To the University of Wyoming:The members of the Committee approve the dissertation of Ye Li presented on

January 31, 2014.

Ye Zhang, Chairperson

Brian F. Towler, External Department Member

Shaochang Wo

Subhashis Mallick

Erin A. Campbell-Stone

APPROVED:

Paul L. Heller, Head, Department of Geology and Geophysics

Gregory K. Brown, Dean, College of Arts & Sciences

Li, Ye, An Uncertainty Analysis of Modeling Geologic Carbon Sequestration in a Naturally

Fractured Reservoir at Teapot Dome, Wyoming, Ph.D., Department of Geology and

Geophysics, January, 2014.

This study presents an uncertainty analysis of Geologic Carbon Sequestration modeling

in a naturally fractured reservoir at Teapot Dome, Wyoming. Structural & stratigraphic,

residual, and solubility trapping mechanisms are the focus of this study, while mineral trap-

ping is not considered. A reservoir-scale geologic model is built to model CO2 storage in the

Tensleep Sandstone using a variety of site characterization data that have been collected,

screened for accuracy, and analyzed. These data are from diverse sources, such as reservoir

geology, geophysics, petrophysics, engineering, and analogs. Because fluid flow occurs in

both matrix and fractures of the Tensleep Sandstone, both systems of heterogeneity must

be incorporated into the geologic model. The matrix heterogeneity of the geologic model is

developed through a hierarchical process of structural modeling, facies modeling, and petro-

physical modeling. In structural modeling, the framework of the reservoir is conditioned to

seismic data and well log interpretations. Based on the concept of flow units, the facies model,

which is conditioned to a global vertical facies proportion curve that acts as soft data, is

built geostatistically by the Sequential Indicator Simulation method. Then, the petrophysi-

cal properties (porosity) are modeled geostatistically within each facies through the Sequen-

tial Gaussian Simulation approach. A Discrete Fracture Network (DFN) is adopted as the

method to model the distribution of open natural fractures in the reservoir. Basic inputs for

the DFN model are derived from FMI logs, cores, and analogs. In addition, in combination

with an artificial neural network analysis, 3D seismic attributes are used as fracture drivers

to guide the modeling of fracture intensity distribution away from the boreholes. In DFN

models, power laws are adopted to define the distribution of fracture intensity, length and

aperture.

To understand the effect of model complexity on CO2 storage predictions, a suite of

increasingly simplified conceptual geologic model families are created with decreasing amount

of site characterization data: a hierarchical stochastic model family conditioned to soft data

(FAM4), a simple stochastic facies model family (FAM3), a simple stochastic porosity model

family (FAM2), and a homogeneous model family (FAM1). These families, representing

1

alternative conceptual geologic models built with increasing reduced data, are simulated

with the same CO2 injection test (20 years of injection at 1,000 Mscf/day), followed by 80

years of monitoring. Using the Design of Experiment, an efficient sensitivity analysis (SA) is

conducted for all families, systematically varying uncertain input parameters, while assuming

identical well configurations, injection rates, bottom-hole pressure constraints, and boundary

conditions. The SA results are compared among the families to identify parameters that have

1st order impact on predicting the CO2 storage ratio (SR) at two different time scales, i.e.,

end of injection and end of monitoring. This comparison indicates that, for this naturally

fractured reservoir, the facies model is necessary to study the sensitivity characteristics of

predicting the CO2 storage behavior. The SA results identify matrix relative permeability,

fracture aperture of fracture set 1, and fracture aperture of fracture set 2 as the statistically

important factors. Based on the results of the SA, a response surface analysis is conducted

to generate prediction envelopes of the CO2 storage ratio, which are also compared among

the families at both times. Its results demonstrate that the SR variation due to the different

modeling choices is relatively small. At the proposed storage site, as more than 90% of

injected CO2 is probably mobile, short-term leakage risk is considered large, and it depends

on the sealing ability of top formations.

yzhang9CalloutThe Tensleep Sandstone has significant porosity and permeability in both the sandstone matrix and in the fracture networks that percolate through the matrix. Ignoring each type of heterogeneity in building and simulating CO2 storage will likely lead to biased or inaccurate CO2 predictions. However, the considerable complexity of both matrix and fracture heterogeneity also requires us to understand the level of detail that needs to be included in building the geologic model, thus resources can be used appropriately. This study explicitly models both matrix and fracture heterogeneity, and a multiple conceptual modeling approach is used to help us understand what details are important to the prediction of CO2 flow and storage. The insights gained will help us understand how fractured reservoir models should incorporate field characterization data and how matrix and fracture heterogeneity, which occurs over disparate scales and which exhibits distinctly different spatial correlation structure and connectivity, should be explicitly resolved in such models. Moreover, the uncertainty in the prediction outcomes, which propagates from both parameter and conceptual modeling uncertainty, can be quantified to understand issues such as storage efficiency and the leakage risk. The storage efficiency is evaluated in this work using the CO2 storage ratio, while the leakage risk is evaluated by examining the extent of scCO2 migration and the size of its footprint in the reservoir.

AN UNCERTAINTY ANALYSIS OF MODELING

GEOLOGIC CARBON SEQUESTRATION IN A

NATURALLY FRACTURED RESERVOIR AT

TEAPOT DOME, WYOMING

by

Ye Li, Ph.D. candidate

A dissertation submitted to theDepartment of Geology and Geophysics

and theUniversity of Wyoming

in partial fulfillment of the requirementsfor the degree of

DOCTOR OF PHILOSOPHYin

GEOLOGY

Laramie, WyomingJanuary 2014

Copyright c 2014

by

Ye Li

ii

Dedicate this work to my parents

iii

Contents

List of Figures viii

List of Tables xv

Acknowledgments xvi

Chapter 1 Introduction 1

1.1 Overview and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Chapter 2 Background and Geologic Review 10

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Parameters Affecting CO2 Storage . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.1 Reservoir Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.2 Fluid Flow Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Geology of Teapot Dome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.1 Structural Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.2 Stratigraphy and Sedimentology . . . . . . . . . . . . . . . . . . . . . 15

2.4 Geologic Characterization Datasets . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.1 Seismic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.2 Core Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.3 Well Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4.4 Outcrop Analogs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

iv

2.4.5 Production Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Chapter 3 Geologic Modeling 23

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Static Site Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.1 Structural Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.2 Property Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Chapter 4 Discrete Fracture Network (DFN) Modeling 52

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.2 Previous Fracture Studies in the Tensleep Sandstone . . . . . . . . . . . . . 54

4.3 Fracture Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3.1 Methods & Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.3.2 Fracture Characterization Data . . . . . . . . . . . . . . . . . . . . . 63

4.3.3 Building a DFN Model . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Chapter 5 Reservoir Simulation 77

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.1.1 Simulation of Naturally Fractured Reservoirs The Dual Porosity Ap-

proach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.1.2 Fluid Flow Simulation in Fractured Reservoirs . . . . . . . . . . . . . 79

5.2 Reservoir Simulation for the Tensleep Sandstone . . . . . . . . . . . . . . . . 80

5.2.1 Geologic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.2.2 Fluid Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.2.3 Relative Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.2.5 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.2.6 Baseline Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

v

5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Chapter 6 Uncertainty Analysis 99

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.2 Overview of Design of Experiment (DoE) methodology . . . . . . . . . . . . 101

6.3 Families of Geologic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.4 Uncertainty Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.4.1 Uncertainty in this study . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.4.2 Shared Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

6.4.3 Family Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Chapter 7 Results and Discussion 120

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7.2 Screening Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7.3 Response Surface (RS) Modeling & Verification . . . . . . . . . . . . . . . . 129

7.4 Monte Carlo (MC) analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7.5 Plume Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

7.6 Summary & Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.7 Discussion & Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

7.7.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

7.7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Appendix A Geologic Modeling 155

A.1 Structural Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

A.1.1 Prepare Input Data for Modeling . . . . . . . . . . . . . . . . . . . . 155

A.1.2 Fault Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

A.1.3 Pillar Gridding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

A.1.4 Layering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

A.1.5 Geometrical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 162

A.2 Property Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

vi

A.2.1 Data Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

A.2.2 Basic Geostatistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

A.2.3 Right Layer Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . 168

A.2.4 Facies Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

A.2.5 Petrophysical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Appendix B ECLIPSE Data Files 177

B.1 Basic Input File the DATA file . . . . . . . . . . . . . . . . . . . . . . . . 177

References 186

vii

List of Figures

1.1 A schematic diagram of the general contributions of different CO2 trapping

mechanisms over time (after [5]). . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1 The hysteresis effect of relative permeability for CO2-brine (data from [49]). 12

