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

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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

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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

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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

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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

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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

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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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REFERENCES 357

358

1. Warren, J.E. and Root, P.J., 1963, The behavior of naturally fractured reservoirs, Soc. Petr. 359

Eng. J., 3(3), 245-255. 360

2. Dean R.H. and Lo, L.L, 1988, Simulations of naturally fractured reservoirs, SPE Res. Eng., 361

3(2), 638-648. 362

3. Dershowitz, B., LaPointe, P., Eiben, T., Wei, L., 2000, Integration of discrete feature 363

network methods with conventional simulator approaches, SPE Res. Evaluation and Eng. 364

3(2), 165-270 365

4. Cacas, M.C., Daniel, J.M., Letouzey, J., 2001, Nested geological modeling of naturally 366

fractured reservoirs. Pet Geosci, 7, 43-52. 367

5. Kemeny, J. and Post, R., 2003, Estimating three-dimensional rock discontinuity orientation 368

from digital images of fracture traces, Computers and Geosciences, 29(1), 65-77. 369

6. Tran, H.N., Chen, Z., Rahman, S.S., 2006, Integrated conditioning global optimization for 370

discrete fracture network modeling, Computers and Geosciences, 32, 17-27. 371

7. Boisvert J., Leuangthing, O., Ortiz, J., Deutsch, C.V., 2008, A methodology to construct 372

training images for vein-type deposits. Computers and Geosciences 34(5), 491-502 373

8. Caers, J., 2013, Editorial: A special issue on benchmark problems, datasets and 374

methodologies for the computational geosciences. Computers & Geosciences, 50, 1-3. 375

9. Arnold, D., Demyanov, V., Tatum, D., Christie, M., Rojas, T., Geiger, S., Corbett, P., 2013, 376

Hierarchical benchmark case study for history matching, uncertainty quantification and 377

reservoir characterization. Computers and Geosciences 50, 4-15 378

10. De Dreuzy, J. R., Pichot, G., Poirriez, B., & Erhel, J., 2013, Synthetic benchmark for 379

modeling flow in 3D fractured media. Computers & Geosciences, 50, 59-71. 380

11. Roubinet, D., De Dreuzy, J. R., Tartakovsky, D. M., 2013, Particle-tracking simulations of 381

anomalous transport in hierarchically fractured rocks. Computers and Geosciences, 50, 52-382

58. 383

12. Roy, A., Shin, Y, Aydin, O., Mukerji, T. and Caers, J., 2014, “The Benchmark Case: A 384

Deterministic Scenario after the Clair Field”: 27th Annual Report, Stanford Center for 385

Reservoir Forecasting, Stanford University, Stanford, CA. 386

14

13. Morton, A., & Milne, A., 2012, Heavy mineral stratigraphic analysis on the Clair Field, UK, 387

west of Shetlands a unique real-time solution for red-bed correlation while drilling. 388

Petroleum Geoscience, 18(1), 115-128. 389

14. Castro, S., Caers, J., and Mukerji, T., 2005, “The Stanford VI reservoir”: 18th Annual 390

Report, Stanford Center for Reservoir Forecasting, Stanford University, Stanford, CA. 391

15. Lee, J. and Mukerji, T., 2012, “The Stanford VI-E reservoir: A synthetic dataset for joint 392

seismic-EM time-lapse monitoring algorithms”: 26th Annual Report, Stanford Center for 393

Reservoir Forecasting, Stanford University, Stanford, CA. 394

16. Avseth, P., Dvorkin, J., Mavko, G., and Rykkje, J., 2000, Rock physics diagnostic of North 395

Sea sands: Link between microstructure and seismic properties, Geophysical Research 396

Letters, 27, no. 17, 2761-2764. 397

17. Gardner, G. H. F., Gardner, L. W., & Gregory, A. R., 1974, Formation velocity and density-398

the diagnostic basics for stratigraphic traps. Geophysics, 39(6), 770-780. 399

18. Castagna, J. P., Batzle, M. L., & Eastwood, R. L., 1985, Relationships between 400

compressional-wave and shear-wave velocities in clastic silicate rocks, Geophysics, 50, 401

no.4, 571 - 581. 402

19. Mallet, J. L. L., 2002, Geomodeling: Oxford University Press, Inc. 403

20. Das, S.K., and Basudhar, P.K., 2006, Comparison study of parameter estimation techniques 404

for rock failure criterion models. Canadian geotechnical journal, 43(7), 764-771 405

21. Chang, C., Zoback, M. D., & Khaksar, A., 2006, Empirical relations between rock strength 406

and physical properties in sedimentary rocks. Journal of Petroleum Science and 407

Engineering, 51(3), 223-237 408

22. Johri, M., Zoback, M. D., & Hennings, P., 2014, A scaling law to characterize fault-damage 409

zones at reservoir depths. AAPG Bulletin, 98(10), 2057-2079. 410

23. Jung, A., Fenwick, D.A., Caers, J., 2013, Training image-based scenario modeling of 411

fractured reservoirs for flow uncertainty quantifications. Computers and Geosciences, 17, 412

1015-1031. 413

24. Hudson, J. A., 1990. Overall elastic properties of isotropic materials with arbitrary 414

distribution of circular cracks, Geophysical Journal International, 102 no.2, 465-469. 415

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

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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