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Geological modeling in GIS for petroleum reservoir characterization and engineering: a 3D GIS-assisted geostatistics approach

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Geological modeling in GIS for petroleum reservoir characterization and engineering: a 3D GIS-assisted geostatistics approach

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GEOLOGICAL MODELING IN GIS FOR PETROLEUM RESERVOIR
CHARACTERIZATION AND ENGINEERING:

A 3D GIS-ASSISTED GEOSTATISTICS APPROACH

by

Diego A Vasquez

A Thesis Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(GEOGRAPHIC INFORMATION SCIENCE AND TECHNOLOGY)

March 2014

Copyright 2014 Diego A Vasquez
ii
DEDICATION

I wish to dedicate this project to all of the citizens who wish to solve the most
challenging scientific problems by implementing cross-disciplinary research and
that are determined to make the world a better place.

I would also like to dedicate this to my friends and family who’ve supported me
throughout the project.
iii
ACKNOWLEDGMENTS

I would like to thank all of my committee members for their guidance and support:
Dr. Jennifer Swift and Dr. Su Jin Lee from the Spatial Sciences Institute, Dr. Behnam
Jafarpour from the Petroleum Engineering Department and Dr. Doug Hammond
from the Earth Sciences Department.

I would also like to thank the engineering and geology consultants who have helped
provide the necessary data for performing this work and who’ve provided
assistance in the field.

In addition, I would also like to send a big thank you to SPE as well as my fellow
colleagues in the Petroleum Engineering, Geology and Geography Departments at
USC.
iv
TABLE OF CONTENTS

Dedication ii

Acknowledgments iii

List of Tables vi

List of Figures vii, viii, ix

List of Abbreviations x

Abstract xi, xii

Chapter One: Introduction 1
1.1 Background 1
1.1.1 Global objective 1
1.1.2 Thesis objective 4
1.2 Analysis Review 7
1.2.1 Kriging review 7
1.2.2 Simulation review 9
1.2.3 Interpolation comparison 12
1.3 Motivation 13
1.3.1 Applicability to Petroleum Engineering 13
1.3.2 Importance of the Energy Industry 15

Chapter Two: Study Area 18
2.1 Geography 18
2.1.1 Physical Geography Overview of Study Area 18
2.2 Geology 20
2.2.1 Geological Setting 20
2.2.2 Geological Structure 22
2.2.3 Sedimentary History Overview 26
2.2.4 Lithology and Stratigraphy 26
2.2.5 Remark on Previous Studies and Field Observations 30

Chapter Three: Data 32
3.1 Hard Data Sources 32
3.1.1 Electrical Data Boring 34
3.2 Software and Data Integration 36
3.2.1 Modeling Software Interoperability 36
3.2.2 Remote Sensing DEM 37
3.2.3 3D Stratigraphic Cross-Section 38
3.2.4 Data Point Set 40
3.2.5 GPS Data Acquisition 41
v
Chapter Four: Methods 42
4.1 Data Exploration and Evaluation 42
4.1.1 Data Input and Transformation 42
4.2 Variogram 47
4.2.1 Variogram Parameters 48
4.2.2 Experimental Variogram 51
4.2.3 Variogram Models 54
4.3 Interpolation 58
4.3.1 Kriging Parameters 58
4.4 Validation 59
4.4.1 Cross-validation 59
4.4.2 Statistical Comparisons 60

Chapter Five: Results 62
5.1 Conditional Simulation 62
5.1.1 Sequential Gaussian Simulation Models 62
5.2 Ordinary Kriging 66
5.2.1 Predicted Models 66
5.3 Volume Explorer 67

Chapter Six: Discussion and Conclusion 69
6.1 Variogram and Simulation Model Remarks 69
6.1.1 Well ID locations 70
6.2 Validation 71
6.2.1 Cross-validation plots 72
6.3 Project Evaluation 77
6.3.1 Comparison of Results 77
6.3.2 Interpretation 79
6.3.3 Final remarks 83
6.4 Conclusion 84

References 87

Appendices
Appendix I: Cross-section with Stratigraphic Log 92
Appendix II: Stratigraphic Column 93
Appendix III: Structural Contour Map 94
Appendix IV: Geological Contour Map 95
Appendix V: Structural Contour/Isopach Map 96
Appendix VI: Integrated Volumetric and Numerical Models 97
vi
LIST OF TABLES

Table 1: Description of Interface Input Parameters 55
for Variogram Modeling in SGeMS

Table 2: Description of Search Ellipsoid Parameters 59
for Kriging Interpolation in SGeMS

vii

Figure 1: Field Database 3

Figure 2: Geography LA Basin 4

Figure 3: Hydrocarbon Scheme 6

Figure 4: Reservoir Eng. Scheme 14

Figure 5: LA Oilfields 20

Figure 6: Surface Geology LA 21

Figure 7: Mahala Reservoirs 22

Figure 8: Geology Chino Fault 24

Figure 9: Cross-Section Chino 25

Fault with legend

Figure 10: Idealized Cross-section 25

Figure 11: Structural Geo-contour 28

Figure 12: Isopach Map 29

Figure 13: Electrical Well Logs 33

Three snapshots: a-c

Figure 14: Spontaneous Potential 35

Figure 15: Pay Zone E-log 36

Figure 16: DEM Study Area 38

Figure 17: 3D Cross-section 39

Figure 18: Blank 3D Point Set 40

Figure 19: Aerial Mapview Lease 41

Figure 20: R Data Logs 43

Figure 21: SP Data Logs 43
LIST OF FIGURES
viii

Figure 22: SP CDF and PDF 44

Figure 23: R CDF and PDF 44

Figure 24: Transformed R 45

CDF/PDF

Figure 25: Raw Q-Q Plot 46

Figure 26: Transformed Q-Q Plot 46

Figure 27: R and SP Scatterplot 47

Figure 28: Variogram Parameters 49

Figure 29: SP Exp. Variogram 51

Figure 30: R Exp. Variogram 52

Figure 31: Vertical Fitted SP

Model
53

Figure 32: Vertical Fitted R

Model
53

Figure 33: Omni Fitted SP Model 53

Figure 34: Omni Fitted R Model 53

Figure 35: Horizontal Fitted SP

Model
54

Figure 36: Horizontal Fitted R 54

Model

Figure 37: Main Variogram Parts 56

Figure 38: SP Variogram Solution 57

Figure 39: R Variogram Solution 58
viii

Figure 40: SP SGS Realizations 62

Six Random Realizations: a-f

Figure 41: R SGS Realizations 63

Six Random Realizations: a-f

Figure 42: R P50 Model 64

Figure 43: R P10 Model 64

Figure 44: R P90 Model 64

Figure 45: SP P50 Model 65

Figure 46: SP P10 Model

65

Figure 47: SP P90 Model 65

Figure 48: R Kriged Model 66

Figure 49: R Variance Model 66

Figure 50: SP Kriged Model 67

Figure 51: SP Variance Model 67

Figure 52: SP Volume Explorer 68

Figure 53: R Volume Explorer 68

Figure 54: Well ID Location Map 71

Figure 55: R Cross-Valid Wells 72-

Thirteen Wells: a-m 74

Figure 56: SP Cross-Valid Wells 74-

Thirteen Wells: a-m 76

ix
x
LIST OF ABBREVIATIONS

3D Three-Dimensional

AAPG American Association of Petroleum Geologists

CA (state of) California

CIPA California Independent Petroleum Association

DEM Digital Elevation Model

DOGG (CA) Division of Oil, Gas and Geothermal Resources

EIA (U.S.) Energy Information Administration

GIS Geographic Information Systems

GPS Global Positioning System

GSA Geological Society of America

IPAA Independent Petroleum Association of America

MATLAB Matrix Laboratory Software

MMbbl One Million Barrels (of oil)

NSWA National Stripper Well Association

OCR Optima Conservation Resources

R Resistivity

SGeMS Stanford Geostatistical Modeling Software

SGS Sequential Gaussian Simulation

SP Spontaneous Potential

SPE Society of Petroleum Engineers

SSI Spatial Sciences Institute

USC University of Southern California
xi

ABSTRACT

Geographic Information Systems (GIS) provide a good framework for solving
classical problems in the earth sciences and engineering. This thesis describes the
geostatistics associated with creating a geological model of the Abacherli reservoir
within the Mahala oil field of the Los Angeles Basin of Southern California using a
variogram-based two-point geostatistical approach. The geology of this study area
features a conventional heterogeneous sandstone formation with uniformly inclined
rock strata of equal dip angle structurally trapped by surrounding geologic faults.
Proprietary electrical well logs provide the resistivity and spontaneous potential at
depth intervals of 10’ for the thirteen active wells in the study area. The dimensions
and shape of the reservoir are inferred from geological reports. An isopach map was
georeferenced, digitized and used to generate a 3D point-set grid illustrating the
boundaries and the volumetric extent of the reservoir. Preliminary exploration of
the input data using univariate and bivariate statistical tests and data
transformation tools rendered the data to be statistically suitable for performing
ordinary kriging and sequential Gaussian simulation. The geological and statistical
characteristics of the study area ensure that these interpolations are appropriate to
employ. Three variogram directions were established as part of the variogram
parameters and then a best-fit statistical function was defined as the variogram
model for each of the two electrical log datasets. The defined variogram was then
used for the kriging and simulation algorithms. The data points were interpolated
across the volumetric reservoir resulting in a 3D geological model displaying the
local distribution of electrochemical properties in the subsurface of
xii
the study area. Data is interchanged between separate modeling programs, Stanford
Geostatistical Modeling Software (SGeMS) and Esri ArcGIS, to illustrate the
interoperability across different software. Validation of the predictive geostatistical
models includes performing a leave-one-out cross-validation for each borehole as
well as computing a stochastic model based on the sequential Gaussian simulation
algorithm, which yielded multiple realizations that were used for statistical
comparison. The reservoir characterization results provide a credible
approximation of the general geological continuity of the reservoir and can be
further used for reservoir engineering and geochemical applications
1
CHAPTER ONE: INTRODUCTION

1.1 Background

Geographic Information Systems (GIS) are a very useful way to integrate
geology with engineering. Geostatistics in particular is an inherently interdisciplinary
branch with direct applications to geology, geography and petroleum engineering
practices (Myers 2013). Since geostatistics involves quantitative analysis, modeling and
simulation of field data using numerical and analytical techniques it is a core component
of petroleum engineering (Dubrule and Damsleth 2001). Due to the focus on modeling of
spatial and spatiotemporal datasets measured at geographical locations, geostatistics is
also a widely used approach in geography and GIS (Burrough 2001). When geostatistics
is applied to petroleum (or hydrology) the focus is on modeling the subsurface
environment constrained to the local geology, thus geostatistics is also an important
discipline in the earth sciences (Journel 2000). Therefore this research provides a good
interdisciplinary opportunity to combine the earth and spatial sciences with petroleum
engineering.

