and porosity/permeability relationships
Detrital composition and diagenesis
Porosity distribution
Influence of diagenesis on reservoir quality
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Acknowledgements
Industry Partners:
Bill Barrett Corporation - Steve Cumella
EnCana USA, Piceance Teams - Brendan Curran,
Mike Dempsey, Danielle Strickler
ExxonMobil, Piceance Basin Team
Don Yurewicz,
Yurewicz, Hollie Kelleher
Williams Production - Lesley Evans
3
Acknowledgements
Contractors and Government:
Elitigraphics – Peter Hutson
Triple O Slabbing - Butch Oliver
USGS Personnel - Phil Nelson, Mark Kirschbaum
USGS Core
C
Research
R
h Center
C t
Tom Michalski, Betty Adrian (current director)
Jeannine Honey, John Rhodes, Josh Hicks,
Terri Huber, Richard Nunn, Devon Connely
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Core sampling and description
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¾
¾
¾
¾
Cut 1” diameter plugs from butt portions of slabbed
core, using water cooled diamond drill bit
Location of core plugs to 0.1 foot
Digital rock typing of each core plug (lithology, grain
size, porosity, sedimentary structures, cementation)
Scanned core slab images and handhand-held digital
photos for core plug locations and documentation of
lithology
t o ogy and
a d sedimentary
sed e ta y structures
st uctu es
Core descriptions from slabbed core when possible
5
Core sampling and description
¾
¾
¾
¾
Logged lithology, grain size, matrix porosity,
sedimentary structures, fractures, trace fossils,
contact relationships and digital rock type at
minimum ½ foot intervals
Comparator for grain size determination
HCl for identification of calcareous cements
Legacy core analysis data and whole core
photographs on file at USGS CRC or from current
well operators
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Barrett Last Dance 43C – Typical Core Chart
7
Digital Core
Description
¾
¾
Sampling designed to
sample across all
lithofacies
5 digit system
z
z
z
z
z
¾
basic type (Ss, Ls, coal)
grain size/sorting/texture
Consolidation/porosity
sedimentary structure
cement mineralogy
Provides lithology log
traces and quantitative
variables for multivariate
analysis
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Digital Rock Types
Grain size/sorting/ shaliness
Visible porosity
10xxx
11xxx
12xxx
xx0xx
xx1xx
xx2xx
2
xx3xx
xx4xx
xx5xx
xx6xx
xx7xx
xx8xx
19xxx
Shale
Silty shale
V shaly sandstone,
sandstone
siltstone
Shaly sandstone
VF sandstone
F sandstone
M sandstone
C sandstone
VC/Matrix
supported
pp
cgl.
g
Conglomerate
05000
2xxxx
30000
Volcanic ash
Limestone
Coal
13xxx
14xxx
15xxx
16xxx
17xxx
18xxx
xx9xx
0-2%, unfractured
0-2% fractured
3 10% unfrac’d
3-10%,
f ’d
3-10%, frac’d
3-10%, highly frac
>10%, unfrac’d
>10%, frac’d
>10%, unfrac’d
V high, weak
consolidation
Unconsolidated
Porosity/ Resistivity logs
GR/Porosity/ Resistivity logs
9
Digital Rock Types, cont.
Sedimentary struc’s
xxx0x Vertical dike
xxx1x Bioturbated
xxx2x Contorted
xxx3x Discontinuous
laminations
xxx4x Continuous
laminations
xxx5x Flaser bedded
xxx6x Ripple laminated
xxx7x Trough & planar
tabular crossbeds
xxx8x Planar laminated,
low angle cross
bedded
xxx9x Massive bedded
Shaliness, vertical and
lateral permeability
Cement
xxxx0 Pyrite
xxxx1
1 Siderite
Sid i
xxxx2 Phosphate
xxxx3 Anhydrite
xxxx4 Dolomite
xxxx5 Calcite
xxxx6 Quartz
xxxx7 Authigenic clay
xxxx8 Carbonaceous
xxxx9 No pore filling
Density/ Resistivity/ PE logs
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15277 - Medium sandstone with
moderate porosity, not fractured,
trough cross bedded,
clay cemented
11
Utility of digital rock typing, continued
¾
¾
¾
¾
¾
¾
Excellent match with GR log traces, core gamma
Precise depth shifting of core analysis data
D
Demonstrates
t t iinfluence
fl
off grain
i size
i and
d shaliness
h li
on
porosity and permeability
Allowed improvement of equations used to calculate
Archie Sw
Sw,, total and effective porosity and significantly
improved estimates of permeability
Rock types are not restricted to a specific depositional
environment
Log analysis identified detrital shale component, but
failed to identify details of grain size and sedimentary
structures
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Correlation of lithofacies and core
analysis data to wireline logs
13
Utility of digital rock typing
¾
¾
¾
Track statistical distribution of lithofacies for
sampling and core analysis data
Provides quantitative variables for multivariate
analysis
The simple variation in grain density from basin to
basin indicates that differences in detrital
composition of sediment, depositional environment,
burial history and diagenesis among basins
requires separate treatment of basins for
assessment of reservoir quality
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Percent of Basin Popula
ation
Grain densities of the
Mesaverde Group
60
Green River
Piceance
Powder River
Uintah
Wind River
Washakie
Sand Wash
50
40
30
20
10
0
2.582.60
2.602.62
2.622.64
2.642.66
2.662.68
2.682.70
2.702.72
2.722.74
15
Thin section preparation
¾
¾
¾
¾
¾
¾
Blue-dyed epoxy, low viscosity, slow cure
BlueVacuum and pressure impregnation in warm
oven
Polished surfaces of billet and mounted
slide
Dual carbonate stained for nonferroan (red)
and ferroan carbonate (various shades of
blue)
Stained for potassium feldspar (K(K-spar is
yellow)
Cover slips
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Thin section petrography
¾
Nikon and Leitz petrographic microscopes
¾ Conventional film and digital photography,
representative magnifications and detailed
features
¾ 300 point counts per sample, automated
point count stage
¾ Calculations in Excel, g
graphic
p
p
plots in
Quattro Pro and Excel spreadsheets
17
Utility of thin section petrography
¾
Detrital composition
z
z
z
¾
Cements
z
¾
Provenance
Radioactive components for GR match
Bulk density of constituent grains
Bulk density of constituent cement (calcite,
dolomite, pyrite, clay)
Distribution of clay
z
z
z
Detrital - laminated, structural, dispersed
(burrowing)
Clay cements – pore
pore--lining, porepore-bridging or
dispersed
Clay mineralogy (visual morphology)
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Utility of thin section petrography
¾
Diagenesis
z
z
¾
Porosity distribution
z
z
¾
Assess the effect of compaction and pressure
solution
Document changes in detrital grains or rock
fabric
Mesoporosity, microporosity, moldic and
intragranular porosity
Compare relative abundance of Meso vs. Micro
Fractures
z
z
Assess the importance of microfractures
Identify fracture cements
19
Paleogeography of Mesaverde Group,
Uinta and Piceance Basins
Early Clagget time,
Middle Judith River time,
Mancos Shale
Iles Formation (Rollins,
Cozette and Corcoran Ss)
Middle Bear Paw time,
Williams Fork Formation
approx 80 mya
approx 73 mya
McGookey, et al., 1972
approx 70 mya
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Depositional environments of the
Mesaverde
¾
¾
¾
¾
¾
¾
Shallow marine and shoreline environments,
including lagoonal
lagoonal, bay
bay--fill and coastal
marsh
Tidal delta, tidal channel, mudflat and tidally
influenced coastal streams
Coal swamps (raised mire) and coastal plain
Fluvial
Fl i l channel,
h
l iincluding
l di tid
tidally
ll iinfluenced
fl
d
Abandoned channel and overbank/splay
Paleosols,, rooted horizons, air fall ash and
Paleosols
lacustrine to shallow marine limestone
21
Example: The Piceance Basin
¾
Core analysis:
z
Routine - 629 samples, SCAL - 46 samples
¾
Mercury invasion and imbibition curves for 8
samples
¾ Core description and petrography :
z
¾
6 wells, 2 shallow bore holes, 1168’ core, 46 thin
section point counts
L analysis:
Log
l i
z
Modern log suites for 5 wells, various vintages and
format for 1 older well and 2 shallow bore holes
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Mesaverde Group cores, Piceance Basin
W Fuels 21011-5
Moon Lake
White River Dome
FR M30-2-96W WRD
Love Ranch
EM WR T63X-2G
RulisonMamm Creek
Grand Valley
Chevron 33-34
Parachute MWX-2 BBC LD 43C-3-792
USGS BC 1
Wms PA 424-34
23
Stratigraphic distribution of samples,
Piceance Basin
33-34
3,500 ft
4,600 ft
5700 ft
10,500 ft
USGS Coal
Resources,
#1 Book
Cliffs
outcrop core
250 ft
6,500 ft
6,600 ft
8200 ft 6,300 ft
8,100 ft
24
30 of 217
Barrett Last Dance 43C – Shallow Marine/Coastal
25
Barrett Last Dance 43C – Coastal Mudstones
26
31 of 217
Barrett Last Dance 43C – Fluvial
27
Lithofacies - Influence of grain size and shaliness on
porosity and permeability
Phi/K Crossplot Mesaverde Group, Piceance Basin
Amb
bient Permeability, in mD
100
10
1
11XXX
12XXX
13XXX
0.1
14XXX
15XXX
0.01
16XXX
17XXX
0.001
0.0001
0
5
10
15
20
Ambient Porosity, percent
28
32 of 217
100
Ambient Permeability, in m
mD
10
1
0.1
11XXX
0.01
0.001
0.0001
0
5
10
15
20
29
100
mD
10
1
0.1
12XXX
0.01
0.001
0.0001
0
5
10
15
20
30
33 of 217
100
mD
10
1
0.1
13XXX
0.01
0.001
0.0001
0.0
5.0
10.0
15.0
20.0
31
100
mD
10
1
0.1
14XXX
0.01
0.001
0.0001
0
5
10
15
20
32
34 of 217
mD
10
1
0.1
15XXX
0.01
0.001
0.0001
0
5
10
15
20
33
mD
10
1
0.1
16XXX
17XXX
0.01
0.001
0.0001
0
5
10
15
20
34
35 of 217
mD
10
1
0.1
16XXX
17XXX
0.01
0.001
0.0001
0
5
10
15
20
35
Influence of burial on porosity and permeability of lithofacies
Fine Grained Ss (15xxx)
Amb
bient Permeability, in mD
100
10
1
250 ‐ 3999 ft
4000 ‐ 6999 ft
7000 ‐ 10,000 ft
0.1
0.01
0.001
0
5
10
15
20
25
36
36 of 217
Influence of burial on porosity and permeability of lithofacies
Medium Grained Ss (16xxx)
100
Ambient Permea
ability, in mD
10
1
250 ‐ 3999 ft
4000 ‐ 6999 ft
7000 ‐ 10,000 ft
0.1
0.01
0.001
0
5
10
15
20
25
37
Detrital Composition of Sandstones
in the Mesaverde Group
¾
Why do we care? Because detrital composition has
an effect on diagenesis and porosity preservation.
¾
In the Mesaverde, quartzose sandstones are
preferentially subject to pressure solution
compaction and quartz overgrowth cementation
(clay cementation may retard overgrowths)
¾
Feldspathic sandstones suffer compaction by grain
rearrangement and brittle
deformation, accompanied by clay cement.
38
37 of 217
¾
Other alterations include dissolution of framework
grains ((Kg
(K-spar
p and carbonate rock
fragments), resulting in moldic porosity.
¾
Ductile deformation of shale, carbonaceous
material, volcanic rock fragments and micaceous
grains, brittle deformation of feldspars
39
¾
¾
¾
¾
Composition ranges from litharenite to feldspathic
litharenite lithic arkose,
litharenite,
arkose sublitharenite
sublitharenite, subarkose
and quartzarenite
Rock fragments include volcanic, sedimentary and
metamorphic grains
Volcanic rock fragments are commonly
altered, resulting in replacement by
clay silicification and partial to complete dissolution
clay,
Sedimentary rock fragments include
shale/mudstone, chert and carbonate grains
40
38 of 217
41
42
39 of 217
43
Detrital Composition, Barrett Last Dance 43C
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Williams Fork Fm
3544.9
3555.4
3577.6
4004.3
4013.3
Top Gas 4363 ft
4393.6
4416.6
5715.4
6042.4
Cameo Coal zone
6337.1
Quartz
Feldspar
Lithic
44
40 of 217
Detrital Composition, MWX‐2
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Williams Fork Fm
5734.1
5838.6
5852.3
6536.3
6542.2
6550.3
7085.5
7133.5
7264.5
7272.8
7276.2
Cozette Ss
Cozette Ss
7851.3
7877.5
7880.1
Corcoran Ss
8106.9
8117.9
Quartz
Feldspar
Lithic
45
SRF – Sedimentary rock fragments
VRF – Volcanic
V l
i rock
k ffragments
t
PRF – Plutonic rock fragments
QM – Quartzose metamorphic
MRF – Micaceous metamorphic
46
41 of 217
Lithic Population, Barrett Last Dance 43C
0.0
5.0
10.0
15.0
20.0
25.0
Williams Fork Fm
3544.9
3555.4
3577.6
4004.3
4013.3
Top Gas 4363 ft
4393.6
4416.6
5715.4
6042.4
Cameo Coal zone
6337.1
Chert
Shale
Dolostone
Volcanic
47
Lithic Population, MWX‐2
0
Williams Fork Fm
5
10
15
20
25
5734.1
5838.6
5852.3
6536.3
6542.2
6550.3
7085.5
7133.5
7264.5
7272.8
7276.2
Cozette Ss
7851.3
7877.5
7880.1
Corcoran Ss
8106.9
8117.9
Chert
Shale
Limestone
Dolostone
Volcanic
48
42 of 217
Cement Distribution in the Mesaverde Group
¾
Pore--lining clay cements
Pore
z
z
¾
Chlorite (common to abundant)
Mixed--layer illite
Mixed
illite--smectite (sparse to moderate)
Pore--filling cements
Pore
z
z
z
z
z
z
z
Siderite (trace)
Pyrite (trace to sparse)
Non--ferroan calcite (sparse)
Non
Quartz overgrowth (trace to abundant)
Ferroan calcite and ferroan dolomite (sparse to common)
Albite (grain replacement and moldmold-filling)
Kaolinite (sparse in one sample in Book Cliff outcrop)
49
Cement Types, Barrett Last Dance 43C
0
5
10
15
20
25
Williams Fork Fm
3544.9
3555.4
3577.6
4004.3
4013.3
Top Gas 4363 ft
4393.6
4416.6
5715.4
6042.4
Cameo Coal zone
6337.1
Quartz Og
Fe Calcite
Chlorite and ML/IS
50
43 of 217
Cement Types, MWX‐2
0
5
10
15
20
25
30
35
Williams Fork Fm
5734.1
5838.6
5852.3
6536.3
6542.2
6550.3
7085.5
7133.5
7264.5
7272.8
7276.2
Cozette Ss
7851.3
7877.5
7880.1
Corcoran Ss
8106.9
8117.9
Quartz Og
Fe Calcite
Chlorite and ML/IS
51
Porosity Distribution in the Mesaverde Group
¾
Mesoporosity
z
z
z
¾
Pore throat apertures <2 micron, > 0.5 micron radius
Intergranular pores, primary and secondary
Moldic pores (partly and completely dissolved
feldspars, carbonate and volcanic rock fragments (large
aspect ratio, pore body/pore throat)
Microporosity
z
z
z
Pore throat apertures <0.5 micron, >0.1 micron radius
P -lilining
PorePore
i and
d porepore-filling
filli clay
l cementt
Intragranular micropores (altered VRF, clay pellets, shale
rock fragments, clay and carbonaceous matrix)
52
44 of 217
Porosity Distribution in the Mesaverde Group
¾
Nanoporosity
z
z
¾
Pore throat apertures <0.1 micron radius
Typical of mudstones, clayclay-sized intergranular, common in
d t it l clay
detrital
l or carbonaceous
b
material
t i l
Fractures
z
z
Macroscopic
Microscopic (primarily crushed feldspars or chert, partings
or separations at quartz overgrowth boundaries)
53
Interparticle and intercrystalline
Mesoporosity
Interparticle and intraparticle
Microporosity
54
45 of 217
Porosity Distribution, Barrett Last Dance 43C
0
5
10
15
20
25
Williams Fork Fm
3544.9
3555.4
3577.6
4004.3
4013.3
Top Gas 4363 ft
4393.6
4416.6
5715.4
6042.4
Cameo Coal zone
6337.1
BP
sBP
Mo
clfBP
55
Porosity Distribution, MWX‐2
0
2
4
6
8
10
12
Williams Fork Fm
5734.1
5838.6
5852.3
6536.3
6542.2
6550.3
7085.5
7133.5
7264.5
7272.8
7276.2
Cozette Ss
7851.3
7877.5
7880.1
Corcoran Ss
8106.9
8117.9
BP
sBP
Mo
clfBP
56
46 of 217
57
Porosity Networks in the Mesaverde Group
¾ Type
z
z
z
z
Conventional porosity – Primary intergranular and
modified intergranular (e.g. quartz overgrowth
cement, secondary intergranular)
Lacking clay cement
Mesoporosity >> Microporosity
Phi=high, K=high, low Swi, efficient drainage, low to
moderate Pc entry pressure
¾ Type
z
z
z
z
I
II
Intergranular and moldic – May include primary
intergranular and secondary intergranular
Trace to absent clay cement
Mesoporosity >> Microporosity
Phi=high, K=moderate , low to moderate Swi, elevated
Srg,, moderate Pc entry pressure
Srg
58
47 of 217
¾ Type
z
z
z
z
Restricted intergranular – ClayClay-lined pores and pore
throats, some moldic and clayclay-filled intergranular
microporosity
moderate to common clay cement
Microporosity > Mesoporosity
Phi=moderate, K=low, moderate to high Swi, elevated
Srg,, increased Pc entry pressure
Srg
¾ Type
z
z
z
z
III
IV
Microintergranular – ClayClay-filled intergranular pores
Moderate to common clay cement
Microporosity >> Mesoporosity
High Swi, Phi=moderate to low, K=low to extremely
low, elevated Srg
Srg,, increased Pc entry pressure
59
¾ Type
z
z
z
V
Nanointergranular– Typical of mudstones, clayNanointergranular–
clay-sized
intergranular, common clay or carbonaceous material
Microporosity only
Phi=moderate to low, K=low to extremely low, high
Swi, extremely high pore entry pressure
60
48 of 217
Type I (shallow burial)
Porosity consists of well connected
primary and secondary intergranular
mesopores, sparse moldic pores,
quartz overgrowth cement.
Quartz cement is sparse.
40X
100X
Lack of pore-lining clay cement
reduces Swi and improves relative
permeability.
USGS CB #1 Book Cliffs, 255.8’
Rock type 15567
Porosity 24.8% amb., Rhob2.64 g/cc
Ka=137.62 mD
Kins=112.2 mD
61
Type I (moderate burial)
Porosity consists of moderately
connected primary and secondary
intergranular mesopores and traces
of pore-lining chlorite clay containing
microporosity
microporosity.
40X
Quartz cement and ferroan calcite are
sparse.
Lack of pore-lining clay cement
reduces Swi and improves relative
permeability.
100X
Barrett Last Dance 43C, 3544.9’
Rock type 16277
Porosity 11.4% Rhob 2.65 g/cc
Ka=0.8716 mD
Kins=0.4287 mD
62
49 of 217
Type II
Porosity consists of poorly to
moderately connected moldic and
secondary intergranular mesopores
with traces of pore-lining ML/IS(?)
clay, containing microporosity.
