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1
A Benchmark Dataset for Fractured Reservoirs 1
2
3 Ankur Roy
1 4
5 Yongduk Shin
1 6
7 Peipei Li
1 8
9 Orhun Aydin
1 10
11 Andre Jung
1, 3 12
13 Tapan Mukerji
1, 2,* 14
15 Jef Caers
4 16
17
18 19 20
1Department of Energy Resources Engineering 21
367, Panama Mall 22
Green Earth Sc. Building, 050 23 Stanford University 24
Stanford, CA 94305-4007 25
26 2Department of Geophysics 27
397, Panama Mall 28 Mitchell Building, 3rd Floor 29
Stanford University 30 Stanford, CA 94305-2215 31
32 3Shell Global Solutions 33
Rijswijk, The Netherlands 34 35
4Department of Geological Sciences 36
367, Panama Mall 37
Stanford University 38
Stanford, CA 94305-4007 39
40
41
*corresponding author (mukerji@stanford.edu) 42
43
2
ABSTRACT 44
A benchmark synthetic fractured reservoir dataset is built comprising about two million grid 45
cells with details on geological, geomechanical and geophysical properties. This synthetic 46
dataset is intended to serve as a test bed for algorithms and workflows aimed at prediction of 47
subsurface geology, reservoir modeling and forecasting in fractured reservoirs. The synthetic 48
model starts with a three-layered subsurface geology reflecting aeolian, fluvial and coastal 49
environments and major sealing faults that dissect the domain into a “core”, “graben” and a 50
“horst” area. The entire reservoir is populated with relevant facies properties, porosity and 51
permeability. Fracture intensity and orientation distributions are computed from geomechanical 52
constraints. The influence of these fractures on elastic properties and seismic responses is 53
evaluated based on computation of the effective elastic stiffness tensor. A subset within the 54
middle-layer of the core region is considered to be the “area of interest”. This region is populated 55
with fractures invoking a discrete fracture network (DFN) model by taking into account fracture 56
intensity and orientations computed from geomechanical constraints. Next, two new intensity 57
maps are generated by assuming an unknown subsurface and that the only available data come 58
from wells drilled into the area of interest and seismic properties. A set of ninety-six DFN 59
models are then generated based on these maps and orientation data from the wells. Finally, 60
these are compared to each other by means of flow response curves. Distance-based sensitivity 61
analysis (DGSA) is invoked for determining DFN parameters that mostly influence flow in a 62
reservoir. 63
Keywords: Faults, DFN, Fracture Intensity, Rock Physics, Seismic Velocity, Clair Field, 64
Sensitivity Analysis, Streamline-based Simulator 65
3
1. INTRODUCTION 66
Fractured reservoirs are challenging to model in both conventional and unconventional 67
resources. Unlike un-fractured systems, where the modeling comes down to structure, facies, and 68
rock properties, the addition of fractures in the modeling workflow add to the complexity but are 69
nonetheless, important because they can have a significant impact on the flow response of the 70
reservoir. Therefore, such reservoirs are widely studied and algorithms are developed for 71
generating fractures and evaluating their flow properties that range from Discrete Fracture 72
Network (DFN) approaches to dual media flow modeling [1-7]. Benchmark reference datasets 73
are very useful for extensive testing of any proposed technique for modeling fractured reservoirs, 74
their characterization, and forecasting before applying them to real cases. While many studies on 75
benchmark problems exist, quite inadvertently, most of such synthetic data sets were generated 76
favoring a specific developed methodology [8]. A more recent publication on benchmark data for 77
subsurface overcomes this and includes full complexity in geological description of un-fractured 78
reservoir [9]. Benchmark case studies also exist on fractures at smaller scales [10, 11]. There is 79
however, a dearth of literature when it comes to a detailed synthetic dataset on fractures at the 80
reservoir scale that can be used by geologists, geophysicists and reservoir engineers for testing 81
different types of algorithms. 82
Generating such a benchmark dataset is a major challenge because a hydrocarbon 83
reservoir is a complex earth system delineated by various types of characteristics. The present 84
research documents a robust dataset comprising details on geologic structure, facies, rock 85
properties and fracture intensity along with field scale seismic responses. Many of the details 86
such as equations invoked in some calculations and the details of steps involved in generating 87
structure, stratigraphy and reservoir properties in specific software (SKUA) can be found in [12]. 88
It has to be kept in mind that this is not a typical “modeling” study. Rather, we assume complete 89
knowledge of the subsurface, and create a “geologically realistic” fractured reservoir from 90
