Lateral and Vertical Discrimination of Thin

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SPE 69485
Lateral and Vertical Discrimination of Thin-Bed Fluvial Reservoirs: Geostatistical
Inversion of a 3D Seismic Data Set
Marcos Victoria, German Merletti, REPSOL-YPF, Alvaro Grijalba Cuenca,SPE, Carlos Torres Verdin,SPE, University of
Texas at Austin
Copyright 2001, Society of Petroleum Engineers Inc.
This paper was prepared for presentation at the SPE Latin American and Caribbean Petroleum
Engineering Conference held in Buenos Aires, Argentina, 25–28 March 2001.
This paper was selected for presentation by an SPE Program Committee following review of
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presented, have not been reviewed by the Society of Petroleum Engineers and are subject to
correction by the author(s). The material, as presented, does not necessarily reflect any
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Abstract
The San Jorge Basin is one of the most prolific hydrocarbon
bearing zones in Argentina.The Cañadon Seco Formation is
characterized by sandstones with thickness usually bellow the
tuning lenght, under these conditions high uncertainty exists in
sandstone prediction when seismic amplitudes are analyzed,
due to interference and tuning effects. This paper presents an
estimation procedure that overcomes these limitations based
on the extrapolation of the well data further away from its
location by Geostatistical Inversion of 3D seismic data.
Although vertical sampling of the seismic data is much less
dense than the one from logging , its higher lateral resolution
is used to complement the high vertical resolution of the well
data. Unlike conventional trace based inversion in which the
source is the seismic data in Geostatistical Inversion the data
source is the well, and the estimated acoustic impedance
values satisfy the seismic data , in this way driving resolution
to an intermediate range between the well and seismic data.
With this procedure stochastic simulations of the petrophysical
variables are generated, (density and lithology) that not only
honour the hard data of the wells but also the seismic data,
and minimize the residual error between the Synthetic model
and the real 3D-Seismic trace. Each simulation (SGSSimulated Annealing and SIS) is itself a possible solution to
the problem and it is called a realization, wich is then
integrated into an average to optimize the certainty of the
predictions. The Acoustic Impedance, density and lithology
models derived from GI have a resolution of 1ms. This
allowed discriminations of lateral variations in the
petrophysics of the reservoir (density porosity) and the
delineation of sand packets of up to 6 meters thick. The
Geostatistical Inversion turned out to be a very powerful tool
for the static reservoir modelling wich can function itself as an
input to the dynamic model (reservoir simulation), guide the
development of the block and assists to the EOR.
Introduction
The Golfo San Jorge Basin is located at the southernmost
region of Argentina in the heart of Patagonia, its long history
of oil production began with the first discovery back in 1907,
since then aproximately 160 million m3 of oil have been
recovered. The area of study is located in the south-eastern
flank of the basin and involves the east section of Cañadon
León oil field, Fig.1
The development of the block follows the discovery of the
productive well named CLORx-1, the production of this well
reached levels that surpass the media of the field. The oil
bearing sandstones are part of the middle cretaceous Cañadón
Seco Formation, the reservoirs produce hydrocarbon generated
in lower cretaceous lacustrine rocks (D-129 Formation).
The oil bearing reservoirs are characterized by thin fluvial
sandstones interspersed with thick shale laminations of
lacustrine and flood-plain origin. The reservoirs are grouped
into two main Members: Caleta Olivia member and Cañadón
Seco member, both are separated by a predominantly thick
shaly cicle called Mb. Pozo O-12, (Biocca et al.). The lateral
continuity of the reservoirs seldom exceeds 2km, mainly the
range is between 1 km to 2 km, the net pay thickness varies
between 0.5m to 5m but in most of the cases is 1m to 3m.
The field is being developed with a 400m well spacing pattern,
due to this, much of the interwell heterogeneities just as the
porosity distribution of the reservoir is laterally under
sampled. The lateral heterogeneity of the sandstone bodies and
their scarse areal distribution make it necessary to backup the
development of the wells with data of higher lateral resolution.
In this way 3D Seismic data combined with well data are
integrated to find a model that allows reservoir
characterization, that is, a model that predicts and delineate the
distribution of heterogeneities and pay between wells.