40X
Quartz cement is prominent,
ferroan calcite is sparse.
Pore-lining clay cement begins to
increase Swi and reduce relative
permeability.
100X
Rock type 15276
Porosity 9.9%
Rhob 2.66 g/cc
Ka=0.0237 mD
Kins=0.0076 mD
63
Type III
Porosity consists of clay-lined
intergranular pores, pore throats
are occluded by clay cement,
causing elevated Swi, reduced
relative permeability and
i
increased
dP
Pc entry
t pressure.
40X
Cements include chlorite or ML-IS
clay, traces of nonferroan or
ferroan calcite, traces of quartz
overgrowths.
Inhomogeneous packing and
over sized intergranular pores
over-sized
indicate the development of
secondary intergranular porosity.
Rock type 15297
Ka=0.0178 mD Kins=0.0019 mD
100X
64
50 of 217
Type III
Porosity consists of clay-lined
intergranular pores, pore throats
are occluded by clay cement,
which causes elevated
Swi, reduced relative permeability
and
d iincreased
dP
Pc entry
t pressure
400X
Cements include chlorite or ML-IS
clay, traces of nonferroan or
ferroan calcite, traces of quartz
overgrowths.
Inhomogeneous packing and
over-sized
over
sized intergranular pores
indicate the development of
secondary intergranular porosity.
400X, XP
.Rock type 15297
Ka=0.0178 mD Kins=0.0019 mD
65
Type IV
Porosity consists almost entirely of
sparse, poorly connected, clay-filled
intergranular microporosity.
Quartz cement is prominent
prominent,
ferroan calcite is sparse.
40X
Pore-filling clay cement causes
elevated Swi, reduced relative
permeability and increased Pc entry
pressure.
Rock type 15286
Porosity 7.9%
Rhob 2.65 g/cc
Ka=0.0211 mD Kins=0.0031 mD
100X
66
51 of 217
Type V
Porosity consists entirely of
sparse, poorly connected
microporosity within interparticle
voids of mudstone and shale matrix.
64X
Cements include siderite, ferroan
calcite and pyrite. Organic matter is
locally common.
Abundant clay causes highly
elevated Swi, severely reduced
permeability and elevated Pc entry
pressure.
p
160X
CER MWX-2, 7085.5’
Rock type 11299
Porosity 2.4%
Rhob 2.70 g/cc
Ka=0.0020 mD Kins=0.00004 mD
67
P
Permeability, ambient, in
n mD
Porosity types, Mesaverde, Piceance basin
100
10
Type I
1
Type II
Type III
Type IV
0.1
Type V
0.01
0.001
0
5
10
15
20
25
Porosity, ambient, in percent
68
52 of 217
Pe
ermeability, ambient, in m
mD
Porosity types, Mesaverde, Piceance basin
250 ‐ 3999 ft minimum burial
100
10
Type I
1
Type II
Type III
Type IV
0.1
Type V
0.01
0.001
0
5
10
15
20
25
69
Pe
mD
Porosity types, Mesaverde Group, Piceance basin
4,000 ‐ 6,999 ft minimum burial
100
10
Type I
1
Type II
Type III
Type IV
0.1
Type V
0.01
0.001
0
5
10
15
20
25
70
53 of 217
Pe
mD
Porosity types, Mesaverde Group, Piceance basin
7,000 ‐ 10,000 ft minimum burial
100
10
Type I
1
Type II
Type III
Type IV
0.1
Type V
0.01
0.001
0
5
10
15
20
25
71
Diagenetic alterations in the Mesaverde
¾
¾
¾
¾
¾
¾
¾
¾
Compaction, ductile and brittle deformation
Clay cements, primarily chlorite and MLML-IS
Quartz overgrowths
Nonferroan calcite
Dissolution of calcite or other precursor cements
Ferroan calcite and ferroan dolomite cements
Replacement of KK-spar by ferroan calcite and
albite formation of moldic porosity
albite,
Dissolution of carbonate rock fragments
72
54 of 217
Brittle deformation of K-spar and Pore-lining clay
cement – Chlorite, ferroan calcite pore fill
Pore-filling chlorite cement with
continued burial
73
74
55 of 217
Pore-lining clay cement – ML/IS
75
76
56 of 217
Inhomogeneous packing and relics of calcite cement indicate
secondary intergranular porosity
77
78
57 of 217
Relic of calcite cement and adjacent
secondary intergranular porosity
Secondary intergranular pores mimic size and
shape of neighboring cement-filled areas
79
80
58 of 217
Secondary porosity, created by dissolution of framework grains
81
Secondary porosity, created by dissolution of framework grains
82
59 of 217
Secondary porosity, created by dissolution
of carbonate framework grains
Alteration of potassium feldspar
83
84
60 of 217
Alteration of potassium feldspar and VRF’s
Alteration of potassium feldspar
85
86
61 of 217
Alteration of plagioclase feldspar
Alteration of plagioclase feldspar
87
88
62 of 217
Alteration of volcanic rock fragments
89
Influence of depositional environment on detrital composition
90
63 of 217
Influence of depositional environment on detrital composition
Influence of depositional environment on diagenesis
91
92
64 of 217
Pore-filling chlorite in a quartzose sandstone
Pore-filling chlorite in a quartzose sandstone
93
94
65 of 217
Conclusions
¾
¾
¾
¾
Rock typing is useful tool for lithofacies
analysis and directing statistical sampling.
Grain size and shale content are the primary
influences on reservoir quality
Compaction and cementation by clay
(primarily chlorite and MLML-IS), quartz and
ferroan calcite further reduce porosity and
permeability
Matrix porosity in the Mesaverde Group
consists of both primary and secondary
intergranular, moldic and clayclay-filled
microporosity
95
Conclusions, continued
¾
¾
¾
Mesofractures, microfractures on the scale of
individual grains
grains, and overgrowth partings are
also present
Porosity type and distribution of clay cements
help explain the variation of permeability for a
given value of porosity
Log
g analysis
y
is complicated
p
by
y the p
presence
of chlorite clay cement (more on that later…)
96
66 of 217
Capillary Pressure and Electrical
Properties for Mesaverde Tight
Gas Sandstones from Western
U.S. Basins
DOE Contract DE-FC26-05NT42660
http://www.kgs.ku.edu/mesaverde
http://www.discovery-group.com
97
67 of 217
Byrnes: Porosity, Permeability, and Compressibility
Capillary and Electrical Properties
for Mesaverde Tight Gas Sandstones
f
from
W
Western
t
U.S.
US B
Basins
i
US DOE # DE-FC26-05NT42660
Core Analysis
•
Porosity & Grain Density
–
–
–
–
•
•
–
–
–
–
–
–
–
–
Lithologic and other controls
Routine helium
In situ
Pore Volume Compressibility
p
y
Permeability
–
–
–
–
–
–
Routine Air
Klinkenberg
Crack & Capillary
Liquid
In situ
Effective & Relative
•
•
•
•
•
Gas oil Oil
Gas-oil,
Oil-water,
water Gas
Gas-water
water
Drainage, imbibition
Steady-state, unsteady-state
Single-phase stationary
Parameters influencing kr
– T, Poverburden, wettability, pore
architecture, capillary number
– Fluid Sensitivity
Saturation & Capillary Pressure
•
Enhanced Oil Recovery
– Chemical (polymer, surfactant, caustic)
– Miscible (CO2, N2, Enriched Gas)
– Thermal (Steam, Combustion)
•
Electrical & Acoustic Properties
– Archie Electrical Properties
• Cementation & Saturation Exponent,
Cation Exchange
– Vp & Vs
•
Rock Mechanics
–
–
Routine Analysis (retort, Dean-Stark)
Air-brine, oil-brine, air-mercury
Centrifuge, Porous-plate, Hg intrusion
I t f i l Tension
Interfacial
T
i
Contact Angle
Wettability
Threshold Pressure
Young’s Modulus, Poisson’s Ratio, Bulk
Modulus
Fracture Pressure
68 of 217
PVTXt
• All petrophysical
properties are
physical-chemical in
nature and dependent
on:
• P – Pressure
– Confining/pore
• V- Volume/Scale
• T – Temperature
• t – time/history
(hysteresis)
• X - Composition (broad
definition)
– Classification (sandstone,
limestone, etc.)
– Compositional (mineralogy)
– Textural (sorting-grain size
distribution, roundness,
angularity)
– Sedimentologic (bedding,
heterogeneity, architecture)
– Porosity/ pore size
distribution
– Fluid
Always consider at what
conditions a property was
measured and over what range of
conditions the measured property
value is valid
Porosity
69 of 217
Core Analysis
•
–
–
–
–
–
–
•
•
Porosity
Classification
Lithologic & other controls
Routine helium
In situ
Pore volume
l
compressibility
ibili
Wireline-log Analysis
–
–
–
–
–
–
–
–
Permeability
–
–
–
–
–
–
Routine Air
Klinkenberg
Crack & Capillary
Liquid
In situ
•
•
•
•
•
Gas-oil, Oil-water, Gas-water
–
T, Poverburden, wettability, pore
•
– Chemical (polymer, surfactant,
caustic)
– Thermal ((Steam,, Combustion))
•
• Cementation & Saturation
Exponent, Cation Exchange
– Vp & Vs
•
Rock Mechanics
–
–
Interfacial
f i l Tension
i
Contact Angle
Wettability
Threshold Pressure
Modulus
Fracture Pressure
70 of 217
Porosity Types - Classifications
Various Porosity Nomenclature – genesis, size distribution, flow contribution
Intraparticle φ
Vuggy φ
Secondary φ
Transparticle φ
F t
Fracture
φ
Nano <0.1 μm
Micro 01.-0.5 μm
Meso 0.5-2 μm
Macro 2-10 μm
Mega 10-100 μm
Micro φ
Ineffective φ
Interparticle φ
Primary φ
Effective φ
Porosity Definition
Porosity, n. The ratio of void space to the bulk volume of rock
containing that void space
φ = Vp/(Vp+Vg)
Isolated φ (minor)
Connected φ
micro φ
φi=isolated
φc=connected = φcmicro+φcmacro+φbound
φcmacro= connected,
d >0.5μm
0
φcmicro= connected, <0.5μm, not bound
bound- φ
= connected, bound to clay or
water φ bound
surface, water of hydration
• Total φtotal = φc+φi=
φcmacro+φcmicro+φbound+φi
• Effective1 φeff = φc (excludes φi)
• Effective2 φeff = φcmacroi+φmicro (exc φi,
φbound)
• Effective3 φeff = φcmacro+φi+φcmicro (exc
φbound)
• Effective4 φeff = φcmacro (exc
φi,φcmicro,φbound)
71 of 217
Packing & Sorting
Control on Porosity
(after Bear , 19
Porosity independent of size
Highly dependent on sorting & packing
Secondary Porosity - Transfer
• Feldspar grain
dissolution
creates
t secondary
d
porosity but
removed material
often
reprecipitates in
nearby pore
space as kaolinite
k li i
or smectite
72 of 217
Porosity Measurement
• Core Analysis
– Helium Boyle’s law - Dry sample, measure bulk volume, injected gas measures
grain volume - measures φc, does not measure φi and may not measure some φbound
– Crushed sample He pycnometer – dry crushed sample material is measured by
Boyle’ss Law technique,
Boyle
technique measures φt
– Liquid Resaturation – dry sample is weighed,saturated with liquid of know density
and weighed saturated, weight difference measures φc, does not measure φi and may not
measure some φbound
– Summation of Fluids – two pieces of native core, one is weighed, crushed, retorted
for oil&water content, and weighed; second has bulk volume measured and mercury
injected into gas pore space, fluid saturations and porosity calculated for combined
volumes – measures combination of φt and φc
– Nuclear Magnetic Resonance – integrated NMR signal is measured on
saturated
t t d sample
l – measures φt
• Wireline Logs
–
–
–
–
–
Core Analysis Data
Density (ρma- ρb)/ (ρma- ρliq)
Sonic
(Δt- Δtma)/(Δtfluid- Δtma)
ResistivityF = a/φm
NMR
Core Analysis Data
Neutron
Helium Porosimeter Precision
• Vg = (Vr +Vc) -P1g/P2gVr
Properly performed error in
grain volume measurement
should be < +0.001 cc
(after Ruth & Pohjoisrinne
73 of 217
Porosity Error Interlaboratory Calibration
• Dotson et al (1951) Avg φ Error = + 0.5
• Thomas and Pugh (1988) Maximum “acceptable” deviation =
+ 0.5;
0 5; 65% of labs in 1987 met that quality assurance criteria
• Quality reviewed data in TGS +0.25 pu (Hunt & Luffel, 1988)
Xmean
std dev
Xmean
std dev
Xmean
std dev
1-inch diameter
1.5 -inch diameter
Porosity (%)
Porosity (%)
Permeability
Permeability
to air, md Ambient Overburden
to air, md Ambient Overburden
Berea Sandstone Samples
248
19.0
18.5
261
18.7
18.2
24
0.5
0.4
22
0.4
0.1
Alundum Samples
111
18.9
18.6
120
19.1
19.2
24
0.8
0.6
22
0.8
0.4
Bedford Limestone Samples
3.2
14.0
13.8
3
13.8
13.7
0.9
0.6
0.5
0.7
0.7
0.7
Interlaboratory comparison - 25 labs (Sprunt et al , 1990)
Routine Porosity Distribution
Routine Porosity Histogram
0.18
Fraction of Popula
ation
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0-2
2-4
4-6
6-8
8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24
Routine Helium Porosity (%)
74 of 217
Porosity Distribution by Basin
Al l B asins
Greater Green River
Washakie
Ui nta
Pi ceance
Wind River
Powder River
0.45
Fraction of Popula
ation
0.40
0.35
0 30
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0-2
2-4
4-6
6-8
8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24
• Distribution influenced by sampling – not
normally distributed
Porosity Statistics by Basin
All
Basins
Mean
ea
Median
St Dev
Minimum
Maximum
Kurtosis
Skewness
Count
7.1
6.2
5.1
0.0
24.9
0.7
1.0
2209
Greater
Green
River
7.3
3
4.6
6.4
0.0
23.6
-0.4
1.0
568
Wind Powder
Washakie Uinta Piceance River River
9.5
9
5
8.7
5.4
0.0
23.8
-0.4
0.5
395
6.1
6
5.9
4.2
0.0
22.2
1.1
0.9
539
6.1
6
6.1
3.8
0.0
24.9
4.5
1.4
596
5.8
5
8
5.5
3.3
0.0
13.2
-0.8
0.1
83
13.2
3
15.1
4.5
2.6
16.9
1.0
-1.5
28
75 of 217
Statistics of Paired Samples
Porosity Histogram
1.0
0.45
0.40
0.9
0.8
0.35
0.30
0.7
0.6
0.25
0.5
0.20
0.15
0.4
0.3
0.10
0.05
0.2
0.1
0.00
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
Fraction of Popula
ation
0.50
Paired Plugs Porosity Ratio
• Histogram of ratio of paired plug porosities to mean
porosity of plug pair. n = 652 x2= 1304
Grain Density
Grain Density Histogram
Fraction of Popullation
0.30
0.25
0.20
0.15
0.10
0.05
0.00
<2.56
2.562.58
2.582.60
2.602.62
2.622.64
2.64266
2.662.68
2.682.70
2.702.72
> 2.72
• Mesaverde grain density is normally distributed
for entire population (n=2200)
76 of 217
Mesaverde Grain Density
All
Basins
Mean
Median
St Dev
D
Minimum
Maximum
Kurtosis
Skewness
Count
2.653
2.654
0 040
0.040
2.30
2.84
15.1
-2.00
2184
Greater
Green Washakie
River
2.648
2.660
2.645
2.662
0 029
0.029
0 034
0.034
2.50
2.47
2.77
2.79
2.6
3.7
0.28
-0.18
566
393
Uinta
Piceance
Wind
River
Powder
River
2.639
2.649
0 052
0.052
2.30
2.80
13.2
-2.82
532
2.660
2.661
0 038
0.038
2.35
2.84
14.0
-1.19
583
2.673
2.673
0 029
0.029
2.51
2.73
10.2
-1.87
82
2.679
2.674
0 026
0.026
2.60
2.75
3.9
-0.28
28
• Statistically meaningful differences exist among
basins
• Low density minerals: carbonaceous fragments
(1.2-1.4 g/cc), K-feldspar (2.57 g/cc),
Illite/smectite (2.60 g/cc)
Grain Density by Basin
Grain Density Histogram
Fraction of Popullation
0.60
0.50
All Basins
Greater Green River
Washakie
Uinta
Piceance
Wind River
Powder River
0.40
0.30
0.20
0.10
0.00
<2.56
2.562.58
2.582.60
2.602.62
2.622.64
2.64266
2.662.68
2.682.70
2.702.72
> 2.72
77 of 217
Generic Porosity vs Confining Pressure
(after Byrnes, 1994)
Crack Compressibility
• Crack porosity is far more
compressible than normal
intergranular porosity
• Walsh & Grosenbaugh (1979)
developed a model for fracture
compressibility
ibili that
h matches
h ddata well
ll
and can be expressed, as shown by
Ostersen for low-k sandstones, by a
linear porosity change with
logarithmic change in stress
(after Walsh & Grosenba
(after Ostensen, 1983)
78 of 217
Stress-Dependence of Porosity
Fraction of Iinitial Porrosity
1.0
0.9
0.8
0.7
0.6
0.5
0.4
10
100
1000
Net Confining Pressure (psi)
10000
• Crossplot of fraction of initial pore volume versus net confining stress for 113
Mesaverde samples. Every sample exhibits a log-linear relationship though
slopes and intercepts differ.
σz
σy
σx
Cformation = ΔVpore/Vpore
Δp
Stress field defined by σx, σy, σz
Effective stress equation:
σhydro = K1σz – K2Pinital + K3 (Pinitial-P)
Cformation
f
ti = K3 Chydro
h d
(after Yale et al, 1993)
K1 = (σx+σy+σz)/3σz; lithostatic stresses
K2 = (1
(1-C
Cb/Cgr); Biot α – effect of pore pressure
K3 = K2 ((1+ν)/(3-3ν)); effect of pore pressure
change, “uniaxial correction”; ν=Poisson’s ratio
Rock Type
Consolidated Sandstone
Friable Sandstone
Unconsolidated Sandston
Carbonate
K1
0.85
0.90
0.95
0.85
K2
0.80
0.90
0.95
0.85
K3
0.45
0.60
0.75
0.55
79 of 217
Type Compressibility Curves
Unconsolidated
Friable
Consolidated
-0.00002805
0.0001054 -0.00002399
300
500
300
0.1395
-0.225
0.0623
0.0001183 -0.00001103
0.00004308
Pore Volum
me Compressibility
(psi/10^6)
A
B
C
D
Cf = A(σ-B)C + D
σ=K1Pover-K2Pi+K3(Pi-P)
60
50
Unconsolidated
Friable
Consolidated
40
30
20
10
0
0
2,000
4,000
6,000
8,000
10,000
Effective Lab Stress (psi)
(after Yale et al, 1993)
Rellative Pore Volume Chan
nge Slope (
1/psi)
0.00
-0.05
-0.10
-0.15
-0.20
-0.25
-0.30
0
2
4
6
8
10
12
14
16
18
20
22
24
• Crossplot of slope of log-linear curves in Figure 4.1.6 with porosity.