1.1.1 Global Objective
A global effort within the scientific community has begun which acknowledges the
need for greater capabilities in information management to: 1) satisfy the continuously
increasing demand for the discovery, management and sustainability of natural resources,
and 2) provide solutions in forecasting natural phenomena for addressing societal
challenges (Sinha et al. 2011). One of the main objectives of this research is to promote
and contribute to the relatively new but rapidly evolving interdisciplinary field of
2
geoinformatics. Geoinformatics is the science that uses spatially related information and
computational technology systems to address complex problems in the earth,
environmental, geographical and related engineering disciplines with the future goal to
provide greater availability of data and tools for serving the needs of the public (Awange
and Kiema 2013). When GIS-assisted approaches are used to acquire, manage and
analyze geo-information in combination with advanced computational techniques,
geoinformatics becomes a powerful tool to efficiently integrate different data and
improve the way scientific information is processed and presented (Krishna et al. 2010).
The development and implementation of information and computing technology as
well as cyberinfrastructure for the earth sciences is expected to help transform the next
generation of interdisciplinary research. The shift to the information age (known as the
“Digital Revolution”) has very significantly affected academia in which earth scientists
increasingly rely more on digital data instead of hard copy. Hence the emergence of
evolving fields such as geoinformatics will be very important for data-intensive research,
especially with the global exchange of information (i.e. the onset of “big data”).
Geographic information systems are complex systems that are comprised of different
components which have separate functions including data, software/hardware and
personnel. When used collectively the components allow for broader approaches to
spatial problem solving. GIS usage specializations relevant to this research include
remote sensing, programming, global navigation and positioning systems, spatial analysis
and modeling, as well as other spatial science disciplines dealing with data visualization
and optimization (Wilson and Fotheringham 2008). The data management system of a
GIS is typically managed via the use of integrated spatial databases that allow for the
3
organization of information and the determination of relationships between the data and
topology. An illustration of the database which was used as a model for the database for
this research and for optimizing field activities, and which contains information about the
study area input data and individual oil reservoir wells, is shown in Figure 1. Additional
more complex programs that can perform GIS geoprocessing functions (e.g.
ModelBuilder) can be used to automate workflows for improving production activities
encountered in day-to-day field work.

Figure 1: Database design utilized for field services by lease operators (OCR 2014).

4
1.1.2 Thesis Objective
The primary objective of this thesis project was to develop a volumetric 3D geological
model of the petroleum reservoir in the study area using GIS to visualize the subsurface
distribution of rock properties shown in Figure 2, the Abacherli reservoir within the
Mahala oil field of the Los Angeles Basin of Southern California.

Interpolation of drilled well or wellbore data involves predicting values of specific
variables at unknown locations based on the measurements obtained from known
locations using statistical principles, thereby creating a continuous surface of the
subsurface field. Earth systems are inherently complex, dynamic and contain various
Figure 2: DEM of study area region with active geological faults (based on USGIN 2011)
5
characteristics that can make reservoir characterization a very burdensome task (Caumon
2010). The inclusion of geological features depends mainly on the depositional
environment and defines the overall geological architecture of a given reservoir (Kelkar
and Perez 2002). Different geological settings may require different geostatistical
approaches (e.g. object-based modeling or variogram-based modeling) in order to
construct an appropriate model that honors the form of the reservoir as closely as
possible. Stationarity, defined in practice as local data averages within a spatial domain
that are approximately constant, is the most important assumption for estimation in
geostatistics. Assuming stationarity in a particular region requires that the model
developed from the sampled data be applicable within the specified study area. In
reservoir analyses this assumption is necessarily subjective because of the inherent
uncertainties in the subsurface and the scarcity of data which prevents researchers from
being absolutely certain about the subsurface geology of a region in which there is
limited wellbore data. In the context of this study, a region of stationarity defines the
continuity boundaries for the study area subsurface or “field”.
Geostatistics is the discipline concerned with determining the extent of that continuity
within the region of assumed stationarity by taking advantage of the notion that values
that are closer to one another are more similar than values further away (i.e. as the
distance between any two values increases the similarity between the two measurements
decreases) (Kelkar and Perez 2002). Following this assumption, geostatistical techniques
are aimed at identifying spatial relationships between variables, such as how neighboring
values are related to each other, in order to estimate values at separate locations. Provided
that field conditions meet the criteria, one reliable approach to define this variability is
6
through a statistical correlation as a function of distance, known as a variogram. In many
cases where geological structures are assumed continuous throughout the reservoir, even
if a few discontinuous lithological layers act as baffles, it is appropriate to assume that the
reservoir can be modeled as a whole by the use of variogram-based modeling. Figure 3
illustrates a typical petroleum deposit scheme in which oil and gas are generated at the
source, migrate in direction of least resistance and are subsequently trapped and
accumulated to form petroleum reservoirs.

Figure 3: Digitized hydrocarbon deposit system (based on AAPG UGM SC 2011)

7
1.2 Analysis Review

1.2.1 Kriging Review
Kriging is a widely used conventional estimation technique that is based on a
linear estimation procedure expected to provide accurate predictions of values within a
volume, over an area or at an individual point within a specified field. In earth science,
kriging is a favored interpolation approach compared to other methods because of its
ability to include the anisotropy that rock layers of a sedimentary material exhibit in
geological formations, thus the models that are obtained via the use of kriging have more
resemblance to the true field geology (SPE PetroWiki 2013). This is in part because the
linear-weighted averaging methods used in kriging techniques depend on direction as
well as orientation, instead of only depending on distance as other interpolation methods
do. The fundamental principle in any kriging technique is that an unknown value at an
unsampled point is estimated by the product of a weighted average of neighboring values,
as explained by the following simplified expression:

( ⃗

) ∑

( ⃗

)

( )

Where ( ⃗

) = value at neighboring location ( ⃗

),

= weight of neighboring value and

( ⃗

) = estimated value at unsampled location. The estimation procedure calculates the
weights (

) assigned to neighboring locations, which depend on the spatial relationship
between unsampled points and neighboring values as well as the spatial relationship
between neighboring points (Kelkar and Perez 2002). The relationships are obtained via
the use of a variogram model.
8
Variations between the different types of variogram-based kriging methods
available are different depending by how the mean value is determined and used in the
interpolation (SPE PetroWiki 2013). Ordinary kriging is by far the most commonly used
kriging approach that allows for the local mean to vary and be re-estimated based on
nearby (local) values thereby easing the assumption of first-order stationarity (Kelkar and
Perez 2002). Ordinary kriging is better suited for this type of analysis because a true
stationary global mean value for data in a reservoir is typically unknown and it cannot be
assumed that the sample mean is the same as the global mean. This is due to the fact that
in any real reservoir the local mean within a neighborhood in the field can easily vary
over the spatial domain.
Ordinary kriging is deemed appropriate and used as the estimation technique in
this analysis. Nevertheless, it is important to consider three other types of kriging
techniques, which include simple kriging, universal kriging and cokriging. As the name
suggests simple kriging is the mathematically simplest technique where a known
stationary mean must be assumed over the entire spatial domain or study area. However,
it is unrealistic to assume that we know the exact mean for all the data locations in the
field given the degree of uncertainty in the subsurface geology, therefore this technique
was not applied in this study. The universal kriging model assumes that there is a general
polynomial trend. However the data is not known to exhibit a trend in a particular
direction and there is no scientific justification to describe a potential trend, so universal
kriging was not deemed to be more appropriate either. Cokriging is a type of kriging
technique that uses spatial correlations from different data variable types to estimate the
values at unsampled locations. In addition to estimating the values at unsampled locations
9
with surrounding samples of the same variable type (e.g. porosity), cokriging also uses
the surrounding samples from different variables (e.g. permeability) provided the
assumption that both variable types are spatially correlated to each other (Kelkar and
Perez 2002). Taking advantage of the covariance between two or more spatially related
variables, and in theory providing a greater ability to make better predictions, cokriging is
an attractive as well as commonly used approach. Nevertheless, the applicability of
cokriging to a particular field depends on if the objective is to provide a stronger
prediction of a more undersampled variable relative to a more well-sampled variable
given a strong correlation between the two variables. For example, if permeability values
were derived from core samples for only a few wells, say 4 or 5, but electrical log values
were obtained for all of the 13 wells and assuming spatial relationships between the cores
and logs, then it would be most appropriate to “cokrige” the permeability samples with
the resistivity/spontaneous potential to provide a better permeability distribution model.
But because both electrical properties in this study, spontaneous potential and resistivity
(“SP” and “R”), are adequately sampled, it was decided that cokriging analysis would not
be included. Nevertheless performing cokriging between SP and R as an additional
analysis in the future may provide useful results and information.

1.2.2 Simulation Review

Another approach besides conventional estimation techniques such as kriging to
characterize heterogeneous reservoirs is the use of geostatistical conditional simulation
techniques. One of the primary differences between the two is that simulation methods
preserve the variance observed in the data by relaxing some of the constraints of kriging,
10
as opposed to only preserving the mean value. Conditional simulation is a type of
variation of conventional kriging and is a stochastic modeling approach that allows for
the calculation of multiple equally probable solutions (i.e. realizations) of a regionalized
variable by simulating the various attributes at unsampled locations, instead of estimating
them (SPE PetroWiki 2013). A “conditional” simulation is conditioned to prior data, or in
other words the hard or raw data measurements and their spatial relationships such as a
variogram are honored. By providing several alternate equiprobable realizations this
approach helps represent the true local variability thereby helping to characterize local
uncertainty. This is one of the most useful properties of a simulation because all models
are subject to uncertainty, in particular geological models because they are based on
partial sampling. This is especially true of reservoir models due to the several different
sources of uncertainty.
Provided that the true value of a geological attribute is a single number but that
exact value is always unknown because of the uncertainty in the field, the practice in
statistical modeling is to transform the single number into a random variable, a variate,
which is a function that specifies its probability of being the true value for every likely
outcome. The two main types of conditional simulation methods are either grid-based
(a.k.a pixel-based) which operate one cell (or point) at a time, or are object-based which
operate on groups of cells arranged within a discretized geologic shape (SPE Petrowiki
2013). During each individual run the corresponding realization starts with a unique
random ‘navigational path’ through the discretized volume providing the order of cells
(or points) to be simulated. Because the ‘path’ differs from each realization-to-realization
the results provide differences throughout the unsampled cells which yield the local
11
changes in the distribution of rock properties throughout the reservoir that are of interest
for accurate geological representations. For example, in this study running several
realizations produced several values per variate, which then allowed for a graphical
representation of the results and an approximation of the variates (Olea et al. 2012). The
method used in this study is the grid-based approach because of the geological
assumption that the geologic facies vary smoothly enough across the reservoir (typical
depositional setting of shallow marine reservoirs) as opposed to sharp changes in the
shape of the sedimentary body. Furthermore, there are different types of simulation
methods including annealing simulation, truncated Gaussian simulation, turning bands
simulation and sequential simulation. Sequential simulation methods are some of the
most widely used in practice and are kriging-based methods where unsampled locations
are sequentially and randomly simulated until all points are included. The order and the
way that locations are simulated determine the nature of the realizations. There are three
types of sequential-simulation procedures, including Bayesian indicator, sequential
Gaussian, sequential indicator. These are based on the same algorithm but with slight
variations. Sequential Gaussian Simulation (SGS) is one of the most popular, it assumes
the data follow a Gaussian distribution. Because SGS is best suited for simulating
continuous petrophysical variables (e.g. resistivity, spontaneous potential, porosity,
permeability) it is deemed most appropriate for this study and thus was used as the
simulation method, detailed in Chapter 4.

