U.S. patent application number 13/967498 was filed with the patent office on 2013-12-19 for generating facies probablity cubes.
This patent application is currently assigned to Schlumberger Technology Corporation. The applicant listed for this patent is Schlumberger Technology Corporation. Invention is credited to Harish Krishnamurthy, Ting Li, Tuanfeng Zhang.
Application Number | 20130338978 13/967498 |
Document ID | / |
Family ID | 44647907 |
Filed Date | 2013-12-19 |
United States Patent
Application |
20130338978 |
Kind Code |
A1 |
Zhang; Tuanfeng ; et
al. |
December 19, 2013 |
GENERATING FACIES PROBABLITY CUBES
Abstract
A method for generating one or more geological models for oil
field exploration. The method includes receiving one or more well
facies logs, a vertical facies proportion curve, a lateral
proportion map, a variogram model and a global target histogram.
The method then includes generating a facies probability cube using
a modified Sequential Gaussian Simulation (SGSIM) algorithm, the
well facies logs, the vertical facies proportion curve, the lateral
proportion map and the variogram model. After generating the facies
probability cube, the method includes matching the facies
probability cube to the global histogram and generating the
geological models based on the matched facies probability cube.
Inventors: |
Zhang; Tuanfeng; (Lexington,
MA) ; Li; Ting; (Beijing, CN) ; Krishnamurthy;
Harish; (Cambridge, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Schlumberger Technology Corporation |
Sugar Land |
TX |
US |
|
|
Assignee: |
Schlumberger Technology
Corporation
Sugar Land
TX
|
Family ID: |
44647907 |
Appl. No.: |
13/967498 |
Filed: |
August 15, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
12837936 |
Jul 16, 2010 |
|
|
|
13967498 |
|
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|
61315098 |
Mar 18, 2010 |
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Current U.S.
Class: |
703/2 ;
703/10 |
Current CPC
Class: |
G01V 2210/6652 20130101;
G01V 2210/665 20130101; G01V 99/005 20130101; G06F 30/20
20200101 |
Class at
Publication: |
703/2 ;
703/10 |
International
Class: |
G06F 17/50 20060101
G06F017/50 |
Claims
1. A method for generating one or more geological models for oil
field exploration, comprising: receiving one or more well facies
logs, a vertical facies proportion curve, a lateral proportion map,
a variogram model and a global target histogram; generating a
facies probability cube using a modified Sequential Gaussian
Simulation (SGSIM) algorithm, the well facies logs, the vertical
facies proportion curve, the lateral proportion map and the
variogram model; matching the facies probability cube to the global
histogram; and generating the geological models based on the
matched facies probability cube.
2. The method of claim 1, wherein the vertical facies proportion
curve is generated based on an interpretation of the one or more
well facies logs.
3. The method of claim 1, wherein the lateral proportion map is
obtained by interpolating one or more facies proportions from the
one or more well facies logs.
4. The method of claim 1, wherein the lateral proportion map is
obtained by calibrating one or more seismic interpretations of the
one or more well facies logs.
5. The method of claim 1, wherein the variogram model is derived
based on the vertical facies proportion curve and the lateral
facies proportion map.
6. The method of claim 1, wherein the variogram model is a Gaussian
variogram model.
7. The method of claim 1, wherein the global target histogram is a
U-shaped beta distribution.
8. The method of claim 7, wherein receiving the global target
histogram comprises receiving a parameter controlled contrast (c)
that is associated with a variance value for the beta
distribution.
9. The method of claim 1, wherein generating the facies probability
cube using the modified Sequential Gaussian Simulation (SGSIM)
algorithm comprises: (a) transforming well facies data into a
plurality of normal score values, wherein the well facies data is
obtained from the well facies logs; (b) selecting a random pixel in
a model of the facies probability cube; (c) determining a kriging
mean and a kriging variance for the random pixel based on the
plurality of normal score values at the random pixel; (d) scaling
the kriging mean based on a difference between a running facies
proportion, a target facies proportion at a Z-layer on the random
pixel, the vertical proportion curve, the lateral proportion map or
combinations thereof; (e) constructing a normal distribution value
at the random pixel based on the scaled kriging mean and the
kriging variance; (f) adding the normal distribution value to the
random pixel in the model; and (g) back transforming the normal
distribution value at the random pixel.
10. The method of claim 9, further comprising repeating steps
(a)-(g) for each pixel in the model of the facies probability
cube.
11. The method of claim 1, further comprising: hierarchically
generating one or more additional facies probability cube;
receiving a multi-facies training image; and generating a
multi-facies model based on the additional facies probability cubes
and the multi-facies training image.
12. The method of claim 1, further comprising: receiving a
multi-facies training image; hierarchically drawing each individual
facies in the facies probability cube; and generating a
multi-facies model using multi-point statistics, the multi-facies
training image and each individual facies in the facies probability
cube.
13. A computer-readable medium for generating one or more
geological models for oil field exploration, the computer-readable
medium having stored thereon computer-executable instructions
which, when executed by a computer, cause the computer to: receive
one or more well facies logs, a vertical facies proportion curve, a
lateral proportion map, a variogram model and a global target
histogram; generate a facies probability cube using a modified
Sequential Gaussian Simulation (SGSIM) algorithm, the well facies
logs, the vertical facies proportion curve, the lateral proportion
map and the variogram model; match the facies probability cube to
the global histogram; and generate the geological models based on
the matched facies probability cube.
14. The computer-readable medium of claim 13, wherein the
computer-executable instructions which, when executed by the
computer, cause the computer to generate the facies probability
cube using the modified Sequential Gaussian Simulation (SGSIM)
algorithm comprises computer-executable instructions, which, when
executed by the computer, cause the computer to: (a) transform well
facies data into a plurality of normal score values, wherein the
well facies data is obtained from the well facies logs; (b) select
a random pixel in a model of the facies probability cube; (c)
determine a kriging mean and a kriging variance for the random
pixel based on the plurality of normal score values at the random
pixel; (d) scale the kriging mean based on a difference between a
running facies proportion, a target facies proportion at a Z-layer
on the random pixel, the vertical proportion curve, the lateral
proportion map or combinations thereof; (e) construct a normal
distribution value at the random pixel based on the scaled kriging
mean and the kriging variance; (f) add the normal distribution
value to the random pixel in the model; and (g) back transform the
normal distribution value at the random pixel.