• The relationship between the slope and porosity can be expressed:
• Slope = -0.00549 -0.155/φ0.5
80 of 217
Relative Pore Volume C
Change
Intercept (1/psii)
1.35
1.30
1.25
1.20
1.15
1.10
1.05
1.00
0
2
4
6
8
10
12
14
16
18
20
22
24
• Crossplot of intercept of log-linear curves in Figure 4.1.6 with porosity. The
relationship between the intercept and porosity can be expressed:
• Intercept = 0.013 φ + 1.08
• The above equations result in a power-law
relationshipp between ppore volume
compressibility and net effective confining
pressure of a form:
log10 β = C log10 Pe + D
• The slope and intercept of the pore volume
compressibility relations can be predicted using:
C = -1.035 + 0.106/φ0.5
D = 4.857 φ-0.038
81 of 217
log Pore Volum e Compressibility Pressure Intercept
log Pore Volume C
Compressibility Pressure Sl ope (1/psi)
-0.95
-0.96
-0.97
-0.98
-0.99
-1.00
-1.01
-1.02
0
5
10
15
20
25
4.80
4.75
4.70
4.65
4.60
4.55
4.50
4.45
4.40
4.35
4.30
4.25
0
Routine Porosity (%)
5
10
15
20
25
log10 β = C log10 Pe + D
• Where:
C = -1.035 + 0.106/φ0.5
D = 4.857 φ-0.038
Porre Volume Compressibility
y (10^6/psi)
1000
100
10
1
100
φ = 21%
φ = 18%
φ = 15%
φ = 12%
φ = 8%
φ = 6%
φ = 4%
φ = 2%
1000
Net Effective Confining Stress (psi)
10000
β =10^[(-1.035+0.106/φ0.5)*log10 Pe+(4.857φ-0.038)]
82 of 217
In situ vs. Routine Porosity
• φi/φo = A logPe + B
φi/φo Slope = A = -0.00549 – 0.155/φ0.5
φi/φo Intercept = B = 1.045 + 0.128/φ
Where:
φi = porosity at defined effective in situ stress Pe,
φo = reference initial porosity
Pe = effective confining stress
A and B are empirical constants that vary with rock
properties
i
Porosity at Pe = 4,0
000 psi (%)
In situ vs. Routine Porosity
24
22
20
18
16
14
12
10
8
6
4
2
0
Mesaverde Study
T ravis Peak
Mesaverde/Frontier
Clinton/Medina
Linear (Mesaverde Study)
0
2
4
6
8
10
12
14
16
18
20
22
24
All Studies:
Mesaverde Study:
φi = A φroutine + B
φi = 0.96 φroutine – 0.73
Travis Peak:
Mesavrd/Frontier
Clinton/Medina:
φi = 0.966 φroutine + 0.02
A>
B>
Routine Porosity
2.0
24.0
Travis
Mesaverde/ Clinton/ Mesaverde
Medina
Study
Peak
Frontier
0.950
0.998
0.966
0.960
-0.300
-0.800
0.020
-0.734
1.6
1.2
2.0
1.2
22.5
23.2
23.2
22.3
83 of 217
Porosity from Wireline Logs
e s y
• Density
• Neutron
• Sonic
• NMR
Permeability
84 of 217
Core Analysis
• Porosity & Grain Density
–
–
–
–
•
• Permeability
–
–
–
–
–
–
Routine Air
Klinkenberg
Crack & Capillary
Liquid
In situ
•
•
•
•
•
Gas-oil, Oil-water, Gas-water
– T, Poverburden, wettability, pore
–
–
–
–
–
–
–
–
Lithologic & other controls
Routine helium
In situ
Pore volume compressibility
•
Interfacial
f i l Tension
i
Contact Angle
Wettability
Threshold Pressure
– Chemical (polymer, surfactant, caustic)
– Thermal (Steam, Combustion)
•
• Cementation & Saturation Exponent,
Cation Exchange
– Vp & Vs
•
Rock Mechanics
–
–
Modulus
Fracture Pressure
Original Darcy Flow Measurement
Q = k A dP
µ dh
Analogs in
Electric and heat flow
i=
1 A dV
d
dx
dQ = KH A dT
dx
85 of 217
Evolution of Permeability Modeling
k=fr2/8
K=Φ/(FsAs2) x (L/La)2
(after Dullien, 1992)
(after CoreLab, 1978)
Current Permeability Modeling
• Permeability
controlled by:
y
–
–
–
–
–
pore body size
pore throat size
distribution
connectivity
larger-scale
architecture
86 of 217
Comparison of Sandstone Pore Volume
Distribution Measured by Hg Porosimetry
and Photomicroscopy
(after Dullien & Dhawan, 1974)
Liquid Permeability
Q = k A dP
µ dL
(liquid)
Q = Volumetric Flow rate (cc/sec)
K = Permeability (Darcies)
A = Cross-sectional area (cm2)
dP = Pressure differential (atm)
m = fluid viscosity (centipoise)
dL = Length (cm)
Q = k A (P12-P22)
µ 2PbzdL
(gas)
87 of 217
Permeability Definitions
• Absolute Permeability (k) – Permeability of rock 100%
saturated with fluid of interest
• Effective Permeability (keg, keo, kew) – Permeability to fluid
of interest when other fluids are also present in pore space
• Relative Permeability (krg, kro, krw) – ke/k, Ratio of effective
to absolute permeability (reference for absolute may be
effective at some condition, e.g. keo,Sw/keo,Swi)
• In situ – under reservoir conditions
• Klinkenberg – Corrected for low pressure gas slippage
effects
• Air – Permeabilityy to air uncorrected for Klinkenbergg
effect
• Routine – Air permeability, generally measured with a
confining stress of less than ~500 psi
Permeability Determination
• Full-diameter
– Influenced by microfractures
– Averages response of
individual beds
– Possible drilling mud invasion
– Less biased
• Plug
– Precisely accurate
– Possible sampling bias
– May
ay miss
ss important
po ta t beds
• Drilled Sidewall
– Greater sampling uncertainty
– Similar to plug
• Probe mini-permeability
– Fast
– Allows high sampling
densityy
– Accurate for k > 1md
• Chip
– Low accuracy
– Severe sampling bias
• Percussion Sidewall
– Shattered
– Under- and over-estimates
properties
• Cuttings
– Rarely used
– Surface-to volume issues
– Sever sampling bias
88 of 217
Klinkenberg Gas Slip
kgas = kliq (1+4cl/r)
= kliq (1+b/P)
Gas
measurable fluid velocity at wall
Where;
Liquid
c = proportionality factor ~ 1
l = mean free path at P
r = radius of capillary
b = proportionality constant
=f(r,l,kliq)
( )
P = ppressure (atm)
Since b is a function of pore radius,
mean free path at P, and liquid
permeability it can vary from one
low k sample to another but values
are generally consistent with the
Heid et al (1950) graph shown
Klinkenberg b factor (psi)
Zero fluid velocity at wall
100
Heid et al, 1950
Jones & Owens, 1981 - low k
10
b = 0.777 kliq0.39
1
0.1
b = 0.867 kliq-0.33
0.01
1E-04 0.001 0.01
0.1
1
10
100
1000
Klinkenberg Permeability (md)
(after Heid et al, 1950)
Klink
kenberg b factor (psi)
General Correlation of Klinkenberg
b Factor and Permeability
100
Heid et al, 1950
Jones & O w ens , 1981 - low k
10
b = 0.777 kliq-0.39
1
0 .1
0.33
b = 0.867
0 867 kliq-0.33
0 .0 1
1 E -0 4 0 .0 0 1 0 .0 1
0 .1
1
10
100
1000
K linkenberg P erm eability (m d)
89 of 217
Correlation between Gas Slip-factor, b, and Permeability
(after Sampath & Keighin, 1982)
In situ Klinkenberg Permeability
Klinkenberg b factor (atm)
1000
100
10
1
0.1
1E-08
1E-07
1E-06
1E-05 0.0001 0.001
0.01
0.1
1
10
100
1000
kgas = kliquid (1 + 4
4cL/r)
L/ ) = kliquid (1+b/P)
Gas
kgas = gas permeability at pore pressure
kliquid is liquid permeability and = Klinkenberg permeability kklink
Liquid
c = proportionality constant (~ 1)
L = mean free path of gas molecule at pore pressure
b = 0.851 kik-0.34 (Present Study)
r = pore radius
b = proportionality constant (=f(c, L, r))
b = 0.867 kliq-0.33 (Jones & Owens)
P = pore pressure (atm)
b = 0.777 kliq-0.39 (Heid)
90 of 217
Measured Insitu Klinkenberg vs Air Permeability
In situ
u Klinkenberg Perm
meability
(md)
100
Sandstone
10
Carbonate
1
0.1
0.01
kik =0.685kia
2
R = 0.98
0.001
0.0001
0.0001
1.12
0.001
0.01
0.1
1
10
In situ Air Permeability (md)
100
(after Byrnes, 2003)
Comparison of Klinkenberg
Prediction Models
1
Klinkenberg Permeability (m
md)
Byrnes, 2003
Jones & Owens, 1981
0.1
0.01
kklink = 0.685 kair1.12
0.001
0.0001
0.00001
0.00001
0.0001
0.001
0.01
0.1
1
Air Permeability (md)
J&O (1980): kklink = 10^(-0.0398 logkair2+1.067logkair-0.0825)
valid for upstream pressure = 100 psi
91 of 217
Effect of Partial Water Saturation on Gas Slip
(after Sampath & Keighin, 1982)
“Averaging” Permeability Data
• Permeability is a vector
• Pseudo-Permeability is
direction dependent
• Pseudo-Permeability
“averaging” is a function of
flow model (3-D
arrangement) assumed
– Dependent on geomodel and
assumptions of smaller scale
permeability distribution
• End-member models
–
–
–
–
Series Flow
Parallel Flow
Random Flow
Vertical flow constraint
• Permeability is
frequently scale
dependent
92 of 217
Typical distributions of Porosity
and Permeability
Permeability Architecture
End Members
Series
Flow
No vertical cross-flow
Vertical crossflow
kv=0, kv=Ckh
Parallel
Flow
Heterogeneous
Flow
93 of 217
• In parallel flow the high perm drives the system
• In series flow the low perm drives the system
• Cross-flow influences parallel flow in closed systems (see Simulation Section)
0.01 md
100 md
100 ft
Karith = 1.010 md
Kgeom = 0.011 md
100 md
1 ft
Karith = 99.000 md
Kgeom = 91.201 md
0.01 md
0.01 md
100 md
100 md
0.01 md
100 md
0.01 md
100 md
Kharm = 0.010 md
Kgeom = 0.011 md
0.01 md
Flow
Kharm = 0.990 md
Kgeom = 91.201 md
Core Plug Sampling with
Bedding
C - Suitable
C
Bedding
Planes
A - Unsuitable
B – Possibly
suitable
94 of 217
Model of Measured vs Composite
Permeability for Layered Samples
Permeability-Porosity Equation : k = 3.65 x 10-5 e(0.68 Φ)
Fraction of Upper Layer Thickness to Total hickness =
0.3
Upper
Base
Porosity
Upper
Base
Average Permeability
Measured
Ratio
Layer
Layer Difference
Layer
Layer
Porosity for Average Permeability Measured/
Porosity Porosity
Permeability Permeability
Porosity
Composite
(%)
(%)
(%)
(md)
(md)
(%)
(md)
(md)
Permeability
0
14
14
0.0000365
0.497
9.8
0.0286
0.348
12.2
2
14
12
0.000142
0.497
10.4
0.0430
0.348
8.1
4
14
10
0.000554
0.497
11.0
0.0646
0.348
5.4
6
14
8
0.00216
0.497
11.6
0.0972
0.349
3.6
8
14
6
0.00841
0.497
12.2
0.146
0.350
2.4
10
14
4
0.0327
0.497
12.8
0.220
0.358
1.6
12
14
2
0.128
0.497
13.4
0.331
0.386
1.2
14
14
0
0.497
0.497
14.0
0.497
0.497
1.0
16
14
-2
1.94
0.497
14.6
0.747
0.929
1.2
18
14
-4
7.54
0.497
15.2
1.124
2.61
2.3
20
14
-6
29.4
0.497
15.8
1.690
9.16
5.4
21
14
-7
58.0
0.497
16.1
2.072
17.7
8.6
22
14
-8
114
0.497
16.4
2.541
34.7
13.6
23
14
-9
226
0.497
16.7
3.116
68.1
21.9
24
14
-10
446
0.497
17.0
3.821
134.1
35.1
Parallel Beds and Sampling
1
Measured or Calc
culated
Permeability (md)
40
Measured Permeability - Kmeas
Calculated Permeability - Kcalc
35
Ratio Kmeas/Kcalc
Upper Bed Porosity
10
30
25
1
20
15
0.1
10
5
40
Measured Permeability - Kmeas
Calculated Permeability - Kcalc
Ratio Kmeas/Kcalc
Upper Bed Porosity
35
30
25
20
0.1
15
0.01
10
5
0.001
Ratio Kmeas/Kcalc & Up
pper
Bed Porosity (%)
Measured or Calculate
ed
Permeability (md)
10
100
0.01
Ratio Kmeas/Kcalc & Upper
Bed Porosity (%)
• When sample contains
parallel beds of
different k the
measured k at the
average porosity is
always greater than the
k calculated for the
composite of the
individual beds
0
9
10
11
12
13
14
15
16
17
Average Porosity (%)
0
7
8
9
10
11
12
13
Average Porosity (%)
95 of 217
General Lithologic Controls on the Effect
of Overburden Pressure on Permeability
Effect of Confining Pressure on
Permeablity
•
Early work by Thomas
and Ward (1972)
Shows the
characteristic decrease
in permeability with
increasing confining
pressure exhibited by
low-permeability
sandstones
Samples from Gas
buggy well, Pictured
Cliffs Fm Rio Arriba
Co., NM and Wagon
Wheel well, Ft. Union
Fm, Sublette Co., WY
1.0
Fraction of Initial Permeabiility
•
0.9
0.8
0.7
0.6
0.5
0.4
0.3
02
0.2
0.1
0.0
0
1000
2000
3000
4000
5000
6000
Confining Pressure (psi)
96 of 217
Effect of Confining Pressure on
Spirit River and Cotton Valley Permeability
(after Walls, 1982)
Permeability Response to Confining
Stress for Varying Crack Aspect Ratios
(after Brower & Morrow, 1983)
k/ki = {1-(16(1-n2)cLc)/(9(1-2n)pwi)s}3
97 of 217
Models of Stress Dependent Permeability
Model Type
Noncrack
Noncrack
Crack
Crack
Asperity
Asperity
Asperity
Model
Capillary tube
Gangi, grain, 1978
Jones &Owens, 1980
Brower & Morrow, 1983
Gangi, bed of nails, 1978
Walsh, exp. dist., 1981
Ostensen, Gauss.,1983
Mesaverde & Frontier
(after Ostensen, 1983)
Equation
.