2.2 A Teapot Dome location map. The field is located within T. 38 - 39 N., R.

78 W. (courtesy of RMOTC [52]). . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 The location of the Teapot Dome field, Tensleep structure depth, and the

proposed CO2 injection well. Structural relationship between Teapot Dome

and Salt Creek fields (after [54]). . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Teapot Dome Geologic Column (after RMOTC [60]). . . . . . . . . . . . . . 16

2.5 A schematic stratigraphic column of reservoir (Tensleep Fm.) and the caprock

(Goose Egg Fm.) (after [63] and [62]). . . . . . . . . . . . . . . . . . . . . . 18

2.6 Cores from the Teapot Dome show fractures (courtesy of RMOTC [64]). . . 19

3.1 An arbitrary cross-section through Teapot Dome (left). A depth-structure

map on the 2nd Wall Creek Sandstone (right) showing location of cross section

line (after [40]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 An amplitude map of the Tensleep Sandstone at Teapot Dome. Basement-

cored faults are shown (after [66]). . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 The fault model of the Tensleep Sandstone at Teapot Dome and 3D seismic

data (in the time domain). Each colored surface with sticks represents a fault

interpreted according to 3D seismic data manually. The model uses 5x vertical

exaggeration. The arrow points to the north. . . . . . . . . . . . . . . . . . . 27

viii

3.4 The structural model of the Tensleep Sandstone. Depth is in feet at subsea

level(in the depth domain). Negative value is below sea level. Colored points

represent well tops. The model uses 5x vertical exaggeration. The arrow

points to the north. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.5 Plain-light thin-section images of different petrophysical facies of the Tensleep

Sandstone (courtesy of Dr. Peigui Yin [62]). . . . . . . . . . . . . . . . . . . 32

3.6 Distribution of petrophysical facies of the Tensleep Sandstone interval of well

54-TPX-10 and comparisons to well logs (courtesy of Dr. Peigui Yin [62]). . 34

3.7 Plot of porosity vs. permeability for different facies of the Tensleep Sandstone

(data from Dr. Peigui Yin). . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.8 Comparison between flow units and petrophysical properties of the plot in

Figure 3.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.9 Comparison between petrophysical facies in [62] and flow units derived in this

study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.10 A North-South stratigraphic cross section of Teapot Dome demonstrates poor

correlation between facies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.11 The experimental variogram and the variogram model of vertical facies (flow

unit 1) in the Tensleep B Sandstone interval. The gray curve represents the

auto-fitted regression curve, and the blue curve is the variogram used during

modeling process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.12 An omni-directional experimental variogram and an omni-directional vari-

ogram model in horizontal direction for flow unit 1 in the Tensleep B Sand-

stone interval. The gray curve represents the auto-fitted regression curve, and

the blue curve is the variogram used during modeling process. . . . . . . . . 43

3.13 A global vertical facies proportion curve generated from all 11 wells at the

study site. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

ix

3.14 A facies model of the Tensleep B Sandstone. Colored vertical lines represent

wells with well logs or cores. The background map is the Teapot Dome base

map, which indicates the relative location of the subsurface model to the

surface. The arrow points north. . . . . . . . . . . . . . . . . . . . . . . . . 45

3.15 Porosity variograms for the Flow Unit 1 (left column) and Flow Unit 2 (right

column) groups. Square=experimental variogram; blue line=fitted variogram

model; gray line=auto-fitted regression curve. . . . . . . . . . . . . . . . . . 47

3.16 Comparison of two porosity models based on the same facies model (Fig-

ure 3.14). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.17 Different correlations between porosity and permeability for flow unit 1. +

R35=11 m is for +1 case, 0 R35=2.8 m is for 0 case, and -

R35=1.0 m is for -1 case respectively (they represent totally different pos-

sible porosity-permeability relations for flow unit 1), when doing screening

test and response surface analysis in later chapters. . . . . . . . . . . . . . . 50

4.1 A schematic cross plot of percent reservoir porosity versus percent reservoir

permeability (percent due to matrix versus percent due to fractures) for the

Nelsons classification. k: permeability; : porosity; m: matrix; f: fracture.

(Modified from [90].) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.2 Lower-hemisphere equal-area net plot of poles to 129 representative through-

going fractures at Teapot Dome. Fractures are considered hinge-parallel if

they strike 20 from the hinge; hinge-perpendicular fractures strike 90 20

from the hinge. In this research, fractures are divided according to Coopers

classification: Fracture Set 1: the hinge-oblique; Fracture Set 2: the hinge-

perpendicular; Fracture Set 3: the hinge-parallel (after [51]). . . . . . . . . . 55

4.3 Examples of four types of fractures in cores. (a)Gouge-filled Fractures; (b)Mineral-

filled Fractures; (c) Partially-filled Fractures; (d) Open Fractures (courtesy of

Dr. Peigui Yin [94]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.4 Partially mineralized vertical extension fracture face in the Tensleep Sand-

stone, at Teapot Dome (courtesy of RMOTC [64]). . . . . . . . . . . . . . . 61

x

4.5 Upper hemisphere of Schmidt stereonet. Points represent the projection of

Pole to a fracture plane interpreted from FMI logs by Koepsell (Schlumberger). 65

4.6 Fracture attributes, such as intensity, aperture, and length that are generated

through power law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.7 Discrete Fracture Networks (DFN) for Fracture Set 1 and Fracture Set 2 in 2D. 72

4.8 DFN for Fracture Set 1 in 2D (above), and the whole DFN of three fracture

sets in 3D (below). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.9 Fracture permeability and porosity generated from the upscaling process by

the Oda method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.1 Dual porosity representation of a fractured reservoir (after [116]). . . . . . . 78

5.2 A typical dual porosity block of matrix containing oil and water (after [118]). 81

5.3 Relative permeability data for CO2-brine systems at in-situ conditoins for a

sample from the Viking Fm. sandstone (data from [125]). . . . . . . . . . . 90

5.4 A smoothed relative permeability based on straight-line relative permeability. 91

5.5 CO2 saturations after injection. Each grid contains two blocks: the outer

block and the inner block. The former one represents the fracture, and the

latter represents the matrix. The color indicates the molar density of CO2.

The arrow points north. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.6 (a) CO2 plume at the end of injection; (b) CO2 plume at the end of monitoring. 95

5.7 Graph showing CO2 dissolved in water, mobile in gas, and trapped in gas over

time. Horizontal axis represents years. Injection begins in 2013, and ends in

2033. Monitoring begins in 2033, and ends in 2113. . . . . . . . . . . . . . . 96

6.1 Generalized Pennsylvanian to Early Permian paleogeography shows setting

for low sea level stand. Arrow represents paleowind direction. Black box :

approximate location of Bighorn County, Wyoming. Red box: approximate

location of Powder River Basin. Dashed line: United States border. Wavy

pattern: the sea distribution. Stippled pattern: major region of the quartz-

sand erg distribution (after [157]). . . . . . . . . . . . . . . . . . . . . . . . . 108

xi

6.2 Satellite images to demonstrate different shapes of dunes and interdunes(after

[158]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.3 Relative permeability data for CO2-brine systems at in-situ conditions for a

sample from the Cardium Fm. sandstone (data from [125]). . . . . . . . . . 114

6.4 Factors varied in the PB design and their ranges of variation. Numbers indi-

cate family ID. Engineering (shared) factors are shared by all model families. 117

7.1 The screening test result for FAM4 at a 90% significance level. Outcome is

the SR at EOI. Statistically significant uncertainty factors in this family are

highlighted. Negative Lenth t-Ratio means increasing value of this factor will

reduce SR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

7.2 The screening test result for FAM4 at a 90% significance level. Outcome is

the SR at EOM. Statistically significant uncertainty factors in this family are

highlighted. Negative Lenth t-Ratio means increasing value of this factor will

reduce SR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7.3 The Screening Design (PB Design) for FAM4. (Part 1) . . . . . . . . . . . . 125

7.4 -(Continued) The Screening Design (PB Design) for FAM4. (Part 2) . . . . . 126

7.5 -(Continued) The Screening Design (PB Design) for FAM4. (Part 3) . . . . . 127

7.6 Response Surface Design for FAM4 . . . . . . . . . . . . . . . . . . . . . . . 128

7.7 Parameter estimates of a second order polynomial RS model of storage ratio

for FAM4 at EOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7.8 An example of RS predicted storage ratio versus simulated storage ratio at