scratch. This is an integrated study that synthetically generates various data types at different 91
scales and involves components of geology, geophysics and reservoir engineering. To impart 92
realism, the setting of the reservoir is based loosely after the Clair field located west of the 93
Shetland Islands on the UK continental shelf. The benchmark reservoir has a geology comprised 94
of three layers reflecting aeolian, fluvial and coastal environments. A set of faults dissect the 95
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entire domain into a “core”, “graben and “horst” conforming to an extensional setting as 96
observed in the Clair field. 97
The next section describes our workflows for creating the facies model, which are then populated 98
with petrophysical and elastic properties using rock physics relations. Fracture intensities and 99
orientations are modeled in the middle-layer and their seismic signatures are computed. 100
Finally, in section 3, we discuss an example of how this synthetic dataset can be put to use by 101
geoscientists. We demonstrate a sensitivity study of fracture parameters and identify those that 102
influence most the production rates. A DFN is first built in a smaller “area of interest” within the 103
middle-layer of the core region by using fracture intensity and orientations in each cell as defined 104
in the Benchmark reservoir such that it represents fractures present in the “true subsurface” and 105
treat this as a reference. This is then upscaled for obtaining effective fracture porosity, 106
permeability and intensity. Then, it is assumed that the Benchmark reservoir which represents 107
the true subsurface is unknown and we only have data from well-logs and seismic velocities 108
from this reservoir. Based on these data, new realizations of matrix porosity-permeability and 109
fracture intensity are generated. Thereafter, ninety-six DFNs are built considering the new 110
fracture intensity values and using fracture orientation data from well-logs. Length, aspect ratio 111
and fracture orientations are varied in creating the DFNs that are finally upscaled for generating 112
effective fracture properties and computing flow responses. 113
114
2. GENERATING THE BENCHMARK DATA 115
2.1 Structure and Stratigraphy 116
The reservoir is created with three units or layers, each reflecting a different geological 117
environment. Fig. 1 shows the structural setting of the Benchmark reservoir built within a 6km x 118
7km domain. Five horizons are created that define these units and a number of faults are added, 119
thus introducing structural complexities. A few major sealing faults dissect the domain into a 120
“core”, “graben” and a “horst” loosely reflecting the structure of the Clair field. Maps and cross-121
sections of the Clair field [13] are used as a guideline for creating the structure and stratigraphy 122
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of the synthetic Benchmark reservoir. Each of the three layers has an average thickness of 150 123
meters and is discretized into 50 vertical grid blocks. 124
After the structural components are created and the domain is gridded with about 2 125
million cells, the reservoir is populated with facies that represent different depositional 126
environments – aoelian, fluvial and coastal or shoreface from bottom to top (Fig. 2). A set of 127
seven facies were created implementing object based modeling: fan and fan-channels in lower 128
section of middle layer, channels in the upper section (running perpendicular to fans) and 129
channels, lobes, drapes in the top layer (coastal). Remaining areas where none of the three facies 130
are present are considered as floodplain, this comprises about 80% of the facies proportion in the 131
top layer and about 50% in the middle layer. The bottom layer is aeolian sandstone. 132
The facies are built using SGeMS (Stanford GEostatistical Modeling Software) and are 133
later imported into SKUA and integrated with the main model. A built-in object-based modeling 134
module in SGeMS, SGeMS-TetrisTiGen that implements simplified geometric representations of 135
geological features is employed. 136
2.2 Initial Reservoir Properties 137
Matrix porosity is simulated by using sequential Gaussian simulation (SGSIM) for each 138
facies individually with different distributions across facies boundaries. The aeolian sand is 139
assigned relatively high porosity while the middle layer is created with low porosity values. The 140
top layer is populated with porosity values larger than the middle layer. The porosity of middle 141
layer is kept low because this is the layer where we will generate fractures and a low porosity-142
permeability unit would enhance the effect of fractures on flow properties. A different target 143
histogram and variogram is used for generating the porosity distribution for each facies using 144
unconditional SGSIM. Fig. 3 shows the resultant porosity distributions that mimic the facies 145