k/ki = (1-2s/E)4
k/ki = {1-2{3p(1-n2)s/4E}2/3}4
k/ki = {1-Slog(Pk/1000)}3
k/ki = {1-(16(1-n2)cLc)/(9(1-2n)pwi)s}3
k/ki = {1-(s/lE)e}3
k = Ls3/12 {ln[(nE(prcs3)1/2)/(2(1-n2)s)]}3
k = 0.76Ls3/12 {ln[(2.48E(s/rc)1/2)/(3p1.5(1-n2)s)]}2
Council Grove Limestones
(after Byrnes et al, 2001)
(after Jones &* Owens, 1980)
Sheet-like Pores in Travis Peak Sandstone
Transmitted light, 100X
Fluorescent epoxy
8,275 ft, k = 0.007 md; SFE Well 2, Waskom Field, Harrison Co., TX
(after Soeder &
Chowdiah, 1990)
98 of 217
Pore
e Size Freque
ency
(%)
Pressure and Pore Throats
25
High P
20
Low P
15
10
5
0
0.01
0.1
1
Pore Throat Diameter (um)
In situ vs Routine Permeability
In situ K
Klinkenberg Perme
eability
(md)
100
10
Council Grove
Mesaverde/Frontier
1
0.1
0.01
logkik = 0.0588 (logkair)3
–0.187 (logkair)2
+1.154 logkair - 0.159
0 001
0.001
0.0001
0.00001
0.001
0.01
0.1
1
10
Routine Air Permeability (md)
100
99 of 217
log
g In situ Klinkenberg Permeability (mD)
Stress dependence of
permeability

3
y = -0.0088x3 - 0.0716x2 + 1.3661x - 0.4574
2
R2 = 0.9262
1

0

-1
-2

-3
-4
-5
-6

-7
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
log Routine Air Permeability Ppore = 100 psi (mD)

Known for many years that lowlow-K
sandstones are stress sensitive
Generalized = f (Ppore, Lith)
1997 Byrnes equation:
kik = 10^[1.34 (logkair) - 0.6]
This study:
kik = 10^[0.0088 (logkair)3 - 0.072
(logkair)2+ 1.37 logkair +0.46]
Statistically similar except for k >
1 mD
no meaningful stress dependence
over 10 mD
Permeablity Distribution
Fraction of Pop
pulation
0.35
0.30
0.25
0.20
0.15
0.10
0.05
100-1
1000
10--100
1-10
1
0.1-1
0
0.01
1-0.1
0.001-0
0.01
0.00
0010.0
001
0.000
0010.00
001
0.0000
0010.000
001
0.00000
0010.0000
001
0.00
Distribution of in situ Klinkenberg permeability measured at 26.7
MPa (4,000 psi) net effective stress for all samples
100 of 217
In situ Klinkenberg Permeability Histogram
Fraction of Pop
pulation
0.60
All Basins
Greater Green River
Washakie
Uinta
Piceance
Wind River
Powder River
0.50
0 40
0.40
0.30
0.20
0.10
100--1000
10
0-100
1-10
0.1-1
0.0
01-0.1
0.001-0.01
0.0
00010.001
0
0.00
00010.0
0001
0.000
00010.00
0001
0.0000
00010.000
0001
0.00
Distribution of in situ Klinkenberg permeability measured
at 26.7 MPa (4,000 psi) net effective stress by basin
Permeability Statistics
All
Basins
Greater
Green Washakie Uinta
River
Mean logk
-2.60
-2.49
-2.03
-2.66
Median logk
-2.93
-3.15
-2.46
-2.86
St Dev log
1.58
1.94
1.78
1.36
Minimum logk
-6.19
-6.19
-5.66
-5.33
Maximum logk
2.31
2.31
2.08
1.88
Kurtosis
0.62
-0.54
-0.39
0.17
Skewness
1.05
0.79
0.76
0.74
Count
2143
555
373
529
Mean
0.0025 0.0032 0.0094 0.0022
Median
0.0012 0.0007 0.0035 0.0014
St Dev
37.9
87.4
59.9
23.0
Minimum
0.000001 0.000001 0.000002 0.000005
a
u
206.0
06 0
206.0
06 0
121.0
0
76.2
6
Maximum
Kurtosis
0.62
-0.54
-0.39
0.17
Skewness
1.05
0.79
0.76
0.74
Count
2143
555
373
529
Piceance
Wind
River
Powder
River
-2.95
-3.44
-1.88
-3.03
-3.36
-2.21
1.13
0.69
1.39
-5.23
-5.11
-4.29
2.05
-1.98
0.55
4.02
-0.49
-0.38
1.48
-0.01
0.50
577
81
28
0.0011 0.0004 0.0133
0.0009 0.0004 0.0062
13.4
4.9
24.5
0.000006 0.000008 0.000051
112.2
0.010
0
0 0
3.53
3
53
4.02
-0.49
-0.38
1.48
-0.01
0.50
577
81
28
101 of 217
Permeability Histogram
1.0
0.18
0.9
0.16
0.8
0 14
0.14
07
0.7
0.12
0.6
0.10
0.5
0.08
0.4
0.06
0.3
0.04
0.02
0.2
0.1
0 00
0.00
00
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
3.0
4.0
5.0
>6
Fraction of Popu lation
0.20
Paired Plugs Permeability Ratio
• Histogram of ratio of paired plug in situ Klinkenberg permeabilities to mean
permeability of plug pair. n = 634 x2 = 1268
Permeability vs Porosity
• Permeability a function of:
Grain size
Shale bed architecture
Pore-throat size
Porosity
g
alteration ((includingg cementation))
Diagenetic
• Porosity is optimal predictor parametric
with lithofacies
102 of 217
Permeability as a Function of
Grain Size and Sorting
(after Jonas & McBride, 1977)
Influence of Grain Size on Permeability
(from Shanley, 2004)
103 of 217
Permeability vs. Porosity by Grain Size
Klinkenberg Permeability (4,000 psi, mD)
K
1000
100
10
1
0.1
0.01
0.001
0.0001
X(4-9)XXX
0.00001
X3XXX
0.000001
X(0-2)XXX
0.0000001
0
2
4
6
8
10
12
14
16
18
20
22
24
In situ calc Porosity (%)
• Generally subparallel trends increasing in porosity range and
permeability at porosity with increasing grain size
• Influence of other variables significant
Dispersed Clay Types in
Sandstones Affecting Flow
Discrete Particle
Kaolinite
Pore-Lining
Chlorite
Montmorillonite
Pore-Bridging
Illite
Mixed-Layer
(after Neasham, 1977)
104 of 217
Influence of
Clay types on
Permeability
Discrete-particle, porelining and porebridging Kaolinite,
Chlorite, and Illite
can each result in
permeability
decrease by a factor
of 1-0.03, 0.2-0.01,
and 0.06-0.003,
respectively
(after Wilson, 1981)
Discrete Particles-Pore Lining Kaolinite
American Hunter Old Road 8360’
(courtesy John Webb)
105 of 217
Pore Lining Clays
Mixed-Layer Illite-Smectite
Chlorite
American Hunter
Old Road 5490 ft
(courtesy John Webb)
Illite - Pore Bridging
106 of 217
• Generalized trend kik = 10[0.3φi-4.75] with 10X error
• Different k-φ trends among basins due to lithologic variation
• Beyond common k↑ with grain size↑, lithologic influence changes with porosity nonlinear
Klinkenberg Perrmeability (4,000 psi, mD)
1000
100
10
1
0.1
Green River
Piceance
Powder River
Uintah
Washakie
Wind River
logK=0.3Phi-3.7
logK=0.3Phi-5.7
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0
2
4
6
8
10
12
14
16
18
20
22
24
1000
• logkik = 0.282φi + 0.182RC25.13 (+4.5X MLRA)
• logkik = 0.034φi2-0.00109φi3 +
0.0032RC2 - 4.13
((+4.1X MNLRA))
• Artificial Neural Network +3.3X
100
10
X9XXX
X8XXX
X7XXX
X6XXX
X5XXX
X4XXX
X3XXX
X2XXX
X1XXX
1
0.1
0.01
0.001
0.0001
0.00001
0.000001
1000
0.0000001
0
2
4
6
8
10
12
14
16
18
20
22
24
in situ Klinkenberg Permeab
bility (mD)
1000
100
10
1
Predicted in situ Klinkenberg Permeability (mD)
Klinkenberg Permeability (4,000 psi, mD)
100
10
1
0.1
0.01
0.001
0.0001
0.00001
0.00001
0.1
0.0001
0.001
0.01
0.1
1
10
100
1000
Measured in situ Klinkenberg Permeability (mD)
0.01
1XX9X
1XX8X
1XX7X
1XX6X
1XX5X
1XX4X
1XX3X
1XX2X
1XX1X
1XX0X
0.001
0.0001
0.00001
0.000001
0.0000001
0
2
4
6
8
10
12
14
16
18
20
22
24
hidden layer: 1
Hidden layer nodes: 10
Mean>
8.239
4.280
6.294 hidden layerStd Dev>
5.260
1.335
2.527 to-output
Input-to-hidden layer weights
weights
Node
Constant Phii
RC2
RC4
Constant
-0.388
1
-0.760
2.946
-2.027
-6.438
-0.885
2
-2.155
4.637
1.279
0.895
2.323
3
-4.999
7.901
0.957
3.167
-2.583
4
-1.484
-0.307
-1.695
6.175
-0.154
5
-4.597
4.582
1.568
0.730
4.022
6
-2.609
0.320
-2.201
-2.257
-2.495
7
-1.765
-1.843
-1.122
0.145
-3.859
8
2.839
-3.146
-9.237
0.264
0.789
9
-1.566
1.029
-1.588
-3.390
2.400
10
2.951
0.778
3.316
0.179
-2.136
Calculated in situ Porosity (%)
107 of 217
•
•
•
Overall trend allows prediction of Kik from porosity with 10X error
Multivariate linear equations using: 1) porosity, 2) rock class (1
(1--3), and for each of three
porosity classes separately (0(0-12%, 1212-18%, >18%), performed separately for each
basin, exhibit an average standard error of prediction of: 00-12%: 3.6+
3.6+2.4X; 12
12--18%:
3.3+
3.3
+3.6X; >18%: 3.1X (for all basins undifferentiated for this high porosity class);
where the range of error for each standard error of prediction indicates the range of
standard error among basins
Beyond common k↑
k↑ with grain size↑, lithologic influence changes are complex and
nonlinear
Klinkenberg Permeab
bility (4,000 psi, mD)
1000
100
10
1
0.1
Green River
Piceance
Powder River
Uintah
Washakie
Wind River
logK=0.3Phi-3.7
logK=0.3Phi-5.7
0 01
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0
2
4
6
8
10
12
14
16
18
20
22
24
Berea
Cotton Valley
Chacra
Cleveland
Wilcox
Travis
Peak
(from Dutton et al, 1993)
Canyon
Frontier-Moxa
Comparison
of Tight Gas
Sand k-f
Trends
108 of 217
Generalized Tight Gas Sandstone
Permeability vs Porosity Trends
In situ Permeability (md)
100
logki = 0.32+0.10 Φi - 5.05+1.48
10
1
0.1
Berea
Cotton Valley
Canyon
Frontier-Moxa Arch
Wilcox
Chacra
Cleveland
Travis Peak
Mesaverde-GGRB
Medina
Mesaverde-Uinta
0.01
0.001
0.0001
0
5
10
15
20
25
Data from various sources including Dutton et al, 1993; Byrnes, 2003; Castle and Byrnes, 2005)
Stressed Permeability Hysteresis
• Loading cycles approach similar values near original
reservoir stress
• Successive loading cycles cease to exhibit further
hysteresis after second loading cycle
(after Thomas & Ward, 1968)
(after Warpinski & Teufel, 1990)
109 of 217
Calculating Directional
Permeability in Festoon
Cross-Bed Sets
(after Weber, 1982)
Shale Bed Continuity
Distribution in Sandstone
p
Environments
Depositional
(after Weber, 1980)
110 of 217
Conclusions
• Grain density, porosity, and permeability measured on ~1500
unique samples and 700 duplicates (5X original proposal)
• Core plugs obtained from 44 wells representing approximately
7,000 feet of described core
• Average grain density for 2200 samples is 2.654+0.033 g/cc
(±1sd)
– but grain density distributions differ slightly among basins &
lithofacies..
lithofacies
• Porosity variance with 11--2 inches (2.5
(2.5--5 cm) = +10% (1sd)
• Pore volume compressibility shows a loglog-linear relationship
characteristic of sheet like pores and cracks
log10 β = C log10 Pe + D where C = -1.035 + 0.106/φ
0.5
D = 4.857 φ-0.038
• Lower porosity rocks exhibit greater pore volume compressibility
than high porosity rocks consistent with observed φi vs φroutine
trends
Conclusions
• Klinkenberg slip term “b” consistent with prior trends to 1 μD
• Geometric mean permeability = 0.0025 mD,
mD, median = 0.0012 mD
• Stress dependence of permeability is consistent with prior work
((Byrnes,
y
1997))
• PorosityPorosity-permeability data exhibit two subtrends with
permeability prediction approaching 5X within each
– Adding rock types or using an ANN model improves perm
prediction to 3.3X – 4X
• Multivariate linear equations using: 1) porosity, 2) rock class (1
(1-3), and for each of three porosity classes separately (0(0-12%, 12
12-18%, >18%), performed separately for each basin, exhibit an
average standard error of prediction of: 00-12%: 3.6
3.6+
+2.4X; 121218%: 3.3+
3.3+3.6X; >18%: 3.1X (for all basins undifferentiated for
this high porosity class); where the range of error for each
standard error of prediction indicates the range of standard error
among basins
111 of 217
Byrnes: Capillary Pressure, Electrical Properties, Relative Permeability
Saturation &
Capillary
Pressure
Water Saturation
• Water saturations in reservoir determined
using three basic methods
– Wireline
Wi li logs
l
• Electric logs
• NMR logs
– Fluid saturations from core
•
•
•
•
Routine core
p g core
Sponge
High-pressure core
Oil- & low-invasion and water-based mud
– Capillary pressure measurements on core
112 of 217
Influence of Core Flushing with
Water-based Mud on Saturations
“Averaging” Saturation Data
i=n
• Saturation is a scalar
but is dimensionless
• Sw should not be
Swaverage
averaged
• BVW is averaged and
then converted back to
Sw
Σ
i=1
=
Swi φi •hi
i=n
Σ φh
i=1
i
i
(Averaging for a well
by thickness)
113 of 217
Buckles Plot – Piceance Basin
Ro
outine Core Water Satura
aiton (%)
100
MWX-1
MWX-2
MWX-3
Buckles 600
Buckles 300
Buckles 240
Buckles 180
90
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Routine Core Porosity (%)
Trendlines shown represent Sw = Aφ-1.1 where A = 180. 240. and 300, respectively.
Differences in trends can be postulated to be due to differences in grainsize
and/or clay type/content.
Buckles Plot – Piceance Basin
Routine Core Water Saturraiton (%)
R
100
480 0-4 935
547 5-5 485
570 0-5 845
90
80
642 0-6 555
708 0-7 180
723 0-7 360
780 0-7 890
810 0-8 120
70
60
Buckle s 78 52 -7 86 3
Buckle s 78 48 -7 87 7
Buckle 78 73 -788 6
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Routine Core Porosity (%)
•
Routine core analysis porosity versus water saturation for the Piceance Basin MWX-2well.
Saturation versus porosity trends exhibit commonly observed Buckles power-law relationship.
Trendlines for depth intervals 7852-7886 shown represent Sw = Aφ-1.1 where A = 180. 240. and
300, respectively. Differences in trends can be postulated to be due to differences in grainsize
and/or clay type/content.
114 of 217
Drop Cohesive Forces
σ
P1
σ
P2
Forceout = π r2 ΔP
Forcein = 2π r σ
At equilibrium:
Fout=Fin
π r2 ΔP = 2π r σ
rearranging
ΔP = 2σ/r
Where :
σ=interfacial tension (dyne/cm)
r = radius (cm)
Capillary Pressure
rcap
Pnw rliq
Pw
rliq = rcap/cosθ
Pc = Pnw-Pw
Pnw Pw
= 2σ/rliq
= 2σcosθ/rcap
q
115 of 217
Capillary Pressure in Uniformly
Variable Capillary
• Pc = 2τ cosθ/r
(after Lake, 2005)
Pc = capillary pressure
τ = interfacial tension
θ = contact angle
r = pore radius
Capillary Rise
Pnw
r
Pnw
Pw
Pnw
h
Pw
Pw
h
h
Pw*
Pw*
Free
Water
Level
Pnw=Pw
Pw*
Water
Pw-Pnw = (ρw-ρnw) h g
116 of 217
Capillary Pressure Equations
• H=
where:
Where:
H = height above free water level
Pcres = reservoir capillary pressure
Pcair-Hg = air-mercury Pc
σbrine = specific density of brine (g/cc)
σoil,gas = specific density of oil or gas (g/cc)
0.433 = conversion from density (g/cc)
to pressure gradient (psi/ft)
Pc = capillary
P
ill
pressure
θ = contact angle
r = pore radius
Pcres = Pcair-Hg τcosθres
Pcres
.
(σbrine-σoil,gas) x 0.433
τcosθair-hg
water
P H
Pw
r = 2τ cosθ/Pc
PhH
oil
PhB
PwB
rH
H
rB
Capillary Pressure Equations
• r = 2τ cosθ/Pc
where:
h
Pc = capillary pressure
θ = contact angle
r = pore radius
• H=
Pcres
.
(σbrine-σoil,gas) x 0.433
• Pcres = Pcair-Hg
air Hg τcosθres
τcosθair-hg
117 of 217
Depth
(after Doveton, 1999)
Capillary Pressure Measurement
Mercury Injection
Porous Plate
Centrifuge
•
•
•
•
Air-mercury
Air-brine
Oil-brine
Gas-oil
• Drainage
• Imbibition
118 of 217
Mercury Capillary Pressure
(after Jennings, 1981)
Capilary Pressure Measurement
In situ Mercury Intrusion
high-P fluid
• Drainageg
imbibition
(n=37)
• Drainage only
(n=90)
• NES = 4000 psi
hi h -P
high
P
core holder
electric
insulator
Pressure
transducer
Core Plug
Core Plug
– Unconfined
(n=150)
– In situ
Resistance
Reference
Cell
• Three different
air-Hg
i H
measurements
Unconfined (routine) Mercury Intrusion
hi h -P
high
P
core holder
Pressure
transducer
mercury in
mercury in
119 of 217
10000
Unconfined
Capillary
Pressure
9000
8000
6000
5000
4000
3000
Air-Hg Capillary Pressure (psia)
7
7000
• C
Capillary
ill
Pressure
P
Varies with
Lithofacies and
associated pore size
distribution and
permeability
2000
1000
0
100
90
80
70
60
50
40
30
20
10
0
Wetting Phase Saturation (% )
Capillary
Pressure Varies
with Lithofacies
and associated
pore size
distribution
Me
ercury Injection Pres
ssure (psia)
10000
1000
0.00025md
0.00049md
0.0012md
0.0017md
0.0018md
0.0030md
0.0040md
0.0057md
0.0085md
0.012md
0.013md
0.032md
0.046md
0.085md
0.25md
0.41md
0.56md
0.84md
2.24md
100
10
0
10
20
30
40
50 60
70
80
90 100
Wetting Phase Saturation (%)
120 of 217
Normalizing Capillary Pressures
• Capillary pressure curves change with permeability and
porosity
• To predict water saturation from capillary pressure it is
necessary to either
– Know the specific conditions at a given point and use a appropriate
measured capillary pressure
– Construct a synthetic capillary pressure curve for the conditions at the
point
– Develop a relation between a normalized capillary pressure function
and saturation
• Two principal approaches for normalization or synthetic curve
construction:
i
– Leverett “J” function (Leverett, 1941)
– Unpublished normalization of Brooks-Corey l function (Brooks and
Corey, 1964)
• Fractal model extension of B-C
Leverett J function
• J(Sw) = CPc (k/φ)0.5/τcosθ
– J = dimensionless Pc function, function of
Sw
– C = conversion constant = 0.2166
– Pc = capillary pressure (psi)
τcosθ = interfacial tension (dyne/cm) X
cosine of the contact angle (degrees)
– k = permeability (md)
–
–φ
= porosity (fraction)
121 of 217
Basic Leverett J Function
• At its simplest a Leverett J
function is constructed by
plotting taking a series of
capillary pressure curves for
samples of different porosity
and permeability and
plotting the J value versus
the water saturation
• From the cross-plot a curve
is constructed that honors
th data
the
d t
• For some formations
Sw = -Alog10J + B
• Valid J<1; For J>1 then
Sw=Swi
•A problem with the Leverett J function
is the wide variance in saturation that
occurs near the “irreducible” water
saturation which is the saturation of
principal interest for many analyses
Leverett J Adjustment for Swi
• Because of the problem that Leverett J functions can have
near the “irreducible” water saturation (Swi) aspects of the
Brooks-Corey method have been adopted to improve the JS correlation
Sw
l ti bby normalizing
li i ffor S
Swii
• Water saturation is normalized using:
– Swe = (Sw-Swi)/(1-Swi) where Swe = effective water saturation,
Sw = water saturation at any given Pc and Swi = “irreducible”
water saturation
– Method is dependent on criteria for defining Swi
• Plot of J versus log Swe is generally linear with a constant
slope, λ, and an intercept, J*, related to the J function
normalized threshold entry pressure.