15. The computer-readable medium of claim 14, wherein the kriging
mean is scaled according to: m sk * new ( i , j , k ) = m sk * ( i
, j , k ) + .lamda. 1 - .lamda. ( V P C ( k ) - p * ( k ) .sigma. T
) + .lamda. 1 - .lamda. ( L P M ( i , j ) - p * ( i , j ) .sigma. T
) ##EQU00007## where m.sub.sk*(i, j, k) is the kriging mean at
pixel (i, j, k), p(k)* is the running facies proportion at the k-th
Z-layer, VPC(k) is proportion read at the k-th Z-layer from the
vertical proportion curve, .lamda. is a servo factor in [0, 1] that
indicates the correction strength, m.sub.sk*.sup.new(i, j, k) the
scaled kriging mean, .sigma..sub.T is a standard deviation of the
global histogram, i.e., .sigma..sub.T= {square root over
(c.times.p.times.(1-p))} and LPM(i, j) is a lateral proportion at
pixel location (i, j), which can be read from the lateral
proportion map, and p*(i, j) is a running facies proportion
calculated from the column at (i, j).
16. The computer-readable medium of claim 14, wherein the kriging
mean is scaled according to: m sk * new ( i , j , k ) = m sk * ( i
, j , k ) + .lamda. 1 - .lamda. ( V P C ( k ) - p * ( k ) .sigma. T
) ##EQU00008## where m.sub.sk*(i, j, k) is a kriging mean at pixel
(i, j, k), p(k)* is the running facies proportion at the k-th
Z-layer, VPC(k) is the proportion read at the k-th Z-layer from the
vertical proportion curve, .lamda. is a servo factor in [0, 1] that
indicates the correction strength, m.sub.sk*.sup.new(i, j, k) is
the scaled kriging mean, and .sigma..sub.T is a standard deviation
of the global histogram, i.e., .sigma..sub.T= {square root over
(c.times.p.times.(1-p))}.
17. A system, comprising: a processor; and a memory comprising
program instructions executable by the processor to: receive one or
more well facies logs, a vertical facies proportion curve, a
lateral proportion map, a variogram model and a global target
histogram; generate a facies probability cube using a modified
Sequential Gaussian Simulation (SGSIM) algorithm, the well facies
logs, the vertical facies proportion curve, the lateral proportion
map and the variogram model; match the facies probability cube to
the global histogram; and generate one or more geological models
based on the matched facies probability cube, wherein the
geological models are used for oil field exploration.
18. The system of claim 17, wherein the global target histogram is
a U-shaped beta distribution.
19. The system of claim 17, the variogram model is a spherical
variogram model, an exponential variogram model, a Gaussian
variogram model or a power variogram model.
Description
RELATED APPLICATIONS
[0001] This application is a continuation of and claims priority to
U.S. patent application Ser. No. 12/837,936 filed 16 Jul. 2010,
titled GENERATING FACIES PROBABILITY CUBES, which in turn claims
priority to U.S. provisional patent application Ser. No. 61/315,098
filed Mar. 18, 2010, titled METHOD FOR RESERVOIR MODELING USING A
GEOSTATISTICAL APPROACH TO GENERATE 3D PROBABILITY CUBES OF BINARY
FACIES WITH GEOLOGICAL CONSTRAINT, both of which are incorporated
herein by reference.
BACKGROUND
[0002] 1. Field of the Invention
[0003] Implementations of various technologies described herein
generally relate to techniques for modeling geological properties
of the earth and, more particularly, to techniques for generating
facies probability cubes that can be used with multipoint
statistics to create a reservoir model.
[0004] 2. Description of the Related Art
[0005] The following descriptions and examples are not admitted to
be prior art by virtue of their inclusion within this section.
[0006] Geological modeling and reservoir characterization provide
quantitative 3D reservoir models based on available reservoir
measurements, such as well log interpretations, experimental
results from core analysis, seismic survey and dynamic fluid flow
responses from field observations (e.g., historic production data)
and pressure change data. One type of reservoir characterization or
modeling technique is stochastic reservoir modeling.
[0007] Stochastic reservoir modeling has gained popularity in
modern reservoir modeling software because of its ability to
constrain its model based on a variety of reservoir data and its
computational efficiency in generating complex reservoir models
with millions of voxels. Stochastic reservoir modeling also allows
users to quantitatively evaluate uncertainties in the model due to
the lack of knowledge of the reservoirs. The data used to constrain
the reservoir models in stochastic reservoir modeling are primarily
classified into two categories: "hard data" or "soft data." Hard
data includes data such as those measured in wells (e.g., well log
data), which are considered to be accurate information and should
be honored during simulations. Soft data are not as accurate as
hard data but typically have larger or better coverage of the
reservoir. Facies probability cubes are considered to be soft data
that have been derived from seismic attributes using well to
seismic calibrations. These types of soft data are important in
guiding inter-well facies prediction and thus, they may be used to
reduce uncertainties in the decision making process for reservoir
management.
[0008] Geostatistics provide variety of algorithms and tools to
build stochastic reservoir models. Generally, there are two
approaches for using geostatistics to build stochastic reservoir
models: a pixel-based approach and an object-based approach. The
pixel-based approach proceeds by gridding the reservoir into pixels
(voxels) and simulating each pixel (voxel) in a random sequence.
Unlike the pixel-based approach, the object-based approach directly
drops the facies (geobody) objects into the simulated reservoir
according to the specified geometric information of these
geobodies. The pixel-based approach provides increased flexibility
for constraining the model according to reservoir data but it often
has poor shape reproduction in the final reservoir models. In
contrast, the object-based approach tends to generate more
realistic shapes of geobodies; however, it becomes more difficult
to constrain the models according to local reservoir observations,
particularly when there are dense well locations.
[0009] In the pixel-based approach, a sequential indicator
simulation (SIS) is often used to create facies models. However, a
newly emerging pixel-based approach named Multi-point statistics
(MPS) is gaining more attention from modelers and is considered to
be part of an advanced facies modeling suite. MPS uses 1D, 2D or 3D
"training images" as quantitative templates to model subsurface
property fields. MPS modeling captures geological structures from
training images and anchors them to data locations. As such, MPS
takes advantage of a 2-point (variogram-based) geostatistical
approach and an object-based approach to create flexibility in data
conditioning while producing more realistic shapes from the
training images. MPS can then integrate soft data, such as a facies
probability cube, to generate geological or reservoir models. The
resulting geological or reservoir models can then be used for oil
field explorations by identifying hydrocarbon deposits in the
Earth.