PB design points for FAM4 at EOM. Comparison is for verification of the RS

fitted model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

7.9 Factors varied in the PB design and their ranges of variation. Numbers indi-

cate family ID. Engineering (shared) factors are shared by all model families. 132

xii

7.10 Cumulative distribution function (cdf ) of the storage ratio for FAM3 (the first

row) and FAM4 (the second row): (left) end of injection; (right) end of mon-

itoring. MC w/ RS is generated with 100,000 MC simulations (exhaustive

cdf ); RS is the cdf constructed using results of the response surface design

runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.11 Cumulative distribution function of the RS-predicted storage ratio for all fam-

ilies: (left) end of injection; (right) end of monitoring. . . . . . . . . . . . . . 135

7.12 Top views: molar density of CO2 (mobile + trapped) as predicted by each

family at EOI, [top face of the model]: (left column) FAM3; (right colum)

FAM4; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

7.13 Top views: molar density of CO2 (mobile + trapped) as predicted by each

family at EOM, [top face of the model]: (left column) FAM3; (right colum)

FAM4; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

7.14 Base views: molar density of CO2 (mobile + trapped) as predicted by each

family at EOI, [bottom face of the model]: (left column) FAM3; (right colum)

FAM4; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.15 Base views: molar density of CO2 (mobile + trapped) as predicted by each

family at EOM, [bottom face of the model]: (left column) FAM3; (right colum)

FAM4; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.16 Comparing the porosity distribution among model families. All the scales are

the same. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

7.17 Comparing the permeability distribution among model families. All the scales

are the same. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7.18 The fracture intensity map of the Tensleep Sandstone B. 1-TPX-10 is the

proposed injection well. Color lines resent the average strikes of fracture sets.

Red: the hinge-parallel; yellow: the hinge-perpendicular; white: the hinge-

oblique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

7.19 The relative location of the CO2 plume at EOM. The background is a base

map of Teapot Dome. The arrow points to the north. . . . . . . . . . . . . 149

xiii

7.20 The CO2 plume from one of simulation runs at the EOM. The model uses 5x

vertical exaggeration. The arrow points to the north. . . . . . . . . . . . . . 150

A.1 Digitizing Key Pillars directly on the 3D seismic data. . . . . . . . . . . . . . 157

A.2 The fault model for the geologic model. . . . . . . . . . . . . . . . . . . . . . 158

A.3 The framework that is generated by the Pillar Gridding process. The white

lines represent the faults built by fault modeling. The blue lines, which are

the framework of the model, constitute grid cells. . . . . . . . . . . . . . . . 159

A.4 The dialog of Make Horizons process. . . . . . . . . . . . . . . . . . . . . . 159

A.5 The dialog of Depth convert 3D grid. . . . . . . . . . . . . . . . . . . . . . 161

A.6 Corner Point grid cells generated by the structural modeling. . . . . . . . . . 163

A.7 The dialog of scale up well log. . . . . . . . . . . . . . . . . . . . . . . . . 165

A.8 Variogram anatomy (courtesy of Dr. Ye Zhang [169]). . . . . . . . . . . . . . 167

A.9 A vertical experimental (or sample) variogram. . . . . . . . . . . . . . . . . 169

A.10 A variogram model (blue line) is fitted to the experimental variogram. Vertical

range = 6.003 (in the red box). . . . . . . . . . . . . . . . . . . . . . . . . . 169

A.11 A variogram generated from a model with a layer thickness of 3 ft. . . . . . 170

A.12 A variogram generated from a model with a layer thickness of 9 ft. . . . . . 171

A.13 A dialog for Data Analysis process. . . . . . . . . . . . . . . . . . . . . . . 172

xiv

List of Tables

4.1 Classification of Naturally Fractured Reservoirs (after [90]). . . . . . . . . . . 53

6.1 Symbols, units, and ranges of the uncertainty factors varied in the hierarchy

stochastic model conditioned to soft data. The azimuth angle is referenced

to East (0 degree). L1, L2, and L3 are modeling choices associated with a

categorical uncertainty factor (see the text for detail). SF=Shared factors;

FF=Family Factors; FU1=Flow Unit 1; FU2=Flow Unit 2. . . . . . . . . . 112

6.2 Symbols, units, and ranges of the uncertainty factors varied in the DFN frac-

ture models. FF=Family Factors; FS1=Fracture Set 1 (the hinge-oblique set);

FS2=Fracture Set 2 (the hinge-perpendicular set); FS3=Fracture Set 3 (the

hinge-parallel set). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

7.1 Significant factors identified by the PB Design for each family that impact

the prediction of the Storage Ratio (SR). Significance level = 90%; EOI: end

of injection; EOM: end of monitoring; FA: Fracture Aperture . . . . . . . . . 124

7.2 Summary of the RS error at the PB design points: Error = RS-predicted SR

- simulated SR at PB points. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

xv

Acknowledgments

There are many people and organizations that have provided me with support to complete

this dissertation. This support has come in the form of financial aid, encouragement, and

the sharing of their personal knowledge.

First and foremost, I wish to thank my advisor Dr. Ye Zhang for the guidance, patience,

and motivation throughout the study. Appreciation is also expressed to Dr. Shaochang Wo

for his efforts and guidance in my study, and for being a member of my Ph.D. committee.

I would like to thank Dr. Erin A. Campbell-Stone for her detailed revision suggestions for

improving my dissertation. Last but not least, I thank the rest of the Ph.D. committee:

Dr. Brian F. Towler and Dr. Subhashis Mallick for their time and input. Their insight and

suggestions have greatly improved my work and my knowledge over these past few years.

I would like to extend my appreciation to Dr. Shuiquan Li and Dr. Peigui Yin, from the

Enhanced Oil Recovery Institute (EORI) of the University of Wyoming, for their guidance

and support during this research.

I also wish to thank the professors and staff at the Department of Geology and Geo-

physics at the University of Wyoming for all of their support.

I am especially grateful to Carolyn Young from the Writing Center of the University of

Wyoming. She provided much help for my writing.

Without the Rocky Mountain Oilfield Testing Center (RMOTC), there would be no

data for analysis and inputs to the model. I would like to thank RMOTC and the U.S.

Department of Energy as the data source. I am also thankful to Schlumberger for supplying

Petrel/ECLIPSE software that were used in this study.

I express my gratitude to Chevron for an internship and financial support. I also would

xvi

like to thank the funding source for this study, the U.S. National Science Foundation (EAR-

0838250).

Lastly, I sincerely thank my parents for their love and encouragement. Without their

continued support, my education would not have been possible.

Ye Li

University of Wyoming

January 2014

xvii

Abbreviations

BC Boundary Condition

BHP Bottom-hole Pressure

DC Dolomit-sand-free, Cemented, dune sandstone facies

DDC Dolomit-sand-rich, Cemented, dune sandstone facies

DFN Discrete Fracture Network

DoE Design of Experiment

DUC Dolomite-sand-free, UnCemented, dune sandstone facies

EOI End Of Injection

EOM End Of Monitoring

EOR Enhanced Oil Recovery

EoS Equation of State

FF Family Factors

FMI Formation MicroImager

GCS Geologic Carbon Sequestration

IDC Interdune sandstone facies, Dolomite-sand-rich, Cemented

IDUC Interdune sandstone facies, Dolomite-sand-rich, UnCemented

LIDAR Light Imaging Detection And Ranging

MC Monte Carlo

NFR Natrually Fractured Reservoir

PB Plackett Burman

RMOTC Rocky Mountain Oilfield Testing Center

RS Response Surface

xviii

SA Sensitivity Analysis

scCO2 supercritical CO2

SF Shared Factors

SGS Sequential Gaussian Simulation

SIS Sequential Indicator Simulation

SR Storage Ratio

TDS Total Dissolved Solids

xix

Chapter 1

Introduction

1.1 Overview and Motivation

Carbon dioxide is believed to be the main cause of global climate change. Due to human

activities, the level of CO2 in the earths atmosphere is rising, with severe implications for

the earths environment. To reduce the amount of CO2 entering the atmosphere, a variety

of actions have been proposed including CO2 capture from industrial sources and storage

underground. This disposal option is called geostorage or Geologic Carbon Sequestration

(GCS) [1]. Injection of supercritical CO2 (scCO2) into deep permeable formations (aquifers)

of mature sedimentary basins is proposed as the most viable approach [2] [3] [4]. The best

candidate formations include unminable coal seams, depleted oil and gas reservoirs, and deep

saline aquifers. This study addresses the fundamental assessment issues in the last category.

In such settings, a variety of physiochemical processes can contribute to CO2 entrapment

and storage. Depending on host rock and fluid characteristics, different trapping mechanisms

dominate at increasing time scales, i.e., cap-rock trapping (or structural & stratigraphic

trapping), residual trapping, dissolution (or solubility trapping), and reaction with solid

matrix (or mineral trapping) (Figure 1.1).