distribution in each layer and some of the target histograms used. For example, the target 146
histogram for channel facies in the top layer (brown) has higher porosity than that of the middle-147
layer (cyan). The matrix permeability is assumed to be isotropic and is computed as a function of 148
porosity for each facies using Kozeny-Carman relationship. 149
The elastic moduli, densities and P- and S-wave velocities of the un-fractured matrix are 150
modeled using standard rock physics workflows, similar to the ones described in [14,15]. The 151
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bulk density of matrix filled with pore water is calculated by using simple volumetric average of 152
mineral component in each facies and a reference pore fluid, assumed to be brine. A theoretical 153
relationship, the constant-cement model [16], is used for calculating P-wave velocity of sand 154
facies, while Gardner’s density-P velocity relation is used to model P-wave velocity of non-sand 155
facies [17]. Established empirical Vp-Vs relations, Castagna’s relations, are used for S-wave 156
velocity of sand and non-sand facies [18]. The background un-fractured medium is considered 157
isotropic and values of shear modulus, bulk modulus, Lame’s parameter, Poison’s ratio and 158
Young’s modulus are calculated from the P- and S-wave velocities and density. The spatial 159
distributions of some of these elastic moduli are shown in Fig. 4. All elastic moduli except 160
Poisson’s ratio have units of stress (GPa). Note how the spatial distribution closely follows the 161
facies distribution. Once the elastic properties are computed for the reference fluid, they can be 162
obtained for any other saturation state using standard fluid substitution models of rock physics 163
(i.e. Gassmann’s equations). 164
2.3 Generating Fracture Intensity in the Middle Layer 165
Fractures are created only within the sand facies of the middle-layer. Since it not a 166
modeling exercise, generating fractures is noticeably different compared to modeling DFNs in a 167
reservoir model. Where statistical data on fractures exist, such as fracture intensity, scale, and 168
their directions, the information on how the fractures have been generated is not required to run a 169
DFN model. However, since this is an exercise in creating ab initio a synthetic dataset, it is 170
assumed that the fractures were formed when the horizons were deformed and faulted to their 171
current shapes. We derive relative fracture intensity from two different sources: (1) stress/strain 172
induced rock failures and, (2) distance from the major faults. 173
For calculating relative fracture intensity from stress-strain, first the principal strain 174
components and their directional vectors are found from restoration/deformation vectors that 175
return the current geological structure to its syn-depositonal condition of flat un-faulted horizons 176
[19]. Then, principal stress components of induced deformation are calculated from elastic 177
properties of rocks by invoking Hooke’s law. Rock strength parameters (friction angles, cohesion 178
strength, and tensile strength) are obtained from either literature (e.g. friction angles; [20]) or 179
empirical relations with other petrophysical properties (e.g. cohesion strength; [21]). Fig. 5 180
shows how stress/strain induced relative fracture intensity is generated. Parameters with relative 181
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values are marked by a “*”, those with fixed values are in red boxes while blue boxes indicate 182
parameters having a range of values. Using Mohr-Coulomb failure criterion, a probability of 183
failure is calculated from the ranges of stress and the ranges of rock strength and is considered as 184
a proxy for relative fracture intensity related to strain/stress induced fracturing. The dip and dip 185
azimuth of the fractures are calculated from the most tensile strain direction (max. principal 186
strain) which is assumed to be the normal to the fracture plane. The median value for fracture dip 187
is about 41°. 188
Major faults have zones of high fracturing around them popularly known as “damage 189
zones”. There have been a number of studies that have focused on the thickness and other 190
geometrical and hydrologic properties of these zones [22]. It has been shown that the fracture 191
intensity within the damage zone falls off with distance from the main fault according to a 192
power-law. Relative fracture intensity, fi based on distance, d from major faults was generated 193
using the following relationship: fi ~ 1/√d. Fig. 6 shows the distance from faults and the 194
resulting relative fracture intensity. Finally, fracture intensity in the middle layer is calculated by 195
linearly adding intensity values arising out of stress/strain induced rock failure and fault induced 196
damage (Fig. 7). 197
2.4 Generating Seismic Responses 198
The entire reservoir is compartmentalized into five zones, each with a different oil-water 199