12
1.2.3 Interpolation Comparison
Both conventional estimation (kriging) and stochastic modeling (sequential
Gaussian simulation) techniques are well proven, but slightly different, approaches to
describe the natural processes and attributes of geological phenomena, in this case the
characterization of a petroleum reservoir. A useful addition is to use both of them in a
study to compare and contrast. To recap the main differences between the two: 1) kriging
provides an estimation of the mean value and its standard deviation at an individual point
given that the variate is represented as a random variable that follows a Gaussian
distribution, and 2) SGS selects a random deviate from the same Gaussian distribution
instead of estimating the weighted mean at each point where the simulation is selected
according to a uniform random number that represents the probability level (Halliburton-
Landmark Software 2011). When including the simulation approach the natural
variability of the local geology counters the blunt smoothing effects of kriging. From the
multiple equiprobable realizations obtained it is possible to characterize uncertainty by
comparing a large number of realizations. Assuming the model is representative of the
field then the true value is expected to fall within the bounds of the probability.
Quantification in terms of probability can be made, for example finding the mean value
of the distribution which corresponds to the highest probability. Both approaches
complement each other and are used in the analysis performed as part of this thesis
research. The mathematical details of these methods are extensive and beyond the scope
of this report. More detailed information on the mathematical and statistical expressions
can be accessed from additional text available in the literature (e.g. McCammon 1975;
Chiles and Delfiner 1999; Kelkar and Perez 2002).
13
1.3 Motivation

1.3.1 Applicability to Petroleum Engineering and Petroleum Geology
Applied geostatistics for geological modeling and simulation is essential for successful
oil and gas production. Reservoir characterization includes determining the distribution,
or the closest possible approximation, of subsurface properties of a geologic system in a
petroleum field. This is essential information for improving resource management,
production development and field operations (Gorell 1995). Geologic outputs obtained
from geostatistical models are used in a variety of important applications for petroleum
and similarly for groundwater resources, including exploration, reservoir engineering and
environmental remediation (Nobre and Sykes 1992). Having a thorough geostatistical
model is very important when it is used in reservoir simulators, inverse models and
geochemical models. Reliable geological models based on geostatistics can be used for
specific practices such as calculating oil production rates, remediating contaminated
aquifers, estimating the recoverable reserves (i.e. oil, gas or water), drilling new
boreholes and determining hydrocarbon migration (Deutsch 2006). The combined use of
geostatistical, simulation and inverse models enable effective reservoir engineering. This
provides the opportunity to predict field performance and further understand reservoir
behavior, which in turn furthers the ultimate goal of optimizing production and
maximizing hydrocarbon recovery (Coats 1969). Reservoir engineering as a sub-
discipline has grown exponentially with the onset of digital technologies and computers
capable of performing larger and more complex sets of calculations. Because of this
“reservoir simulation revolution” and the increasing demand for energy, geostatistical
14
modeling will remain a key engineering tool in natural resource development (Stags and
Herbeck 1971).
The schematic diagram provided in Figure 4 illustrates the general workflow cycle of
the “field” from a reservoir engineering perspective. First a geostatistical model
(geological continuity) is developed and input into a fluid flow model (reservoir
simulator) that predicts field production, then an objective function (inverse model) is
developed to integrate dynamic data (field observations) and adjust the necessary
parameters (history match) until the simulations are reasonably close to the observations.
The complete process assists in the validation of all model(s) included in a given
analysis, thus providing the opportunity to achieve a validated decision-making tool
ensuring that optimal field performance is achieved in the future.

Figure 4: Reservoir engineering results illustrating reservoir characterization/simulation scheme.

15
1.3.2 Importance of the Energy Industry
The energy industry is an extremely important part of the Unites States economy
and will remain a key component for economic growth in the following decades.
Petroleum is currently the most important player in the energy industry and is expected to
continue to be the main source of energy throughout our human timescale. Petroleum
affects virtually every aspect of the industrialized world and is found in most synthesized
materials in use today, from the fuel we use (cars, jets, boats) to our electronics and
beauty products. Therefore, control of this resource is imperative for the development and
stabilization of human well-being (Ranken Energy 2014). In 2011 the U.S. consumed an
estimated 18.8 MMbbl/day plus around 19.1 MMbbl/day of refined petroleum products,
or around 22% of the global production, making it the largest consumer in the world (EIA
2012). Recent resurgence in domestic oil and gas production has led to a remarkable oil
boom, in great part due to the use of advanced recovery technologies for the extraction
from unconventional resources. This is dramatically transforming the nation’s energy
market and has put the U.S. on the verge of becoming the world’s largest oil producer
(Thompson 2012). In 2012 the U.S. experienced the largest increase in the world of crude
oil and natural gas production, providing extraordinary opportunities for independent
producers in the upstream industry (Bell, Julia 2013). Independent oil companies operate
most of the national oil production, accounting for around 42% offshore and 72%
onshore (averaging 68%) (PolitiFact 2014). Approximately 80% of the domestic oil wells
in the U.S. are classified as stripper wells (i.e. wells yielding ≤ 10 bbl./day), and
production from stripper wells makes up about 20% of the total domestic production
(NSWA 2014). Furthermore the U.S. is the only country with significant stripper well
16
output. The production from independent companies in California alone comprises
around 70% of total oil and 90% of gas production in the state with a fair share coming
from small to midsized companies (CIPA 2014). Therefore crude oil production from
independent sources will continue to play an imperative role on the road to energy
independence and economic stability. It is important to mention that the amount of oil
extracted during primary oil recovery, especially with outdated practices used in the mid-
20th century, typically only ranges between 5-15% of the total recoverable oil. When
combined with secondary or tertiary recovery production may only reach between 40-
60% of the total oil reserves (Tzimas et al. 2005). Since mature oil fields such as the
Abacherli reservoir in the Mahala field have only been subjected to primary recovery
using outdated technology, much interest and investment is focused on reviving these old
fields, which are guaranteed to retain most of their extractable reserves still intact. With
innovative solutions and growing technology, mature oil fields including the Mahala have
the potential to become significant contributors to the national oil and gas boom,
especially with the use of functional operations such as: horizontal drilling, hydraulic
fracturing, gas injection and other enhanced oil recovery techniques. Mature reservoirs
produce more than 80% of the world oil production. In addition, the rate of production
from new (non-mature) discoveries has consistently dropped since the turn of the century
(Alvarado and Manrique 2010; Delshad, Mojdeh 2013; EOIR 2013). Therefore mature
reservoirs and associated stripper wells comprise an essential part of the energy industry,
so increasing production from these assets is very important for ensuring economic
security and meeting the growing energy demand. As part of an old large oil field with
the vast majority of its recoverable reserves still in play, the Abacherli reservoir in the
17
Mahala oil field is a good candidate for evaluation and revival. The social motivation of
this work and contribution to society is providing computational results for the
management of an indispensable natural resource, petroleum. Because of the
interconnection between the energy industry with the economy as well as public and
political interests, this research project could have a significant impact on the economy.
Information derived from this study will be used to take action and make substantial
improvements in oil reservoir extraction from the Abacherli reservoir in the Mahala oil
field in the future. Lastly, the academic motivation of this work is to help contribute to
the rapidly evolving cross-disciplinary research between the natural and applied sciences.

18
CHAPTER TWO: STUDY AREA
2.1 Geography

2.1.1 Physical Geography Overview of Study Area
This project evaluates the Abacherli reservoir within the Mahala oil field of the
Los Angeles Basin of Southern California, shown in Figure 2. Situated between the
intersection of Los Angeles, Riverside, Orange and San Bernardino county lines, the
reservoir is part of the Chino Hills highlands and immediately connected to the Chino
Hills State Park. Based on distance calculations obtained from field observations using
GPS/GIS tools, the Abacherli lease is estimated to have a total surface area measuring
approximately 1.0 km
2
and a rugged terrain with variable elevation ranging from 500’ to
1,200’ above sea level, consisting of hills dissected by deep canyons. The study area field
is geographically located on the southern Californian pacific coast of the North American
Cordillera, which is the major mountain chain extending throughout the western
continent.
Along the American west coast are numerous major mountain ranges known
collectively as the pacific mountain system. In southern California, more specifically,
there are collections of different mountain ranges including the Peninsular Ranges and
the Transverse Ranges. The ecology of this region is typical of terrestrial ecosystems of
southern California, transitioning from coastal to the desert environments and consisting
mostly of shrubland (e.g. chaparral) and woodlands (Schoenherr 1992). The Santa Ana
Mountains, part of the Peninsular Ranges, are a north-south trending range that
geographically and geologically divide Los Angeles, marking the easternmost border of
19
the LA basin and county. Within these mountains, the Chino Hills highlands mark the
beginning of the Santa Ana range from the north. The Chino Hills are the foothills to the
southern section of the east-west trending San Gabriel Mountains of the Transverse
Ranges and act as a bridge connecting the Peninsular Ranges to the south, with the
Transverse Ranges to the north immediately adjacent to the Puente Hills (California State
Parks 2013). The location of Chino Hills is of geographic importance because of its
relation to major metropolitan cities and its connection to mountain ranges, ecosystems
and local watersheds. In fact, the southeastern part of the study area extends into the
Santa Ana River valley. The map provided in Figure 2 displays the major geologic faults
of the region overlain on a digital elevation model (DEM) that further illustrates the
topography of the study area. Figure 5 illustrates the oil fields within the Los Angeles
Basin of southern California. The significant deposits of petroleum in the region can be
attributed to the deposition of organic-rich sediments in the basin and their effective
accumulation in part due to the major geologic forces at work, such as faulting, folding.
20

2.2 Geology

2.2.1 Geological Setting
The following geologic map, Figure 6, of Southern California illustrates some of
the overall bedrock and lithology of the region.
Figure 5: Oilfields of the Los Angeles basin (based on DOGG 2013)
21

Regional geographic features and landscapes are shaped by California’s complex
but young and active geology. Active tectonic forces have resulted in dominant fault
zones where structural formations have allowed for the large accumulation of
hydrocarbons. Southern California in particular is in a pivotal location where a great
continental transform fault (San Andreas) divides two of the world’s major tectonic
plates. Energy released from geological activity along these plates has resulted in massive
stress fields that have triggered the generation of several faulting and folding mechanisms
(Wright, Thomas 1987). The two most important structural mechanisms that are
responsible for the formations of the Mahala oil field are the Whittier and Chino faults;
these are the two upper segments that branch off of the major Elsinore Fault Zone, which
is part of the trilateral split of the intercontinental San Andreas Fault system (Figure 2).
There are four known and producing reservoirs in the Mahala oil field, listed as follows:
Figure 6: Geology of Southern California study area region (Madden and Yeats 2008)
22
Mahala, West Mahala, Prado Dam and Abacherli, and there are an additional three
known reservoirs in the vicinity of the field as shown in Figure 7.