By trapping mechanisms, we mean any chemical or physical processes through which

CO2 can be stored in a geologic environment such that it is unlikely to escape. The efficiency

of long-term storage in permeable formations is directly related to each of the trapping

1

Figure 1.1: A schematic diagram of the general contributions of different CO2 trappingmechanisms over time (after [5]).

2

mechanisms involved. There are four major trapping mechanisms [6] (Figure 1.1). During

the injection phase, a plume of supercritical CO2 (scCO2), which is injected into a deep

aquifer, may migrate upwards driven by buoyancy, and structural & stratigraphic trapping

are the main contributors preventing the scCO2 from escaping to the surface [7]. During

injection, scCO2 moves through the formation and displaces the resident brine. However,

as it continues to migrate (i.e., after injection ceases), brine will start to replace scCO2 in a

process called imbibition, leaving some scCO2 trapped in the pores by capillary forces. This

is called residual trapping. Over time, scCO2 dissolves into formation brine and becomes

either immobilized (if the velocity of the aquifer flow is negligible) or is carried away down

hydraulic gradients if the aquifer flow is significant [6] [8] [9]. Mineral trapping is considered

the safest long-term mechanism to sequestrate CO2, as it transforms it into an immobile

solid; however, this process can be very slow, which may take millennia [10] [11]. Clearly,

the dominant CO2 trapping mechanism can change with time.

Supercritical CO2 is lighter than formation brine and will rise under buoyancy from the

point of injection. Since the success of geostorage depends on whether significant leakage

will develop in a site evaluation, it is critical to understand both the storage efficiency of

the injected scCO2 and the extent of lateral and vertical migration. At a given storage site,

both the storage efficiency of the CO2 in the subsurface and its potential leakage back to

the surface are the key performance outcomes to be considered. Because we cannot conduct

a pilot test directly in the field, at Teapot Dome and many potential sites, to evaluate CO2

geostorage because of the large cost and time requirements, mathematical modeling and

simulation are the focus of this study.

To evaluate CO2 geostorage, mathematical modeling of CO2 flow in a storage reser-

voir provides an essential quantitative tool. It lies at the heart of every GCS assessment

study; thus to date, numerous simulation studies have been conducted to model CO2 flow

in a variety of settings [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [8] [25] [26].

Depending on the study objective, assumptions are often employed in terms of model for-

mulations, constitutive relations, and parameterizations of the subsurface environment. In

particular, aquifer homogeneity is often assumed at various scales, which is constrained by

3

the quality and accessibility of site-specific data. However, permeability heterogeneity is

the rule rather than exception in natural aquifers [27]. It exerts important controls on CO2

migration [28] [29] [30], while studies also suggest that models incorporating high-resolution

heterogeneity are required to accurately assess the various storage mechanisms [31] [6] [32].

However, heterogeneity in simulations is frequently generated with stochastic algorithms

subject to a range of limitations, e.g., smoothness and statistical homogeneity are common

artifacts as opposed to preferential flow paths and non-stationarity exhibited by natural

aquifers. In modeling geostorage, it is thus desirable to incorporate both high-resolution and

geologically realistic heterogeneity. On the other hand, because of the homogeneity assump-

tion, effective parameters are routinely used in modeling field injections, and a fundamental

question remains: what is the impact of effective parameterizations (alternatively, the unre-

solved heterogeneity) on model predictions of CO2 flow and its storage efficiency? To answer

this question, detailed three-dimensional permeability characterization is required. However,

in deep aquifers, information on permeability is commonly lacking. Detailed measurements,

if available, are limited to those of bore-hole data, while such sampling is often too sparse to

resolve the main heterogeneity features. Permeability is also site-specific, e.g., some faults

are fluid conduits while others are barriers [33]. Without site-specific information on per-

meability (and its spatial variation), the extent of CO2 migration subsequent to injection is

difficult to quantify.

In evaluating a storage site, reservoir simulation is performed using a geologic site model

characterizing subsurface structure, facies, and other geologic heterogeneity. However, geo-

logic carbon sequestration is frequently considered a cost center. In order to resolve de-

tailed reservoir heterogeneity, increasing subsurface characterization effort is required. The

greater the detail, the higher the cost. For the type, amount, and accessibility of data at a

given site, different geologic models can be built, ranging from simple to complex. Petro-

physical properties, for instance, can be alternatively modeled assuming homogeneity [34]

or heterogeneity [35], the latter requiring advanced modeling techniques supported by ad-

ditional and often detailed data. Although such data can be obtained from drilling and

logging the aquifer or from high-resolution geophysical surveys, extensive data acquisition

4

is not realistic at large scales where industrial CO2 storage is concerned, due to the cost

constraint in data collection and analysis. Furthermore, potential leakage from well-bores

must be minimized, limiting the number of boreholes that can be drilled. A critical issue in

GCS is therefore to determine the right types of data to collect, and, based on these data,

the right type of model to construct, leading to a cost-effective strategy of data collection

to support the building of site models. Such models, as input to reservoir simulation, will

ideally lead to adequate, or sufficiently accurate predictions of the desired outcomes, while

models are not overly detailed and thus cost-prohibitive to construct. However, there are

many uncertainty factors in modeling that can affect CO2 migration, its storage efficiency,

and leakage, including intrinsic permeability of the geologic formation and cap-rocks, relative

permeability, and relationships between porosity and permeability. These uncertainties may

be very important for controlling CO2 storage and leakage, or they may exert only a minor

influence on these performance outcomes. Given the variety of uncertainty factors, their

range of variations, and their possible interactions, how they affect CO2 storage and leakage

and what may be the most important factors for predicting these performances outcomes

over multiple time scales remain unanswered. At a given storage site, these questions have

significant implications for the types of field and laboratory characterization data to collect,

and based on these data, the types of analysis and modeling activity that should be carried

out in a GCS assessment study.

Towards this overall objective of developing cost-effective models, this study conducts an

uncertainty analysis of CO2 storage in the Tensleep Sandstone1 at Teapot Dome, Wyoming.

Even though there are several kinds of datasets, such as seismic data, well logs, core mea-

surements, and production data, much uncertainty exists concerning the three-dimensional

(3D) porosity and permeability distributions in the Tensleep Formation because much of the

data has not been interpreted and interpolated, and data limitation/uncertainty is poorly

understood. Reservoir heterogeneity, however, is known to exist in this formation, as will

be discussed in Chapter 3. The large distances between wells, furthermore, give rise to

uncertainty as to the appropriate geologic modeling method that can capture the inter-

1the Tensleep Sandstone and the Tensleep Formation are equal and interchangeable in this thesis.

5

well heterogeneity in this reservoir. In fact, alternative modeling methods appear equally

suitable, whereas the effect of different methods on porosity/permeability prediction and

therefore CO2 storage modeling is unknown.

The goal of this study is to understand geologic complexity in modeling CO2 storage

in the Tensleep Sandstone and the associated data needs, including both site static and

dynamic data. In modeling GCS, a variety of uncertainty factors exist, including geologic

factors influencing reservoir porosity and permeability distribution, and engineering factors

influencing gas trapping and migration. The uncertainty factors that exert the most signifi-

cant impact on CO2 predictions are of the most interest these are the factors that need to

be better characterized, reducing their uncertainties and therefore uncertainty in predictions.

In building and simulating a reservoir model, nevertheless, as more complexity is built into

it, more geologic uncertainty factors can come into play [36] [37]. To address this issue, this

study evaluates multiple conceptual Tensleep Sandstone models to determine if the list of

the most important factors (i.e., those factors whose variations have significant impact on

a prediction outcome) will change with the modeling choice. In addition, because CO2 flow

is typically dominated by viscous force during injection and gravity force during monitoring,

the list of the most important factors influencing its predictions may change over time, as well

as the uncertainty in the predictions. The study outcome will therefore be evaluated over

different time scales, i.e., end of injection and end of monitoring. Finally, a large reservoir

model is built for the storage formation for which the computational challenge in carrying

out a full uncertainty analysis is significant. This study therefore adopts the efficient Design

of Experiment (DoE) and Response Surface (RS) methodology for analyzing both parameter

importance and prediction uncertainty.

The Tensleep Sandstone at this location has significant porosity and permeability in

both the sandstone matrix and in the fracture networks that percolate through the matrix.