• The calculation of water saturation requires knowledge or
back-calculation of Swi:
J = J* Swe(1/λ)
122 of 217
Normalization: Leverett J Function
9
0.00025md
8
0.00049md
0.0012md
0 0017md
0.0017md
7
Leverett J Function
• J function
works poorly
for mixed
lithofacies and
between basins
• Does work OK
for single
lithofacies in a
small area
0.0018md
0.0030md
6
0.0040md
0.0057md
5
0.0085md
0.012md
4
0.013md
0.032md
0.046md
3
0.085md
0 25md
0.25md
2
0.41md
0.56md
1
0.84md
2.24md
0
0
10
20 30
40
50
60
70 80
90 100
Normalized Brooks-Corey
• Brooks and Corey (1966) showed that a log-log
plot of Pc versus Swe often exhibits a linear trend
with slope,
slope λ,
λ and intercept equal to the threshold
entry pressure
• logSwe = -λlogPc + λlogPce for Pc>Pce
–
–
–
–
Pc=capillary pressure
Pce = threshold entry pressure
Swe = (Sw-Swi)/(1-Swi)
λ = slope of log-log plot
Capillary pressure parameters, λ and Pce, are
correlated with permeability and/or porosity to
develop Pc curves
123 of 217
10000
Normalization: BrooksCorey Capillary Pressure
9000
8000
7000
• Transform taking logarithm of Pc and Sw
• λ represents pore throat size distribution
• Standard unimodal curves can be reduced
to intercept (Pce = extrapolated threshold
entry) and slope (λ)
6000
5000
4000
3000
2000
1000
0
0
10
20
30
40
50
60
70
80
90 100
10000
Air-Hg Capillary
y Pressure (psia)
Air-Hg Capillary Pres
ssure (psia)
10000
1000
-2.05
Pc = 1.54E+07Sw
2
R = 0.997
Pce
λ
1000
100
100
0
10
20
30
40
50
60
70
80
90
100
10
100
Change in Methane Density with
Pressure and Temperature
Meth
hane Density (g/cc)
ρ=0.03861-0.0003331T+5.943*10-5P-4.287*10-9P2+1.226*10-13P3
0.32
0.30
0.28
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0 08
0.08
0.06
0.04
0.02
0.00
Pressure (psia)
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
90
100 110 120 130 140 150 160 170 180 190 200 210 220 230
Temperature (deg F)
124 of 217
Brine Density vs P-T-X
Bw = (1 +ΔVwp)x(1-ΔVwT); Bw =FVFw
γw = 1+ 6.95x10-6 XTDS; γw = specific gravity, X mg/l
ΔVwT = -1.0001x10-2 + 1.339x10-4T+5.5065x10-7T2
ΔVwp = -1.953x10-9pT-1.7283x10-13p2T-3.5892x10-7p-2.2534x10-10p2
De
ensity (g/cc)
1.30
65 F, 15 psi
1.25
65 F 1000 psi
1.20
65 F, 10000 psi
1.15
100 F, 1000 psi
1.10
100 F, 10000 psi
ρw =
γw/Bw
65 F, 5000 psi
100 F, 15 psi
100 F, 5000 psi
200 F, 15 psi
200 F, 1000 psi
1.05
200 F,, 5000 psi
p
200 F, 10000 psi
1.00
300 F, 15 psi
300 F, 1000 psi
0.95
300 F, 5000 psi
300 F, 10000 psi
0.90
0
50
100
150
200
250
300
Total Dissolved Solids (mg/l/1000)
Discrepancy in High P,T MethaneWater Interfacial Tension
80
J&N M
Modeled IFT (dyne/cm)
• IFT data of Hough,
Raza, and Wood
(1951) exhibits
hibi IFT
<30 dyne/cm at
higher P,T
• Data of Jennings &
Newman (1971)
exhibit higher values
• J&N data more
consistent, HRW
may have had
unknown problem
with system
elastomer seal
contamination
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
HRW Measured IFT (dyne/cm)
125 of 217
Relationship Between Pore Throat
Diameter and Permeability by Lithology
Principal Po
ore Throat Diameter (μm)
100
0 445
y = 2.61x0.445
R² = 0.9259
10
1
0.1
Ss lithic
Ss arkosic
Ss quartzose
Ls interparticle
Ls chalk
Ls moldic
Ls oomoldic
0.01
0.001
0.000001 0.00001
0.0001
0.001
0.01
0.1
1
10
100
1000
10000
Insitu Klinkenberg Permeability (md)
Principal Pore Throat Diameter (μm))
100
10
Dp = 7.17(k/φ)0.49
R2 = 0.83
1
0.1
Lithology
Ss lithic
Ss arkosic
Ss quartzose
Ls interparticle
Ls chalk
Ls moldic
Ls oomoldic
0.01
0.001
0.000001
0.00001
0.0001
0.001
0.01
0.1
1
10
100
1000
Porosity Normalized Permeability (kik/φa, md/%)
126 of 217
Princip
pal Pore Throat Diameter (μm
m)
100
Dp = 7.17(k/φ)0.49
R2 = 0.83
10
Lithology
Ss lithic
1
Ss arkosic
Ss quartzose
Ls interparticle
0.1
Ls chalk
Ls moldic
Ls oomoldic
Mesaverde Hi
0.01
Mesaverde Lo
Power (Lithology)
0.001
0.000001
0.00001
0.0001
0.001
0.01
0.1
1
10
100
1000
Porosity Normalized Permeability (kik/φa, md/%)
Relationship Between Threshold Entry
Pressure and Permeability
Air-Mercury Threshold Entrry
Pressure (psi)
10000
kak
kmk
kik
1000
100
10
-0.44
y = 64.66x
2
R = 0.82
1
1E-06 0.00001 0.0001
0.001
0.01
0.1
1
10
100
Klinkenberg Permeability (mD)
127 of 217
1000
100
10
1
R091
255.9 ft
0
k = 113 m D
φ = 24.5%
113 mD
10
20
30
40
50
60
70
80
90
100
100
10
10
20
30
40
50
60
70
80
90
100
100
10
20
30
40
50
60
70
80
90
100
20
30
40
50
60
70
80
90
100
8 mD
90
100
0.2 mD
100
10
10
20
30
40
50
60
70
80
1000
100
10
B029 1
11460.6 ft
k = 0.02550mD 10
φ = 4.4%
20
30
40
50
60
70
80
90
100
0.02 mD
1000
100
10
PA424 1
4606.5 ft
0 m D10
k = 0.00107
φ = 12.7%
20
30
40
50
60
70
80
90
100
1000
100
10
B029 1
13672.5 ft
0 m D10
k = 0.000065
φ = 2.6%
20
30
40
50
60
70
• no significant
difference in high-low
pairs at high K
• increasing Pce
separation with
decreasing K
• merging of curves at
35-50% Sw
• smaller pores are in
protected pore space
• users of Winland R35
need to adjust for
confining stress
10000
10000
10
1000
LD43C 1
4013.25 ft
0
k = 0.190 mD
φ = 12.9%
A
Ai r-Hg Capillary Pressure (psia)
1000
E946 1
6530.3 ft
k = 0.04160mD 10
φ = 9.5%
0.001 mD
10
10000
10000
0.04 mD
100
10000
1000
E946 1
6486.4 ft
0
k = 0.637 mD
φ = 12.2%
1000
R780 1
2729.9 ft
0
k = 7.96 mD
φ = 19.2%
Air-Hg Capillary Pressu
ure (psia)
Air-Hg Capillary Pressu
ure (psia)
10000
0.6 mD
Stress effect on Pc
10000
10000
80
90
100
0.00007 mD
Thresho
old Entry Pore Diame ter
(μ m)
100
0.50
y = 11.77x
2
R = 0.77
10
1
y = 11.28x0.50
R2 = 0.93
01
0.1
A
0.01
1E-06 0.00001 0.0001
0.001
0.01
0.1
1
10
100
Klinkenberg Permeability/Porosity (mD/%)
Threshold Entry Gas Column
Height (ft))
10000
C
1000
y = 6.75x
6 75x-0.50
R2 = 0.93
100
10
1
1E-06
y = 6.48x-0.50
2
R = 0.77
1E-05 0.0001 0.001
0.01
0.1
1
10
• threshold entry
pressure is
predictable from
√K/φ at any
confining
pressure
• correct
unconfined Pce
to insitu Pce
based on perm
change with
stress
100
128 of 217
Threshold Entry Pore Diame ter
(μ m)
100
Stress effect on Pc
1000
100
10
R091 1
255.9 ft
0
k = 113 mD
φ = 24.5%
10
20
30
40
50
60
70
80
90
100
0.6 mD
100
10
10
20
30
40
50
60
70
80
90 100
100
10
E946 1
6530.3 ft
k = 0.04160mD 10
φ = 9.5%
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
A
8 mD
0.01
1E-06 0.00001 0.0001
0.001
0.01
0.1
1
10
100
100
10
10
20
30
40
50
60
70
80
90
100
0.2 mD
1000
100
10
20
30
40
50
60
70
80
90
100
1000
20
30
40
50
60
70
80
90
100
0.02 mD
90
100
0.00007 mD
1000
100
10
B029 1
13672.5 ft
0 mD10
k = 0.000065
φ = 2.6%
20
30
40
50
60
70
80
y = 6.48x-0.50
10
C
10
y = 6.75x-0.50
R2 = 0.93
100
100
10000
1000
PA424 1
4606.5 ft
0 mD10
k = 0.00107
φ = 12.7%
10000
1000
B029 1
11460.6 ft
k = 0.02550mD 10
φ = 4.4%
10
LD43C 1
4013.25 ft
0
k = 0.190 mD
φ = 12.9%
Air-Hg Capil lary Pressure (psia)
1000
10000
0.001 mD
100
10000
10000
0.04 mD
y = 11.28x0.50
R2 = 0.93
10000
1000
E946 1
6486.4 ft
0
k = 0.637 mD
φ = 12.2%
1
0.1
R780 1
2729.9 ft
0
k = 7.96 mD
φ = 19.2%
Air- Hg Capillary Pressure ( psia)
10000
1000
Threshold Entry Gas Column
Height (ft)
113 mD
10000
10000
0.50
y = 11.77x
2
R = 0.77
10
2
R = 0.77
1
1E 06
1E-06
1E 05 0.0001
1E-05
0 0001 0.001
0 001
0 01
0.01
01
0.1
1
10
100
• threshold entry pressure
is entirely predictable
from √K/φ
√K/φ ratio at any P
Brooks-Corey Slope
• PSD expressed by Pcslope
• Pcslope = f (k)
• Pcslope ↓ with P ↑
Leverett J(Sw) =
Pc (k/φ)0.5/τcosθ
Poor fit because
Pcslope ≠ C = f(k, lith)
5
Brooks-C
Corey Capillary
Pressure Slope
Implicitly assumes
Pcslope = Constant
in situ
unconfined
y = -0.0304Ln(x) + 1.87
2
R = 0.0216
4
y = -0.037Ln(x) + 1.256
2
3
R = 0.052
2
1
0
1E-05 0.0001 0.001
0.01
0.1
1
10
100
1000
129 of 217
Height a
above free water (ft)
Modeled Pc curves
1000
900
Modeled Pc
Curves
k=0.0001 mD
k=0.001 mD
800
700
600
k=0.01 mD
k=0.1 mD
k=1 mD
k=10 mD
500
400
300
200
100
0
Modeled Pc curves
Pc properties evolve
over time as
diagenesis changes
porosity and pore
architecture
Height above frree water (ft)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1000
100
k=0.0001 mD
k=0.001 mD
k=0.01 mD
10
k=0.1 mD
k=1 mD
k=10 mD
1
0.0
0.1
1.0
Hysteresis of
Capillary
Pressure
• Non-wetting
residual
saturation to
imbibition
S
Snwr
= f(Snwi)
f(S i)
4
Drainage-Imbibition
Cycles
3
5
2
1
Midale Dol
φ = 23%
(after Larson & Morrow, 1981)
130 of 217
Capillary Pressure Hysteresis in
Coarse Sand Pack
(after Klute, 1967)
Drainge-Imbibition
• what is the residual trapped gas when a reservoir
leaks or along a gas migration path?
Approx. Height above Free Waterr
Level (ft)
10000
0000
Primary Drainage
First Imbibition
Secondary Drainage
Second Imbibition
Tertiary Drainage
Third Imbibition
1000
100
10
1
0.1
0
10
20
30
40
50
60
70
80
90
100
131 of 217
10000
10000
Primary Drainage
First Imbibition
Secondary Drainage
Second Imbibition
Tertiary Drainage
Third Imbibition
kik
1000
Air-Hg C apillary Pressure (psia)
100
10
1
E393
7001.1ft
φ = 17.4%
= 28.9 mD
0
10
20
30
40
50
60
70
80
90
100
Air-Hg Capil lary Press
sure (psia)
Air-Hg Capillary Press
sure (psia)
100
10
10
20
30
40
50
60
70
80
90
100
30
40
50
60
70
80
90
100
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
100
10
Airr-Hg Capilla ry Pressure (psia)
Airr-Hg Capillary Pressure (psia)
100
10
1
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
100
10
1
S685
6991.2 ft (B)0
φ = 8.6%
= 0.0063 mD
10
20
30
40
50
60
70
80
90
100
10000
10000
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
Air-Hg Capillary Pressure (psia )
20
10000
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
100
10
1
E458
6404.8 ft (A) 0
φ = 9.5%
= 0.0019 mD
10
1000
1
R829
5618.3 ft (B)0
φ = 9.2%
= 0.287 mD
10000
B646
8294.4 ft (B) 0
φ = 7.6%
= 0.022 mD
10
10000
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
1
E393
7027.2 ft
0
φ = 15.0%
= 1.93 mD
100
1
B049
9072.1 ft (A) 0
φ = 12.3%
= 6.74 mD
10000
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
10
20
30
40
50
60
70
80
90
100
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
100
10
KM360 1
8185.7 ft (B)0
φ = 5.9%
= 0.00070 mD
10
20
30
40
50
60
70
80
90
100
Capillary
Pressure
Hysteresis
• Composite primary
drainage trend
consistent with
single--cycle drainage
single
• Imibition curves
exhibit
hibi high
hi h trapping
i
• Trapped saturation
increases with
increasing initial
saturation
Trapping increases with
increasing initial saturation
(after Lake 2005)
132 of 217
Residual Non-wetting
Phase Saturation
Residual N
Nonwetting Phase Saturation (S
Snwr)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Initial Nonwetting Phase Saturation (Snwi)
Residual Gas Saturation
C = 1/[(Snwr-Swi)-1/(Snwi-Swi)]
Snwr = 1/[C + 1/Snwi]
C = 0.55 (min ε); Swi = 0
all
unconfined
hysteresis
confined
all
unconfined
hysteresis
confined
all
unconfined
hysteresis
confined
Swirr
definition
Swirr = 1-Snwmax
Swirr = 1-Snwmax
Swirr = 1-Snwmax
Swirr = 1-Snwmax
Swirr = 0
Swirr = 0
Swirr = 0
Swirr = 0
Swirr = 0, Snwi<70%
Swirr = 0, Snwi<70%
Swirr = 0, Snwi<70%
Swirr = 0, Snwi<70%
Land C
C
Land C
Snwr
Snwr
Average Standard Minimum Standard Std Error
Error
Error
Error
C=0.55
0.57
0.329
0.53
0.077
0.077
0.61
0.294
0.59
0.087
0.088
0.61
0.383
0.51
0.056
0.057
0.44
0.249
0.45
0.088
0.085
0.73
0.443
0.63
0.073
0.073
0.78
0.360
0.71
0.080
0.081
0.75
0.562
0.59
0.057
0.057
0.61
0.316
0.54
0.078
0.078
0.70
0.054
0.053
0.83
0.062
0.061
0.70
0.052
0.051
0.50
0.038
0.039
Residual Nonwetting
g Phase Saturation (Snwr)
1.0
Sample
Condition
unconfined Snwi= 1-Snwmax
unconfined hysteresis
Land C =0.59, Swirr=0
Land C=0.71, Swirr=0
Land C =0.55, Swirr=0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
133 of 217
Residual
Saturation
C = 1/[(Snwr-Swi)-1/(Snwi-Swi)]
Snwr = 1/[C + 1/Snwi]
C = 0.55 (min ε); Swi = 0
Residual Non
nwetting Phase Saturation (Snwr)
1.0
unconfined
0.9
confined
Land C=0.66, Swi=0
0.8
Land C =0.54, Swi=0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Primary Drainage
First Imbibition
Secondary Drainage
Second Imbibition
Tertiary Drainage
Third Imbibition
1000
100
10
1
0
10
20
30
40
50
60
70
80
90
100
Air-Hg Capil lary Pressurre (psia)
Air-Hg Capillary Pressurre (psia)
100
10
10
20
30
40
50
60
70
80
90
100
30
40
50
60
70
80
90
• Snwi and Snwr are ~ = for Sw >
80%
• e.g.,
e g for Swi of 30%
30%, Swr is ~50%
100
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
100
10
Air-Hg
g Capilla ry Pressure (psia)
Air-Hg
g Capillary Pressure (psia)
100
10
10
20
30
40
50
60
70
80
90
100
1.0
10
20
30
40
50
60
70
80
90
100
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
100
10
1
S685
6991.2 ft (B)0
φ = 8.6%
= 0.0063 mD
10
20
30
40
50
60
70
80
90
100
10000
10000
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
Air-Hg Capillary Pressure (psia )
20
10000
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
100
10
1
E458
6404.8 ft (A) 0
φ = 9.5%
= 0.0019 mD
10
1000
1
R829
5618.3 ft (B)0
φ = 9.2%
= 0.287 mD
10000
1
B646
8294.4 ft (B) 0
φ = 7.6%
= 0.022 mD
10
10000
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
1
E393
7027.2 ft
0
φ = 15.0%
= 1.93 mD
100
1
B049
9072.1 ft (A) 0
φ = 12.3%
= 6.74 mD
10000
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
10
20
30
40
50
60
70
80
90
100
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
100
unconfined
0.9
confined
Land C=0.66, Swi=0
0.8
Land C =0.54, Swi=0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
10
KM360 1
8185.7 ft (B)0
φ = 5.9%
= 0.00070 mD
Residual Nonwetting Phase Saturation (Snwr)
E393
7001.1ft
φ = 17.4%
= 28.9 mD
Residual Gas
Saturation
10000
10000
kik
Air-Hg C apillary Pressure (psia)
0.0
10
20
30
40
50
60
70
80
90
100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
134 of 217
• Trapping
constant, C
consistent
with
cemented
sandstone
1.0
Complete trapping, C=0
Vuggy, isolated moldic, C=0.3
Mesaverde high C =0.35
Mesaverde Ss, C=0.55
Mesaverde low, C=0.9
Cemented Ss, C=0.7
Berea, C=1.7
Unconsolidated sucrosic
Unconsolidated,
sucrosic, oolitic
oolitic, C=3
C 3
0.9
Residu
ual Nonwetting Phase Saturattion (Snwr)
Residual
gas
saturation
0.8
07
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Electrical
Properties
135 of 217
Wireline log
analysis tools
unkn
1000
Timur : Constant Exponent
0.001
MD
1000
Timur : Variable Exponent
0.001
md
1000
1:240 MD in F
Permeability - 1
Core
0.001
0.4
0.4
0.4
0.4
0
Reservoir Components
Porosity
V/V
PHIX
V/V
Oil
V/V
Water
V/V
Shale
V/V
Permeability - 2
Core
0
0.0
0
0.001
0.001
0.001
unkn
Timur : Sw-Sw(Density)
unkn
Timur : Sw/Sw(Density)
1000
unkn
1000
1000
0
2
CPHI
0
unkn
0
Water
Oil
6400
0
0
1
6425
6450
• Lithofacies identification
• Accurate porosity
calculation
• Water saturation
calculations
Gas
6475
6500
6525
6550
MWX2
Resistivity of a simple rock model
with straight pores
Porosity
1
(Φ)
Resistivity
Rw
(Ro)
The ‘formation factor’ (F) is defined as the ratio Ro/Rw
8
0
F = 1/φ
136 of 217
For a rock with a
tortuous pore network ....
m
F = 1/φ
This is the first Archie equation,
where ‘m’ is known as the ‘cementation exponent’
The resistivity of hydrocarbonbearing rocks
1
8
Ro
0
Water saturation (Sw)
Resistivity (Rt)
The ‘resistivity index’ (I) is defined as the ratio Rt/Ro
n
I = 1/Sw
137 of 217
Putting it all together ...
the Archie equation
F=
Ro
Rw
=
a
Φm
I
=
Rt
Ro
a
Rw
m
=
Sw φ * R t
(
=
1
n
Sw
1/n
)
Core measurement of the
formation factor, F
core p
plug
g
A ro Rw
Φ
L
138 of 217
When F and φ are plotted on
logarithmic graph paper ...