contact (OWC). In order to create seismic properties considering initial fluid saturation and 200
OWC, fluid substitution must be done on elastic properties. For the top and bottom layers where 201
the block properties are isotropic, bulk and shear moduli of the rock with new fluid saturations 202
are obtained by applying Gassmann’s equations on the initial elastic moduli with reference pore 203
fluid (brine) described in section 2.2. P- and S-wave velocities were computed from elastic 204
moduli and density. Fig. 8 shows the P-wave and S-wave velocity for the top and the bottom 205
layers with the initial saturation. The middle layer is excluded. While P-wave velocity above 206
OWC is noticeably lowered by fluid substitution, S-wave velocity does not vary much. This is 207
because the density difference is relatively small, and the shear modulus is not changed by 208
changing fluid phases, when considering low frequency waves (~ 25-50 Hz) appropriate for 209
surface seismic frequencies. 210
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Once aligned fractures are introduced in the middle layer, the elastic properties are no longer 211
isotropic. First, stiffness tensor for each grid block was generated for dry matrix and fractures by 212
invoking the Hudson’s crack model [24]. It may be noted that any other appropriate effective 213
medium crack model can also be used in this step for computing the effective elastic tensor of 214
rocks with aligned fractures. All such models involve idealizations with respect to the fracture 215
geometry and different approximations related to multiple fracture-to-fracture elastic 216
interactions. Hudsons’ model, like many other crack models, assumes penny-shaped cracks and 217
calculates effective medium stiffness tensors by superposing correction terms on a background 218
isotropic medium. The effective elastic anisotropy depends on the crack density (related to 219
fracture intensity) and aspect ratio. Brown-Korringa’s equations [25] (or equivalently, the 220
anisotropic form of Gassmann’s equations) were then used for fluid substitution to calculate 221
stiffness tensors with initial fluid saturations. Once the elastic tensor is obtained for every grid 222
block, the seismic phase velocities for P-waves and fast and slow S-waves in any arbitrary 223
direction of wave propagation can be calculated using the Christoffel’s equation [26]. 224
Instead of using computationally expensive full-waveform anisotropic elastic wave 225
propagation to generate the synthetic seismic response, we chose a computationally cheaper 226
approximation based on upscaling grid-block scale seismic velocities to the appropriate seismic 227
resolution. A low-pass filter derived from a Born approximation is used to generate 228
representations of seismic imaging responses of velocity and impedance field [27]. The filter, 229
calculated in the Fourier domain, depends on the source-receiver geometry with respect to the 230
target zone being imaged, and the signal bandwidth. We use a source-receiver spread of -6000m 231
to +6000m, target depth of 2.5km and frequency range of 25-50Hz. Fig. 9 shows P-wave 232
impedance (Z-direction) for the middle-layer at gird-scale and field-scale resolutions. 233
234
3. AN EXAMPLE USE OF THE BENCHMARK DATA 235
The Benchmark reservoir we have created will be useful to researchers who are interested 236
in extensive testing of their algorithms for prediction of subsurface geology, reservoir modeling 237
and forecasting performance in fractured sandstone reservoirs. Such endeavors can range from 238
exercises where a new set of properties are created within some volume of interest from well 239
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data and some auxiliary data to ones involving model selection for generating training images. 240
Knowing the “true” subsurface as a reference can be of advantage because in real world 241
scenarios there is no direct information on this. In this section, we demonstrate one such 242
application of this dataset. We take a two-step approach. First, generate a DFN within a subset 243
region of the core within the middle layer, our “area of interest”, by using fracture intensity and 244
orientations in each cell as defined in the Benchmark reservoir such that it represents all fractures 245
present in the “true subsurface” and treat this as a reference. Next, assume that the true 246
subsurface is actually unknown and that the only data we have are well-logs for porosity, fracture 247
intensity and orientation and, some seismic attributes. Then, using this sparse “dataset” we 248
generate several DFN models that endeavor to capture our reference DFN in terms of its flow 249
response. In the process, we attempt to identify fracture parameters that have the most impact on 250
field production. 251
A DFN is built in a smaller 3km x 2km region which is our “area of interest”. A different, 252