2.2.2 Geological Structure
Compressional forces from the Whittier and Chino faults have resulted in
deformation in the area, including large anticline-syncline folding structures between
these two faults, such as the Mahala anticline. Located on the geographic extreme eastern
edge of the Puente Hills/Chino Hills and located on the geologically extreme eastern edge
of the LA basin, the Mahala anticline is an asymmetric northwest-trending breached
anticline extending over three miles in length (Dorsey, Ridgely 1993). The anticline is
thrust-faulted by the chino fault, which is directly responsible for the uplift of the region
Figure 7: Reservoirs in the Mahala oilfield study area (Olson 1977)
23
and is the primary structural feature of the Abacherli reservoir. The chino fault trends to
the northwest and has a dip range between 50-70 to the southwest (dipping ≤ 50° at
depths less than 1,000’ and around 70° at depths exceeding 3,0000’) (Olson, Larry 1977).
The Chino fault thrust segmented the northeastern-most limb of the Mahala anticline fold
dividing the area into a hanging wall above the fault and a footwall below the fault. It is
estimated that movement along the fault occurred during the Pleistocene epoch (Olson,
Larry 1977). This local mechanism is responsible for setting up the updip fault trap for
the oil accumulation of the Abacherli reservoir, such as the footwall block in the
segmented limb of the faulted Mahala anticline within the Chino fault zone. The reservoir
itself is a tilted homocline with steeply but uniformly dipping beds to the northeast with
an approximate strike of 315°. The reservoir dip angle ranges between 40-70° with an
average of 60°, and the dip angle is largest closer to the fault and decreases with distance
from the fault. There are two unnamed northeast-southwest trending sealing faults which
merge southwest of the Abacherli area that cap the reservoir at its northern and southern
edges, effectively serving as the boundaries of the reservoir.
Figure 9 is a cross-section of line E-E’ from Figure 8 below. Both Figures
illustrate some of the local lithology and main structures of the chino fault zone within
the chino fault area. The column on the right of Figure 9 is the legend for both Figures,
providing a reduced version of the stratigraphic column. Figure 10 is an additional cross-
section for the location of interest helping to illustrate the local stratigraphy. The
“Michelin Zone” in the cross-section is the primary sandstone formation that produces
most of the oil in the lease. Appendix I and II illustrates additional information on the
stratigraphic sequence.
24

Figure 8: Geological map of study area (Madden and Yeats 2008)
25

Figure 9 (above): Cross-section of Chino fault zone for line E-E’ of Figure 8. Stratigraphic
Legend (right) applies to both Figures 8 and 9. (Madden and Yeats 2008)
Figure 10: Idealized cross-section of Chino fault zone (DOGG 1992)
26
2.2.3 Sedimentary History Overview
Part of the greater Los Angeles Basin, the Mahala field is on par with the
geological history of the rest of the basin. Basin formation occurred during the Neogene
period (approximately 15 million years ago) with major subsidence and deposition
occurring between the Upper Miocene until the Lower Pleistocene epochs (approximately
between 11.5 to 2.5 million years ago) (Mayuga, 1970). The depositional environment is
known to be a marine to moderately deep marine environment with sediment being
deposited via the transport mechanisms of the sea and rivers which allowed for the
accumulation of large sediment deposits to be further transformed into hydrocarbons. The
United States Geological Survey (USGS) report by Durham and Yerkes 1964 estimates
the water depth of the Mahala field vicinity at the time of deposition to have been
approximately 2,000’, with turbidity currents as the main transport method (Dorsey,
Ridgely 1993).

2.2.4 Lithology and Stratigraphy
The strata in the area are first divided into series depending on their age, then the
series are divided into separate formations according to their sequence. Then the
formations are further divided into members according to their producing intervals, such
as production zones and lithology. Appendix II illustrates the full stratigraphic column
for the Mahala area and surrounding vicinity. Based on the known well penetrations the
strata in the field range from Late Cretaceous to Holocene, with the oldest (lowest)
Cretaceous section supposedly underlain by a basement of Mesozoic age consisting of
granodiorite and associated plutonic rocks of the Southern California batholith from a
27
depth of 5,000’ to 7,000’ (Olson, Larry 1977). Following the law of superposition we
expect that the layering order of the sedimentary rocks will follow the sequence on the
stratigraphic column (i.e. oldest on bottom and youngest on top). However, the
movement of the thrust fault has reversed the normal order by pushing up rocks of a
lower layer over rocks of a higher layer, so older strata southwest of the Chino fault, such
as the Yorba shale member, are thrust over younger strata to the northeast, for example
the Sycamore Canyon sand member. Therefore the overthrust hangingwall block above
the fault contains the lower permeability shale member, and the footwall block including
the Abacherli reservoir oil field contains the higher permeability oil-rich sand member
(Olson, Larry 1977).
The “Michelin Zone” of the ‘Sycamore Canyon’ member within the Upper
Miocene ‘Puente’ formation is the only stratigraphic layer analyzed in this study.
Therefore this is the only zone discussed herein. Additional information on the entire
stratigraphic column and other associated strata is available in the literature (e.g. Madden
and Yeats 2008). The Michelin Zone is predominantly a sandstone facies with some
interbedded thin layers of silty and shaly sands underlain by poorly consolidated basal
conglomerates (Dorsey, Ridgely 1993). Observations on the lithology include:
 Sand- tan to brown color with fine to coarse grain size
 Shale and Siltstone – white to buff to light gray and dark gray ultrafine grain size
 Conglomerates- Pebble to cobble size, hard, poorly consolidated by calcareous
matrix
28
 Key foraminifera identified – Rotalia garveyensis, Bolivina barbarana and
Bolivina Hughesi (biostratigraphy of Upper Miocene foraminiferal fauna of
California)
Figure 11 is a geologic contour map of adjacent reservoirs illustrating their areal extent in
the field. Additional structural contour maps are included in Appendix III, IV and V.

Figure 11: Structural and geological contour map of Mahala oil field (Olson 1977)
29
Figure 12 is an isopach map, the contours of which help detail the thickness of the
stratigraphic formation of interest. This map was subsequently digitized for use in this
study to establish the boundaries of the reservoir, to compile the point set shown in
Figure 22, and the areal outline shown in Figure 23, all utilized in this analysis.

Due to very limited core data, values for the production sand characteristics are
rough estimates. Dorsey’s 1993 study provides estimates of an average permeability of
500 md and an average porosity of 27% (Dorsey, Ridgely 1993). Although the values are
Figure 12: Isopach map of Abacherli reservoir (Dorsey 1993)
30
probably overestimated, the sand characteristics are expected to be well within the
characteristic sand range favorable for conventional crude oil production.

2.2.5 Remark on Previous Studies and Field Observations
Most of the information obtained from previous geological work for the Mahala
oil field is endorsed as true geological characteristics, conditions and representations of
the field including the Abacherli reservoir. The necessary geological assumptions are
made for the continuation of the analysis, however the only major exception is the
suggestion of cross-faults within the reservoir as shown in Figure 12. Dorsey’s (1993)
geological review suggests that there are at least six cross-faults that divide the reservoir
into separate fault blocks. However, in this study this interpretation is deemed rather
unsuitable based on direct field observations and the analysis conducted. The existence of
these cross-faults is questionable mainly because of the general continuity across the
whole reservoir apparent from the geostatistical analysis discussed in this thesis, as well
as the synchronous field observations of well pressures on either side of a given proposed
cross-fault. In the case of these well pressures, change in one well causes a pressure
change in another well across a proposed fault signifying that there must be connectivity
between the wells. Even if cross-faults are present and do affect the local geology, the
geostatistical analysis performed in this study assumes pre-fault conditions in which the
entire reservoir is modeled as a single unit in order to make an overall study viable. Most
geological interpretations are subject to case-specific interpretations. The objective of this
project is not to refute previous geological work but to model the strata as accurately as
possible in the analyses performed. More detailed information on previous geological
31
work conducted in the study area is available in the literature, for example in Olson,
Larry 1977, Dorsey, Ridgely 1993, and Madden and Yeats 2008.

32
CHAPTER THREE: DATA
3.1 Hard Data Sources
The primary data used in this report consists of well logs located at specific
coordinate locations displaying the electrical properties of rocks and their fluids in the
borehole. This data represents a geophysical exploration test that provides information on
the lithology and other geological characteristics at different points within the reservoir.
When combined with additional physical and chemical information of the subsurface a
useful description and better evaluation of the field can be made. Electrical properties are
given as resistivity values (‘R’) measured in ohms (Ω) and spontaneous potential values
(‘SP’) measured in millivolts (mv) for the active wells in the field.
The entire Mahala oil field has had several dozens of wells drilled since its initial
discovery. All of the thirteen wells drilled within the Abacherli reservoir are still in good
production today, and their log values are used as the hard data in this report. Several
other dry, unproductive wells were drilled in the immediate vicinity around the reservoir
that helped define the extent of the reservoir area and confirm the presence of no-flow
boundaries (OCR, LCC 2014). Because the reservoir consists of a single small to
medium-sized geological unit comprised of the same sand facies throughout, the wellbore
data within the known reservoir boundaries are expected to show coherent statistical
properties throughout the field. Thus in order to conduct the statistical analyses
performed in this study, stationarity within the boundaries of the Michelin sand layer of
the reservoir must be assumed in order for this study to be viable.
For any type of computational analysis it is imperative to know and understand
the integrity of the data. Schlumberger Limited performed the borehole logging of the
33
thirteen wells used in this study (OCR, LLC 2014). Log values are measurements
obtained from borehole equipment which consists of wireline instruments directed down
into the subsurface of the earth that record the measurements at depth via direct contact
of electrical sensors with rocks and their fluids (Schlumberger 2014). The wireline
services produced a continuous dataset (recorded as a log) for each of the drilled wells,
and this raw data was used as the hard data points utilized in this analysis. Snapshots of
sections of different well logs are shown in Figure 13 a through c. Vertical quantitative
data values were obtained for 10’ intervals to depths ranging down to 3,050’ from
surface.

a b c

Figure 13(a-c): Electrical well logs from the Mahala field (KMT Oil Co., Inc 2013)
34
3.1.1 Electrical Data Boring
Spontaneous Potential (‘SP’) measures the differences in static electrochemical
potential and ionic concentration in pore fluids of rocks that is caused by the charge
separations due to the diffusion of ions (Radhakrishna, I. and Gangadhara, T. 1990). Ions
in porous and permeable media diffuse differently than ions in impermeable media. The
difference in voltages between a reference electrode and the ground electrode is caused
by the electric current given off by the sensor at depth as a response to its electric charge.
The charge depends on the buildup of ions. This ionic concentration can be high, low,
positive or negative depending on the characteristics of the rock material including its
mineralogy, permeability and porosity. Greater ion exchange occurs in porous and
permeable rock media causing a higher response in the SP log (SPE PetroWiki 2013).
Similarly the concentration of ions in connate water depends on the mineral components
of the formation rocks Generally, large and negative deflections in SP indicate the
presence of permeable beds, thus SP values have been extensively used to help detect
permeable and porous formation beds, for instance to identify the location of reservoir
rocks (Schechter, David 2014). Figure 14 illustrates how the distribution of an electric
current changes between beds of different permeability due to the behavior of ions in
separate geologic media, and how it affects the SP electrical measurements in a well log.
35

Resistivity (‘R’) measures the electrical resistance of the fluid in the pores of the
rock. It is the inverse of electrical conductivity and quantifies how strongly a material
readily opposes (or resists) the movement of electric current (William, Lowrie 2007).
Rocks, sediments, and their fluids within a borehole will have different properties that
cause the resistivity in the materials to vary. By measuring the degree of resistivity down
a borehole it is possible to characterize the formation downhole. Although most rocks are
insulators, the fluids within their pores are conductors, however the big exceptions are
hydrocarbon fluids, which do not conduct electricity. When a formation contains oil, the
resulting resistivity will be high and recorded as a “spike” in the log, thus resistivity these
logs have been extensively and efficiently used to detect the presence of hydrocarbons.
Both the SP and R values combined provide a good tool to characterize geological
formations. Large positive R deflections and large negative SP deflections are clear
indicators of permeable hydrocarbon-containing formations (a.k.a “pay zones”). Figure
18 is an illustration of a pay zone that has been logged showing the spikes in R and the
Figure 14: Spontaneous Potential illustration (PetroWiki 2013)

36
opposite spikes in SP. Resistivity values range from 0 to 60 (6mV intervals) and
Spontaneous Potential values range from -50 to 50Ω (1ohm intervals).