1
Φ
m= 3
0.1
m= 2
m= 1
0.01
1
10
F
100
1000
Regional Water Chemistry
Database
DOE Contract DE-FC-02NT41437
Billingsley et al
Advanced Resources International
• Historical
Hi t i l D
Data
t
• 3200 Well Locations
–Greater Green River Basin and Wind River Basin
• 8000 Chemical Analyses
• Access/Excel Formats
139 of 217
m in sandstones
Archie (1942) observed the range in value of
m in sandstones:
1.3
unconsolidated sandstones
1.4 - 1.5
very slightly cemented
1.6 - 1.7
slightly cemented
1.8 - 1.9
moderately cemented
2.0 - 2.2
g y cemented
highly
Guyod gave the name “cementation exponent” to m,
but noted that the pore geometry controls on m were
more complex and went beyond simple cementation
m variability
Core measurements of
formation factor and
porosity in a Cherokee
sandstone sample, with
a computed value of
cementation exponent m
for each core sample
from:
m
F = 1/φ
140 of 217
Archie Cementation Exponents
35
30
Mesaverde Frontier
Mesaverde-Frontier
25
20
Medina
15
10
2.1-2.2
2.0-2.1
1.9-2.0
1.8-1.9
1.7-1.8
1.6-1.7
1.5-1.6
0
1.4-1.5
5
1.3-1.4
Percent of Populatio
on (%)
40
Archie Cementation Exponent (m, a=1)
Water Saturation Calculations
•
•
•
•
•
Archie
Simandoux
Fertl
Dual-Water
Waxman-Smits
141 of 217
Simandoux
• Developed theoretically primarily for
Gulf Coast application
Where
φ = effective porosity
• Rw = water resistivity
• Rt = formation true resistivity
• Rsh = shale or clay resistivity
• Vsh = volume of shale
Fertl
• Developed for shaly sandstones in Rocky Mountains
Where
φ = effective porosity
• Rw = water resistivity
• Vsh = volume of shale
• A = Constant
142 of 217
Dual-Water/Waxman-Smits
• (Clavier, Coats, and Dumanoir, 1984)
Swt - Swb
Sw =
1 - Swb
Where
φt = total porosity
• Rwf = formation water resistivity
• Rwb = bound water resistivity (Rwa in shales)
• Swt = total water saturation
• Swb = bound water saturation (various methods for determination
– e.g., Swb = α vq Qv; vq = 0.28 cc/meq25oC, α(XNaCl) ≈ 1
Clay Surface Area & Cation
Exchange Capacity
Clay Type
Cation Exchange
Morphology
Specific Surface
Pure Clay Clay in Sandstone Capacity (Meq/100g)
Kaolinite
15-18
0.05-0.20
3-15
Books
Fans
Smectite
85-100
0.5-2.0
80-150
Honeycomb
Illite
90-115
1.5-10
10-40
SmectiteIllite
(mixedlayer)
85-115
0.5-10
10-150
Curled flakes with
projecting and
fibrous mat
Similar to Smectite
& Illite
Chlorite
40-60
0.5-2.0
10-40
Cardhouse, rosette
(after Grim, 1968; Gaida et al, 1973)
143 of 217
Waxman and Smits (1969)
Calculated Water Saturation
• Redefined the Archie equation including the
influence of conductive clays
Co = (1/F*) (Cw + BQv)
• Co = core conductivity at Sw=100% (mho/m)
Cw = water conductivity (mho/m)
F* = salinity/clay conductivity independent formation factor
Qv = cation exchange capacity of the core (meq/cc)
B = specific counter-ion activity [(equiv/l)/(ohm-m)]
• F*/F = (1 + BQv/Cw)
Waxman-Smits
Water Saturation Calculations
• Sw = [(F*Rw) Rt(1+ RwBQv/Sw)]1/n*
• F* = salinity/clay conductivity independent formation factor
Qv = cation exchange capacity of the core (meq/cc)
B = specific counter-ion activity [(equiv/l)/(ohm-m)]
• Qv ≈ CEC(1-φ)ρ
( φ)ρma/100φ
φ
144 of 217
Waxman-Smits-Thomas
Sw = n *
a*
φm *
Rw
⎛
⎞
R
BQ
⎜
⎟
w
v
Rt ⎜⎜1+
Sw ⎟⎟⎠
⎝
F* = a*/φm* Intrinsic Formation Factor; free of excess conductivity
m*
p
; free of excess conductivityy
Intrinsic cementation exponent;
n*
Intrinsic saturation exponent; free of excess conductivity
Rw
Resistivity of brine at temperature (ohm-m)
B
Equivalent counterion conductance at temperature (1/ohm-m)/(equiv / liter)
Qv
Cation exchange capacity per ml pore space (meq/ml)
Qv Lab Methods
• Wet Chemistry
– Utilizes crushed rock with high surface area
– Requires sample porosity & grain density to
compute Qv
– Crushing can improperly exposes Qv sites not
present in native pores
• Multiple Salinity (Co vs Cw)
– Flow-through
Fl
th
h off multiple
lti l salinity
li it bbrines
i
on core
– Preserves distribution of clays and Qv
– time – intensive
145 of 217
Multiple-salinity Analysis
Core Conductivity (CO), 1/Ro
Bmax Q v
F*
CO =
Cw B Qv
+
F*
F*
Slope @ Bmax brines = 1/F*
Clay-rich sandstone
Excess conductivity
CO =
Clean sandstone
1
C
⋅ CW = W
F
F
0
BmaxQv
Brine Conductivity (CW), 1/Rw
Porosity dependence of “m”

Empirical:
m = 0.234 ln φ + 1.33
Dual porosity: m = log[(φ
log[(φ-φ2)m1 + φ2m2]/log φ

φ2 = 0.35% m1=2, m2=1; SE both = 0.11
rock behaves like a mixture of matrix p
porosityy and
cracks or fractures
both models fit data
φ = bulk porosity
φ2 = fracture porosity
m1 = matrix
cementation
exponent
m2 = fracture
cementation
exponent
In situ Archie C
Cementaiton Exponent
(m, a=1, X brrine=40KppmNaCl)

2.2
2.1
2.0
1.9
1.8
1.7
1.6
15
1.5
1.4
1.3
1.2
1.1
1.0
0
2
4
6
8
10
12
14
16
18
20
22
146 of 217
Archie Cementation Exponent
• Empirical:
m = 0.95 - 9.2φ + 6.35φ0.5
• Dual porosity: m = log[(φ-φ2)m1 + φ2m2]/logφ
•
•
•
•
φ = bulk porosity
φ2 = fracture or
touching vug
porosity
m1 = matrix
cementation
exponent
m2 = fracture or
touching vug
cementation
exponent
Archie Ceme ntation Exponent (m, A=1)
2.4
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
m1 = 2.1,
2 1 φ2 = 0.0005
0 0005
m1 = 2.0, φ2 = 0.001
m1 = 1.8, φ2 = 0.002
m2 = 1
High:
Int:
Low:
15
1.5
1.4
1.3
1.2
1.1
1.0
0
0.02 0.04 0.06 0.08
0.1
0.12 0.14 0.16 0.18
0.2 0.22 0.24
Porosity (fraction)
Archie porosity (cementation) exponent

Nearly all cores exhibit some salinity dependence
tested plugs with 20K, 40K, 80K, and 200K ppm brines
1.0
Core C
Conductivity (mho/m)
0.9
n=335
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
2
4
6
8
10
12
14
16
18
20
22
Brine Conductivity (mho/m)
147 of 217
Archie Cementation Exponent vs. Rw
In situ Arrchie Cementation Ex
xponent,
(m, A=1)
2.3
Nearly all cores
exhibit some salinity
dependence
tested p
plugs
g with
20K, 40K, 80K, and
200K ppm brines

2.2
2.1

2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.01
0.1
1
Brine Resistivity (ohm-m)
Multi-salinity Archie m
Archie
e Cementaiton Expo
onent (m,
a=1)
2.4
2.2
2.0
1.8
1.6
1.4
200K
1.2
80K
40K
1.0
20K
0.8
0
2
4
6
8
10
12
14
16
18
20
22
• Archie m decreases with decreasing salinity
148 of 217
In situ Archie m vs log Rw
w Slope
Slopem-logRwvs Porosity
Each core exhibits a highly linear
m vs logRw
Mean value for all cores:
0.2
0.1
0.0
-0.1
Average Slopem-Rw = -0.27+0.32 (2
-0.2
standard deviations)
-0.3
where Slopem-Rw = slope of mRw versus
logRw.
-0.4
-0.5
-0.6
y = 0.0118x - 0.3551
R2 = 0.1198
-0.7
-0.8
0
2
4
6
8
10
12
14
16
18
20
22
Slopes exhibit a weak correlation
with porosity . This correlation
can be used to improve the
prediction of m at any salinity:
Slopem-Rw = 0.00118 φ – 0.355 (φ - %).
Estimation of Archie m
• Each core exhibits a highly linear m vs logRw
• Mean value for all cores:
– Average Slopem-Rw = -0.27+0.32 (2 standard deviations)
– where
h Slope
Sl m-Rw = slope
l
off mRw versus logRw.
l R
• Slopes exhibit a weak correlation with porosity . This correlation
can be used to improve the prediction of m at any salinity:
– Slopem-Rw = 0.00118 φ – 0.355 (φ - %).
• Combining the above equations the Archie cementation exponent
at any given porosity and reservoir brine salinity can be predicted
using:
– mX = m40 + Slopem-Rw (log RwX + logRw40K)
– mX = (0.676 logφ + 1.22) + (0.0118 φ-0.355) x (logRwX + 0.758);
– mX = 1.95 + (0.0118 φ-0.355) x (logRwX + 0.758);
•
•
•
φ<14%
φ>14%
where mx = m at salinity X
m40 = m at 40K ppm NaCl, log RwX = log10 of resistivity of brine at salinity X
logRw40K = log10 of resistivity of 40K ppm NaCl = 0.758
149 of 217
Salinity dependence of “m”
20K ppm
2.50
y = 0.2267Ln(x) + 2.2979
2
R = 0.6619
Axis Title
2 00
2.00
1.50
Series1
Log. (Series1)
1.00
40K ppm
0.50
3.00
0.00
0.000
y = 0.2328Ln(x) + 2.409
0.050
0.100
0.150
0.200
2
R = 0.6547
2.50
0.250
• m = a ln φ + b
• a, b = f (salinity)
• low porosity rocks hold
more gas than we
thought
insitu porosity (%)
Axis Title
2.00
Series1
1.50
80K ppm
Log. (Series1)
1.00
3.00
y = 0.2149Ln(x) + 2.4354
0.50
2
R = 0.5132
2.50
0.050
0.100
0.150
insitu porosity (%)
0.200
0.250
2.00
Axis Title
0.00
0.000
200K ppm
Series1
1.50
Log. (Series1)
3.00
1.00
y = 0.1621Ln(x) + 2.3222
2
R = 0.3633
2.50
0.50
2.00
0.050
0.100
0.150
insitu porosity (%)
0.200
0.250
Axis Title
0.00
0.000
Series1
1.50
Log. (Series1)
1.00
0.50
0.00
0.000
0.050
0.100
0.150
0.200
0.250
insitu porosity (%)
Critical Gas
Saturation
150 of 217
Overview
– little krg data at Sw >
65% : Does p varyy or
Sgc vary or both?
– little Swc data: how is
Swc = f (kik)? Or what is
krw exponent ?
Ga
as Relative Permeability
0.1
0.01
0
10
20
30
40
50
60
70
80
90
100
Water Saturation
1
Relative Permeability (fraction)
• Previous work indicated
that krg could be
modeled using: Corey
q with p=1.7
p
& Sgc ~
eqn
0.15-0.05*log10kik
• Swc ~ Swi600
• Issues
Western Sandstones
1
g-10 md
w -10 md
g-1 md
w -1 md
g-0.1 md
w -0.1 md
g-0.01 md
w -0.01 md
g-0.001 md
w -0.001 md
0.1
0.01
0.001
0.0001
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Swc>Swi
0
0
Swi
krg
krw
Swc
Sgc 1
0
0
gas-only
production
Heightt above Free
Water Level
Pc
drainage
curve
ater
water-only gas&wa
production production
• At Sg<Sgc no gas flow only water flow
• At Swc<Sw<(1-Sgc) transition zone both gas & water flow
• At Sw<Swc no measurable water flow
only gas flow
Rela
ative Permeability
• Krg - relative permeability to gas
• Krw - relative permeability to water
• Sgc - critical gas saturation (Sg
necessary for
f connective
ti gas path)
th)
• Swc - critical water saturation (Sw
below which water relative
permeability is zero or less than
measurable threshold
• Swi - “irreducible” water saturation
(Sw at which further increase in Pc,
hydrocarbon column height, results in
S decrease
Sw
d
lless th
than some criteria
it i
1
Capillarry Pressure
Relative Permeability
and Capillary Pressure
Sgc
Transition
zone
Free water level
1
Water Saturation
151 of 217
Relative Permeability Scaling
Linear
Relative Perm
meability
Logarithmic
1
0.1
0.01
0
0
0.001
0.0001
0.00001
0.000001
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Water Saturation
Water Saturation
• A
As saturations
t ti
approachh the
th critical
iti l saturation
t ti for
f eachh phase
h
the
th
relative permeability for that phase changes by orders of
magnitude
• At saturations above critical saturations the relative
permeability to the remaining flowing phase changes less than
an order of magnitude
Relative Permeability Reference Frame
• krg = kreg/kr?
• Relative permeability is the ratio of the effective
permeability of one phase to a baseline
permeability
bili - traditional
di i l references
f
are:
– kr = ke/kabsolute; where kabs may be kair,kwater, koil kklink
– kr = ke/kenw,Swc or kr = ke/kenw,Swi
• kabs is the absolute permeability
–
–
–
–
In high k rocks kwater ~ kklink ~ kabs (~ kair)
In high k rocks kenw,Swc
Swii
en S c ~ kabs and Swcc~S
In low k rocks kwater<kklink
In low k rocks keg,Swi < kklink
• User must choose reference frame - (carefully)
152 of 217
Relative Permeability Reference Frame
Selection of
–
–
–
Relative Perm
meability
•
For most reservoir simulation programs
kr cannot exceed 1
In reservoir Swi can be < Swc but it
achieved the low Sw by water flow at
krw << krw,Swc
1
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
kref = kwater
Water Saturation
10
1
Relative Perme
eability
•
kreference = kwater
kref = keg,Swc
results in krg > 1 at Sw < Swc
Relativ
ve Permeability
10
•
0.1
0.01
0
0
0.001
0.0001
0.00001
0.000001
1
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
kref = kklink
Water Saturation
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
kref = keg,Swc
Water Saturation
Generalized Drainage & Imbibition
Relative Permeability Curves
Generalize Drainage Curves
Generalized Imbibition Curves
(after Sahimi, 1994)
153 of 217
Gas Relative Permeability of LowPermeability Tight Gas Sandstone
• Referenced to kklink
• Measurements
performed at Sw
<Swi by evaporation
• Note shift to lower
krg at a given Sw
with decreasing ki
Effect of Confining Pressure on Relative
Permeability for Tight Gas Sandstone
•
•
•
•
•
Note data points
showing little effect of
significant
g
change
g in
confining pressure on
krg
Ward & Morrow
(1987) data indicate
that krg under pressure
may be 10% less than
at low pressure
Referenced to kklink,P
Measurements
performed at Sw <Swi
by evaporation
Note shift to lower krg
at a given Sw with
decreasing ki
154 of 217
Gas Relative
Permeability is
Similar using
different
techniques to
obtain water
saturation
(after Walls, 1982)
Influence of Confining Pressure on Gas Permeability with
Core at Different Water Saturations
(after Walls, 1982)
155 of 217
Effect of Confining Pressure on Relative
Permeability for Tight Gas Sandstone
Data of Randolph (1983)
show moderate effect of
confining stress on kr at
low water saturation but
increasing effect with
increasing Sw
(after Randolph, 1983)
Single-phase Stationary krg Curves
• Relative gas permeability data, representing
krg values obtained at several saturations,
saturations
were compiled from published studies
(Thomas and Ward, 1972; Byrnes et al ,
1979; Sampath and Keighin, 1981; Walls,
1981; Randolph, 1983; Ward and Morrow,
1987)
156 of 217
Western Sandstones
Gas Relative Permeab
bility
1
Bounding curves
consistent with
single-point data
0.1
0.01
0
10
n=43
20
30
40
50
60
70
80
90
100
Water Saturation
Single-point krg,Swi Data
• Relative gas permeability data,
data representing krg
values obtained at a single Sw and krg values
obtained for a single sample at several saturations,
were compiled from published studies (Thomas
and Ward, 1972; Byrnes et al , 1979; Jones and
p and Keighin,
g
1981; Walls,
Owens, 1981; Sampath
1981; Randolph, 1983; Ward and Morrow, 1987;
Byrnes, 1997; Castle and Byrnes, 1997; Byrnes
and Castle, 2001)
157 of 217
Single-Sw Gas Relative Permeability
All Tight Gas Sandstones
Gas R
Relative Permeab
bility
1.0
1-10 md
0.1-1 md
0.05-0.1 md
0 01 0 05 md
0.01-0.05
d
0.005-0.01 md
0.001-0.005 md
0.0001-0.001 md
1 md
0.1 md
0.01 md
0.001 md
0.0001 md
0.9
08
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
10
20
30
40
50
60
70
80
90
100
Water Saturation (%)
Relative Permeability to Gas – at Stress
Multiple reservoir intervals – GGRB (n = 583)
1.0
0.8
Krg/4000
Byrnes
data
0.6
0.4
0.2
0
0
10
20
30
40
50
60
70
80
90
100
(Shanley et al, 2003)
158 of 217
Single-Sw Gas Relative Permeability
Gas R
Relative Permeab
bility
1
0.1
1-10 md
0.1-1 md
0.05-0.1 md
0.01-0.05 md
0.005-0.01 md
0.001-0.005 md
0.0001-0.001 md
1 md
0.1 md
0.01 md
0.001 md
0.0001 md
0.01
0.001
0
10
20
30
40
50
60
70
80
90
100
Relative Permeability Modeling
• Early workers (e.g., Burdine, 1953) modeled kr based on KozenyCarmen equation and capillary pressure curves and associated pore
size distribution where kr was expressed as a function of the fraction of
ppore space
p
occupied
p and the relative size occupied
p
• Example: Wyllie & Spangler (1958)
Sw
krw = [(Sw-Swc)/(1-Swc)]2
Tortuosity Term
Gates and Lietz (1950)
1
∫0
krg = [1-(Sw-Swc)/(1-Sgc-Swc)]2
dSw
Pc2
dSw
Pc2
∫0
1
∫S
w
1
∫0
Mean Hydraulic
Radius Term
Burdine (1953)
dSw
Pc2
dSw
Pc2
159 of 217
Corey (1954) Equation
• Corey (1954) making the approximation that 1/Pc2
= C(Sw-Swc)/(1-Swc), i.e., is linear with ΔSw over a
range of saturations, simplified the BurdineP
Purcell
ll ddrainage
i
ttype equations
ti
tto:
Sw-Swc
(1- 1-S
krg =
gc-Swc
Sw-S
Swc
1-Swc
(
krw =
Sw-Swc 2
2
) (1- ( 1-S ) )
wc
4
)
•Exponents often modified to adjust for different pore
size distribution
Key Features of Krg
Sw-Swc,g 1.7
Sw-Swc,g 2
11-Swc,g
gc-Swc,g
Swc decreases with decreasing ki
Swc
krg =
(1- 1-S
)( (
1
))
1-10 md
0.1-1 md
0.05-0.1 md
0.01-0.05 md
0.005-0.01 md
0.001-0.005 md
0.0001-0.001 md
1 md
d
0.1 md
0.01 md
0.001 md
0.0001 md
0.001
0
10
20
30
40
50
60
(where<0 then 0)
Scg = 0.15 - 0.05*log10kik
krg, at any given Sw
increases with
increasing ki
krg,Sw
0.1
0.01
Swc,g = 0.16 + 0.053*log10kik
70
80
90
100
Krg curve shapes are
approximately
identical for widely
different lithofacies
Sgc
Sgc increases with decreasing ki
160 of 217
Key Features of Gas Relative
Permeability in Low Permeability Rocks
Swc,g decreases with decreasing ki
Swc,g
1
krg, at any given Sw
increases with
increasing ki
krg,Sw
0.1
1-10 md
0.1-1 md
0.05-0.1 md
0.01-0.05 md
0.005-0.01 md
0.001-0.005 md
0.0001-0.001 md
1 md
d
0.1 md
0.01 md
0.001 md
0.0001 md
0.01
0.001
0
10
20
30
40
50
60
70
80
90
100
Krg curve shapes are
approximately
identical for widely
different lithofacies
Sgc
Sgc increases with decreasing ki
Why is Sgc Important?