Ignoring each type of heterogeneity in building and simulating CO2 storage will likely lead to

biased or inaccurate CO2 predictions. However, the considerable complexity of both matrix

and fracture heterogeneity also requires to understand the level of detail that needs to be

included in building the geologic model, so resources can be used appropriately. This study

6

explicitly models both matrix and fracture heterogeneity, and a multiple conceptual model-

ing approach is used to help understand what details are important to the prediction of CO2

flow and storage. The insights gained will help understand how fractured reservoir models

should incorporate field characterization data and how matrix and fracture heterogeneity,

which occurs over disparate scales and which exhibits distinctly different spatial correlation

structure and connectivity, should be explicitly resolved in such models. Moreover, the un-

certainty in the prediction outcomes, which propagates from both parameter and conceptual

modeling uncertainty, can be quantified to understand issues such as storage efficiency and

the leakage risk. The storage efficiency is evaluated in this work using the CO2 storage ratio,

while the leakage risk is evaluated by examining the extent of scCO2 migration and the size

of its footprint in the reservoir.

1.2 Thesis Organization

This thesis is composed of seven chapters. Chapter 1 is to introduce the overview and the

motivation of this study. Chapters 2, 3, 4, and 5 describe the modeling investigations of the

Teapot Dome. Chapters 6 and 7 describe uncertainty analysis and related results.

In chapter 2, Background and Geologic Review, parameters that affect CO2 storage

are briefly discussed. An overview of the Teapot Dome geology is presented next. The

available geologic characterization datasets are introduced.

In chapter 3, Geologic Modeling, the step-by-step geologic modeling approach of the

Tensleep Formation at Teapot Dome is introduced. A hierarchical stochastic model (for the

matrix) is built through structural modeling, facies modeling, and petrophysical modeling.

First, structural modeling is discussed, which builds the main framework of the Tensleep

Formation model and provides basic geometry of grid cells. Then, property modeling, which

normally contains two main steps, facies modeling and petrophysical modeling, is presented.

The concept of facies/flow units, which is the base of facies modeling, is introduced, fol-

lowed by reservoir characterization of the Tensleep Formation. Based on the Winland R35

method [38], the Tensleep Formation is categorized into two facies/flow units. After this

7

categorization, a facies model of the Tensleep Formation is built through the Sequential In-

dicator Simulation (SIS) approach. Based on the facies model, the petrophysical modeling

is completed via two steps: (1) a porosity model is first built for each facies (flow units)

using Sequential Gaussian Simulation (SGS); (2) a permeability model is derived from the

porosity model based on the relationship between porosity and permeability that follows the

Winland R35 equation [38].

In chapter 4, Discrete Fracture Network (DFN) Modeling, natural fractures in

reservoir rocks and their modeling are discussed. Some basic concepts related to fractures and

naturally fractured reservoirs are first introduced. Previous fracture studies in the Tensleep

Sandstone, which provide a set of preliminary understanding of the fractures as well as

necessary data for fracture modeling, are then presented. Finally, fracture characterization

data are interpreted and discussed in detail, and a discrete fracture network model is built

based on the data.

In chapter 5, Reservoir Simulation, fluid flow simulations for modeling the migration

of the injected CO2 are presented. First, basic concepts of fluid flow simulation in naturally

fractured reservoirs, such as the dual porosity approach, and the recovery processes in frac-

tured reservoirs, are introduced. The matrix model generated in chapter 3, and the fracture

model built in chapter 4, provide essential geologic information for the reservoir flow sim-

ulation. Fluid properties, relative permeability, boundary conditions and initial conditions

are discussed. Results of a baseline simulation using representative parameter values are

presented.

In chapter 6, Uncertainty Analysis, using results of reservoir flow simulation, an

uncertainty analysis of CO2 storage in the Tensleep B Sandstone2 is conducted according

to the Design of Experiments (DoE) and Response Surface (RS) principles. An overview

of DoE methodology is, first, presented. The approaches and steps of uncertainty anal-

ysis adopted in this study are then introduced. Based on the DoE, a suite of increasingly

simplified conceptual geologic model families are created with decreasing amount of site char-

acterization data: a hierarchical stochastic model family conditioned to soft data (FAM4),

2As shown in Figure 2.5, the Tensleep B Sandstone (the B Sandstone) is the main producing formationin the Tensleep Formation and is also the proposed storage interval for the CO2 sequestration experiment.

8

a simple stochastic facies model family (FAM3), a simple stochastic porosity model family

(FAM2), and a homogeneous model family (FAM1). Within the context of model building,

two categories of uncertainty factors, shared factors and family factors, are discussed.

In chapter 7, Results and Discussion, for the CO2 storage ratio (SR), results of the

uncertainty study are presented in 4 sections: (1) screening test outcomes; (2) Response

Surface (RS) modeling and verification; (3) Monte Carlo (MC) analysis to assess the SR

uncertainty; (4) visualization of end-member CO2 plumes and footprints. In each section,

results are analyzed at two output times: end of injection (EOI) and end of monitoring

(EOM). Implication of the study outcomes and insights obtained is summarized and dis-

cussed before future works are presented.

In appendix A, Geologic Modeling, detailed operations to build the matrix geologic

model are presented. Basic steps to build a structural model are introduced first. They

include preparing input data, fault modeling, pillar gridding, layering, and geometrical mod-

eling. Then processes of how to build a property model are presented.

In appendix B, ECLIPSE Data Files, the basic input file for ECLIPSE (the DATA

file) is attached.

9

Chapter 2

Background and Geologic Review

2.1 Introduction

Although deep saline aquifers in the US can provide large storage capacities to sequester

100 years of CO2 emissions from all the coal-fired power plants [39], oil and gas reservoirs

are preferred short-term targets for Geologic Carbon Sequestration (GCS), since there are

possible cost offsets from CO2 flooding in a process termed as Enhanced Oil Recovery (EOR).

The Teapot Dome Field Experimental Facility, which is fully owned by the US gov-

ernment, has been designated to conduct carbon-storage experiments. Long-term scientific

research and technical development can be guaranteed by Federal ownership. Besides, this

field has plenty of existing static and dynamic field and laboratory characterization data, in-

cluding seismic, cores, well-logs and production data, all of which are in the public domain.

These data are the basis for characterizing and interpreting structural and stratigraphic

attributes of the subsurface reservoirs at this site [40].

In this chapter a research project of uncertainty analysis of CO2 geologic sequestration in

a fractured sandstone reservoir at Teapot Dome will be discussed. First, parameters affecting

CO2 storage are introduced. Then, the geology of Teapot Dome and available datasets will

be described.

10

2.2 Parameters Affecting CO2 Storage

At the field scale, simulation of CO2 storage involves a large number of variables and pa-

rameters which govern the performance of GCS. CO2 plume migration is controlled by the

complex interplay of viscous, capillary, buoyancy forces, and reservoir heterogeneity and its

structure.

2.2.1 Reservoir Heterogeneity

Geologic heterogeneity is the rule rather than the exception in natural aquifers [27]. In oil/gas

reservoirs, heterogeneity has a strong control on the hydrocarbon displacement process [41].

Studies have concluded that heterogeneity also exerts important influences on scCO2 migra-

tion [42] [28] [29] [30], while some research suggests that models incorporating high-resolution

heterogeneity are required to accurately assess the various storage schemes [31] [6] [43]. How-

ever, heterogeneity in simulation is frequently generated with stochastic algorithms subject

to a range of limitations, e.g., smoothness and statistical homogeneity are common artifacts

as opposed to preferential flow paths and non-stationarity exhibited by natural aquifers. In

modeling geostorage, it is thus desirable to incorporate both high-resolution and geologically

realistic heterogeneity. However, in deep aquifers, information on detailed heterogeneity is

commonly lacking. Detailed measurements, if available, are limited to well data, while such

sampling is often too sparse to resolve the main heterogeneity features. Without site-specific

information on permeability (and its spatial variation), the extent of the scCO2 plume sub-

sequent to injection is difficult to quantify.

2.2.2 Fluid Flow Properties

Other sources of uncertainty also exist in simulating deep injection, further contributing to

the predictive uncertainty of a modeling study. In particular, under supercritical conditions,

the fluid phase relative permeabilities (one for brine; one for scCO2) are highly uncertain.

The relative permeability of scCO2-brine systems determines CO2 injection, migration, and

the immobile CO2 due to irreducible saturation in pore space [44]. Therefore, it is a key

11

Figure 2.1: The hysteresis effect of relative permeability for CO2-brine (data from [49]).

parameter in numerical simulations to predict CO2 storage [45].

Recent experiments have demonstrated hysteresis effects on the relative permeability

of scCO2-brine system between the drainage and imbibition curves [44] [46] [47]. Hysteresis

refers to irreversibility, or directional saturation phenomena as exhibited by the relative

permeability and capillary pressure when a given phase saturation is increased or decreased

[6] [48]. This phenomenon is illustrated by Figure 2.1.

A saline aquifer is a medium that is initially filled with water, and it is water wet.