3.2 Software

3.2.1 Modeling Software Interoperability
This study provided a good opportunity to showcase the interoperability between
different geographic and modeling software. The transfer of data via common exchange
formats allows for data to be inputted and outputted between separate computing
programs, including popular systems such as Stanford Geostatistical Modeling Software
(SGeMS), Esri ArcGIS, Microsoft Excel and Mathworks MATLAB. The two primary
software used for the geostatistical modeling done in this thesis research include SGeMS
Figure 15: Pay zone electrical log (KMT Oil Co., Inc 2013)

37
2.0 and ArcGIS 10.1. As the most popular Geographic Information System in the world,
ArcGIS has several integrated applications including ESRI ArcScene for 3D analysis and
modeling, ArcMap for 2D analysis and modeling, ArcCatalog for database management
and ArcGlobe for 2D and 3D mapping and visualizing larger datasets (Esri 2012). Since
SGeMS is specifically designed for geostatistical modeling it was used for the 3D
variogram-based modeling and conditional simulation performed in this study, then these
data output were transferred to ArcGIS. ArcGIS and its functional components were used
for organizing, georeferencing, digitizing, visualizing and managing most of the field
data. Besides electrical well logs other sources include remote sensing, GPS and
additional geological information.

3.3.1 Remote Sensing DEM
Remote sensing data obtained from the USGS national map viewer platform was
downloaded to provide a DEM of the oil field study area. Geographic coordinates of the
oil field were input into the USGS server and the elevation information was then
downloaded and georeferenced in ArcGIS (USGS 2014). The DEM grid set, consisting of
grid blocks of about 1-arc second resolution (or 30 meters), was imported into ArcScene
and converted to a 3-D elevation map of the field. An aerial map was then draped on top
of the DEM to provide a realistic visualization model of the topography for the area of
interest (Appendix VI). Figure 16 illustrates a close-up 3D DEM representation for the
area of interest draped over a full spectrum color ramp to better illustrate the variable
elevation.

38

3.2.2 3D Stratigraphic Cross-section
As previously discussed, significant deflections in the logs indicate zones of high
and low values; these changes in rock properties indicate the interfaces between different
geological facies. With this information it is possible to determine the thickness of
individual rock units and thus determine the local stratigraphic boundaries. Knowing the
facies and thicknesses of geological units at specific depths and coordinate locations
within the reservoir makes it possible to develop a cross-section for the area. ArcScene
allows for creating and mapping 3D models, thus it is a useful tool to create and maintain
the volumetric models used in this study.
The depths of the tops and bottoms of the rock strata were interpreted from the
logs at each respective borehole and were input into ArcScene. A continuous surface was
created connecting all of the 13 points on the top of each formation and a separate
continuous surface was created connecting all of the 13 points at the bottom of each
Figure 16: DEM of study area with legend (based on USGS 2014)
39
formation for all of the facies. Next a volume within each formation was generated
resulting in a 3D geologic cross-section illustrating the local lithological boundaries of
the strata in the field. For visualization purposes, Figure 17 illustrates the stratigraphy of
the reservoir as well as the log values for all of the wells. Appendix VI provides
illustrations of the cross-section at different angles as well as processed models
transferred from SGeMS and MATLAB and integrated into ArcScene.

Figure 17: 3D cross-section
40
3.3.3 Data Point Set
Figure 18 is an image of the point set grid used in the interpolation. After
georeferencing the isopach map (Figure 12) and digitizing the dimensions of the
reservoir, ArcGIS tools were used to create an ultra-high resolution point data set with
the specified volumetric dimensions of the field. The blank point set served as the
interpolation medium where each of the individual points were populated after running
the ordinary kriging and conditional simulations. One of the drawbacks of performing
simulations on an ultra-high resolution point set is the time required to run all of the
simulations. Due to the large size of the data point set (> 1.5 million points) running all of
the simulations was computationally demanding, taking a total time of over one month
for completely performing all 101 realizations to run on a Dell XPS-8300 desktop with a
Windows 7 professional 64-bits operating system.

Figure 18: Blank 3D point set
41
3.3.4 GPS Data Acquisition
Figure 19 is an aerial map view of the field with the boundaries of the reservoir
obtained by digitizing the isopach geology map (Figure 12). Additional information in
Figure 19 includes GPS-derived positions of production lines, water lines, tanks, wells
and valves. GPS data points, lines and polygons were obtained via direct measurement
using an ultra-high precision Geo-XH GPS unit and subsequent data corrections were
done using GPS pathfinder software and then imported into ArcGIS. The GPS unit and
software were obtained from the University of Southern California’s Spatial Sciences
Institute. The Trimble GPS Geo-XH unit is an ultra-high precision data collection device,
with precision to a few millimeters (GSI Works 2009).

Figure 19: Mapview of study area lease (based on GPS 2013)
42
CHAPTER FOUR: METHODS
4.1 Data Exploration and Evaluation

4.1.1 Data Input and Transformation
Exploration of the data of the datasets allows an assessment of their suitability for
the proposed analyses. An important preliminary step in the evaluation of the data is to
examine the spatial distribution of the datasets. Because the kriging and conditional
simulation techniques used in this study are methods for interpolating values that are
modeled by a Gaussian process, it is necessary for the sample data to have a normal
distribution. Simple univariate and bivariate statistical tests were performed to determine
if data need transformation to become Gaussian. The well locations and log values for the
thirteen active wells in the stratigraphic formation of interest in the Michelin Zone were
entered into SGeMS software. A Probability Density Function (PDF), Cumulative
Distribution Function (CDF) and QQ-plot of the two variables as well as a scatter plot
analysis illustrating the correlation coefficient between both variables were obtained.
Resulting Figures from the preliminary statistical analyses are illustrated from Figure 22
to Figure 26.

Figure 20 and 21 illustrate the spatial distribution of the wellbores, surrounded by a
bounding box representing the overall volume of the field, including color-coded R and
SP values and legend.

43

Figure 22 shows the PDF and CDF outputs of the raw SP dataset. The dataset follows an
acceptable normal distribution and therefore it can be assumed that it does not need to
undergo further transformation to be used in this analysis.
Figure 20: Resistivity Data logs
Figure 21: Spontaneous Potential Data logs
44

Figure 23 shows the PDF and CDF of the raw R dataset. Since the data exhibit a
significant positive skew to the right and thus is not normally distributed, it is therefore
preferable to transform this dataset to normality.

Figure 22: Spontaneous Potential CDF and PDF
Figure 23: Raw Resistivity PDF and CDF
45
The R dataset was transformed to resemble a normal distribution by using the
histogram transformation tool in the SGeMS utilities box. Figure 24 shows the PDF and
CDF of the normally transformed R dataset.

Figure 25 is a Q-Q plot of both SP and R probabilities plotting their quantiles
against each other. This graph compares the shapes of the two probability distributions
and also allows one to better determine if the data is close to a normal distribution. For
the compared probability distributions to be normal, the plotted points should lie within a
straight line. The closer all points are to a straight line the closer the samples are to a
normal distribution. This graph illustrates that there is a significant offset, indicating a
clear deviation from normality.
Figure 24: Transformed Resistivity PDF and CDF
46

Figure 26 is the Q-Q plot of the SP dataset with the normally transformed R
dataset. In this Figure the linear relationship between the two variables (points plotted
across a straighter line) indicates a more normal distribution.

Figure 25: Raw Q-Q plot between R and SP
Figure 26: Transformed Q-Q plot of SP and R
47
Figure 27 is a scatterplot of SP and R including the linear regression line
illustrating the correlation between both variables and their coefficient.

The correlation coefficient for SP and R is -0.665. The strong negative correlation
(as SP goes up R goes down and vice versa) follows the field expectation as described in
the data section. Although this correlation is not needed for ordinary kriging it provides
more useful information and allows a better evaluation for potential cokriging as a future
study.

4.2 Variogram
Several attempts experimenting with different parameters, conditions and components
were tried in the variogram modeling for this study. Correct variogram modeling requires
Figure 27: Scatterplot between R and SP
48
practice and a fair amount of guesswork. The defined variogram model is at best an
approximation of a best-fit function describing the spatial relationship of the variables in
the field.

4.2.1 Variogram Parameters
A useful initial technique to help estimate the variogram is to restrict the
maximum distance at which the variogram is computed to ensure sufficient pairs for a
given distance while still allowing for a reliable estimate of the variogram for that given
distance. A very common approach to select that restricted distance is to use around half
of the maximum possible distance within the region of assumed stationarity and use it as
the lag distance (Kelkar and Perez 2002). Because a variogram is symmetric this
approach also ensures that all pairs on either side of a given location are included in the
model, and adding 180° to a given direction provides the same variogram estimate. In
addition, another common rule of thumb is to use approximately half the distance of the
lag separation as the lag tolerance (Babish, G. 2000). It is important to note that these lag
assumptions are not necessarily relevant for every case. The conditions (geologic
structure, well geometry, depositional setting) of different oil field reservoirs can require
significantly different lag parameters. However, as noted in the geology section and
illustrated in Figure 19, the wells in this field are oriented or located in nearly a straight
line and their spacing is consistently distributed at closely uniform intervals. In addition,
the area of the field is not too large geographically so the entire reservoir system is
analyzed as a whole. These factors simplify the decision-making process for defining the
distance and direction of the variogram model.
49
Once the data is inputted into the modeling software and determined to be
appropriate for the kriging analysis, an experimental variogram model can be defined.
Figures 23 and 24 show the initial data input of the wells. The first step is to choose the
parameters that will estimate the variogram, the lag components that define the distance
and the directional components that define the direction/orientation. In SGeMS the three
lag distance components are: 1) number of lags, 2) lag separation and 3) lag tolerance and
the four lag direction components are: 1) azimuth, 2) dip, 3) tolerance and 4) bandwidth.
Figure 28 displays the lag distance and direction parameters used.