coarser gird is first created here such that it can be used directly for purposes of flow simulation 253
at a later stage. Properties are copied to this grid from the previous finer one as shown in Fig. 7 254
(fracture intensity). Information on fracture orientation and intensity is used for building the 255
DFN with a uniform length distribution (mean length ~ 5m) and a median aperture value of ~ 256
1mm, the length to height ratio being one. These values are chosen so they may represent 257
subseismic fractures. After the DFN is generated, fracture porosity, permeability, shape factor 258
and intensity values are upscaled. Following the steps laid down in [23], the upscaled fracture 259
porosity is threshold at 0.4E-05 for creating a binary indicator grid identifying cells to be 260
modeled with either dual or single media (matrix only) porosity-permeability values. Fig. 10 261
shows the DFN, upscaled porosity and the dual media/single media grid thus obtained. This grid 262
will be used for generating flow responses. 263
Two new fracture intensity maps are chosen from a handful of realizations simulated 264
using conditional SGSIM conditioned to fracture intensity from wells as hard data and seismic 265
data as secondary or soft data using collocated cokriging within SGSIM. The fractures are below 266
seismic resolution and a number of fracture parameters are uncertain. To investigate the 267
sensitivity of these fracture parameters on the flow response, we use experimental design and use 268
these two intensity maps in conjunction with varying length, aspect ratio and orientation, 269
10
generating a total of ninety-six DFN models. Each DFN has two sets of fractures because well 270
data from our area of interest shows two sets of fractures with dip azimuths around 0° and 255 as 271
seen in Fig. 11. The parameters thus explored are explained in table-I. For each map, three 272
different types of relative lengths are considered for the two sets: long-long, short-short and 273
long-short. For each length-type, uniform and power-law distributions are used in order to 274
investigate the effect of length distribution. The ratio between fracture height and fracture length 275
(aspect-ratio) is assigned values of 1:1 and 1:2. While keeping the dip of the first set fixed at 30°, 276
the dip of the second set is given values of 40° and 70° to represent moderate versus steeply-277
dipping fractures. Finally, instead of merely using fixed values for the orientations of the fracture 278
sets, the spatial distribution of the fracture normals are modeled as either tight or dispersed by 279
drawing values from a Fisher distribution and using a K-parameter of 100 and 30 respectively. 280
Now that we have built the ninety-six discrete fracture networks, we need to upscale 281
them to get effect reservoir properties and translate them to dual-medium reservoir models for 282
flow simulation. First, the fractures are upscaled to get the effective porosity, permeability and 283
shape factors. Then, as in the reference DFN case, a cutoff value of the upscaled fracture 284
porosity is used to create a binary indicator grid identifying dual media cells and single media 285
cells [23]. Fig. 12 shows one of the 96 DFNs and its corresponding dual-medium indicator grid. 286
In addition to varying the parameters discussed in table-I that have been used to build the ninety-287
six DFNs, we also simulated two different scenarios of matrix properties to inspect the effect of 288
matrix in such a reservoir. The matrix porosity is generated from the available well-data using 289
conditional SGSIM. The matrix permeability is then generated using CO-SGSIM by 290
conditioning to the well data and simulated porosity. Thus, in the end, there are 96 x 2 = 192 291
flow responses in total that are used as inputs for distance-based general sensitivity analysis 292
(DGSA) [28]. 293
A commercial streamline-based simulator, 3DSL is used for computing flow simulations 294
with two injector wells and two producer wells (Fig. 13). 3DSL invokes the formulae laid down 295
by Di Donato et al. [29] and assumes matrix/fracture transfer of oil/water based on imbibition 296
only. While the production rate may not be accurate compared to a full field flow simulator, it 297
does not affect the end-results because the goal here is to compare the responses of different 298
11
models and not estimate production rates of a particular field. The response curves, field oil-299
production rate for all 192 runs are shown in Fig. 13. 300
We analyze the impact of DFN parameters (Table I) and matrix properties, using DGSA 301
with these 192 response curves. This technique clusters models into several groups based on 302
some distance between them. For our purpose, Euclidean distance is calculated between the flow 303
response curves and k-medoid algorithm is used to cluster the responses. Fig. 15 shows the final 304
sensitivity analysis results and indicates that the parameters that are most sensitive in dominating 305