During CO2 injection into the aquifer, the scCO2 is a non-wetting phase, and it follows

the drainage curve of the scCO2-brine relative permeability to invade the pore space. This

is a drainage process in which the CO2 is in the form of a continuous, connected cluster.

After CO2 injection, water displaces scCO2 under capillary pressure as water is the wetting

12

Figure 2.2: A Teapot Dome location map. The field is located within T. 38 - 39 N., R. 78W. (courtesy of RMOTC [52]).

phase. The scCO2 will follow the imbibition curve of the relative permeability. During this

imbibition process, scCO2 gets disconnected in the form of blobs or ganglia. It is, therefore,

trapped as an effectively immobile phase [6].

2.3 Geology of Teapot Dome

The Teapot Dome oil field, also known as Naval Petroleum Reserve No.3 (NPR-3), is the

last United States government owned oil field [50]. It is 30 mi north of Casper, Wyoming,

and located at the southwestern edge of the Powder River Basin (Figure 2.2) [51]. The field

covers nearly 10,000 acres [50].

13

Figure 2.3: The location of the Teapot Dome field, Tensleep structure depth, and the pro-posed CO2 injection well. Structural relationship between Teapot Dome and Salt Creekfields (after [54]).

Teapot Dome is an elongated asymmetric, doubly plunging, basement-cored, Laramide-

age anticline, which has a north-northwest axis [51]. It is considered as an extension of the

larger Salt Creek anticline, with the Salt Creek anticline to the north and the Sage Spring

Creek and Cole Creek oil fields to the south (Figure 2.3) [53].

Teapot Dome, a basement-cored anticline, is one of several productive hydrocarbon

structural traps within the Rocky Mountain region. The same types of structures can be

found in many other areas around the world [55] [56] [51]. As basement-cored anticlines can

provide excellent four-way closure, which can trap a significant amount of hydrocarbons,

they become exploration targets. Permeability anisotropy associated with such structures

directly controls final recovery of these trapped hydrocarbons [56].

14

2.3.1 Structural Elements

Teapot Dome is a SW-verging anticline that has steep dips (20-50) on the west flank and

shallow dips (

Figure 2.4: Teapot Dome Geologic Column (after RMOTC [60]).

Pennsylvanian Tensleep Sandstone with the overlying Goose Egg Formation is discussed in

the following because Tensleep has been chosen as the first reservoir target for the proposed

CO2 injection experiments, i.e. the target CO2 storage reservoir in this research.

The Tensleep Formation (The Tensleep Sandstone)

The Pennsylvanian Tensleep Formation covers a large extent in Wyoming, Montana, and

Colorado and is the most promising target for CO2 storage, because of its enormous volume.

The Tensleep Formation is a thick, continuous, porous and permeable eolian sandstone con-

taining oil or brine [50]. The Tensleep in the Lost Soldier and Wertz Fields in Wyoming

and its equivalent formation, Weber Sandstone, at Rangely field in Colorado have accommo-

dated injected CO2 as part of an Enhanced Oil Recovery method for roughly 20 years. The

Tensleep Sandstone, which holds two thirds of Wyomings oil, is an important producing

16

unit in Wyoming [59].

Through study of analogs, Zhang [61] concluded that the Tensleep Sandstone consists

of multiple sequence boundaries as a result of frequent and high-amplitude sea level changes.

Zhang also stated that generally from bottom to top, the Tensleep Sandstone changes from

dominantly marine, with abundant crinoids and corals, thick tabular carbonate beds and

thick sandstone layers, to dominantly terrestrial, with thick eolian cross-bedded sandstones,

scarce fossils, and thick and discontinuous carbonates.

Zhang [61] stated that the Tensleep Sandstone comprises thick-bedded porous and per-

meable eolian deposits with average porosity of 8% and 80 mD average permeability. Sabkha

and shallow marine dolomites, interbedded with these eolian deposits, are thin but form

widespread extensive beds. Due to their low permeability, the dolomites act as flow baffles

or barriers. Although many vugs, fractures and stylolites are observed in dolomites, such beds

do not constitute permeable reservoir because of extremely low permeability. Sandstones,

the reservoir rocks, are separated in several intervals by these extremely low permeability

dolomites. As shown in Figure 2.5, the B Sandstone (the Tensleep B Sandstone) is the

main producing formation and is also the proposed storage interval for the CO2 sequestration

experiment [61] [50].

The Tensleep Sandstone at Teapot Dome are divided into the lithofacies of eolian dune,

interdune, and sand sheet, which are comprised of fine- to very fine-grained, quartz arenites,

with local concentration of dolomite sand grains. Lamination and grain size vary widely as a

function of the depositional environment. Porosity and permeability are therefore determined

by both the depositional units and the degree of cementation and compaction, which further

aggravate reservoir heterogeneity [62].

The Permian Phosphoria Formation, which is locally called the Goose Egg Shale, overlies

the Tensleep Sandstone as a cap rock. It is the regional seal of the Tensleep Formation across

Wyoming [50]. At the Teapot Dome field, the Goose Egg Formation comprises over 300 ft

of shale, carbonate, and anhydrite. More than 35 million barrels of oil and dissolved gas

has been trapped under this seal at Teapot Dome, indicating good evidence of its long term

sealing effectiveness [50].

17

Figure 2.5: A schematic stratigraphic column of reservoir (Tensleep Fm.) and the caprock(Goose Egg Fm.) (after [63] and [62]).

18

Figure 2.6: Cores from the Teapot Dome show fractures (courtesy of RMOTC [64]).

Fractures

At the Teapot Dome, both core data and outcrops indicate that the Tensleep Sandstone

contains well developed natural fractures. Fractures provide substantial permeable pathways

in these eolian sandstone reservoirs, which form dual porosity networks that are challenging

to characterize and integrate into reservoir modeling and numerical simulations. A more

detailed discussion will be presented in chapter 4 that will describe the process of building

a Discrete Fracture Network (DFN) model.

19

2.4 Geologic Characterization Datasets

Teapot Dome covers nearly 10,000 acres with more than 2,200 wells, about 1,200 of which may

be accessed by public. About 600 of those total 2,200 wells are producing, and more than 400

have depths greater than 2,700 ft. Importantly, public-domain databases exist at the Teapot

Dome field. These databases include cores, well logs, mud logs, completion descriptions, and

production data. These data are fundamental to our effort of characterizing the structural

and stratigraphic attributes and reservoir heterogeneities at the subsurface [54].

2.4.1 Seismic Data

A set of full-field three-dimensional (3D) seismic data was acquired by the Rocky Moun-

tain Oilfield Testing Center (RMOTC), which is colocated with the Department of Energy

(DOE)s office that manages and operates Teapot Dome. This set of 3D seismic data, con-

sisting of 345 in-lines and 188 cross-lines with a bin size of 110 ft, is also in the public

domain [54].

A post-stack migrated volume was interpreted in time-domain by EXCEL Geophysical

Services Company in Denver, Colorado [65]. The interpreted horizons include the tops for

the Second Wall Creek formation (KF2), Fall River formation (Dakota), Lakota/Morrison

formation, Crow Mountain formation, Red Peak formation, Tensleep formation, and Precam-

brian basement. This seismic dataset also includes 2D seismic data, synthetic seismograms,

and time-depth tables. However, it does not include the interpretations of faults.

2.4.2 Core Data

There are about 35 wells that have penetrated the Tensleep Sandstone at Teapot Dome,

including 13 cored wells [54]. Sedimentary attributes and fractures have been characterized

for a subset of the cores. Porosity and permeability are tested from core samples and provide

limited information on the subsurface at the well locations. Petrophysical characterizations

and lithofacies descriptions have been carried out based on these core data [62] [64].

20

2.4.3 Well Data

The 35 wells, which have penetrated the Tensleep Sandstone, all have traditional well-log

suites that have been digitized. Most of these well-log suites contain spontaneous potential

logs, resistivity logs, gamma ray logs, and porosity logs including sonic logs, density logs,

and neutron logs [60].The well-log dataset includes well headers, directional surveys, and

formation log tops, all of which are basic well data used to build geologic model of this

study.

Six recent wells have FMI (Formation Micro Imager) logs [64], which can be used to

characterize reservoir fractures (induced, open and seal) at the in-situ condition. FMI can

also be used to interpret dune cross-bedding orientations [66].

2.4.4 Outcrop Analogs

Outcrops supplement sparse subsurface data with outcrop-derived measurements. The Tensleep

Sandstone outcrops in the nearby Alcova anticline were studied in [67]. LIDAR (Light Imag-

ing Detection and Ranging), which has the ability to detect fracture planes with area 1 m2,

was adopted to characterize natural fractures in the Alcova anticline. Some key parameters,

like fracture dip, fracture azimuth, fracture spacing, and fracture height-to-length aspect

ratio, can be determined by fracture data extracted from the LIDAR dataset [67].