Lag distance is the product of the number of lags and the lag separation, i.e.
( ). The maximum distance between any
Figure 28: Variogram direction and distance parameters
50
two pairs of points in this field, for instance the distance between the two wells that are
farthest apart, is 4,300’. Therefore the maximum lag distance the model was initially
targeted to have is around 2,150’. After several attempts with the given directions, a lag
number of 39 and a lag separation of 55 provided promising preliminary variogram plots.
A lag tolerance half the value of the lag separation was targeted, so the value selected is
27 ( ) rounded down to the nearest whole.
The variogram for a 3D model is commonly expected to include as a minimum,
three directions: 1) a vertical directional component to account for variability with respect
to depth in any given borehole, 2) an omni-directional component to account for global
variability throughout the field, to see the overall picture, and 3) at least one horizontal
directional component covering the major directions in the field.
Four components in the SGeMS software define the directionality of the
variogram, including: 1) the azimuth, which corresponds to the direction on a planar
surface measured in degrees from 0°-360°, 2) the dip, which corresponds to the angle of
descent relative to the azimuth measured in degrees from 0°-90°, 3) the tolerance which
corresponds to the angle of tolerance of the directional variogram measured in degrees
from 0°-90°, and 4) the bandwidth, which corresponds to the maximum width of the area
resulting from the directional variogram (Remy, Boucher and Wu 2009). The azimuth
and dip, analogous to geologic strike and dip, are two important components reflecting
the major axes in a 3D environment, and the tolerance and bandwidth help further refine
the directions of interest to accommodate the intended directionality of the field. By
manipulating the variogram azimuth, dip, tolerance and bandwidth it is possible to
capture the structural geology of the field (strike, dip, rake, plunge) and hence end up
51
with a true volumetric (3D) estimation resembling the geology. Once a general direction,
(azimuth and dip) is established then the tolerance and bandwidth choices, which are
more flexible because they are based on subjective decisions, should be adjusted until an
interpretable variogram structure is identified.

4.2.2 Experimental Variogram
Three variogram directions were established: a vertical direction, an omni-
directional and a horizontal direction following the geological geometry (strike) of the oil
field reservoir. The components for all directions are shown in Figure 28. The tolerance
and bandwidth were manipulated until a clear variogram structure was obtained. Figures
29 and 30 illustrate the experimental variogram in all three directions for both datasets
after a decipherable structural trend was identified.

Figure 29: SP experimental variogram in all three directions

52

In Figures 29 and 30 if Cartesian coordinate plane orientation is assumed and the figure is
divided into four separate figures, or quadrants, Quadrant I in the upper right represents
the omni-direction, Quadrant II in the upper left represents the vertical direction,
Quadrant III in the lower left represents the horizontal direction, and Quadrant IV in the
lower right represents a plot of all the directions combined. Quadrant IV is useful to
visualize the complete extent of the entire variogram.

The first direction established is the vertical direction with an azimuth of zero, a dip of
90°, a tolerance of 5° and bandwidth of 200 (Figure 28). The interpreted variogram
Figure 30: R experimental variogram in all three directions
53
structure for each dataset in this direction as well as the fitted function is shown in
Figures 31 and 32.

The second direction established is the omni-direction with an azimuth of 0°, a dip of 0°,
a tolerance of 91° and a bandwidth of 200 (see Figure 28). The interpreted variogram
structure for each dataset in this direction as well as the fitted function is shown in
Figures 33 and 34.

Figure 31: SP Fitted vertical variogram model
Figure 33: Fitted SP Omni-directional variogram
model
Figure 32: R Fitted vertical variogram model
Figure 34: Fitted R Omni-directional
variogram model
54
The third direction established is the horizontal direction aligned along the major trend of
the wells with an azimuth of 120°, a dip of 10°, a tolerance of 40° and a bandwidth of 500
(see Figure 28). The interpreted variogram structure for each dataset in this direction as
well as the fitted function is shown in Figures 35 and 36.

4.2.3 Variogram Models
Once the distances and directions are established (see Figure 28) to get
interpretable structures (Figures 29 and 30), then the variogram can be modeled to
represent the statistical function. Two requirements that must be honored in modeling the
variogram are: 1) the condition of positive definiteness, and 2) the use of a minimum
number of parameters and models to model the variogram (Kelkar and Perez 2002).
Because the model types available in the computing software (exponential, spherical,
Gaussian) are already known to satisfy the condition of positive definiteness, by using
any of these, or linear combinations of them, it is automatically assumed that the model is
positive definite, thus satisfying condition one. As previously discussed, the variogram
estimation parameters direction and distance capture the most important reservoir
Figure 35: SP fitted horizontal variogram model
Figure 36: R fitted horizontal variogram model
55
structures including geologic strike and dip, and orientation or trend of wells. It is
assumed that the essential spatial features of the oil field reservoir are thus included in the
model, which satisfies condition two. The model types available in the software are
assumed to have a sill contribution, which is a constant value after a certain lag distance
called the range, as shown in Figure 37. The components in the modeling software user
interface used to characterize the variogram model are described in the following table.

SGeMS Variogram Model Components
Interface
Input
Description
Nugget
Effect
The initial abrupt jump to the first value at the beginning of the entire
variogram model. Non-continuity only at the origin is due to either
measurement error or variation at a scale smaller than the sampling
distance.
Number of
Structures
Number of (nested) variogram structures composing the variogram
model. An accurate fit to a variogram model may be best constructed
using a combination of multiple model functions (a.k.a. nested
structures), especially to model variability at different scales.
Sill
Contribution
Effect of the sill, or the maximum variance of the variogram. Sill is the
limit (represented graphically as where the function flattens out) of the
variogram model after a specific distance a.k.a the range.
Type The type of variogram model. SGeMS includes only models for
variograms that have a sill: Spherical, Exponential and Gaussian. The
model type depends on the function used to approximate the variogram
(determines the overall shape of the model).
Ranges
(Max,Med,
Min)
Ranges along each of the three directions of the anisotropy ellipsoid in
the variogram structure (maximum, medium and minimum) used to
approximate the model. Depending on the direction(s) specified these
ranges help refine the shape/extent of the function.
Angles Measurement in degrees for each of the three angles (directions) of the
3D anisotropy ellipsoid in the variogram structure: azimuth, dip and
rake. Rotation of the angles along the orthogonal planes of a Cartesian
coordinate system positions the 3D ellipsoid in space

Table 1: Interface input description of variogram model components
56
Once a nugget constant and the number of structures in the whole variogram
model are selected, then each individual nested structure is further defined by the
subsequent parameters listed in the table: the variance contribution (sill), the variogram
function (type), and anisotropy characterized by a 3D ellipsoid defined by the ranges and
angles (Remy, N., Boucher, A. and Wu, J. 2009). This 3D ellipsoid is defined by the six
parameters of the ranges and angles where the three angles, azimuth, dip, and rake,
represent the direction of the major, medium and minor axes, and the ranges represent the
radii of the axes along the three directions. More detailed information on variogram
modeling inputs and conditions is available in the following references: Chiles and
Delfiner 1999, and Remy, Boucher. and Wu 2009. Figure 37 illustrates the main
components of a typical variogram model, including lag distance, variance, sill, nugget
and range.

Several experiments with the variogram design in terms of the modeling
components and variogram parameters were undertaken for both the SP and R datasets.
After different options were tested, the following variogram model inputs displayed in
Figure 37: Illustration of main variogram model components (based on Landscape
Toolbox Wiki 2014)
57
Figures 38 and 39 for SP and R illustrate the final variogram models used for both the
interpolation functions. These variogram models were used for the subsequent ordinary
kriging and conditional simulation procedures.

Figure 38: Complete variogram model for Spontaneous Potential
58

4.3 Interpolation

4.3.1 Kriging Parameters

Once the variogram models are defined and saved they can be loaded into
the kriging toolbox in the SGeMS program followed by simple selections of the grid, data
and the type of estimation (e.g. ordinary kriging) necessary to run the analyses. Because
the kriging algorithm used in the modeling software requires a 3D ellipsoid to be
specified in order to represent a search volume in 3D, the only remaining task was to
define the search ellipsoid (Remy, Boucher and Wu 2009). The search ellipsoid was
represented by a search space surrounding the interpolation point, and only the points that
fell within this search space were considered to take part in the kriging calculations, for
Figure 39: Complete variogram model for resistivity
59
instance in defining the extent and volume to look for values to be used in the
interpolation. The search ellipsoid, which is characterized in the same way as the
variogram anisotropy ellipsoid, consists of minimum and maximum conditioning data
(min/max number of data points to be included in the algorithm), max/med/min ranges
and the 3-directional angles. After several experimental kriging runs were conducted, the
parameters used to define the search ellipsoid for the analyses determined to be the best
were selected, provided in Table 2. . These results are described in detail in Chapter 5.
Search Ellipsoid Parameters
Conditioning Data Min Max
2 20
Ranges Max Med Min
3000 1650 200
Angles Azimuth Dip Rake
128 2 3

4.4 Validation

As part of the kriging interpolation procedure the kriging variance was also
calculated and the resulting models mapped the variance in the oil field reservoir. This
procedure can help define the areas with higher or weaker variance in the estimation.

4.4.1 Cross-validation

To know how well the models predict the values at unknown locations in the
field, in other words to test the integrity of the methods and determine their effectiveness,
it was necessary to perform validation procedures on the predicted models. An
appropriate technique is cross-validation which consists of leaving one data location out
Table 2: Search ellipsoid parameters used for kriging
60
(i.e. one well) and performing the estimation to predict the values at that excluded
location, repeating the process by removing one different well location at a time and re-
running the estimation until all the well values have been interpolated. Once the predicted
values were obtained for the data at all the measured locations, they were compared to the
known values to help determine the quality or accuracy of the model. The observed
values, which consisted of actual values from the logs, were plotted against the estimated
values predicted values from the model, then compared and contrasted to evaluate their
differences. In this manner, cross-validation at each well for both datasets was performed.

4.4.2 Statistical Comparisons
By generating several realizations using the sequential Gaussian simulation
algorithm based on the same kriging parameters, uncertainty can be characterized by the
multiple possibilities that exhibit local variation. The uncertainty at individual locations
throughout the field can be ascertained by examining the differences among several
equiprobable plots which will display the local variations and distributions in the oil field
reservoir. In this sense, if uncertainty at a particular location is relatively small then a
number of images will display similar simulated values at that location, and conversely if
uncertainty at a particular location is relatively large then a majority of images will
display the differences in simulated values at that location (Kelkar and Perez 2002).

As previously stated, the primary objective of performing a stochastic simulation
is to create a model for the probability distribution of the unknown variables. Because the
variables are conditioned to the information provided from the field data which is
61
assumed to be a true representation of the subsurface geology, then their values are
reasonably expected to fall within the limits of the simulated probability distribution.
Summary statistics on the simulation output provide a measure of the uncertainty of the
model, and specific statistical calculations on the suite of realizations provide estimated
probabilities.

Calculating the median or mean of the provided multivariate distribution where
the median (mean) at each cell is computed from the values of all realizations at that cell
location will yield a map with the highest probability of representing the true model. This
probability model can be compared to the predicted (kriged) model to provide a better
assessment of the analysis. The similarity between the predicted and the probability
models provides a degree of confidence in the estimated model. In addition to the median
probability (i.e. P50) the P10 and P90 quantiles provide uncertainty ranges or error bars
in the simulated median value, providing more confidence that the true expected mean
falls within the simulated range. A total of 48 realizations for R were obtained and a total
of 53 realizations for SP were obtained. These results are described in detail in Chapter 6.

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CHAPTER FIVE: RESULTS
5.1 Conditional Simulation
5.1.1 Sequential Gaussian Simulation Models
In terms of final results of this thesis research, Figure 40 a-f comprises six random
realizations of SP distribution across the oil field reservoir, visualized using SGS.