[0010] In addition to being used in multipoint statistics facies
modeling, probability cubes are also used for other modeling
approaches, such as object-based modeling and pixel-based
Sequential Indicator Simulation (SIS), to further constrain the
simulated earth models. As such, facies probability cubes play an
important role in geological modeling or reservoir
characterization. In particular, facies probability cubes can
assist in geological modeling or reservoir characterization when
well data is scarce. However, automatically generating facies
probability cubes that are geologically sound remains a
challenge.
SUMMARY
[0011] Described herein are implementations of various technologies
for generating facies probability cubes and using the facies
probability cubes to generate geological models for oil field
exploration. In one implementation, a method generating geological
models may include receiving one or more well facies logs, a
vertical facies proportion curve, a lateral proportion map, a
variogram model and a global target histogram. The method may then
include generating a facies probability cube using a modified
Sequential Gaussian Simulation (SGSIM) algorithm, the well facies
logs, the vertical facies proportion curve, the lateral proportion
map and the variogram model. After generating the facies
probability cube, the method may match the facies probability cube
to the global histogram and generate the geological models based on
the matched facies probability cube.
[0012] The claimed subject matter is not limited to implementations
that solve any or all of the noted disadvantages. Further, the
summary section is provided to introduce a selection of concepts in
a simplified form that are further described below in the detailed
description section. The summary section is not intended to
identify key or essential features of the claimed subject matter,
nor is it intended to be used to limit the scope of the claimed
subject matter.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] Implementations of various technologies will hereafter be
described with reference to the accompanying drawings. It should be
understood, however, that the accompanying drawings illustrate only
the various implementations described herein and are not meant to
limit the scope of various technologies described herein.
[0014] FIG. 1 illustrates a schematic diagram of a logging
apparatus in accordance with implementations of various techniques
described herein.
[0015] FIG. 2 illustrates a flow diagram of a method for generating
a facies probability cube in accordance with implementations of
various techniques described herein.
[0016] FIG. 3 illustrates a flow diagram of a method for generating
a multiple facies model constrained by a facies probability cube in
accordance with implementations of various techniques described
herein.
[0017] FIG. 4 illustrates a flow diagram of a method for generating
a multiple facies model constrained by a facies probability cube in
accordance with implementations of various techniques described
herein.
[0018] FIG. 5 illustrates a flow diagram of a method for performing
a modified Sequential Gaussian Simulation (SGSIM) algorithm in
accordance with implementations of various techniques described
herein.
[0019] FIG. 6 illustrates a computer network into which
implementations of various technologies described herein may be
implemented.
[0020] FIG. 7 illustrates an example of a vertical proportion curve
in accordance with implementations of various techniques described
herein.
[0021] FIG. 8 illustrates an example of a lateral proportion map in
accordance with implementations of various techniques described
herein.
[0022] FIG. 9 illustrates an example of well facies data in
accordance with implementations of various techniques described
herein.
[0023] FIG. 10 illustrates an example of a fluvial sand probability
cube in accordance with implementations of various techniques
described herein.
[0024] FIG. 11 illustrates an example of two Probability Density
Function (PDF) curves of a Beta distribution for different
parameter controlled contrasts in accordance with implementations
of various techniques described herein.
[0025] FIG. 12 illustrates an example of a Cumulative Density
Function (CDF) curve in an original probability space and a CDF
curve in a normal score space in accordance with implementations of
various techniques described herein.
[0026] FIG. 13 illustrates an example of four facies training image
in accordance with implementations of various techniques described
herein.
[0027] FIG. 14 illustrates an example of a reservoir model with
four facies in accordance with implementations of various
techniques described herein.
[0028] FIG. 15 illustrates a diagram for creating a reservoir model
in accordance with implementations of various techniques described
herein.
DETAILED DESCRIPTION
[0029] The discussion below is directed to certain specific
implementations. It is to be understood that the discussion below
is only for the purpose of enabling a person with ordinary skill in
the art to make and use any subject matter defined now or later by
the patent "claims" found in any issued patent herein.
[0030] The following provides a brief description of various
technologies and techniques for generating facies probability
cubes. In one implementation, a computer application may receive a
vertical facies proportion curve, a lateral proportion map, a
variogram model and a global target histogram to generate the
facies probability cube. The vertical proportion curve may indicate
the amount in which the facies deposits change within varying
depths. The lateral proportion map may be a 2 dimensional map in
the XY plane that represents the variation of lateral proportions
of certain facies in terms of an average proportion along the Z
direction. The variogram model may be a quantitative tool in
conventional 2-point geostatistics that measures the spatial
variability of a geo-variable. Generally, the vertical facies
proportion curve and the lateral proportion may be determined based
on well facies data in well facies logs. The variogram model may be
determined based on an automatic or computerized interpretation of
the well facies data or it may be received from a user based on
his/her interpretation of the well facies data or other relevant
data. The global target histogram may be received from a user and
may be defined as probability distribution such as a U-shaped beta
distribution.
[0031] After receiving the vertical facies proportion curve, the
lateral proportion map, the variogram model and the global target
histogram, the computer application may generate a facies
probability cube using a modified Sequential Gaussian Simulation
(SGSIM) algorithm. The modified SGSIM algorithm may use the
vertical facies proportion curve, the lateral proportion map and
the variogram model to estimate facies proportions in a facies
probability cube. The modified SGSIM algorithm may estimate the
facies probability cube by increasing or reducing a kriging mean
based on the vertical facies proportion curve (VPC) and the lateral
proportion map (LPM). The adjustment with regard to the vertical
facies proportion curve (VPC) and the lateral proportion map (LPM)
may be performed based on the following formula:
m sk * new ( i , j , k ) = m sk * ( i , j , k ) + .lamda. 1 -
.lamda. ( V P C ( k ) - p * ( k ) .sigma. T ) + .lamda. 1 - .lamda.