2.4.5 Production Data

The production data demonstrates that the Tensleep Sandstone is under strong water drive

[65]. In other words, the Tensleep Sandstone connects to a large aquifer. These data provide

a clue to the boundary condition (BC) of this reservoir.

2.5 Summary

In this chapter, we have presented an introduction to the background of Geologic Carbon

Sequestration (GCS), as well as parameters that affect GCS, and an overview of Teapot

21

Domes geology. The understanding and the dataset related to Teapot Domes geology are

the basis for modeling, which will be discussed in detail in the next chapters.

22

Chapter 3

Geologic Modeling

3.1 Introduction

The geologic model is also designated as the static (reservoir) model (in the oil industry,

it is also referred to as the reservoir model), because it is built on static data, such as

geological, geophysical, and petrophysical measurements and for example, well logs, core

measurements, and seismic data, etc. These data are constant and do not vary with time.

In contrast, dynamic data varies with time, like fluid saturations, bottom-hole pressure

(BHP) and formation pressure. The flow (reservoir) simulation model is also referred to as

the dynamic model that is utilized to simulate behavior of dynamic data over time.

In the lifetime of an oil field, models play a crucial and fundamental role in understand-

ing and predicting reservoirs characteristics and performance. A model is a quantitative

digital representation that incorporates every available piece of information from diverse

data sources, such as geology, geophysics, petrophysics, and engineering, to maximize the

value of these data.

The objective of model studying is to provide one or several alternative models that rep-

resent the spatial variation of geologic properties, such as facies, porosity, and permeability.

Models can normally be built by two distinct approaches: deterministic and stochastic. The

former one can provide only one definite model whereas the latter one can produce different

equiprobable static reservoir models, or different realizations [68].

23

A geologic model (static model) integrating large amounts of data delivers basic input

to a flow simulation model (dynamic model). Flow simulation models based on stochastic

geological models can produce a distribution of predictions, and this procedure transfers

uncertainties from geological models to fluid flow predictions [69]. Therefore, through eval-

uating simulation outcomes, i.e., CO2 storage performance metrics, uncertainties during

modeling and simulation can be assessed.

3.2 Static Site Model

A model is a simplified representation of some aspects of the subsurface reality. As modeling

is always about simplifications, we will only focus on the important ones [70]. It is widely

believed that reservoir models can only mimic reality, not reproduce reality [71].

This chapter describes the step-by-step geologic (static site) modeling approach of the

Tensleep Formation at Teapot Dome in Wyoming. A hierarchy stochastic model is built

through processes of structural modeling, facies modeling, and petrophysical modeling.

3.2.1 Structural Modeling

The structural model describes the main framework of the Tensleep Formation at Teapot

Dome, and it provides basic geometry of grids (or cells). These grids are assigned with facies

or petrophysical attributes by following a property modeling process.

Fault Modeling of the Tensleep Sandstone Fault modeling is a procedure to generate

faults in the Tensleep Formation. The purpose of this process is to define the shape of each

fault that can be conditioned on data, such as seismic interpretation and cross section. [70].

Faults can be digitized directly on seismic data. In this study, faults were interpreted

based on the post-stack migrated 3-D seismic data. Although Petrel provides an Automatic

fault extraction function, it did not work well with the Teapot Dome data and the result was

disappointing. We had to interpret faults manually. Following previous interpretation and

information (Figure 3.1, Figure 3.2), five faults were interpreted, including a west bounding

24

Figure 3.1: An arbitrary cross-section through Teapot Dome (left). A depth-structure mapon the 2nd Wall Creek Sandstone (right) showing location of cross section line (after [40]).

thrust fault (Figure 3.3).

Structural Modeling of the Tensleep Sandstone Well logs and 3D seismic interpreta-

tions at the Teapot Dome were integrated at the regional scale to obtain formation horizons

for the Tensleep Sandstone: Tensleep A Sandstone, and Tensleep C1 Dolomite (Figure 3.4).

The horizons are truncated to the west by the thrust fault. In creating the horizons, seismic

interpretations from RMOTC dataset were utilized and were constrained by well tops along

formation contacts. Based on the horizons, a 3-D structural model of the Tensleep Sandstone

was built, spanning an average thickness of approximately 100 ft. (For detailed procedures

to build this structural model please refer to Appendix A).

The completed structural model contains 18532280, total 4, 765, 600 grids with an

average grid spacing of 90 ft in the I direction, 90 ft in the J direction, and 3 ft in the

K direction. In the next step (Property Modeling), these grids will be assigned geologic

attributes to characterize reservoir heterogeneity.

During structural modeling, most of the data we used, such as the seismic data, the

25

Figure 3.2: An amplitude map of the Tensleep Sandstone at Teapot Dome. Basement-coredfaults are shown (after [66]).

26

Figure 3.3: The fault model of the Tensleep Sandstone at Teapot Dome and 3D seismicdata (in the time domain). Each colored surface with sticks represents a fault interpretedaccording to 3D seismic data manually. The model uses 5x vertical exaggeration. The arrowpoints to the north.

27

Figure 3.4: The structural model of the Tensleep Sandstone. Depth is in feet at subsealevel(in the depth domain). Negative value is below sea level. Colored points represent welltops. The model uses 5x vertical exaggeration. The arrow points to the north.

28

interpreted faults and horizons, and well tops, are in some sense definite (i.e., in this research,

it is assumed that there is no uncertainty in these data). Therefore, the structural model,

or structural-stratigraphic model, is sometimes referred to as a deterministic model.

Structural models are traditionally built based on consolidating data from well logs,

cross sections, and isopach maps. As cross sections and isopach maps are commonly created

from limited data, the accuracy and resolution of such data are not definite. Furthermore,

even though well data often have high resolution, the interpolation approach has to be

used to derive inter-well information because of a small support volume of well data. The

3-D seismic data for this research can characterize elementary structural information with

enough resolution, such as faults, horizons, and boundaries. Thus, the structural model based

on such 3-D seismic data provides the most accurate possible framework of the Tensleep

Sandstone, and grid geometry for the following property modeling.

3.2.2 Property Modeling

The property model is a process with which attribute values, discrete or continuous, are

populated into every grid cell of the structural model. It typically includes two main steps:

facies modeling and petrophysical modeling.

Facies/Flow Units In geology, a facies is a body of rocks with a set of specified character-

istics [72]. In modeling, facies has various definitions: for example, lithofacies, or lithology,

is used to define a depositional environment and/or a type of deposit; electrofacies indicates

log responses which characterize and differentiate different layers; seismic facies is the sum of

seismic attributes; petrophysical facies describes homogeneous petrophysical behavior (static

and dynamic); rock-type in reservoir engineering corresponds to a numerical expression of

elementary dynamical petrophysical grouping after homogenization [73].

Traditional discrimination of rock types is based on subjective observations; neverthe-

less, permeability can change by several orders of magnitude within a given rock type. This

means that even if we can have explicit lithofacies classification over the entire reservoir, it

cannot be utilized in reservoir simulation, because it is not able to characterize permeability

29

distribution that is critical to the effective description of a reservoir.

The concept of flow units that integrate geologic and engineering data into a system

for reservoir descriptions is proposed in [74]. A flow unit is defined as the representative

volume of total reservoir rock within which geological and petrophysical properties that

affect fluid flow are internally consistent and predictably different from properties of other

rock volumes (i.e., flow units). [74] Thus, a flow unit is a reservoir volume in which fluid flow

has similar characteristics and is continuous laterally and vertically [75]. According to [74],

Flow units are defined by geological properties, such as texture, mineralogy, sedimentary

structures, bedding contacts, and the nature of permeability barriers, combined with quan-

titative petrophysical properties, such as porosity, permeability, capillarity, and fluid satu-

rations. [74] Flow units do have some relation to geologic facies but are not consequentially

consistent with facies boundaries. Studies in the subsurface and in surface outcrops also

support the notion that flow units do not always coincide with geologic lithofacies [74]. At

the microscopic scale, pore-throat attributes control fluid flow. The pore geometry is in turn

controlled by geologic properties. Flow units, which are generated by various associations

of these geologic properties, will have similar fluid flow properties. Hence, a flow unit can

contain several geologic facies types, depending on their depositional texture, mineralogical

constituent, and sedimentary structures [76] [77].

The flow unit can be utilized to divide a reservoir into appropriate zones that approxi-

mate the architecture of the reservoir at a scale that is consistent with reservoir simulations.