Figure 40a – SP Realization 1 Figure 40b – SP Realization 2

Figure 40c – SP Realization 3 Figure 40d – SP Realization 4

Figure 40e – SP Realization 5 Figure 40f – SP Realization 6

Figure 40 (a-f): Six random SP SGS realizations

63
Figure 41 (a-f) includes 6 realizations of R distribution across the oil field reservoir.
` Figure 41a – R Realization 1 Figure 41b – R Realization 2

Figure 41c – R Realization 3 Figure 41d – R Realization 4

Figure 41e – R Realization 5 Figure 41f – R Realization 6

The calculated median (P50) as well as the P10 and P90 probability simulation models
from all the realizations are also included. Figures 42-44 illustrate the P50 map as well as
the P10 and P90 maps for R with designated color bars. Figures 45-47 illustrate the P50
map as well as the P10 and P90 maps for SP with designated color bars.
Figure 41 (a-f): Six random R SGS realizations

64

Figure 42: Resistivity P50 map
Figure 43: P10 Resistivity map
Figure 44: P90 Resistivity map
65

Figure 45: Spontaneous Potential P50 map
Figure 46: P10 Spontaneous Potential map
Figure 47: P90 Spontaneous Potential map
66
5.2 Ordinary Kriging
5.2.1 Predicted Models
The kriged model and its associated variance map for R are included as Figures 48 and
49. Figures 50 and 51 illustrate the predicted map and its associated variance map for SP.

Figure 48: Resistivity ordinary kriging interpolated map
Figure 49: Resistivity variance map from ordinary kriging model
67

5.3 Volume Explorer

The “volume explorer” tool in the SGeMS modeling software allows exploring of
the 3D distribution of properties across the estimated volume of the field. Figures 52 and
53 display a snapshot of the “inside” of the SP and R models. This is an important tool
because static images mostly show the outside of a model and may not provide an
Figure 50: Spontaneous Potential ordinary kriging interpolated map
Figure 51: Spontaneous Potential variance map from ordinary kriging model
68
adequate representation of the entire 3D volume distribution. The scale of Figure 52 is
identical to that of Figure 50 and the scale of Figure 53 is identical to that of Figure 48.

Figure 52: Spontaneous Potential 3D volume map
Figure 53: Resistivity 3D volume map
69
CHAPTER SIX: DISCUSSION AND CONCLUSION

6.1 Variogram and Simulation Model Remarks

The experimental variogram in the vertical direction (top left corner, or Quadrant
I, of Figures 29 and 30) for both datasets exhibit periodic behavior, which represents
cyclical geological processes. This is known as the “hole effect” in geostatistics and is
typically experienced when modeling a variogram in the vertical direction. In
depositional environments sediment is deposited in layers during geological events, thus
this repetition of cycles will be reflected in the vertical continuity of the layers in the
field. In these variograms the transition from one facies to another can be clearly defined.
Interpretation from both of the vertical-directional variograms indicates that the
formation is continuous in the vertical direction up to around 350’ and then becomes
discontinuous but regains continuity at greater distances. This trend is expected to
continue throughout different depths across the field. The fitted vertical variogram
functions (Figures 31 and 32) only include those values to 350’ and ignore the rest
because it is of most interest to only capture the extent of that continuity. In addition, the
average thickness of the formation is only 378’, so by modeling to 350’ we are capturing
all the continuity necessary for building a valid 3D model for this formation. The other
two variogram directions show the overall and the horizontal continuity trends in the
field, both of which exhibit very similar patterns. The fitted functions (Figures 33 through
36) were plotted in order to include most of the points. A few points which were
considered as possible local outliers were neglected in order to obtain a reasonable
structural function for the variogram model, discussed further in the project evaluation.
Overall, the trend of the study area is well captured in both of the variogram models.
70
Since all of the realizations of the conditional simulations honor the same constraints
because they are coming from the same data distribution, it is not possible that one
realization image is more likely to occur than any other. Therefore the apparent
differences between realized images is representative of the local uncertainty, and
visualizing the variability between simulations provides a reasonable assessment of
uncertainty. Provided the distribution is representative of the real oil field reservoir then
the true reservoir values are expected to fall within the bounds of the distribution while
the calculated statistical summaries of the simulations (P10, P50, P90) illustrate the
probabilities of occurrence.

6.1.1 Well ID Locations
Figure 54 is a 2D map displaying the well locations of each borehole in the
reservoir area, labeled by unique well identification number. The well ID numbers were
assigned based on the order that the wells were drilled. The spatial configuration of wells
is important to note for the discussion and interpretation of results.

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6.2 Validation
Figures 55 and 56 (a-m) display the cross-validation results of all wells for both
datasets. The well number is the well ID number (Figure 54). The results include the
observed data (log values) plotted along with the estimated data (kriged values) versus
subsea depth. All the plots include low, medium and high value thresholds as well as
horizontal error bars of the standard deviation of the observed data for each borehole.

Figure 54: Well ID location map
72
6.2.1 Cross-validation plots
Figure 55 (a-m) provides R cross-validation graphs which represent the differences
between the observed values and the estimated values.

` Figure 55a – R Cross-Validation Well #1 Figure 55b – R Cross-Validation Well #2

Figure 55c – R Cross-Validation Well #3 Figure 55d – R Cross-Validation Well #4

Figure 55e – R Cross-Validation Well #5 Figure 55f – R Cross-Validation Well #6

Figure 55 (a-f, continued on page 73): Resistivity cross-validation results for all wells

73

Figure 55g – R Cross-Validation Well #7 Figure 55h – R Cross-Validation Well #8

Figure 55i – R Cross-Validation Well #9 Figure 55j – R Cross-Validation Well #10

Figure 55k – R Cross-Validation Well #11 Figure 55l – R Cross-Validation Well #13

Figure 55 (g-l, continued from page 72): Resistivity cross-validation results for all wells

74

Figure 55m – R Cross-Validation Well #14

Figure 56 (a-m) displays SP cross-validation graphs, which depict the differences
between observed values and estimated values.

Figure 56a – SP Cross-Validation Well #1 Figure 56b – SP Cross-Validation Well #2

Figure 55 (m, continued from page 73): Resistivity cross-validation results for all wells

Figure 56 (a-b, continued on page 75): Spontaneous Potential cross-validation results for all wells

75

Figure 56c – SP Cross-Validation Well #3 Figure 56d – SP Cross-Validation Well #4

Figure 56e – SP Cross-Validation Well #5 Figure 56f – SP Cross-Validation Well #6

Figure 56g – SP Cross-Validation Well #7 Figure 56h – SP Cross-Validation Well #8

Figure 56 (c-h, continued from page 74): Spontaneous Potential cross-validation results for all wells

76

Figure 56i – SP Cross-Validation Well #9 Figure 56j – SP Cross-Validation Well #10

Figure 56k – SP Cross-Validation Well #11 Figure 56l – SP Cross-Validation Well #13

Figure 56m – SP Cross-Validation Well #14

Figure 56 (i-m, continued from page 75): Spontaneous Potential cross-validation results for all wells

77
6.3 Project Evaluation
Both of the kriged models illustrate static representations, in 3D, of the
distribution of SP and R throughout the field. The intent of kriging interpolation is to
estimate, or provide the best possible approximation of the overall continuity in this study
area. The conditional simulations provide complementary information to help determine
the local variation and quantify uncertainty in a probabilistic sense while providing a
degree of confidence in the models. The cross-validation provides a direct measurement
of the estimation accuracy.

6.3.1 Comparison of Results
Both the spontaneous potential (SP) and resistivity (R) kriged models appear to
follow an expected continuity trend based on the local geology of the field, and both of
their corresponding variance maps help indicate the local variance in their predictions.
Both of the simulations and their calculated statistical outputs provide useful
representations of the field variabilities and their probabilistic ranges. Comparing the R
kriged model with the calculated R P50 simulation mean value model (Figure 48 and
Figure 42), it appears that the overall trend remains generally consistent between both
models with the exception of a few small areas in the upper half of the field. Comparing
the SP kriged model with the calculated SP P50 simulation mean value model (Figure 50
and Figure 45) it appears that most of the continuity is also well preserved, especially in
the lower half of the field. However, small to moderate dissimilarity appears within the
upper half of the oil field reservoir. The dissimilarities that are most apparent occur
mainly near opposite edges, which is probably due to lack of data from boreholes drilled
78
near the edges of the study are (i.e. no conditioning data points). In addition, the distances
from the observed locations (i.e. logged wells) are larger, therefore we can expect greater
uncertainty in those locations. Aside from the expected larger variances near the corners
of the study area due to the edge wells being farther away from real/observed values, and
some of the localized variances that can be seen from the variance maps (Figures 49 and
51), the P10 and P90 maps appear to show a modest margin of probability in the
distribution in which the P50 median (or average) falls between the lower and upper
quantiles (P10 and P90). The noticeable differences apparent in both datasets in the upper
half of the oil field reservoir are probably related to the larger variability experienced in
the upper half of the field.
From the cross-validation it is possible to gauge the accuracy of the estimation given the
assumptions made in the modeling process, since the standard deviation error bars help
provide a “tolerance range”. Although the SP and R values obtained for the same well
locations and at the same depths do show a strong (negative) correlation, the spatial
relationships within each set differ significantly. The interpolation and validation
procedures conducted in this study help quantify these relationships. Observance of the
raw data indicates correlation trends will likely differ between both datasets due to
different modest deviations within each set of wellbores. Also, the cross-validation
results point out the individual wells that deviate the most.

The R well#1 is the well with the largest error in the R dataset, followed by the
southernmost R well#4. Although these wells plot in a consistent manner close to the
observed values, most of the calculated values fall outside the bounds of the standard
79
deviation (Figures 55 and 56). The estimated values for the rest of the wells in this
dataset appear to plot reasonably close to the observed values. However, close
examination of the results reveals that the estimations for all of the wells between R
well#1 and R well #4 (i.e. wells #11, 3, 13, 9, 8 and 14 in the lower half of the field)
appear to plot slightly better in terms of accuracy than all of the wells north of well #1
(i.e. wells #10, 2, 5 and 5 in the upper half of the field).

In contrast to the R data plots, the SP well#7 estimated values deviate the most from the
observed data, also plotting outside the bounds of the standard deviation. Most of the
other wells within this dataset plot reasonably close to the observed values, however there
are some significant differences noted, including well #4 (located at the southern edge)
and well #6 (located at the northern edge) which both show significant deviation. The
same overall field observation noted from the R results appears to also be evident in the
SP results, where all the wells in the lower half (south of the dataset outlier) provide
slightly closer approximations relative to all the wells in the upper half (north of the
dataset outlier). The “dataset outlier” for the SP values is well #7, and for the R values it
is well #1. Also included in this observation is the significant deviation of these two wells
at the boundaries, where one is located at the northern edge and one at the southern edge
of the field.

6.3.2 Interpretation
In summary, the cross-validation results as well as the compared interpolation
results indicate that the wells with slightly larger errors include the two wells at the
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north/south edges of the field (well #4 and well #6) as well as the outlier for each dataset
(well #7 for SP and well #1 for R). Also, all of the wells north of the outlier for each
dataset (in upper half of field) show slightly higher errors than all of the wells south of
the outlier (in lower half of field).