( L P M ( i , j ) - p * ( i , j ) .sigma. T ) ##EQU00001##
where m.sub.sk*(i, j, k) is kriging mean at pixel (i, j, k), p(k)*
is running proportion of the facies at the k-th Z-layer, VPC(k) is
proportion read at the k-th Z-layer from the VPC, .lamda. is a
servo factor in [0, 1] that indicates the correction strength,
m.sub.sk*.sup.new(i, j, k) is adjusted kriging mean, .sigma..sub.T
is the standard deviation of the global target histogram, i.e.,
.sigma..sub.T= {square root over (c.times.p.times.(1-p))} and
LPM(i,j) is lateral proportion at pixel location (i, j), which can
be read from the LPM, and p*(i,j) is a running facies proportion
calculated from the column at (i, j). After generating the facies
probability cube, the computer application may perform an inverse
normal score transform on the facies probability cube in a Gaussian
space to match the global target histogram.
[0032] FIGS. 1-15 illustrate one or more implementations of various
techniques described herein in more detail.
[0033] FIG. 1 illustrates a schematic diagram of a logging
apparatus in accordance with implementations of various techniques
described herein. FIG. 1 shows a borehole 32 that has been drilled
in formations 31 with drilling equipment, and typically, using
drilling fluid or mud that results in a mudcake represented at 35.
A logging device 100 is shown, and can be used in connection with
various implementations described herein. The logging device 100
may be suspended in the borehole 32 on an armored multiconductor
cable 33. Known depth gauge apparatus (not shown) is provided to
measure cable displacement over a sheave wheel (not shown) and thus
the depth of logging device 100 in the borehole 32. Circuitry 51,
represents control and communication circuitry for the
investigating apparatus. Although circuitry 51 is shown at the
surface, portions thereof may typically be downhole. Also shown at
the surface are processor 50 and recorder 90. Although logging
device 100 illustrated herein is shown to be a wireline logging
tool, it should be noted that other tools such as a logging while
drilling tool may be used in connection with various
implementations described herein.
[0034] The logging device 100 may represent any type of logging
device that takes measurements from which formation characteristics
can be determined, for example, by solving complex inverse
problems. The logging device 100 may be an electrical type of
logging device (including devices such as resistivity, induction,
and electromagnetic propagation devices), a nuclear logging device,
a sonic logging device, or a fluid sampling logging device, or
combinations thereof. Various devices may be combined in a tool
string and/or used during separate logging runs. Also, measurements
may be taken during drilling and/or tripping and/or sliding.
Examples of the types of formation characteristics that can be
determined using these types of devices include: determination,
from deep three-dimensional electromagnetic measurements, of
distance and direction to faults or deposits, such as salt domes or
hydrocarbons; determination, from acoustic shear and/or
compressional wave speeds and/or wave attenuations, of formation
porosity, permeability, and/or lithology; determination of
formation anisotropy from electromagnetic and/or acoustic
measurements; determination, from attenuation and frequency of a
rod or plate vibrating in a fluid, of formation fluid viscosity
and/or density; determination, from resistivity and/or nuclear
magnetic resonance (NMR) measurements, of formation water
saturation and/or permeability; determination, from count rates of
gamma rays and/or neutrons at spaced detectors, of formation
porosity and/or density; and determination, from electromagnetic,
acoustic and/or nuclear measurements, of formation bed
thickness.
[0035] In one implementation, the measurements obtained by logging
device 100 may include well facies data in the well logs (facies
logs). Facies logs may indicate the absolute presence or absence of
a targeted facies at different spatial locations. Targeted facies
may include channels, levees, crevasses, shale background and the
like.
[0036] FIG. 2 illustrates a flow diagram of a method 200 for
generating a facies probability cube in accordance with
implementations of various techniques described herein. In one
implementation, method 200 may be performed by a computer
application. The following description of method 200 is made with
reference to method 500 of FIG. 5 and diagram 1500 of FIG. 15. It
should be understood that while method 200 indicates a particular
order of execution of the operations, in some implementations,
certain portions of the operations might be executed in a different
order.
[0037] At step 210, the computer application may receive well
facies data from well facies logs. Well facies logs may be well
logs that have been acquired at various locations in a survey area
such as boreholes and the like, as described above with reference
to FIG. 1. Well facies logs may indicate the absolute presence or
absence of a targeted facies at different spatial locations. An
example of well facies data is provided in FIG. 9.
[0038] At step 220, the computer application may receive a vertical
facies proportion curve (VPC). FIG. 7 illustrates an example of a
VPC. FIG. 15 illustrates how the VPC 1510 may be used in method
200. The VPC may illustrate the change of facies deposits in the
earth with the variation of depths. The change of facies deposits
in the earth may occur due to a geological sedimentation process,
which may evolve periodically as progradation and retrogradation
patterns. These patterns may result when sea levels rise and drop
alternatively. This phenomenon is ubiquitous in sequence
stratigraphy at large scales, but the cyclical nature of the
patterns may also be found at small scales. As such, the amount of
specific facies deposits changes with the variation of geological
times or depths leading to a systematic vertical trend of facies
proportions. For example, in a fluvial-dominated deltaic
environment, the sand deposit may be high at the bottom of a
reservoir unit, become lower in the middle of the reservoir unit
and becomes high again at the top of the reservoir unit. Coarsening
or fining upwards characteristics in geological deposition for a
certain facies is also a trend indicator of the deposition of that
facies.
[0039] In one implementation, VPC can be calculated from well
facies logs (from step 210) interpretation, geological conceptual
models or analogs similar to the reservoir under study. If well
facies data are available, the well facies data may be combined
with geological interpretations of the seismic area to generated
interpreted well facies data. The interpreted well facies data may
then be used as anchors in generating facies probability cubes,
i.e. they indicate the absolute presences/absences of the targeted
facies at different spatial locations: probability is 1 for its
presence and 0 for its absence. The vertical facies proportion
curve can be calculated by extracting the facies proportion along
each vertical layer (i.e., Z-layer) of a modeling grid. In case of
very sparse wells, the calculated proportion curve may not be
reliable and hence, its modification and editing may be performed
based on geological interpretations or analogs similar to the
studied reservoir.
