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«INTEGRATION OF GEOMORPHIC EXPERIMENT DATA IN SURFACE-BASED MODELING: FROM CHARACTERIZATION TO SIMULATION A DISSERTATION SUBMITTED TO THE ...»

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INTEGRATION OF GEOMORPHIC EXPERIMENT DATA IN

SURFACE-BASED MODELING: FROM

CHARACTERIZATION TO SIMULATION

A DISSERTATION

SUBMITTED TO THE INTERDISCIPLINARY PROGRAM OF

EARTH, ENERGY, AND ENVIRONMENTAL SCIENCES

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Siyao Xu March 2014 © 2014 by Siyao Xu. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons AttributionNoncommercial 3.0 United States License.

http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/rj323qf2670 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Tapan Mukerji, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Jef Caers I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

George Hilley Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost for Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives.

iii iv ABSTRACT Dynamic process distributing geobodies, defined as geological dynamic processes in this dissertation, are the determinants of spatial heterogeneity of petrofacies, which further affect reservoir performances. But a dynamic process is normally not considered by conventional static reservoir modeling techniques, e.g. two-point statistics, multiple point statistics, and object-based methods. The surface-based method is the only static reservoir modeling technique that explicitly considers a geological dynamic process.

Moreover, the surface-based method is an open and flexible framework that is capable of integrating various techniques to generate realistic model realizations. However, current implementations of geological dynamic processes in surface-based models rely on imprecise conceptual rules, which normally involve a large number of empirical coefficients and subjective decisions to quantify qualitative concepts. This does not appear to be an ideal treatment, since workloads in reservoir uncertainty estimation are increased along with empirical coefficients and subjective decisions. The demand of an improved implementation of geological dynamic processes that is more proper for the Monte Carlo uncertainty estimation led to the research in this dissertation. Contributions of this dissertation include a treatment to extract erosion rules from the records of an experiment, a solution to identify a geomorphic experiment to a real depositional system, and a new strategy to implement a geological dynamic process in surface-based models using geomorphic experimental data.

v The shale drape coverage in deepwater environments is a key parameter to the sand body connectivity in a reservoir. Proper modeling of shale drape coverage requires understanding of erosion geometries, which must be extracted from changes of intermediate topography of the depositional process. However, intermediate topography is normally not maintained in the stratigraphy of real depositional systems, thus understanding on the erosion geometry is always limited. To study this issue, we developed a workflow based on a geomorphic experiment, where the intermediate status was available in the records. An experiment of a delta basin with recorded intermediate topography was used to demonstrate this workflow. Sequential correlated patterns of erosion and deposition were extracted from intermediate topographies. A surface-based model of lobes and distributary channels was built based on input statistics of experimental erosion-deposition geometries. Since the geomorphic experiment was at a different scale than any real scale depositional system, we proposed to measure the cumulative distribution functions of dimensionless ratios to characterize correlations between erosion depth and deposition thickness in the experiments.

Static reservoir models in the oil industry are always required to be specified to the real scale system of a reservoir. Thus, the selected experiment to provide information for a surface-based model is required to be as similar to the system of the reservoir as possible. However, no hydrodynamic or stratigraphic method has been developed to estimate similarities between an experiment and a specific real depositional system. A solution is provided to identify one experiment that is most similar to a given real system from a set of optional experiments. The solution estimates a similarity between lobe stacking patterns of two systems, which are characterized by the cumulative distribution functions of pairwise lobate proximity measurements. The similarity is estimated with a bootstrap two-sample hypothesis test on the two cumulative distribution functions.





Since lobate bodies in experiments can be identified hierarchically from small scales to large scales depending on decisions of the interpreter, the solution also includes an automatic method to quantify lobe hierarchies and to choose lobate stacking patterns at vi various scales of interpretation. This solution is applied to estimate the similarity between two delta fan experiments and two published real systems.

Based on statistical similarity analysis, an experimental lobe pattern was identified as the pattern with the highest similarity to a real system. A natural assumption is that the forward process forming identified experimental lobate pattern is also similar to the process forming the given real lobate pattern. In this sense, an experimental lobe pattern is a prior scenario of the spatial-temporal lobe distributing process and is input to the surface-based model. A new surface-based model for a lobate environment was developed, in which the lobe migration mechanism was implemented based on the correlated random walk. The input lobe pattern was treated as a sequence, characterized by statistics of migration distance and migration orientation shifting angle.