Therefore, critical geologic information can be incorporated into reservoir simulation with-

out greatly complicating the models [74]. After building the geologic model, the flow unit

is considered a better choice than other facies type for numerical reservoir simulation. Thus

we will use flow units to create the facies model. In the following chapter, facies is used

interchangeably with flow unit. In some literature, flow unit is also termed as hydraulic

(flow) units.

30

Reservoir Characterization of Tensleep Sandstone

Reservoir Characterization of the Tensleep Sandstone Several geologists studied the

Tensleep Sandstone based on texture, mineralogy and sedimentary structure, and concluded

that it was deposited in both eolian and marine environments [78] [79] [80] [81].

Outcrop and subsurface studies show that the Tensleep Sandstone contains interbedded

eolian sandstone, marine sandstone and dolomitic sandstone. Sea level fluctuation caused

this cycle phenomena. Eolian sandstones are formed at low sea level and dolomitic sandstones

are created when the sea level rises [82] [80].

In general, every para-sequence in the Tensleep Sandstone can be divided into two units:

the lower and the upper. Marine facies dominate the lower unit while eolian facies prevail

over the upper unit. Normally, tabular-planar cross-bedding in eolian dune sandstone facies

indicates high-porosity and high-permeability zones, whereas eolian interdune facies, shore-

face/foreshore marine sandstone facies, normal marine carbonate and its equivalent dolomitic

sandstones are zones of low porosity and permeability. Nevertheless, depositional textures

and diagenetic modifications cause the eolian sandstones to be surprisingly heterogeneous.

Additionally, natural fractures make this heterogeneous situation more complex [62] [80].

As mentioned before, reservoir lithofacies in the Tensleep Sandstone can be divided into

eolian dune, inter dune, and sand sheet. Porosity and permeability change with depositional

environments. Furthermore, cementation and compaction affect the porosity and perme-

ability to intensify the heterogeneity of the reservoir. Cements in the Tensleep Sandstone

are mainly micro-crystalline dolomite and anhydrite, which can reduce porosity and cause

anisotropic permeability. Dolomite sand grains are ductile and can be distorted under me-

chanical compaction to destroy porosity and permeability as a result of the filling of the

inter-granular space. Considering this diagenetic modification, the Tensleep Sandstone is

classified into six petrophysical facies: (1) uncemented, dolomite-sand-free, dune sandstone

facies (DUC), (2) cemented, dolomite-sand-free, dune sandstone facies (DC), (3) cemented,

dolomite-sand-rich, dune sandstone facies (DDC), (4) uncemented, dolomite-sand-rich, inter-

dune sandstone facies (IDUC), (5) cemented, dolomite-sand-rich, interdune sandstone facies

(IDC), and (6) cemented, dolomite-sand-rich sand sheet facies [62] (Figure 3.5).

31

(a) DUC (b) DC

(c) DDC (d) IDUC

(e) IDC (f) Sand Sheet

Figure 3.5: Plain-light thin-section images of different petrophysical facies of the TensleepSandstone (courtesy of Dr. Peigui Yin [62]).

32

According to the above petrophysical facies classification, core data from the Tensleep

well 54-TPX-10 have been characterized in [62], as shown in Figure 3.6, which measured and

plotted porosity and permeability of each petrophysical facies from the Tensleep interval

(Figure 3.7).

The work from [62] indicates that the distributions of petrophysical properties between

facies are different and there is a intimate correlation between facies and petrophysical prop-

erties. In addition, there are overlaps among cemented, dolomite-sand-free, dune sand-

stone facies (DC), cemented, dolomite-sand-rich, dune sandstone facies (DDC), uncemented,

dolomite-sand-rich, interdune sand facies (IDUC), and cemented, dolomite-sand-rich, inter-

dune sandstone facies (IDC). In other words, the distributions of petrophysical properties

are not unique in some facies. Hence, flow units are adopted as an approach to characterize

facies of the Tensleep Sandstone.

Flow Units of the Tensleep Sandstone

If there is sufficient core description, such as the work in [62], we could categorize them

according to the classification of facies from [62] and build a facies model based on them.

However, we just have one well having such petrophysical facies classification. Even though

we have well log data, they could not yield an accurate clue to lithofacies or petrophysical

facies. Although Petrel provides a neural network tool to help classify well log data, it

does not lead to any satisfying results. Although the results are similar compared to the

petrophysical facies classification based on cores in [62], they are not accurate enough. As our

research is about uncertainty of modeling, we do not want to bring some extra uncertainties,

and need a definite facies classification. As a result, flow unit is chosen as an approach to

classification of facies.

Because rock types are classified according to petrophysical properties which pertain

to fluid behavior such as porosity, permeability, capillary pressure, and saturation [83], rock

types and flow units are similar because both of them are classified by properties important

to fluid flow. Therefore, we can borrow a category method from rock types to classify flow

units. There are different methods to classify rock types: for example, K-Phi cross plot;

33

Figure 3.6: Distribution of petrophysical facies of the Tensleep Sandstone interval of well54-TPX-10 and comparisons to well logs (courtesy of Dr. Peigui Yin [62]).

34

Figure 3.7: Plot of porosity vs. permeability for different facies of the Tensleep Sandstone(data from Dr. Peigui Yin).

35

Winland method; Pittman method; and rock quality index(RQI) [84].

The Winland equation, or Winland R35, is a method to calculate pore-throat radius

using core porosity and permeability measurements. The R35 of a given rock type not only

can reflect depositional and diagenetic texture, but it can also impact fluid flow [38]. As

a result, R35 estimated from core or well logs, can be utilized to categorize zones that can

be used by both geologists and reservoir engineers. This approach is ideally suited to our

research, because the Tensleep Sandstones porosity and permeability varies with different

depositional environments and are further modified by diagenetic processes. And reservoir

simulation, which describes fluid flow in a reservoir, will be run based on a 3D geologic model

of the Tensleep Sandstone. As our research includes both geologic modeling and fluid flow

simulation, an approach that can be used in both procedures is preferred. Consequently, the

Winland equation is adopted to classify facies of the Tensleep Sandstone.

The Winland equation depicts an empirical relationship among porosity, permeability,

and pore aperture radius corresponding to the 35th percentile of mercury saturation for a

mixed suite of sandstones and carbonates. The equation is as following:

logR35 = 0.732 + 0.588 logKair 0.864 log (3.1)

where R35 is the pore aperture radius corresponding to the 35% mercury saturation,

Kair is the uncorrected air permeability (in mD), and is porosity (in %) [85] [86].

There are 12 wells that contain porosity and permeability data derived from laboratory

core tests. After a quality check, 11 wells were designated to be used in classifying flow

units. These have similar and predictable fluid flow characteristics respectively. Two flow

units with different reservoir performance are distinguished by the ranges of R35.

(1) Flow unit 1 is defined as having an R35 ranging above a threshold of 0.85 m. This

kind of flow unit corresponds to high-porosity and high-permeability zones where fluid can

easily flow.

(2) Flow unit 2 has an R35 less than 0.85 m. Such flow units correspond to a low-

porosity and low-permeability location where there are normally tight reservoirs or non-

reservoirs.

36

Figure 3.8: Comparison between flow units and petrophysical properties of the plot in Fig-ure 3.7.

We compared this flow unit category to the petrophysical facies based on cores in [62],

as shown in Figures 3.8 and 3.9 .

The black line in Figure 3.8 represents R35 = 0.85. The facies of the points above this

black line are flow unit 1; the ones below this line are flow unit 2. Almost all uncemented,

dolomite-sand-free, dune sandstone facies (DUC), and some of the cemented, dolomite-sand-

free, dune sandstone facies (DC) belong to flow unit 1, whereas almost all interdune fa-

cies (uncemented, dolomite-sand-rich, interdune sandstone facies (IDUC), and cemented,

dolomite-sand-rich, interdune sandstone facies (IDC)), cemented, dolomite-sand-rich, dune

sandstone facies (DDC), and some part of cemented, dolomite-sand-free, dune sandstone fa-

cies (DC) are attributed to flow unit 2. This indicates that flow units do have some relation

with petrophysical facies, but are not absolutely consistent with them. This also testifies the

statement in [74] that flow units do not always coincide with geologic lithofacies [74].

37

Figure 3.9: Comparison between petrophysical facies in [62] and flow units derived in thisstudy.

38

The Relationship between Porosity and Permeability The relationship between

porosity () and permeability (k or log k) is traditionally assumed to be linear. This assump-

tion is simply based on observation. However, approaches from experiments, for instance the

Winland equation, do not illustrate that permeability is a linear function of porosity. Flow

units