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MARCOS VICTORIA, et al
The present study describes the use of Geostatistical Inversion
to optimize the reservoir characterization of the block, taking
advantage of the high vertical resolution from the log data and
the high lateral sampling given by 3D seismic data.
In this way Geostatistical Inversion analysis provides a
variety of models wich are consistent with well data and
honors the 3D seismic information. All models depicts
plausible solutions, and have a finer vertical sampling than the
standard 3D seismic analysis.
Volumes of total acoustic p-impedance, density (porosity) and
lithology are yielded by the simulation process, afterwards,
those different but possible solutions, are averaged into one
final volume (for each physical property) that best describes
the fine scale distribution of lithology and porosity and
improves the development of the block. Further studies will
include the results of Geostatistical Inversion in dynamic
reservoir simulations.
Input Data
The subsurface of Cañadon León prospect , was highlighted
by a 240km2 3D seismic volume (20km x 12km with a 25 m
bin size), the dominant frecuency is 35 Hz and considering the
velocity of the studied interval it yields a tuning thicknes of
18m, far above the resolution needed to discriminate the sand
bodies individually. Four key wells guided the Geostatistal
analysis Fig.1, c, all of them were edited in order to remove
the bad borehole effect due to washouts and invasion and tied
properly to the seismic, using a time-depth relation and
information from a VSP acquired in CLORx-1 well.
Computed petrophysical logs (such as effective porosity, shale
volume an water saturation) were available for many of them.
A structural framework was carefully interpreted prior to the
process of inversion and then refined using reflectivity data
derived from the process of trace based inversion, the key
horizons are shown Fig.2
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Full log resolution analysis shows that sands in the interval of
interest are low acoustic impedances, and that the embedding
shales are high acoustic impedances.
When the same log is transformed to the seismic bandwith
domain, by means of a high cut filter, the response of the
reservoirs changes and must be carefully analyzed, Fig. 4
Not only we can not assume that all reservoirs are highs, but
also a thickness-porosity vs acoustic impedance relation must
be considered. Thick porous sand packets ( 15m up) are
relative lows, the higher the porosity the lower the impedance,
but for equivalent stratigraphyc units, thick tight sands (low
porosity) are highs. Thin sands independently from porosity
are highs, mostly due to a problem of resolution and
interference caused by the embedding shales, Fig 5 A, B
An schematic like cartoon describing the behaviour of
P-impedance as a function of thickness and petrophysics for
sand packets, is shown in Fig. 6
All these conclusions lead us to interpretet this particular
acoustic impedance volume in a different way from previous
studies, and let us conclude that the relative position of the oil
field within the Golfo San Jorge Basin , plays an important
role when analyzing the seismic response of the reservoirs,
and should also be considered.
Constrained Sparse Spike Inversion
The transformation of the seismic trace into a pseudo acoustic
p-impedance log is called trace based inversion, in such
process the “wavelet effect” is removed from the seismic in
order to find the best reflectivity model, which is itself a
bandlimited (seimic frequency domain) aproximation to the
reflectivity of the subsurface. As we deal with bandlimited
data, (it lacks the low frequencies), the solution to the problem
is non-unique, it means, several combinations of acoustic
impedances can yield the same reflectivity model, which once
convolved with the seismic wavelet reproduces properly the
input seismic trace, Fig. 7
Description of the Problem
Only two seismic data set had been inverted in the basin
before performing this study, the two prospects were located
far enough from each other, and the analysis of both acoustic
impedance data set had yielded similar results, sand packets
were “seen” as intermediate to high values of acoustic
impedance, Fig. 3
With this assumption in hand we began to analize the new log
and seismic data set. One important step to do before
transforming the seismic data into acoustic impedances is to
know how is the acoustic response of the reservoirs, this
knowledge allows us to estimate if the inversion process will
succeed or not in predicting the vertical and lateral distribution
of sand packets in a priori basis.
In this way the agreement between the modeled seismic trace
(synthetic) and the real seismic trace is necessary but is not the
condition that narrows the solution space, therefore other
conditions must be taken into account.