1
P = 1.7
Sgc = f (kik)
0.1
0.01
P=f (kik)
Sgc = 10%
0.001
0.0001
0.00001
0
10
20
30
40
50
60
70
80
90
100
Water Saturation
161 of 217
Definitions
• Critical-gas saturation has been defined variously as
– minimum gas saturation at which the gas phase flows freely
(Firoozabadi et al., 1989)
– maximum gas saturation before any gas flow occurs (Moulo
and Longeron, 1989)
– gas saturation at which gas freely flows to the top of a
reservoir (Kortekaas and Poelgeest, 1989)
– gas saturation at which gas is produced at the outlet of a core
(Li and Yortsos, 1991)
– Li andd Yortsos
Y
(1993) appropriately
i l clarified
l ifi d a robust
b
definition as the gas saturation at which the gas forms a
system-spanning cluster (and consequently flows freely). This
definition is consistent with the critical percolation threshold
at which the gas is connected to all parts of the system and not
just flowing in a subset of the system.
Measured Sgc
• 0.006 < Sgc < 0.38
– Solution-gas laboratory-measured (Hunt and Berry, 1956; Handy, 1958; Moulu and
Longeron, 1989; Kortekaas and Poelgeest, 1989; Firoozabadi et al., 1989; and
Kamath and Boyer, 1993)
• 0.03 < Sgc < 0.11
– 0.0008 mD < kik < 0.031 mD, n =11, Chowdiah (1987)
•
Sgc=0.01
– k = 0.10 mD, Colton sandstone sample, Kamath and Boyer (1993)
• Sgc = 0.10
– solution gas drive, k = 0.10 mD, Colton sandstone sample, Kamath and Boyer
(1993)
• Sgc=0.02
– Torpedo sandstone, k = 413 mD, Closmann (1987)
• 0.045 < Sgc < 0.17
– Schowalter (1979) , n=10, 0.01 mD < k < 30.09 mD
162 of 217
Published Single-Saturation Gas
Relative Permeablity
G as Realtive Permeability
y
1.00000
0 10000
0.10000
0.01000
Thomas & Ward, 1972
Byrnes et al, 1979
Jones & Owens, 1980
Sampath & Keighin, 1981
Walls, 1981
Chowdiah, 1990
Morrow et al, 1991
Byrnes, 1992
Byrnes, 1997
Byrnes & Castle, 2000
0.00100
0.00010
0.00001
0
10
20
30
40
50
60
70
80
90 100
Measurement of Snwc (Sgc)
– Percolation threshold of Hg
detected by resistivity drop of
>200x105 to <5 ohm
– Able to determine Pc
equilibrium saturation after
non-equilibrium
q
breakthrough
g
– Determine pore throat size
difference between entry
threshold and percolation
threshold
ΔV
Hg in
Core
• Confined mercury intrusion
with electrical conductivity
• Advantages
oil
High P Vessel
Pnetconfining = 4,000 psi
163 of 217
Critical Non-wetting Phase Saturation
Critical Non-wetting
g Phase
Saturation
0.22
0.20
MICP-inflection
0.18
Electrical Resistance
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0 02
0.02
0.00
0.00001 0.0001
0.001
0.01
0.1
1
10
100
1000
• Electrical conductivity and Pc inflection indicate 0% < Snwc < 22%
• Higher Snwc in complex bedding lithofacies
Measurement of Snwc (Sgc)
N2 in
micropipette
gas bubble
Core
• Confined gas injection
• Advantages
– Sample water wet
– Expulsion
l i off first
fi gas bubble
b bbl is
i
highly sensitive
– Sgc from both Vgas and weight
change
• Disadvantages
– Potential saturation gradient
g
– Solution gas development at
high pressure
– Pore volume change with stress
and possible hysteresis
oil
High P Vessel
Pconfining = 4,000 psi
164 of 217
50
45
40
35
30
25
20
15
10
5
0
Sgc Histogram
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
00
0.0
04
0.0
08
0.12
0.16
20
0.2
0.2
24
0.2
28
0.3
32
0.3
36
0.4
40
0.4
44
0.4
48
Frequency
Critical Gas Saturation
• Sgcavg = 0.066+0.13 (2 stdev)
• Wide variance
Critical Gas Satu
uration
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
00
0.0001 0.001
0.01
0.1
1
10
100
• Sgc is low for high permeability samples and fraction of
population shows increasing Sgc with decreasing permeability
165 of 217
How does Sgc get so high?
• In cross-bedded sandstone
series intrusion requires
Pc=threshold of lowest k
facies
• Sgc = f(Pc1&Pc2, V1/V2,
Sgc1&Sgc2, Pc equilibrium,
architecture)
1
Gas-Water Capillary P
Pressure (psi)
140
0.1 md
0.01 md
0.001 md
120
100
1
80
60
40
2
20
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
2
Sgc=5%
1
1
2
Sgc=5%
Sgc=75%
Sgc=75%
Sgc vs
bedding
Corey and Rathjens
(1956)
166 of 217
Invasion direction
Sgc and Percolation
• Sgc (L) = A LD−E
(Wilkinson and Willemsen, 1983)
1) Percolation Network (Np) - Macroscopically
homogeneous, random distribution of bond
sizes, e.g., Simple Cubic Network (z=6)
– L is network dimension
– A is a numerical constant (for
simple cubic network A = 0.65)
– D is the mass fractal dimension
of the percolation cluster
– E is the Euclidean dimension
3) Series network (N ) - preferential samplespanning orientation of pore sizes or beds of
different Np networks perpendicular to the
invasion direction.
• As L → ∞ Sgc → 0
– Sgc = 21.5% for L = 10
– Sgc = 2.4% for L = 1000
– Sgc = 0.8% for L = 10000)
Gas-Water Capillary Pressurre (kPa)
1000
2) Parallel Network (NII) preferential
orientation of ppore sizes or beds of different
Np networks parallel to the invasion
direction.
4) Discontinuous series network (N d) ppreferential non-sample-spanning
p p
g orientation
of pore sizes or beds of different Np networks
perpendicular to the invasion direction.
Represents continuum between N and Np.
• Experimental results can be
explained using four - pore
network architecture models
0.001 md
900
0.1 md
800
700
600
A
B
500
400
300
200
100
0
0.0 0.1 0.2
0.3 0.4 0.5 0.6 0.7
0.8 0.9 1.0
Water Saturation
Sgc and
percolation theory
Invasion direction
1) Percolation Network (Np) - Macroscopically
homogeneous, random distribution of bond
sizes, e.g., Simple Cubic Network (z=6)
3) Series network (N ) - preferential samplespanning orientation of pore sizes or beds of
different Np networks perpendicular to the
invasion direction.
• critical gas saturation
strongly controlled by
sedimentary structures/rock
f bi
fabric
• any bedding parallel
laminations result in low
Sgc
2) Parallel Network (NII) preferential
orientation of pore sizes or beds of different
Np networks parallel to the invasion
direction.
4) Discontinuous series network (N d) preferential non-sample-spanning orientation
of pore sizes or beds of different Np networks
perpendicular to the invasion direction.
Represents continuum between N and Np.
• experimental results can be
explained using four - pore
network architecture models
Gas-Water Capillary Press
sure (kPa)
1000
0.001 md
900
0.1 md
800
700
600
500
A
B
400
300
200
100
0
0.0 0.1 0.2
0.3 0.4 0.5 0.6 0.7
0.8 0.9 1.0
Water Saturation
167 of 217
Prediction of Sgc
•
Four pore network architecture models:
–
–
–
–
•
•
•
•
percolation (Np)
parallel (N//)
series (N⊥)
discontinuous series (N⊥d)
Analysis suggests that Sgc is scale- and bedding-architecture dependent in
cores and in the field.
Sgc is likely to be very low in cores with laminae and laminated reservoirs
(N//)) and low (e.g., Sgc < 0.03-0.07 at core scale and Sgc < 0.02 at reservoir
scale) in massive-bedded sandstones of any permeability (Np)
In cross-bedded lithologies exhibiting series network properties (N⊥), Sgc
approaches a constant reflecting the capillary pressure property differences and
relative
l ti pore volumes
l
among th
the bbeds
d iin series.
i For
F th
these networks
t
k Sgc can
range widely but can reach high values (e.g., Sgc < 0.6)
Discontinuous series networks, representing lithologies exhibiting series
network properties but for which the restrictive beds are not sample-spanning
(N⊥d), exhibit Sgc intermediate between Np and N⊥ networks.
CMG IMEX
Single 1-ft thick HighPermeability Layered
Reservoir Simulation Model
•
•
•
•
1ft – 0.01, 0.1, 1, 10, 100 md
keg=0.004,0.04,0.4,4,40 md
Swc= 0.34, krg = 0.38
kbase= 0.004 md, kvert = 0.0004md
168 of 217
Base Model – keg=0.004 md
Cumulative Gas (scf)
1.E+09
1.E+08
1.E+07
1.E+06
J-01
J-02
J-03
J-04
Time (m-yr)
J-05
J-06
khigh = 4 md, kbase = 0.004 md
Cumulative Gas (scf)
1.E+10
1.E+09
1.E+08
1.E+07
J-01
J-02
J-03
J-04
Time (m-yr)
J-05
J-06
169 of 217
Effect of highk thin-bed on
recovery
relative to
recovery
without bed
Influence of Vertical Permeability
170 of 217
Bioturbation
Lenticular bedded
isolated lenses
Lenticular bedded
thick connected lenses
Wavy bedded
Shaly Sandstone
core
• Core through
g non-bioturbated interval would indicate ggood k in lenses
• Series flow indicates long-range permeability would be reduced to
permeability of shale k < 1μd
• Bioturbation decreases k of lenses by 5-10X but preserves average k
• Beneficial effect of bioturbation decreases with increasing sand:shale
ratio but amount of k decrease also decreases
Plug
Permeability Scales
DST-Well Test
Wireline- log
Establish role of
Heterogeneities
& Fractures
Lease-Reservoir
Establish role of
Heterogeneities
& Fractures
F t
FullDiameter
Core
171 of 217
Conclusions
• Drainage capillary pressure (Pc) can be modeled using
equations for threshold entry pressure (Pte) and Brooks-Corey λ
slopes.
• Capillary pressure (Pc) exhibits a log-log threshold entry
pressure (Pte)
(Pt ) versus kik/φi trend
t d andd variable
i bl Brooks-Corey
B k C
slopes.
• Snwr ↑ with Snwi ↑ Land-type relation: 1/Snwr-1/Snwi = 0.55
• Capillary pressure (Pc) is stress sensitive as expected
– threshold entry pressure is predictable from √K/ φ at any
confining pressure
g ppores consistent with
• Confiningg ppressure decreases largest
permeability decrease but has little influence on smaller pores
(pores largely protected by matrix)
• Residual gas saturation increases with increasing initial gas
saturation
– Land
Land--type relation: (1/Snwr
(1/Snwr))-(1/
(1/Snwi
Snwi)) = 0.55
Conclusions
• Multi-salinity measurements of Archie cementation exponent, m, have
been completed on 408 samples at various salinities for each sample
– 20,000 ppm NaCl, 40,000 ppm, 80,000 ppm, and 200,000 ppm
– Three times the number proposed
• Nearly all core exhibit some dependence of conductivity and
cementation exponent on salinity
• The salinity dependence of m is weakly negatively correlated with
porosity
• Using equations developed the Archie cementation exponent can be
predicted for any given porosity and formation brine salinity
• Archie cementation exponent (m) decreases with decreasing porosity
below approximately 6%
– Can
C be
b modeledd l d empirical
i i l or by
b a duald l porosity
it model
d l
172 of 217
Conclusions
• Analysis suggests that Sgc is scale- and bedding-architecture dependent in
cores and in the field.
• Sgc is likely to be very low in cores with laminae and laminated reservoirs
( //)) andd low
(N
l ((e.g., Sgc < 0.03-0.07
0 03 0 0 at core scale
l andd Sgc < 0.02
0 02 at reservoir
i
scale) in massive-bedded sandstones of any permeability (Np)
• In cross-bedded lithologies exhibiting series network properties (N⊥), Sgc
approaches a constant reflecting the capillary pressure property differences
and relative pore volumes among the beds in series. For these networks Sgc
can range widely but can reach high values (e.g., Sgc < 0.6)
• Discontinuous series networks, representing lithologies exhibiting series
network
t
k properties
ti but
b t for
f which
hi h th
the restrictive
t i ti beds
b d are nott samplel
spanning (N⊥d), exhibit Sgc intermediate between Np and N⊥ networks.
173 of 217
Krygowski: Log Responses in Tight Shaly Gas Sands
Properties
P
ti off Mesaverde
M
d Ti
Tight
Tightht-Gas
G
Log Responses in Tight Shaly Gas Sands
Dan Krygowski
1
Denver, Colorado
The geologic environment
¾
Complicated lithology/mineralogy
z
z
z
¾
Quartz
Mixture of clays
clays, maybe diagenetic products
(Vcl/Vsh)
Low porosity, <15%
(Phi)
Fluids
z
z
z
¾
Quantities
of interest
Gas (water saturation, Sw < 1)
Relativelyy fresh waters
High irreducible water saturation
Permeability
z
(Sw)
((Rw))
(Swirr)
(k)
Low, and of interest
2
174 of 217
A Mesaverde
example
2.65
ExxonMobil
Willow Ridge T63X-2G
Rio Blanco county, CO
Piceance Basin
3
Environmental effects on the logs
¾
Complicated lithology/mineralogy
z
Presence of clay
• Ga
Gamma
a ray,
ay, SP:
S decreased
dec eased response
espo se as co
compared
pa ed to
nearby shales.
z GR may also be affected by radioactive KK-feldspar.
• Porosity measurements
z Density porosity: slightly lower
z Neutron porosity: higher
z Sonic porosity: higher
• Resistivity: lower, from additional clay conductivity.
z May make water saturation calculations higher
than actual saturations.
4
175 of 217
Environmental effects II
¾
Fluids
z
Gas
•
•
•
•
z
Gamma ray: no change. SP: decreased response
Density porosity: slightly higher
Neutron porosity: lower
Sonic porosity: variable
Relatively fresh water
• Clay conductivity will be a larger percentage of the total
conductivity than in a salt water case.
• Resistivityy decreased from equivalent
q
clean case;
z Shaly sand version of Archie needed?
z
High irreducible water
• WaterWater-free production even with elevated water
saturations.
5
Environmental effects III
¾
Permeability
z
Low, but of interest
• Logs,even
ogs,e e NMR logs,
ogs, do
don’tt measure
easu e pe
permeability,
eab ty, but
we can infer permeability from log response.
• Many equations; functions of porosity and irreducible
water saturation.
⎛ Phi 6 ⎞
⎟
z An example: Timur:
KT = 62500 ∗ ⎜
⎜ Sw 2 ⎟
irr ⎠
⎝
• We can get Swirr from BVWirr, irreducible bulk volume
water: BVW = Phi
Phi*Sw
Sw, and BVWirr = Phi*
Phi Swirr
z
and BVW can give us some indication of fluids
that will be produced (water vs no water).
6
176 of 217
Quantities, parameters of interest
¾
Clay/shale volume
z
Density/neutron: problematic because of gas
effects on the neutron.
z
SP: hydrocarbon
effects will make
Vsh too high.
Gamma ray:
probably
p
y the best.
Use linear unless
other data indicates
otherwise.
Shale volume, Vsh
• In general, neutron porosity has issues in the Rockies.
z
Vsh may be needed for the
following quantities...
BakerAtlas, 1984
Radioactivity Index, IRA
Gamma Ray Index, IGR
7
More quantities of interest
¾
Porosity, Phi
z
Need matrix and fluid parameters
• Variable
a ab e matrix
at pa
parameters
a ete s are
a e not
ot uncommon.
u co
o
PHID =
RHOma − RHOB
RHOma − RHOfl
PHIS =
z
DT − DTma
2 DT − DTma
or = *
DTfl − DTma
3
DT
May need shale/clay parameters: Vsh, shale
values for specific measurements: density,
neutron,
t
…
• Effective porosity from total porosity, Vsh, and shale
response.
PHIDeff = PHID − Vsh ∗ PHIDSH
8
177 of 217
Porosity in a gas zone
¾
Single porosity measurement
z
Can the matrix and fluid parameters in the
volume of investigation
g
be sufficiently
y estimated
to produce a reasonable porosity?
• Most porosity measurements are in the flushed zone.
¾
Porosity measurement combinations:
density and neutron
z
If the neutron is good, this is actually a good
estimate
ti t off hydrocarbonhydrocarbon
h d
b -corrected
t d crossplot
l t
porosity.
1
⎛ PHIDe 2 + PHINe 2 ⎞ 2
⎟
PHIE = ⎜
⎜
⎟
2
⎝
⎠
9
More quantities, for saturation
¾Water
z
saturation, Sw
Water resistivity, Rw
• Produced waters yield Rw values that are much too
fresh (water of condensation in the gas).
• NOT SP!
Rwa vs GR
• Pickett plot or Rwa,
150
apparent water resistivity GRshale
Rwb
125
Archie parameters, a,
m (variable), n
• Local knowledge; Pickett
plot
z
Which form of Archie’s
equation?
• Vsh & Rsh; or Rwf &
Rwb
100
GR
z
75
50
data
25
GRclean
0
0.1
Rw, Rwf
1
10
100
Rwa
If Rwf = Rwb, use Archie.
10
178 of 217
Rwa in the Mesaverde
Rwb
Rw, Rwf
11
Another saturation parameter method
¾“Super
BVWirr can
also be
estimated
from a log
plot.
Slope = f(saturation exponent,n)
Pickett plot
Rw
increasing BVW BVWirr
1
Porosity
z
Getting a number of parameters.
decrreasing Sw
z
Pickett” plot
data
0.1
Slope = -1/cementation exponent, m
Sw = 1
0.01
1
10
100
1000
Resistivity
12
179 of 217
Pickett with Mesaverde data
From slope,
saturation exponent, n = 2.0
Rw = 0.064
Sw = 1
BVW = 0.1
06
0.6
04
0.4
02
0.2
0.04
0.05
BVWirr
= 0.026
From slope,
cementation exponent, m = 1.85
13
Which saturation equation to use?
¾
The most commonly used in the Rockies:
z
Archie
1
⎞2
⎛ a ∗ Rw
Sw = ⎜
⎟
⎝ Phi m ∗ Rt ⎠
z
In conductivity space
(Ct = 1000/Rt):
Ct = a ∗ Sw n ∗ Phi m ∗ Cw
Dual Water
Sw = [a number of versions are published…]
⎡⎛ Swb ⎞
⎤
Swb
Ct = Sw n ∗ Phi m ∗ ⎢⎜1 −
∗ Cwb ⎥
⎟ ∗ Cwf +
Sw
Sw
⎠
⎣⎝
⎦
14
180 of 217
Mesaverde
data again
What about permeability?
¾
Timur (and other equations) requires Swirr.
• Swirr is a proxy for surface area.
z
We can get Swirr from BVWirr:
Swirr = BVWirr / PHI
z
But the permeability numbers are suspect (at
best).
• Core data is needed to calibrate the permeability
calculation, calibration being done by modifying the
porosity and saturation exponents.
z
NMR logs can provide permeability
• They measure both Phi and BVWirr.
• But they still need calibration to core for quantitative
values.
16
181 of 217
…and bulk volume water, BVW…
¾
If Sw < 1, and BVW is a constant, the zone
has a good chance of producing waterwater-free.
z
z
But we can
can’tt determine the production volumes
volumes.
If BVW > 0.05, there’s a good chance that the
well will produce no fluids at all.