field productions are fracture intensity, fracture length-type, matrix properties and fracture dip. 306
However, comparing to the other three sensitive parameters, fracture dip is less important as its 307
average standardized L1-norm distance is below one. Aspect ratio, fracture length distribution 308
and K-parameter are found to be not as important. Fig. 16 shows MDS plots of the 192 flow 309
responses in 2D. In each figure, models are color coded based on the parameter whose influence 310
is visualized. Fracture intensity, fracture length-type and matrix properties are shown in figs. 16 311
a, b and c respectively. It is no surprise that models with different fracture intensity form tighter 312
clusters. Models with long-long (black circles) and short-short (blue) fractures form two clusters 313
while those with long-short fractures (green) are found in both groups. Finally, models with 314
different matrix properties do not form distinct clusters because this parameter is the least 315
influential one amongst the three. 316
While this is one of the simpler example uses of the Benchmark dataset, it is important to 317
point out that this data may be used for more sophisticated applications. For example, one might 318
be interested in building training images and generate MPS-based realizations from them, in 319
conjunction with auxiliary (seismic) data as well as hard (well) data to see if a single DFN model 320
of a reservoir with data from one production phase can be used to forecast recovery during a later 321
phase in a new, relatively underexplored zone. Similarly one can test the impact of different 322
seismic attributes (e.g. azimuthal travel-time anisotropy, shear-wave splitting, etc.) on 323
constraining the sub-seismic fracture distributions. 324
325
326
327
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4. CONCLUDING REMARKS 328
This research documents the workflow for creating a synthetic Benchmark fractured 329
reservoir that we hope will prove useful to researchers who want to test their proposed 330
algorithms for fractured reservoir modeling, characterization, forecasting, and management 331
before applying them to real cases. It is a robust dataset with information on structure, 332
straigraphy, reservoir properties, fracture intensity and orientation and seismic responses at field-333
scale. An important aspect of this exercise is the integration of geological restoration analysis 334
with geomechanical and rock physics models for assessing the spatially varying seismic response 335
of fractured reservoirs. We also demonstrate an example application of this dataset whereby a 336
DFN with is created in an area of interest by considering cell-by-cell information on intensity 337
and orientation values of the Benchmark. This DFN acts as a reference case and is compared to 338
94 DFNs generated using sparse data from wells drilled into the Benchmark reservoir and its 339
field-scale seismic properties. This is done by the means of comparing flow response curves. 340
Finally, DGSA is invoked in delineating fracture parameters that are most influential in 341
controlling flow properties. This project lays the foundation for future work that may include a 342
range of possible applications from MPS-based realizations from training images, auxiliary 343
variables from seismic properties and hard-data from wells to running flow simulations for 344
evaluating the role of fractures in sandstone reservoirs. 345
The Benchmark dataset along with the “reference DFN” is available on Stanford Digital 346
Repository at: http://purl.stanford.edu/bp332mt0871 347
348
Acknowledgments 349
We would like to thank Tim Lane and Aoife Toomey of BP for their collaboration and support 350
and acknowledge the contributions from Emmanuel Gringarten of Paradigm for providing 351
technical support for SKUA and arranging workshops for the users. In addition, we thank 352
Streamsim Technologies for the use of 3DSL and studioSL. Funding for this project has been 353
made possible by sponsors of the Stanford Center for Reservoir Forecasting group, special 354
thanks to BP for providing funding for part of this research. Finally, we also thank Madhur Johri 355
of BP for his intellectual and technical inputs. 356
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25. Brown, R., and Korringa, J., 1975, On the dependence of the elastic properties of a porous 416
rock on the compressibility of the pore fluid, Geophysics, 40, 608-616 417
15
26. Auld, B. A., 1990, Acoustic fields and waves in solids, vol. 1, 2, Robert E. Krieger Pub. Co. 418
27. Mukerji, T., Mavko, G., Rio, P. 1997, Scales of reservoir heterogeneities and impact of 419
seismic resolution on geostatistical integration, Mathematical Geology, 29, no. 7, 933-950. 420
28. Fenwick D., Scheidt C. and Caers J., 2014, Quantifying Asymmetric Parameter Interactions 421
in Sensitivity Analysis: Application to Reservoir Modeling: Mathematical Geosciences, 422
Volume 46, Issue 4, 493-511. 423