[0040] At step 230, the computer application may receive a lateral
facies proportion map (LPM). FIG. 8 illustrates an example of a
LPM. FIG. 15 illustrates how the LPM 1520 may be used in method
200. The lateral proportion map may be a 2 dimensional map in the
XY plane that represents the variation of lateral proportions of
certain facies in terms of an average proportion along the Z
direction. In this manner, the lateral proportion map may
illustrate lateral trends such as progradation or transition. In
one implementation, the computer application may obtain the lateral
facies proportion map by interpolating facies proportion from each
well facies log or by calibrating seismic interpretations of each
well facies log. The information included in the lateral facies
proportion map may be useful when facies depositions have apparent
lateral trends, such as progradation or a transition as observed
from received seismic data, well facies log interpretations or
conceptual models.
[0041] The computer application may create lateral proportion maps
based on well facies data using any smooth interpolator, such as a
kriging technique in 2-point geostatistics or moving averaging
algorithms. For instance, at each well location, the computer
application may calculate a facies proportion. The facies
proportion value may then be considered to be one of the hard data
used as an anchor point to control the smooth interpolator. In one
implementation, the computer application may also add interpreted
trends into the LPM by adding data from "pseudo" wells. In any
case, by integrating LPM into reservoir modeling, the computer
application may be able to generate a facies probability cube that
has more realistic results.
[0042] At step 240, the computer application may receive a
variogram model from a user. The variogram model may be a
quantitative tool in conventional 2-point geostatistics that
measures the spatial variability of a geo-variable. The variogram
model may be used to control the anisotropy of the spatial
distribution of a geo-variable by changing the correlation ranges
and the orientations of major/minor axis of the variogram model. As
such, the variogram model may be specified by a user to govern the
anisotropic distribution of probability values in the facies
probability cube.
[0043] The variogram model may be derived by the computer
application based on well facies data or may be specified by a user
based on his/her interpretation of the well facies data or other
relevant data. If the variogram model is derived by the computer
application, the computer application may derive the variogram
model from the vertical facies proportion curve and the lateral
facies proportion map. The vertical facies proportion curve may be
used to infer the vertical range of the variogram model, and the
lateral facies proportion map may be used to infer the horizontal
correlations of the variogram model. If a local azimuth field that
reflects the orientation of facies deposition is available, the
computer application may also use the local azimuth field to build
the variogram model.
[0044] Generally, the computer application may receive one of four
commonly used variogram models: spherical, exponential, Gaussian
and power variograms. It has been shown that the Gaussian variogram
model, as compared with the other three variogram models, may
create smoother results in generating the facies probability cube
and therefore may be more suitable to generate facies probability
cubes. However, it should be noted that method 200 described herein
is not limited to the Gaussian variogram model.
[0045] At step 250, the computer application may receive a global
target histogram from a user. The global target histogram may be a
probability distribution used to constrain the facies probability
cube. In one implementation, the global target histogram may be a
U-shaped beta distribution. As such, the two end peaks of the
U-shaped beta distribution may correspond to the likelihood of
facies presence/absence in the entire probability cube.
Additionally, the mean of the Beta distribution may be forced to
match the global facies proportion in the reservoir while the
variance of the Beta distribution may be a user-defined parameter
that allows the user to control the variation or "sharpness" of the
resulting probability cube.
[0046] The probability density function (PDF) of Beta distribution
is defined in classic statistics as:
f ( x , .alpha. , .beta. ) = x .alpha. - 1 ( 1 - x ) .beta. - 1
.intg. 0 1 u .alpha. - 1 ( 1 - u ) .beta. - 1 u = .GAMMA. ( .alpha.
+ .beta. ) .GAMMA. ( .alpha. ) .GAMMA. ( .beta. ) x .alpha. - 1 ( 1
- x ) .beta. - 1 = 1 B ( .alpha. , .beta. ) x .alpha. - 1 ( 1 - x )
.beta. - 1 ##EQU00002##
where .GAMMA. is the gamma function. The expected value, second
moment and variance of a Beta random variable X with parameters
.alpha. and .beta. are:
E ( X ) = .alpha. .alpha. + .beta. ##EQU00003## E ( X 2 ) = .alpha.
( .alpha. + 1 ) ( .alpha. + .beta. ) ( .alpha. + .beta. + 1 )
##EQU00003.2## Var ( X ) = .alpha. .beta. ( .alpha. + .beta. ) 2 (
.alpha. + .beta. + 1 ) ##EQU00003.3##
[0047] To match a specified global facies proportion (p) and a
user-defined tuning factor (c), the following relationships may be
established:
E(X)=p
Var(X)=c.times.p.times.(1-p)
where 0.5<c.ltoreq.1.0; 0<p.ltoreq.0.5. The specified global
facies proportion (p) denotes the proportion of a particular facies
in the facies probability cube, and the user-defined tuning factor
or parameter controlled contrast (c) is associated with the
variance or spread of the Beta distribution. The link between the
two parameters p and c and the two parameters .alpha. and .beta. in
Beta distribution is defined as:
.alpha. = p .times. 1 - c c ; ##EQU00004## .beta. = ( 1 - p )
.times. 1 - c c ##EQU00004.2##
[0048] This equation ensures 0<.alpha.<.beta.<1.0. As a
result, the two peaks of the PDF of the Beta distribution occurs at
x=0 and at x=1.0 such that the peak at x=0 is higher than the peak
at x=1.0 because the target facies proportion p is less than 0.5.
If, however, the target facies proportion is more than 0.5, the
complementary facies of the target facies may need to be considered
to ensure that 0<.alpha.<.beta.<1.0. Additionally, if c
increases from 0.5 to 1.0, the facies probability cube may tend to
include more contrast. The largest contrast is reached when c=1.0,
which means that every value in the probability cube is either 1 or
0 and thus the probability cube becomes a binary cube. FIG. 11
illustrates an example of two Probability Density Function (PDF)
curves of a Beta distribution for different parameter controlled
contrasts c, which may control the spread of the Beta
distribution.
[0049] In one implementation, if the global target histogram is a
U-shaped beta distribution as described above, the computer
application may also receive the parameter controlled contrast (c)
for the beta distribution. Although the global target histogram has
been described as a U-shaped beta distribution, it should be
understood that in other implementations the global target
histogram may be a different type of distribution.
[0050] At step 260, the computer application may generate a facies
probability cube using a modified Sequential Gaussian Simulation
(SGSIM) algorithm. The conventional Sequential Gaussian Simulation
(SGSIM) algorithm, as described in Deutsch, C. V. and Journel, A.