As several mathematical solutions geologically feasible can
meet the criteria, it is necessary to impose some restrictions,
since we can know from key wells how is the lateral
variability of impedances, a track of allowed impedances can
be built to be used in the inversion process, thus rejecting all
the possible mathematical solutions with no geologic sense,
Fig. 8
Again, the result of the inversion lacks the compaction trend
because of the bandlimited character of the seismic wavelet,
but it is possible to build a geologic model by interpolating
SPE 69485
LATERAL AND VERTICAL DISCRIMINATION OF THIN-BED FLUVIAL RESERVOIRS: GEOSTATISTICAL
INVERSION OF A 3D SEISMIC DATA SET
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the acoustic impedance data from the wells and then high cut
filter it to 4Hz / 6Hz. The merging of both data yields a new
class generally called total or absolute acoustic impedance, in
wich every trace is a pseudo acoustic impedance log (this data
is no more interface dependent as it is the seismic, but
property lithology dependent), Fig. 9, 10
the local probability density function at random located grid
points. The unknowns are generated (Sequential Gaussian
Simulation) by multiple random draws, however, although
volumes encountered are consistent with histograms and
variograms we are not completly sure these sets of simulated
values satisfy the 3D seismic volume.
Interpretation work has been done in both volumes,
Bandlimited acoustic impedance and Total acoustic
impedance, in a back and forth quality control basis, since the
low frequency geologic model can be affected by the
interpolation process, this may lead us to misinterpret the data.
This problem is solved by applying a technique based on a
random-walk sthochastic simulation of acoustic impedances
with an acceptance-rejection criteria based on fit to the seismic
data, thus the outcome of the process is less dependent on
variogram than standard geostatistical techniques. The
volumes of acoustic impedances are broad band, and have
higher frequencies than input seismic Fig.12
The reflectivity data having a higher resolution than 3D
Seismic presents an optimum scenario to delimit top and base
of acoustic impedance events that best describe the vertical
and lateral sand distribution, in a standard interpretation basis,
Fig.11
More sophysticated 3D visualization techniques can be
foccussed directly to impedance data, in order to get 3D
bodies consistent with lithology and connectivity criteria.
In addition to inverting for acoustic impedance values, a
stochastic co-simulation process yielded independent
simulations for both density and lithology.
Results
Geostatistical Inversión of Acoustic Impedance
The model of lithology properties, which is acoustic
impedances, works well when it comes to characterize sand
packets response, but it fails when a finer heterogeneity
model is needed.
Geostatistical Inversion
Histograms and three dimensional variograms were
computed corresponding to both inputs, wireline data (in this
case p-impedance and bulk density) and p-impedance from a
priori trace based inversion, and were used to drive the
geostatistical simulations constrained by 3D seismic data,
Fig.13 and Fig.14.
Quick look to the methodology
Each one of the steps involved in the geostatistical inversion
process has been described carefully by several authors (see
for instance Haas and Dubrule (1994), Pendrel and van Riel
(1997), Torres Verdin et al., (1999), etc.), it is not the scope of
this paper make an strict description of the whole process, but
presents results showing the power of geostatistical inversion
in “resolving” sand bodies distributions not seen by the
conventional inversion process in the area of study.
Geostatistical modeling honors the data at the well location
(hard data) and simulates the values where they are unknown,
3D seismic guides the process in the sense that each simulated
model of acoustic impedance is a plausible geologic solution
and satisfies the 3D seismic data. A solid geologic model is
the framework in wich histograms and variograms are
estimated and respect the structure and the stratigraphy of the
model. Stationarity is assumed for each layer within the solid
model. In the vertical direction, variograms are estimated from
well data, whereas in the horizontal direction the estimation
comes from the inverted acoustic impedance model.
The knowledge of the 3D spatial continuity (vertical and
horizontal variograms) is crucial in finding property values in
locations in wich they are unknowns. Histograms, variograms
and neighbouring data values are used (Kriging) to estimate
Once the statistics were computed, and the spatial
continuity model was known, 10 full independant simulations
of acoustic impedance were done, the geostatistical inversions
were performed with a vertical resolution better than 2ms, in
this case 1ms, all of the geostatistical analysis supporting the
simulations were made consistent with this sampling intervals,
thus driving the vertical resolution to an intermediate point
between well data and 3D seismic data. This new model of pimpedance with higher lateral and vertical resolution is
considered to refine the horizontal model of lateral variability
(horizontal variograms), then, thirty geostatistical simulations
of p-impedance were done, each one of the these multiple
realizations was in agreement with the input seismic data.