• Pore throats are blocked by water.
17
Mesaverde
with
permeability
and BVW
182 of 217
Conclusions
¾
The combination of gas, shaly formations,
and low porosity has adverse affects on all
the logging measurements.
z
z
¾
Some of the effects counteract each other; i.e.,
gas and clays on neutron porosity.
Generally, the difference between wet zones and
pay is more subtle.
So, what specifically have we learned about
the Mesaverde in the Rockies?
z
The story continues…
19
183 of 217
Whittaker: Standard Log Analysis
Properties of Mesaverde Tight
Tight--Gas
Standard Analysis
Stefani Whittaker
1
Denver, Colorado
OUTLINE
¾
DATA PREPARATION
z
z
z
z
z
z
Gather Data and Initial Clean up
Calc. In situ Core Data
Import corrected core data, rock type numbers,
and point count numbers
Shifting: Core data, point count data and rock
type data
Pick tops and zones
Setting up zone parameters
2
184 of 217
¾
CALCULATION:
z
z
z
z
z
z
Calculate Vsh
Total and Effective Porosities
Calculate Sw
Look at a Pickett Plot
Calculate SWI
Calculate perm
3
Gathering WellWell-Log Data
¾
Required Curves
¾
Depth
p Matching
g
¾
Merging Multiple Runs
¾
Tool Pick
Pick--up
¾
Neutron Matrix Conversion
¾
Normalization
4
185 of 217
Calculating In
In--situ Core Data
Klinkenberg Corrected
Porosity
CPHIinsitu = CPHI − 0.008
Permeability
log Kinsitu = 1.341(log kroutine ) − 0.6
*Note: Alan Byrnes equation from The Mountain Geologist; Volume 34; Number 1;
“Reservoir Characteristics of Low-Permeability Sandstones in the Rocky
Mountains”; pg. 42.
There is a mistype in the publication, the above equation is
the CORRECT equation.
5
Importing Data
1)
In Situ Core Data
●
●
2)
Rock Type Data
•
•
3)
Conventional Core Data
KGS analyzed Core Data (Appended _KGS)
Core description 5 digit rock type code
5 digit code can be compared to GR
Point Count Data
•
•
Thin Section Point Count Data
The total radiation term (VRAD_TS) can
be compared to the Vsh curve in the logs.
6
186 of 217
VANHCMT_TS
VCCMT_TS
VCO3CMT_TS
VKSP_TS
Volume of anhydrite in thin section
Volume of clay cement in thin section
Volume of carbonate cement in thin section
Volume of Potassium Feldspar in thin section
VKVRF_TS
Volume of Potassium rich volcanic rock fragments in thin section
VOSRF_TS
Volume of of other sedimenary rock fragments in thin section
VOVRF_TS
Volume of other volcanic rock fragments in thin section
VPLAG_TS
Volume of Plagioclase Feldspars in thin section
VQTZ_TS
VQTZ TS
VQTZCMT_TS
VRAD_TS
VSSRF_TS
VVISPOR_TS
Volume of quartz in thin section
Volume of quartz cement in thin section
Volume of Radioactive Elements in thin section
(VRAD_TS = VKSP_TS + VKVRF_TS + VSSRF_TS + VCCMT_TS + VOVRF_TS)
Volume of Shaley sedimentary rock fragments in thin section
Volume of Visible Porosity in thin section
Depth Shifting Core Data
¾
Rock Type Number was compared to the GR.
¾
Data Shifted together:
•
•
•
•
Conventional Core Data
KGS analyzed Core Data
Point Count Data
Rock Type Data
8
187 of 217
Picking Tops and Zones
1
1.
PI Dwights scout tickets for formation tops
tops.
2.
Zones were chosen based on changes in
petrophysical properties to “tighten the
log/core correlation
•
•
•
GR
Porosity
Induction
9
Standard Discovery Group
Shaly Sand Process
1.
2
2.
3.
4.
5.
6.
Set up Parameters
Calculate Vshale
Calculate Porosity (Total, Effective, Cross
Cross--Plot)
Calculate Water Saturation
Calculate Bulk Volume Water and
Bulk Volume Water Irreducible
and Calculate Irreducible Water Saturation
Calculate Permeability
10
188 of 217
Setting up zone Parameters
¾
Deep Resistivity
Rt = Rdeep
¾
Rho Matrix
From Header Data
¾
Neutron Matrix
From Header Data
¾
Vshale Model
Linear using GR
¾
Water Sat. Model
Archie’s (m=1.85, n=2, a=1)
¾
BVW Model
Effective Porosity
¾
Permeability Model
Timur Model
Parameters for Permeability were varied by zone:
•Permeability Porosity Exponent [KPHIEXP] (Ranged from 5.0 - 9.25)
•Permeability Irreducible Water Saturation Exponent [KSWIEXP] (Ranged from 1.5 - 2.0)
11
Calculate Vsh
¾
Used the GR with the Linear method to calculate Vsh.
V sh =
¾
GR log − GR clean
GR sh − GR clean
Rockyy Mountain Region
g
Suggestions:
gg
GR_CLEAN = 1010-15 API
GR_SHALE = 9090-100 API
(Will vary from well to well)
12
189 of 217
Total Porosity
¾
Total Porosity
z PHIN = Converted from LS units to
desired output lithology units.
z
PHID =
z
PHIS =
RHOMA − RHOB
RHOMA − RHOFL
(Wyllie Time
Average Equation)
Δt log − DTMA
DTF − DTMA
13
Cross-Plot Porosities
•Take RHOB and Neutron Φ and cross plot them to get a PHIDN
PROS:
-Corrects for grain density
-Eliminates most of the gas
effect
CONS:
-Requires a good NPHI log
190 of 217
Effective Porosity
PHINE = PHIN − (Vsh * PHINSH )
PHIDE = PHID − (Vsh * PHIDSH )
PHISE = PHIS − (Vsh * PHISSH )
PHIDNE = PHIDN − (Vsh * PHIDNSH )
(Diminish the effect of Shale)
15
Total Φ
Diminishes Shale Volume
Diminishes
1. Grain Density Differences
2. Gas Effect
3. Shale Volume
191 of 217
Calculate Sw
Archie’s Water Saturation equation
z
z
z
z
a=1; n=2; m=1.85 (Rocky Mountain Suggestion)
Rw = Zoned (Pickett Plot or Rwa plot)
Used Neutron/Density crossplot Effective Porosity
Rt = Deep Resistivity
Sw = n
aRw
φ m Rt
17
BVW, BVWI and SWI
Two ways to find BVW, BVWI, and SWI
1) Calculate and visual estimation
2) Graphically using Pickett Plot
Calculate:
BVWT = PHIX * S w
BVWe = PHIE * S w
Then look at a consistently flat part on the BVW and
visually pick the BVWI
SWI = BVWI / PHI
18
192 of 217
100% Water Sat. when a=1
Pickett Plot
Iso BVW lines
BVWI
193 of 217
Calculate Permeability
¾
Used the Timur Model for permeability
K coef = 62500
K KPHIEXP ~ 5.0 − 9.25
(Determined by zone)
K KSWIEXP ~ 1.5 − 2.0
(Determined by zone)
K log = K coef
PHIX KPHIEXP
SWI KSWIEXP
21
Piceance Basin
Error introduced =
Vshale
Φ, m&n
Φ, SWI
Kexp.
Left to right more error introduced
194 of 217
Green River Basin
Washakie Basin
195 of 217
Uinta Basin
Wind River Basin
196 of 217
Cluff: Advanced Log Models
Properties of Mesaverde Tight
Tight--Gas
Advanced Log Analysis
Bob Cluff
The Discovery Group Inc.
Inc
2009 AAPG Annual Convention Short course #1
1
Denver, Colorado
Outline
rock typing
¾ variable m model for Sw
¾
z
¾
as an alternative to obtuse shaly sand models
permeability modeling
2
197 of 217
Advanced rock typing
¾
most rock typing methods follow some form of φ-K
separation or BVW separation
z
z
z
¾
Winland R35 isoiso-lines
K/
K/φ
φ ratios
BVW classes
or, some kind of statistical relationship with logs is
sought
z
z
z
single variate comparsions (e.g. GR vs grain size)
multivariate comparisons, cluster analysis, etc.
neural networks (a fancy form of multivariate nonnon-linear
regression)
3
Winland equation
¾
¾
¾
¾
Developed by Amoco in 1970’s
Empirically derived eqn from a large Pc dataset,
Weyburn field in Canada
Eqn published by Kolodzie, 1980 (SPE 9382)
Rock types defined by “equi“equi-pore throat size”
classes, or “port” sizes, as determined from Pc at
35% Snw
z
z
z
z
¾
macroports = 22-10 μm
mesoports
p
= 0.5 – 2 μm
microports = 0.1 – 0.5 μm
nanoports < 0.1 μm
implicit is pore throat sizes control hydrocarbon
entry and relate to pay quality
4
198 of 217
Winland R35 “port” size classes
log R35 = 0.732 + 0.588 log Kair – 0.864 log φ (%)
in-situ Klin
nkenberg gas permeability (MD
D)
1000
R35
“macroports”
100
2
10
0.5
“microports”
1
0.1
0.1
“nanoport”
0.01
0.02
0.001
0.0001
Note: essentially all Kmv TGS
fall into the nanoport rock type
0.00001
0.000001
0.0
5.0
10.0
15.0
20.0
25.0
in-situ porosity (%)
5
K/
K/φ
φ ratio isoiso-lines
K/phi ratio = Ka (mD) / φ (v/v)
in-situ Klinkenberg gas permeability ((MD)
1000
K/phi
100
50
10
5
1
0.5
0.1
0.01
0.05
0.005
0.001
0.0001
Note: most smpls are at K/f < 0.5
and would fall into 3 or 4 classes,
but without natural breaks
0.00001
0.000001
0.0
5.0
10.0
15.0
20.0
25.0
in-situ porosity (%)
6
199 of 217
K/phi methods
¾
you can compute K/phi ratio from ambient or in
in--situ
core data, or from log K and phi
z
z
¾
compute Winland R35 from standard eqn or cook
your own eqn from our dataset!
z
z
¾
divide it into classes that make sense for your area
no natural divisions in the overall database
we have NOT done this for you
LOTS of ways to slice and dice this large a database
basic Winland classes have limited utility in very
tight rocks like these, almost everything falls into
the “nanoport” size range
7
Rock types from logs
we have digital rock types from core
description depth shifted to log data
¾ seems like we should be able to pull rock
types out of the log data by xx-plots or
statistical analysis
¾ Well, maybe its not so easy.........
¾
8
200 of 217
Digital core database @ 0.5 ft resolution
GR log plot vs rock #
¾
GR to rock # correlation is outstanding!
201 of 217
GR vs Rock number
but over the entire database, the
rock type classes broadly overlap
Why is that?
¾
GR logs are not normalized
z
z
z
it looks good on a single well basis, but gets
smeared out over multiple
p cores/wells
uncorrected environmental effects
all vendors GR tools are not alike
the 13000 rock class will always be a
problem, by nature of the definition they
span
p a broad range
g of Vsh
¾ only the higher rock classes (1st 2 or 3
digits) are likely to fall out in the best of
cases
¾
12
202 of 217
ILD vs. GR xplot colored by major rock #
11000 to 12999’s separate
cleanly from 15000’s, but
the 13000’s overlap all
NPHI--RHOB by major rock #
NPHI
again the 15000’s split
cleanly from 12000’s,
while 13000’s overlap
the entire field
203 of 217
DT - RHOB colored by major rock #
nothing separates on this,
because DT and RHOB
are too similar in their
lithology response
Rock typing summary
there is a lot of data here, we didn’t push the
boundaries of what could be done by any
means
¾ BUT, from our analysis, the results do not
look promising
¾ very, very difficult to pull out subtle rock type
signatures from a limited suite of open hole
measurements if the base lithology does not
change much
¾ only grain size comes out cleanly, but with a
broad overlap between classes
¾
16
204 of 217
Saturation model
basic model assumes Archie with TGS
average m, n values
¾ Shaly sand models (e
(e.g.
g Dual Water) all
yield similar results because fm. waters are
saline and shales are not highly conductive
¾ core data suggests m varies as a function of
both porosity and average salinity
¾
17
When F and φ are plotted loglog-log
1000
m= 2
m= 3
100
m= 1
F
10
1
0.01
0.1
φ
1
log F = -m log φ
18
205 of 217
tested plugs with 20K, 40K, 80K, and 200K ppm brines
Nearly all cores exhibit some salinity dependence
¾
¾
1.0
In situ Arc
chie Cementation Exponent,
(m, A=1)
2.3
0.9
Core
e Conductivity (mho/m)
n=335
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
2
4
6
8
10
12
14
16
18
20
22
22
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0.01
Brine Conductivity (mho/m)
0.1
1
Brine Resistivity (ohm-m)
19
All data, all salinities
Archie C
Cementaiton Exponent (m
m, a=1)
2.40
2.20
2.00
1.80
1.60
1.40
1.20
200K
80K
1.00
40K
20K
0.80
0
2
4
6
8
10 12 14 16 18 20 22
In situ Porosity (% )
20
206 of 217
20K ppm
2.50
¾
y = 0.2267Ln(x) + 2.2979
2
R = 0.6619
Axis Title
2.00
¾
1.50
Series1
Log. (Series1)
1.00
40K ppm
0.50
0.00
0.000
3.00 0.100
0.050
0.150
0.200
¾
m = a log φ + b
intercept b drops with
decreasing salinity
slope is ~ constant
0.250
insitu porosity (%)
y = 0.2328Ln(x) + 2.409
2
R = 0.6547
2.50
Axis Title
2.00
Series1
1.50
Log. (Series1)
1.00
80K ppm
200K ppm
0.50
3.00
0.00
0.000
3.00
y = 0.2149Ln(x) + 2.4354
0.050
0.100
0.150
2.50
0.200
y = 0.1621Ln(x) + 2.3222
y 0.1621Ln(x) + 2.3222
2
R = 0.5132
0.250
2
R = 0.3633
2.50
insitu porosity (%)
2.00
Series1
1.50
Log. (Series1)
Axis Title
Axis Title
2.00
Log. (Series1)
1.00
0.50
0.50
0.00
0.000
0.050
0.100
0.150
insitu porosity (%)
0.200
0.250
Series1
1.50
1.00
0.00
0.000
0.050
0.100
0.150
0.200
0.250
insitu porosity (%)
21
Simple procedure to compute Sw
¾
determine Rw @ Tf conventionally
z
z
z
¾
Pickett plots – focus on the lower porosity, wetter
sandstones
produced waters
your best guess.......
convert Rw to 75
75°°F by chart lookup or Arps
equation
22
207 of 217
Pickett Plot example
Rw = 0.306
pick m at low porosity
end, where BVWirr ~ BVW
Williams PA 424424-34
Piceance basin
Kmv above “top gas”
Pickett plot Rw 0.306 ohmm @ 160
160°°F = 0.7 @ 75°
75°F (9K ppm)
208 of 217
Our new procedure
¾
compute m at 40K ppm from RMA regression:
m40k = 0.676 log φ + 1.22
e.g. for 10% φ : m = 0.676 + 1.22 = 1.896
¾
correct m for salinit
salinity effect b
by
m = m40k + ((0.0118 φ – 0.355) * (log Rw + 0.758))
¾
e.g. for 10% φ, Rw = 0.7 @ 75°
75°F
m = 1.896 + ((0.0118 * 10 – 0.355) * (log 0.7 + 0.758))
m = 1.896 + ((--0.237 * 0.603) = 1.753
¾
¾
cap m at 1.95 (~12% porosity)
this corrects for variation in both porosity and fm
salinity space
25
Practical impact
Nominally, most of us use an m close to 2,
but usually slightly less, for tight gas sand
evaluations (e.g.
(e.g. 1.85, 1.90)
¾ Variable m that DECREASES with
decreasing porosity leads to lower Sw’s
¾ Therefore, there is more gas in the tight
rocks than we thought.
¾ Above 10% porosity there is very little
difference
¾
26
209 of 217
Example: Low porosity, wet zone
Moderate porosity, wet
210 of 217
“High” porosity gas zone
m is HIGHER than base case, so Sw is higher!
20Kppm example, Natural Buttes
improvement in HCPV in shoulders
211 of 217
30K ppm example, Wamsutter
no change
Sw summary
335 Kmv samples run at multiple salinities
¾ Archie porosity exponent m varies with
¾
z
z
¾
porosity
salinity
m ↓ as porosity ↓
m ↓ as salinity ↓
behavior is consistent with increasing
electrical efficiency with decreasing porosity,
whatever the pore scale architecture
z
z
very likely that the surface conductivity is highly
connected with low effective m
pore--pore throat conductivity is Archie with m
pore
close to 2
32
212 of 217
Capillary tube model for m
m
1.0
>1
~2
m=1
>2
Herrick & Kennedy,
1993, SPWLA Paper HH
33
E0 vs porosity, 40K ppm data
TableCurve 2D v5.01
213 of 217
¾
¾
¾
¾
variable m Archie model can be implemented with a
simple equation relating m to porosity and formation
water salinity
m is constant above ~12%
12% porosity at 1
1.95
95
lowering m at 5
5--12% φ increases GIP
see no impact below ~5% porosity
z
z
z
¾
BVWirr is typically 3
3--5%
no longer calculate Sw’s >> 1
Sw = 1 at low φ validates Rw
much simpler than Dual Water or WW-S formulations
for TGS, easier to implement, and it gets you the
same answer
35
Permeability
permeability has historically been a problem
to estimate from log data
¾ dynamic property that we are trying to
correlate with static properties
¾
z
¾
problem is there are no 1:1 functional
relationships between any of the static
properties, like porosity, and permeability.
so, we fudge....
g
36
214 of 217
Permeability from logs
¾
Porosity--permeability cross
Porosity
cross--plots
z
z
z
z
regression equations developed for each basin
and p
presented p
previously
y
with an accurate log porosity, you can predict K
within a SE of about 4X to 5X
if you add information such as grain size or rock
type, you can do even better
only a fraction of what is possible to do has been
done
done, but basic eqn’s
eqn s by basin are presented in
the project data store
37
Klinkenb
berg Permeability (4,000 ps
si, mD)
1000
100
10
1
0.1
Green River
Piceance
Powder River
Uintah
Washakie
Wind River
logK=0.3Phi-3.7
logK=0.3Phi-5.7
0.01
0.001
0.0001
0 00001
0.00001
0.000001
0.0000001
0
2
4
6
8
10
12
14
16
18
20
22
24
38
215 of 217
Kozeny & TimurTimur-type eqn’s
¾
Kozeny equation
K = A * φ3 / S2,
where S = surface area/bulk volume
¾
Timur eqn (and its derivatives) are of this general
form, but use Swi as a proxy for the internal surface
area term
K = 0.136 * φ4.4 / Swi2
K = 62,500 * φ6 / Swi2
K = A * φB / SwiC
¾
¾
(original Timur eqn)
(Schlumberger eqn)
(general form)
We treat A, B, C as local variables and fit p
parameters by
y trial
and error or using a multivariate solver (e.g. Excel Solver)
note: NMR eqn’s (e.g. Coates & SDR or T2GM) are basically
the general Timur eqn, but use Swi and φ from NMR instead
of indirect estimates
39
216 of 217
41
Thank you!
¾
Q&A period (if
(if time available)
available)
Visit our project website portals:
or
http://www.discovery--group.com/projects_doe.htm
http://www.discovery
42
217 of 217

Lithofacies and Petrophysical Properties of Mesaverde Tight

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