G., 1998, GSLIB: Geostatistical Software Library and User's Guide.
Oxford University Press, New York, p. 369 (Deutsch and Journel,
1998), is a popular geostatistical algorithm that is used to
simulate a petrophsyical properties distribution of any continuous
variable, such as porosity or permeability in a model (i.e., facies
probability cube). It is a pixel-based sequential simulation
approach under a multi-Gaussian assumption.
[0051] The SGSIM algorithm first transforms well log data into
standard normal values using a process called normal score
transformation. The well log data is transferred into standard
normal values for practical purposes because the continuous
variables may not follow a Gaussian distribution. FIG. 12
illustrates an example of a Cumulative Density Function (CDF) curve
in the original probability space and a CDF curve in the normal
score space. The algorithm then proceeds by selecting a random
pixel (or voxel in 3D) in a model. Because of the multi-Gaussian
assumption, the SGSIM algorithm may make a determination of a
conditional cumulative density function (ccdf) at the selected
pixel to determine the probability of the existence of a continuous
variable at the selected pixel location. In order to make the
determination of the conditional cumulative density function (ccdf)
at the selected pixel, the SGSIM algorithm solves a local kriging
system to obtain an estimated kriging mean and variance based on
well data obtained from well logs that are within the neighborhood
of the selected pixel in the model. The SGSIM algorithm then
constructs a normal distribution at the selected pixel using the
estimated kriging mean and variance. After constructing the normal
distribution at the selected pixel, the SGSIM algorithm may add the
normal distribution value to the model at the selected pixel. This
process is then repeated for each pixel in the model until all of
the pixels have been selected.
[0052] After applying the SGSIM algorithm to each pixel in the
model in the standard normal space, a simulation of the original
(probability) variable may be obtained by performing a back
transformation of the normal score model to the original space. By
using the conventional SGSIM algorithm, the variogram model is used
to control the spatial anisotropic distribution of the
(probability) variable and a global target histogram of the
original variable is forced to be reproduced during the back
transformation.
[0053] FIG. 5 illustrates a flow diagram of a method 500 for
performing a modified Sequential Gaussian Simulation (SGSIM)
algorithm in accordance with implementations of various techniques
described herein. The following description of method 500 describes
the process used at step 260 of method 200. The modified SGSIM
algorithm is a variation of the conventional SGSIM algorithm that
may be used to create facies probability cubes such that the facies
probability cubes are constrained by the vertical facies proportion
curve, the lateral proportion map, the variogram model and the
global target histogram received at steps 220-250. Like the
conventional SGSIM algorithm, the modified SGSIM algorithm may
first transform well log data into standard normal values using a
process called normal score transformation. (Step 510). The
modified SGSIM algorithm may then select a random pixel (or voxel
in 3D) in a model of the facies probability cube. (Step 520). Next,
in the simulation stage, the modified SGSIM algorithm may solve a
local kriging system at the selected pixel to determine a kriging
mean m.sub.sk* and a kriging variance .sigma..sup.2.sub.sk based on
well data obtained from well logs that are within the neighborhood
of the selected pixel in the model. (Step 530).
[0054] Up to this step, all the procedures remain the same as the
traditional SGSIM algorithm. However, in order to constrain the
facies probability cube to the vertical proportion curve, the
modified SGSIM algorithm may increase or decrease the kriging mean
m.sub.sk* according to the difference between a running facies
proportion and a target facies proportion at the Z-layer at
selected pixel. (Step 540). The running facies proportion is
defined as the simulated facies proportion before the simulation
reaches the selected pixel, and the target facies proportion is the
proportion value of the target facies at the selected pixel as
indicated from the vertical proportion curve. In order to calculate
the running proportion, the computer application may perform a back
transformation of the simulated pixels from the normal score values
into the original probability space.
[0055] In one implementation, the modified SGSIM algorithm is
configured to increase or decrease the kriging mean m.sub.sk*
without changing the kriging variance. As such, the chance for
drawing a larger or smaller probability value in the original space
will be high unless the kriging variance is also scaled. In order
to scale the kriging mean m.sub.sk* without changing the kriging
variance, the modified SGSIM algorithm may progressively adjust the
kriging mean m.sub.sk* at each pixel to match the vertical
proportion curve. The adjustment with regard to the vertical facies
proportion curve (VPC) is performed based on the following
formula:
m sk * new ( i , j , k ) = m sk * ( i , j , k ) + .lamda. 1 -
.lamda. ( V P C ( k ) - p * ( k ) .sigma. T ) Equation 1 )
##EQU00005##
where m.sub.sk*(i, j, k) is the kriging mean at pixel (i, j, k),
p(k)* is running proportion of the facies at the k-th Z-layer,
VPC(k) is the proportion read at the k-th Z-layer from the VPC,
.lamda. is a servo factor in [0, 1] that indicates the correction
strength, m.sub.sk*.sup.new(i, j, k) is the adjusted kriging mean,
and .sigma..sub.T is the standard deviation of the global target
histogram, i.e., .sigma..sub.T= {square root over
(c.times.p.times.(1-p))}.
[0056] As shown in equation 1 above, if the running facies
proportion at the k-th Z-layer is larger than the target vertical
proportion, the kriging mean will be reduced. Alternatively, if the
running facies proportion at the k-th Z-layer is smaller than the
target vertical proportion, the kriging mean will be increased. As
a result, a smaller or a larger normal score value will likely be
used to gear the simulated probability values in the original space
towards the final facies probability cube such that they match the
input vertical proportion curve.
[0057] If the servo factor .lamda. is 0, the modified SGSIM
algorithm does not make a correction to the probability values. A
larger servo factor (i.e., approaching 1.0), however, corresponds
with a stronger correction factor for the reproduction of the
vertical proportion curve in the resulting facies probability cube.
When the vertical proportion curve has an erratic variation cycle
or trend, it may compromise the resulting probability spatial
continuity, which is typically governed by the variogram model.
Therefore, a reasonable selection of the servo factor is used to
balance a trade-off between the vertical proportion curve trend
reproduction and the variogram model.
[0058] In addition to making the adjustment to the kriging mean
m.sub.sk* with regard to the vertical facie.sub.s .sup.Proportion
curve, the modified SGSIM algorithm may also make an adjustment to
the kriging mean m.sub.sk* with regard to the lateral proportion
map based on the following formula:
m sk * new ( i , j , k ) = m sk * ( i , j , k ) + .lamda. 1 -
.lamda. ( V P C ( k ) - p * ( k ) .sigma. T ) + .lamda. 1 - .lamda.