Fig. 15 shows plan views of the correlation between the
measured and simulated seismic data sets for 3 independent
simulations , the correlation is acceptably high, we see that an
almost 99.8% agreement is reached for each one of them.
By applying statistics we can summarize the information in
our results, in the same cell we are able to generate for
instance the mean and standard deviation for the p-impedance
values for that cell, it is clear that the standard deviation
decrease to cero in the vicinity of key wells, it reminds us that
well data drives the simulation process. The accuracy of the
prediction decrease away from wells, in this particular case we
feel very confident up to 1 well-spacing.
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When comparing the previous acoustic impedance model
(derived from trace based inversion) with the mean of multiple
simulations derived from geostatistical inversion we can
clearly observe an improvement in the lateral and vertical
resolution of the latter, not only this allows us to vertically
discriminate sand bodies of up to 5-7m thick, but also lateraly
map thiner acoustic impedance events that corresponds to
sandstone, Fig. 16.
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a lithology model that perfectly satisfy the input 3D seismic
data and wireline data.
We have shown that Geostatistical Inversion by integrating all
the available data can be used to improve the imaging and
interpretability of sand packets in Mb. Caleta Olivia.
Also to discriminate its lateral and vertical distribution, as
well as to build a finer model of heterogeneity in the interwell
spacing, which finally can be used in reservoir flow simulators
to support the water flooding proyect of the block.
Geostatistical Inversión of Density and Lithology
Acknowledgments
Three lithology categories were recognized based on
statistics and cross-plots analysis in this project : shales, tight
sands and porous sands. Full statistics analysis were computed
for each particular lithology group separately, see Fig.17.
The relationship between density and acoustic impedance,
depicted in Fig.18, is lithology dependent, in this way, it is
possible to simulate a lithology type (using a lithology PDF),
then we can randomly draw a sample of density for that
particular lithotype which is finally used to draw a random
sample of acoustic impedance via the joint PDF that relates
density with acoustic p-impedance.
Again these simulated values of p-impedance once
convolved with the seismic wavelet must generate a synthetic
trace that satisfy the input 3D seismic. The stochastic
simulations results yields prediction of lithology type, acoustic
p-impedance and density (porosity), Fig. 19
Standard interpretation and 3D visualization techniques
were applied to the high-resolution cubes in order to laterally
map the distribution of lithology and porosity within the
CLORx-1 block.
Fig.20 shows an arbitrary line across the CLORx-1 well, 6
time dependent intervals were analyzed, the lithology volume
(this is the result of the count of the number of ocurrencies of
a given lithotype, referred as to lithology mode) presents an
optimum scenario to directly extract lithology attributes from
those windows such as Net sands and Gross sands. Extra
works must be done to refine the framework, in order to
generate a higher number of time windows that encompass
individual sand units.
The resulting volumes containing a higher lateral and
vertical variability and a finer sampling time interval (1ms)
will be converted to depth to be imported into a reservoir flow
simulator.
Conclusions
For sand packets corresponding to Caleta Olivia Mb. the
acoustic response can be a high or a low in the p-impedance
values depending on the petrophysics (porosity). By applying
Geostatistical Inversion we can reduce the uncertainty in the
prediction of a particular lithology group (sands), by building
We thank Division Regional Sur (REPSOL-YPF) for
permission to publish this paper and those people from the
Department of Petroleoum Engineering – University of Texas
at Austin who helped us in performing this study.
References
1. A.Grijalva Cuenca, C.Torres Verdin, H. Debeye “ Geostatistical
Inversión of 3D Seismic Data to Extrapolate Wire Line
Petrophysical Variables Laterally Hawai From the Well”.
SPE Annual Technical Conference, Dallas 2000.
2.R.Lattimer, S Bahret, C Sullivan, R. Horine, W Mills, V. Sturrock “
Reservoir characterization using Geostatistical inversion for the
Amberjack Field, offshore Gulf of Mexico”. SEG, Annual
meeting, technical program. Houston, 1999
3. J. Pendrel, P. van Riel, “Using Seismic Inversion and Geostatistics
to Estimate Porosity: A Western Canadian Reef Example”.
CSEG. 1997.
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Fig.1- A- Location of Golfo San Jorge Basin and Cañadon Leon prospect.
B- Structural map showing wells distribution and position of study area.