The apparent estimation discrepancies are probably related to the fact that well #4 is the
southernmost well located in an almost isolated southeastern corner of the reservoir, and
well #6 is the northernmost well and is also the thinnest borehole (100’ of formation with
only 10 log values). The relatively larger accuracy error of these two wells located at the
study area boundaries can be attributed to their locations compared to the configuration
of other wells in the field and their less than optimal proximity to the other boreholes.
The clustered borehole locations have more conditioning data and so are expected to
provide slightly more accurate estimates. Given a general consistency between the kriged
and simulated models in addition to the same general trend expressed from the cross-
validation of both electrical datasets, the assumption can be made that the spatial
continuity in the lower half of the field is very strong (from well #4 up to somewhere
between well #7 and well#1), and in the upper half (from well #1 to well#6) it is strong
but slightly less continuous. Nevertheless, this assumption does not include the notion
that the reservoir is divided into separate segments or compartments. Based on the
observations discussed herein the integrity of the overall trend throughout the entire field
is continuous enough to consider and treat the reservoir as a whole. Based on the results
of this study, and although there a few slightly statistically deviated wells (or minor
81
localized zones), it is suggested that the reservoir is intact with a generally strong
continuity trend mimicking the geologic attitude of the field.

It is very important to provide final clarifications on the uncertainties associated with the
necessary assumptions that are expressed in the results and how it relates to the
confidence that can be attributed to the models. As mentioned in Chapters 1 and 3 the
assumption of stationarity for the entire reservoir must be made as a necessary subjective
decision. Stationarity is assumed in order to build a single geological model for the entire
study area. Also, as mentioned in Chapters 2 and 4 the wellbores are aligned along the
plane parallel to the geological strike of the field. Because all of the wells are
preferentially directed along this plane there is inherently more certainty in the data
obtained in this direction (northwest-southeast) compared to the perpendicular direction
(southwest-northeast). Due to a lack of data in the southwest-northeast direction relative
to northwest-southeast, it is apparent that there is significant directional uncertainty (i.e.
more uncertainty) in the model results along the lateral southwest-northeast direction.
Because the assumed continuities throughout the reservoir volume are constrained to and
are a direct result of the chosen variogram model parameters, the variability in the
parameters for the variogram models define the global continuity in the field. As can be
seen from the similarities between the variogram in the northwest-southeast trend and
omni-directions the continuity in the study area is preferential in the plane parallel to the
well alignment, and the uncertainty in the estimation in this direction is less significant.
Similarly, because a coherent continuity trend is captured in the vertical direction for
most of the thickness of the formation layer, the uncertainty in the estimation in this
82
direction is also less significant. According to the data in this analysis the confidence
levels (i.e. from maximum continuity to minimum continuity) follow this order, from
greatest to least: first the vertical direction, second the well alignment direction, and third
the direction perpendicular to the orientation of the wells.

Despite the many benefits of conventional estimation techniques (as discussed in Chapter
1) one of the common weaknesses of kriging, which relies on a variogram model, is that
it is completely dependent upon the input data, and because of data limitations it is
necessary to make large assumptions for an entire field which typically yield results with
directional uncertainty in continuities across the study area. As future work, to reduce the
uncertainty in this study area along the lateral plane perpendicular to the well orientation
(i.e. southwest-northeast direction), additional variogram models should be computed
using available data from wellbores drilled outside of the southwestern and northeastern
boundaries of the reservoir in order to determine any correlations with the continuities
defined in this project.

To summarize, based on all of the assumptions discussed with regards to this specific oil
reservoir, including the model parameters and directional uncertainties of the field, there
are various levels of confidence. Because of the previously mentioned similarities
between the simulated and predicted maps as well as the cross-validation results we can
assume more confidence in the variogram and continuity results for both the trends in the
vertical direction and in the direction of the wellbore alignment in the field. We can
assume less confidence in the variogram and continuity results for the trend in the
83
direction perpendicular to the wellbore alignment because of larger uncertainties in this
direction and thus weaker predictions. In addition, because of the local active geology
consisting of continuous thrust faulting that extends the reservoir along its northwest-
southeast plane and thins the geologic units of interest along its southwest-northeast
plane, it can be expected that the trend along the plane perpendicular to the geologic
strike of the study area will not be as continuous. Thus the geological representations of
the field obtained from the interpolation analyses presented as the final results of this
thesis appear to provide acceptable reservoir models that can be used at individual
discretion for subsequent engineering analyses and field operations, as long as all of the
relevant uncertainties of the field are taken into consideration.

6.3.3 Final remarks
Geostatistics is applied to several disciplines including environmental science,
oceanography, geology, meteorology and epidemiology for specific operations such as
petroleum production, water production, mining, weather prediction and even disease
spreading. Ongoing research within this field is vast and it is likely to remain a very
important modeling approach in the sciences and engineering. Although the data utilized
in this study include the electrical properties of rocks and their fluids, the same (or
similar) methodology can be applied to different datasets including hard data and soft
data values obtained from other sources such as seismic, geochemical sampling, core
sampling or remote sensing. For example, in applications to geochemistry and hydrology,
geostatistical modeling using chemical and geochemical data can help quantify the flow
and transport of subsurface constituents in aqueous systems (e.g. pollutants, solutes,
84
particles) and thus provide a better assessment of water resources including groundwater
quantity and quality (e.g. remediation of contaminant plumes and aquifer productivity).

The discipline of geostatistics is a core component of reservoir characterization and is a
necessary step to obtain an adequate geological model of the reservoir that can be
integrated into a fluid-flow numerical simulator to predict hydrocarbon production, then
further formulated into an inverse model and adjusted to match field responses. The
whole reservoir characterization-simulation-engineering process is a dynamic and
continuous process that allows scientists, engineers and operators to understand, predict
and to some extent control the reservoir in order to achieve optimal field performance.

6.4 Conclusion
The use of geostatistics provides an effective way to integrate earth science and
spatial science with engineering. This research project has demonstrated the necessary
steps to develop a geological model that characterizes the distribution of subsurface
properties using a two-point geostatistics approach. Additionally this study has directly
exemplified how GIS tools can be combined with engineering techniques based on
geological concepts and use genuine field data to solve complex real-world problems
with the aid of software interoperability. The oil field represents a conventional
petroleum reservoir and preliminary evaluation of the hard data obtained from direct
subsurface field measurements presents ordinary kriging and sequential Gaussian
simulation as valid methods for the aforementioned analysis and modeling. A satisfactory
variogram was defined incorporating geological and statistical assumptions, and used for
85
the kriging and conditional simulation interpolations to map the field properties in a
volumetric extent. The procedures taken to construct the variogram as well as the major
aspects and the different components of these techniques including the variogram
parameters, kriging parameters and interpolation conditions are discussed throughout the
report. Results include 3D static models and multiple possible realizations of the spatial
distribution of electrical properties of rocks and their fluids throughout the field domain.
And because of the direct relationship of SP and R with additional reservoir properties
and their associated characteristics (such as permeability, porosity, water saturation) the
geostatistical outputs provide useful information that can be used for further field
modeling including numerical and inverse modeling. With the information provided and
especially with the addition of subsequent engineering analyses such as reservoir
simulation and history matching, it is possible to make more informed decisions for field
operations aimed at improving petroleum development and management, including
activities such as drilling and waterflooding.
Validation procedures included statistical calculations to assess local uncertainty and
variability, as well as direct measurement comparisons. By way of comparing and
evaluating the analyses the interpretable conclusion is that the modeling techniques
performed do indeed provide a proper approach for reservoir characterization. Although
the structural continuity of the reservoir appears to retain general consistency throughout
the entire field, there is an apparent continuity trend (based on keen observations) where
the upper half of the reservoir becomes slightly less continuous relative to the lower half.
This small to modest apparent change reflected from the field continuity is probably due
to geological phenomena attributed to the major thrusting experienced in the area.
86
Moreover, the confidence level in the models and interpreted results and the associated
uncertainties due to the inherent variability and limitations in modeling subsurface
geological formations always need to be taken into consideration. The interoperability of
this project between GIS, engineering and geology alike is expected to promote the
growing field of geoinformatics and thus help bridge the gap in interdisciplinary
collaboration for data intensive research in the natural and applied sciences.

87
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92
APPENDIX I: Cross-section with stratigraphic log of adjacent reservoirs in Mahala
Obtained from CA DOGGR 1992 Report #TR12

93
APPENDIX II: Stratigraphic Column of Mahala Oilfield
Obtained from DOGG Report #TR18

94
APPENDIX III: Structural Contour Map of Chino Fault Zone
Obtained from USGS NEHRP 2008 report # 04HQGR0107

95
APPENDIX IV: Geological Contour Map
Obtained from DOGG Report #TR18

96
APPENDIX V: Structural Contour/Isopach Map of Mahala and West Mahala
Fields
Obtained from CA DOGGR 1992 Report #TR12

97

APPENDIX VI: INTEGRATED VOLUMETRIC AND NUMERICAL MODELS
Obtained from combining Matlab, SGeMS, Excel and ArcGIS using Reservoir Data

Abstract (if available)

Abstract Geographic Information Systems (GIS) provide a good framework for solving classical problems in the earth sciences and engineering. This thesis describes the geostatistics associated with creating a geological model of the Abacherli reservoir within the Mahala oil field of the Los Angeles Basin of Southern California using a variogram‐based two‐point geostatistical approach. The geology of this study area features a conventional heterogeneous sandstone formation with uniformly inclined rock strata of equal dip angle structurally trapped by surrounding geologic faults. Proprietary electrical well logs provide the resistivity and spontaneous potential at depth intervals of 10’ for the thirteen active wells in the study area. The dimensions and shape of the reservoir are inferred from geological reports. An isopach map was georeferenced, digitized and used to generate a 3D point‐set grid illustrating the boundaries and the volumetric extent of the reservoir. Preliminary exploration of the input data using univariate and bivariate statistical tests and data transformation tools rendered the data to be statistically suitable for performing ordinary kriging and sequential Gaussian simulation. The geological and statistical characteristics of the study area ensure that these interpolations are appropriate to employ. Three variogram directions were established as part of the variogram parameters and then a best‐fit statistical function was defined as the variogram model for each of the two electrical log datasets. The defined variogram was then used for the kriging and simulation algorithms. The data points were interpolated across the volumetric reservoir resulting in a 3D geological model displaying the local distribution of electrochemical properties in the subsurface of the study area. Data is interchanged between separate modeling programs, Stanford Geostatistical Modeling Software (SGeMS) and Esri ArcGIS, to illustrate the interoperability across different software. Validation of the predictive geostatistical models includes performing a leave‐one‐out cross‐validation for each borehole as well as computing a stochastic model based on the sequential Gaussian simulation algorithm, which yielded multiple realizations that were used for statistical comparison. The reservoir characterization results provide a credible approximation of the general geological continuity of the reservoir and can be further used for reservoir engineering and geochemical applications.

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Asset Metadata

Creator Vasquez, Diego A. (author)

Core Title Geological modeling in GIS for petroleum reservoir characterization and engineering: a 3D GIS-assisted geostatistics approach

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 04/17/2014

Defense Date 03/17/2014

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag 3D GIS,conditional simulation,geoinformatics,geospatial technology,geostatistics,GIS,kriging,Modeling,OAI-PMH Harvest,ordinary kriging,petroleum geology,petroleum production,reservoir characterization,reservoir engineering,sequential Gaussian simulation,simulation,variogram

Format application/pdf (imt)

Language English

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Advisor Swift, Jennifer N. (committee chair), Hammond, Douglas E. (committee member), Jafarpour, Behnam (committee member), Lee, Su Jin (committee member)

Creator Email davasquez01@live.com,diego.vasquez@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-380265

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