( L P M ( i , j ) - p * ( i , j ) .sigma. T ) ( Equation 2 )
##EQU00006##
where LPM(i, j) is lateral proportion at pixel location (i, j),
which can be read from the LPM, and p*(i, j) is the running facies
proportion calculated from the column at (i, j). Based on equation
2, the modified SGSIM algorithm may constrain the facies
probability cube according to the vertical proportion curve and the
lateral proportion map. (Step 550).
[0059] It should be noted that two different servo factors could be
used in equation 2, but by keeping the two servo factors the same
the input parameters of the algorithm may be simplified.
[0060] After scaling the kriging mean m.sub.sk*, the modified SGSIM
algorithm may construct a normal distribution at the selected pixel
using the estimated kriging mean and variance. (Step 550). After
constructing the normal distribution at the selected pixel, the
modified SGSIM algorithm, like the conventional SGSIM algorithm,
may add the normal distribution value to the model at the selected
pixel. (Step 560). The modified SGSIM algorithm may then back
transform the value at the selected pixel to the target space and
update the running proportions. (Step 570). This process is then
repeated for each pixel in the model until all of the pixels have
been selected.
[0061] At step 270, the computer application may perform an inverse
normal score transform in Gaussian space to the facies probability
cube generated at step 260 in order to match the global target
histogram received at step 250. FIG. 10 illustrates an example of a
fluvial sand probability cube generated using method 200. FIG. 15
illustrates how the fluvial sand probability cube 1530 may have
been generated using the VPC 1510 and the LPM 1520 as described in
method 200.
[0062] In one implementation, the modified SGSIM algorithm may
require that consistency exists between the three inputs: global
facies mean (p), vertical proportion curve and lateral proportion
map. The consistency means both the average of the vertical
proportion curve and the average of the lateral proportion map may
be close to the global mean (p). Otherwise, the resulting
probability cubes do not guarantee the reproduction of the input
constraints.
[0063] FIG. 3 illustrates a flow diagram of a method 300 for
generating a multiple facies model constrained by a facies
probability cube in accordance with implementations of various
techniques described herein. The following description of method
300 is made with reference to method 200 above and diagram 1500 of
FIG. 15. In one implementation, method 300 may be performed by a
computer application.
[0064] Method 200 generates a facies probability cube by targeting
one facies at a time. As a result, the probability cubes reflect
the spatial variation of the likelihood of the selected facies. In
reservoir modeling, however, there are often more than two facies
present within the earth. Users rarely build multiple facies
probability cubes for each facies at one time due to the difficulty
of making each facies probability cube consistent with each other.
To overcome this difficulty, method 300 and method 400, described
below, may be used to create a multiple facies model based on the
facies probability cube generated by method 200.
[0065] At step 310, the computer application may receive a facies
probability cube that may have been generated using method 200
described above. The facies probability cube as described in method
200 may also be described as a binary (grouped) facies probability
cube that includes information pertaining to a single facies. For
instance, the binary facies probability cube may be used to
indicate the probability of whether sand exists or does not exist
in an area of the earth.
[0066] At step 320, after receiving the binary facies probability
cube, the computer application may hierarchically generate an
additional binary facies probability cube. As such, the computer
application may recursively generate an additional dimensions or
facies on the binary facies cube received at step 310. In this
manner, the computer application may repeat method 200 using the
received binary facies probability cube. However, when repeating
method 200, the computer application may generate a quaternary
facies probability cube to indicate the presence of an additional
facies. For instance, if the facies probability cube received at
step 310 represented locations where sand exists in the survey
area, at step 320, the computer application may recursively
evaluate the locations where sand exists in the received facies
probability cube such that the sand locations will be categorized
into a different facies such as levees, crevasse or background.
[0067] Method 300 may be repeated using the newly generated binary
facies probability cube to determine another binary facies
probability cube. As such, method 300 may be repeated until each
individual facies probability cube has been created. At step 325,
the computer application may determine whether each individual
facies probability cube has been created. If each individual facies
probability cube has been created, the computer application may
proceed to step 330. If each individual facies probability cube has
not been created, the computer application may return to step
310.
[0068] After creating each individual facies probability cube, at
step 330, the computer application may receive a multi-facies
training image. FIG. 13 illustrates an example of a multi-facies
training image.
[0069] At step 340, the computer application may generate a
multiple-facies model based on each individual facies probability
cube. FIG. 14 illustrates an example of a multiple-facies model.
FIG. 15 illustrates how the multi-facies model 1540 is
generated.
[0070] FIG. 4 illustrates a flow diagram of a method 400 for
generating a multiple facies model constrained by a facies
probability cube in accordance with implementations of various
techniques described herein. The following description of method
400 is made with reference to method 200 above and diagram 1500 of
FIG. 15. In one implementation, method 400 may be performed by a
computer application.
[0071] At step 410, the computer application may receive a binary
(grouped) facies probability cube that may have been generated
using method 200 described above. The facies probability cube may
include the highest level or category of the facies group.
[0072] At step 420, the computer application may receive a
multi-facies training image. The multi-facies training image may be
used to obtain a multi-facies model using a multi-point statistics
algorithm. As mentioned above, FIG. 13 illustrates an example of a
multi-facies training image.
[0073] At step 430, the computer application may hierarchically
draw each individual facies at each simulated pixel in the binary
facies probability cube. In one implementation, in order to
hierarchically draw each individual facies, the computer
application may use user-defined proportions for each facies of the
multi-facies model. Using the defined proportions, the binary
facies probability cube of step 410 and the training image of step
420, at step 440, the computer application may generate the
multi-facies model using the multi-point statistics algorithm,
described in Conditional Simulation of Complex Geological
Structures Using Multiple Point Statistics. Mathematical Geology,
v. 34, p. 1-22 (Strebelle, 2002). In one implementation, method 400
may be more practical when there are distinct and clear facies
associations in the training image. By generating the multi-facies
model using the multi-point statistics algorithm, the computer
application may generate the multi-facies model once without using
a hierarchical refining process as described in method 300. As
mentioned above, FIG. 15 illustrates how the multi-facies model
1540 is generated.