C- Close-up view of key wells that guided the Geostatistical Inversion of the block.
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Fig.2- Arbitrary line through some wells from the block, color density logs shows effective porosity, wigle
Type logs are spontanous potential and seismic is shown as background. The key structural framework
is in red. Postack seismic traces in this particular case fails to do direct lithology predictions.
Fig.3- Acoustic Impedance response of sand packets from different prospects in the Golgo San
Jorge basin. High values of AI, are represented by warm colors, lithology log is SP (wigle trace).
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Fig.4- Stratigraphyc setting and compaction compartments for one of the studied wells. Hydrocarbon producing interval
is represented by fluvial sandstones from Mb. Caleta Olivia. Well P-Impedance has been high cut filtered to 65 Hz in
order to see the acoustic impedance response of the reservoir in the seismic bandwidth domain. In color density (leftpanel) is shown the trend compaction of the block, the more dramatic changes occurs at the sequence boundaries or
major discontinuity surfaces.
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Fig.5, A- Full log resolution wireline data, density porosity (background), SP (yellow), P-Impedance (blue), P-Velocity (red),
reservoirs with different thickness responds with minimum acoustic impedance (white arrows), the embedding shales
shows higher acoustic impedance than sands. The net pay interval shows an almost constrast P-Velocity, therefore the
decrease in the impedance value is dominated by bulk density of the sand.
B- Same log data set high cut filtered to the seismic resolution domain, thin sands (1-7m) and tight sands (1-15m)
responds as maximum values of P-Impedance, thick porous sands are “seen” as minimum of P-Impedance.
Fig.6- Schematic cartoon descibing the behaviour of P-Impedance as a function of thickness and
petrophysics of sand packets.
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Fig.7- Influence of sand thickness and porosity on acoustic impedance data derived from seismic trace-based
inversion. For equivalent stratigraphic interval (blue arrow), acoustic impedance decreses due to an increase in the
effective porosity of net pay. The thickness interval (>15m.) is equivalent for both wells.
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Fig.8- Compaction trend along with acoustic p-impedance filtered to seismic bandwidth, black lines represents the
track of allowed impedances. Seismic wavelet, along with its amplitude and phase spectrum.
Fig.9- Show a total acoustic impedance (left), and a band-limited acoustic impedance arbitrary lines (right).
Fig.10- Shows a total acoustic p-impedance arbitrary line (background, left panel) with reflectivity overlaid
(wigle trace). On the right panel it is clear the broader bandwidth (higher frequencies) of the reflectivity with
respect to 3D Seismic (background).
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Fig.11- Total acoustic p-impedance, plan view of porous sand packets distribution corresponding to
the time window interval encompassed by black markers (above).
Fig.12- Pseudo acoustic impedance trace from standard trace-based inversion and from geostatistical
inversion (blue), the high frequency is recovered from well logs, note the possibility to discriminate thin sand
packets due to an improvement in resolution.
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Fig.13- Depicts histograms of the key wells (left) and inverted impedance model (right), the normal Gaussian
transformation applied to be used in the process is in blue.
Fig.14- Shows the variograms of p-impedance from 5 key wells, in red is the exponential function that best fit the
variogram.
Fig.15- Correlation maps for 3 independent realizations, the misfit between seismic and synthetic is
low, an almost 99.8% of correlation is reached in each simulation.
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Fig.16- Arbitrary line showing acoustic impedance from trace-based inversion (a) and Geostatistical
Inversion (b), a finer model is yielded and sand packets up to 5m note can be discriminated
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Fig.17- Lithology cut-offs derived from the density-impedance cross-plot, SP is color coded.
Fig.18- Shows the density-impedance relationship, in red is drawn the correlation
line for shales, green for tight sands and black for porous sands.
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Fig. 19- Shows the result of 30 stochastic reaalizations, lithology and density are simulated in order to
find acoustic impedance traces that when convolved with the seismic wavelet yields a synthetic trace
that satisfy the input seismic; the simulations are integrated into an average to reduce the uncertainty
of the model
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Fig.20- Lithology model, shales (black), tight sands (brown), porous sand (yellow), along with time windows in
which gross and net sand values has been extracted. The 2D color coded maps of net sands are vertical
stacked samples of porous within the interval.
SPE 69485

Lateral and Vertical Discrimination of Thin

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