29. Di Donato G., Huang W., and Blunt M., 2003, Streamline-based dual porosity simulation of 424
fractured reservoirs, SPE 84036, Proceedings of the SPE Annual Technical Conference and 425
Exhibition, Denver, Colorado, U.S.A., 5-8 October 2003. 426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
16
Table I: Parameters variations used in the experimental design for generating 96 DFNs 442
Parameter Scenarios Considered
Fracture Intensity Map 1 Map 2
Length Long-Long Short-Short Long-Short
Length Distribution Uniform Power-law
Aspect Ratio 1:1 1:2
Dip 30° -40° 30° -70°
K-parameter 30 100
17
FIGURE LIST
Figure 1: Structural setting of Benchmark reservoir showing faults and horizons. Faults
separating the core, horst and graben are shown in red, others are in yellow
Figure 2: Three-layer stratigraphy of Benchmark reservoir
Figure 3: Layer-wise facies controlled porosity distribution. Note: each facies has a different
target histogram used for creating the porosity using unconditional SGSIM
Figure 4: Elastic properties of the unfractured brine-saturated rock matrix in the benchmark
reservoir: bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio
Figure 5: Schematic diagram showing generation of stress-strain induced relative fracture
intensity. Starred (*) parameters have a range of values
Figure 6: Fracture intensity in the fault damage zones derived from distance to faults
Figure 7: Combined fracture intensity shown in 7km x 6km geologic grid (cell-size: 30m x 30m
x 3m) and 3km x 2km flow grid (cell-size: 60m x 60m x 7m) constructed for volume of interest
Figure 8: Initial saturation of the benchmark reservoir and corresponding P-wave and S-wave
velocities. Middle layer is excluded
Figure 9: P-wave impedance (Z-axis) for middle layer at fine scale and field scale. Note how
channels become “blurred” when filtered to field scale-resolution
Figure 10: Generation of dual-single media grid from DFN via upscaling and thresholding
porosity values. Cells with values below threshold are single-media cells in blue while dual
media cells are in red
Figure 11: Rose diagram of dip azimuth from well data showing two dominant trends, 0° and
255°
Figure 12: A typical DFN model out of the 96 realizations and its corresponding dual-
media/single media indicator grid
Figure 13: Locations of injector wells (blue) and producer wells (red) within region of interest
Figure 14: Field oil production rate with time (days) for 192 realizations
Figure 15: Results of sensitivity analysis with DGSA using proxy flow responses in fig. 14
Figure 16: MDS plots of 192 flow responses: models are color coded based on the parameter
whose influence is visualized: (a) fracture intensity (b) fracture length-type (c) matrix properties
18
Figure 1: Structural setting of Benchmark reservoir showing faults and horizons. Faults separating the
core, horst and graben are shown in red, others are in yellow
Figure 2: Three-layer stratigraphy of Benchmark reservoir. Each layer is about 50m thick
19
Figure 3: Layer wise facies controlled porosity distribution. Note: each facies has a different
target histogram used for creating the porosity using unconditional SGSIM
Figure 4: Elastic properties of the benchmark reservoir (brine saturated): bulk modulus, shear
modulus, Young’s modulus, Poisson’s ratio
20
Figure 5: Schematic diagram showing generation of stress-strain induced relative fracture
intensity from considering mode of failure. Starred (*) parameters have a range of values
Figure 6: Relative fracture intensity in fault damage zones derived from distance to faults
21
Figure 7: Combined fracture intensity shown in 7km x 6km geologic grid (cell-size: 30m x 30m
x 3m) and 3km x 2km flow grid (cell-size: 60m x 60m x 7m) constructed for volume of interest
Figure 8: Initial Saturation of the benchmark reservoir and corresponding P-wave and S-wave
velocities. Middle layer is excluded
22
Figure 9: P-wave impedance for middle layer at fine scale and field scale. Note how channels
become “blurred” when filtered to field scale-resolution
Figure 10: Generation of dual-single media grid from reference DFN via upscaling and
thresholding porosity values. Cells with values below threshold are single-media cells in blue
while dual media cells are in red
23
Figure 11: Rose diagram of dip azimuth from well data showing two dominant trends, 0° and
255°
Figure 12: A typical DFN model out of the 96 realizations its corresponding dual-media/single
media indicator grid
24
Figure 13: Locations of injector wells (blue) and producer wells (red) within region of interest
Figure 14: Field oil production rate with time (days) for 192 realizations
25
Figure 15: Results of sensitivity analysis with DGSA using proxy flow responses in fig. 14
26
(a)
(b) (c)
Figure 16: MDS plots of 192 flow responses: models are color coded based on the parameter
whose influence is visualized: (a) fracture intensity (b) fracture length-type (c) matrix properties
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