[0074] Generally, method 300 may be used when many facies exist and
one-level facies grouping is not enough to resolve the variability
of spatial facies heterogeneity, but it calls for many intermediate
steps. Conversely, method 400 may be more practical when there are
distinct and clear facies associations in the training images. As
such, method 400 may recursively draw facies at each simulated
pixel/voxel during the sequential simulation by the following
rules: [0075] Assume there are A.sub.1, A.sub.2 . . . A.sub.M
(M>2) facies and group them into 2 groups: A=A.sub.1+A.sub.2+ .
. . +A.sub.S and .about.A=A.sub.s+1+A.sub.s+2++A.sub.M. [0076] For
a conditioning data B searched within a neighborhood of the
currently simulated pixel/voxel, read the
P(A|B)=P(A.sub.1|B)+P(A.sub.2|B)+ . . . +P(A.sub.2|B) from the
search tree and combine with the underlying facies probability
value (soft data) noted as P(A|C) using the Tau model, described in
Journel, A. G., 2002, Combining Knowledge From Diverse Sources: An
Alternative to Traditional Data Independence Hypotheses.
Mathematical Geology, v. 34, p. 573-596 (Journel, 2002), to obtain
P(A|B, C). [0077] Draw facies from P(A|B, C) and P(.about.A|, C).
If facies group A is drawn, renormalize P(A.sub.1), P(A.sub.2), . .
. , P(A.sub.S) to 1.0 and draw from these S facies; if facies group
.about.A is drawn, renormalize P(A.sub.s+1), P(A.sub.s+2), . . . ,
P(A.sub.M) to 1.0 and draw from these M-S facies. [0078] Assign the
simulated facies, which is one of A.sub.1, A.sub.2 . . . A.sub.M,
to the simulated pixel/voxel and then move to the next simulation
pixel/voxel.
[0079] FIG. 6 illustrates a computer network 600 into which
implementations of various technologies described herein may be
implemented. The computing system 600 (system computer) may include
one or more system computers 630, which may be implemented as any
conventional personal computer or server. However, those skilled in
the art will appreciate that implementations of various techniques
described herein may be practiced in other computer system
configurations, including hypertext transfer protocol (HTTP)
servers, hand-held devices, multiprocessor systems,
microprocessor-based or programmable consumer electronics, network
PCs, minicomputers, mainframe computers, and the like.
[0080] The system computer 630 may be in communication with disk
storage devices 629, 631, and 633, which may be external hard disk
storage devices. It is contemplated that disk storage devices 629,
631, and 633 are conventional hard disk drives, and as such, will
be implemented by way of a local area network or by remote access.
Of course, while disk storage devices 629, 631, and 633 are
illustrated as separate devices, a single disk storage device may
be used to store any and all of the program instructions,
measurement data, and results as desired.
[0081] In one implementation, well facies logs may be stored in
disk storage device 631. The system computer 630 may retrieve the
appropriate data from the disk storage device 631 to predict
effective permeabilities according to program instructions that
correspond to implementations of various techniques described
herein. The program instructions may be written in a computer
programming language, such as C++, Java and the like. The program
instructions may be stored in a computer-readable medium, such as
program disk storage device 633. Such computer-readable media may
include computer storage media and communication media. Computer
storage media may include volatile and non-volatile, and removable
and non-removable media implemented in any method or technology for
storage of information, such as computer-readable instructions,
data structures, program modules or other data. Computer storage
media may further include RAM, ROM, erasable programmable read-only
memory (EPROM), electrically erasable programmable read-only memory
(EEPROM), flash memory or other solid state memory technology,
CD-ROM, digital versatile disks (DVD), or other optical storage,
magnetic cassettes, magnetic tape, magnetic disk storage or other
magnetic storage devices, or any other medium which can be used to
store the desired information and which can be accessed by the
system computer 630. Communication media may embody computer
readable instructions, data structures or other program modules. By
way of example, and not limitation, communication media may include
wired media such as a wired network or direct-wired connection, and
wireless media such as acoustic, RF, infrared and other wireless
media. Combinations of any of the above may also be included within
the scope of computer readable media.
[0082] In one implementation, the system computer 630 may present
output primarily onto graphics display 627, or alternatively via
printer 628. The system computer 630 may store the results of the
methods described above on disk storage 1029, for later use and
further analysis. The keyboard 626 and the pointing device (e.g., a
mouse, trackball, or the like) 625 may be provided with the system
computer 630 to enable interactive operation.
[0083] The system computer 630 may be located at a data center
remote from the region were the earth formations were obtained
from. The system computer 630 may be in communication with the
logging device described in FIG. 1 (either directly or via a
recording unit, not shown), to receive signals indicating the
measurements on the earth formations. These signals, after
conventional formatting and other initial processing, may be stored
by the system computer 630 as digital data in the disk storage 631
for subsequent retrieval and processing in the manner described
above. In one implementation, these signals and data may be sent to
the system computer 630 directly from sensors, such as well logs
and the like. When receiving data directly from the sensors, the
system computer 630 may be described as part of an in-field data
processing system. In another implementation, the system computer
630 may process seismic data already stored in the disk storage
631. When processing data stored in the disk storage 631, the
system computer 630 may be described as part of a remote data
processing center, separate from data acquisition. The system
computer 630 may be configured to process data as part of the
in-field data processing system, the remote data processing system
or a combination thereof. While FIG. 6 illustrates the disk storage
631 as directly connected to the system computer 630, it is also
contemplated that the disk storage device 631 may be accessible
through a local area network or by remote access. Furthermore,
while disk storage devices 629, 631 are illustrated as separate
devices for storing input seismic data and analysis results, the
disk storage devices 629, 631 may be implemented within a single
disk drive (either together with or separately from program disk
storage device 633), or in any other conventional manner as will be
fully understood by one of skill in the art having reference to
this specification.
[0084] While the foregoing is directed to implementations of
various technologies described herein, other and further
implementations may be devised without departing from the basic
scope thereof, which may be determined by the claims that follow.
Although the subject matter has been described in language specific
to structural features and/or methodological acts, it is to be
understood that the subject matter defined in the appended claims
is not necessarily limited to the specific features or acts
described above. Rather, the specific features and acts described
above are disclosed as example forms of implementing the
claims.
* * * * *