Both control the random walk behavior of lobe migration. Only three cumulative distribution functions from the input pattern and two empirical coefficients were introduced by the random-walk-based lobe migration mechanism. Compared to tens of empirical coefficients, the new mechanism was more appropriate for uncertainty estimations using a Monte Carlo method. Demonstrations also show that realizations of the new model were hierarchically similar to the input lobe sequence analogous to the similarity between realizations of multiple point statistics and the training image.

viiACKNOWLEDGEMENTS

Turning back and recalling the past four years, I would like to express the most sincere gratitude to my advisor Professor Tapan Mukerji, who has been supporting and guiding me through my time in Stanford. When I came here as a general geoscientist and software engineer, Tapan tolerated my naï questions with his great patience and ve led me to the correct path. Tapan is knowledgable. Every time an obstacle appeared in my research, a conversation with Tapan was the best way to organize my chaotic mind, refine the problem, and locate a good solution. He has also been a good friend when I have had difficulties in life.

I would also like to express my gratitude to Professor Jef Caers, whose active mind is one of the richest sources of ideas. Jef’s talk and comments in every seminar introduced his insightful opinions on research, guiding me toward meaningful and promising directions. My work would not be in the current form without Jef.

I would like to appreciate all those I have been talking to through the duration of my Ph.D., including Tim McHargue, George Hilley, and Gary Mavko. Tim’s precious experiences from the very frontier of Surface-based modeling and critical comments from George and Gary were the base pillars of successful research.

My appreciation also goes to Professor Chris Paola and his students: Antoinette Abeyta, Sarah Baumgardner, and Dan Cazanacli. Without Chris’ data and valuable viii responses, our ideas at SCRF would not be implemented. It was my honor to witness and contribute to the beginning of a successful collaboration between SCRF and SAFL.

I also benefitted quite a lot from my three internships at Shell. Names I must mention are Omer Alpak, J-C Noirot, Matt Wolinsky, Long Jin, Tianhong Chen, and Paul Gelderblom. Any work and conversation with you enhanced my understanding about the industry, which was the required background for my research.

I am thankful to my colleagues and friends in SCRF: Andre Jung, Orhun Aydin, Lewis Li (please forgive me for not listing all of them here), from whom I have always received both help and fun. We have built a perfect community for work and life. It is my honor to be a member of SCRF.

I also appreciate my best friend Yang Liu, who was my unofficial mentor. I have learned much from him in research and in stories of this industry, and I will always remember other fun memories we have had, for example, those tickets.

I would like to say thanks to Professor Milton E. Harvey, who granted me selfless help through my two years in Ohio. I will never forget our discussions, covering topics from research to baseball and from politics to food.

I have always been thankful to live and study within the community of Department of Energy Resource Engineering, where you can always find helpful friends.

I dedicate this dissertation to Dr. Ning, my sweetie. I will bear in mind that Christmas, when the primary idea of this work and our wedding came true in Redwood City, the most romantic place in the Bay Area.

This dissertation is also dedicated to my mum, dad, and grandma.

–  –  –

Abstract

ACKNOWLEDGEMENTS

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

CHAPTER 1 INTRODUCTION

1.1 REVIEW OF STATIC RESERVOIR MODELING ALGORITHMS

1.2 CHOOSING MODELING ALGORITHMS

1.3 SURFACE-BASED MODELING AND CHALLENGES

1.4 THE PROPOSED APPROACH

1.5 THESIS OUTLINE

CHAPTER 2 EROSION RULES IN SURFACE-BASED MODELING: GEOMORPHIC

EXPERIMENTS AS THE KNOWLEDGE DATABASE

2.1 INTRODUCTION

2.1.1 Model Setting: Deepwater Turbidite System

2.1.2 Erosion in Static Reservoir Modeling

2.2 METHODOLOGY

2.2.1 Surface-Based Modeling

2.2.2 Building a Distributary Channel-Lobe Systems

2.2.3 Geomorphic Experiments

2.3 SIMULATION RESULTS

2.4 CHAPTER SUMMARY

CHAPTER 3 THE STATISTICAL EXTERNAL SIMILARITY BETWEEN LOBATE

ENVIRONMENTS: LINKING EXPERIMENTS TO REAL-SCALE SYSTEMS

3.1 INTRODUCTION

3.2 METHODOLOGY

x 3.2.1 Experimental Data and Preprocessing

3.2.2 Stage One – Automatic Lobe Hierarchy Quantification

3.2.3 Stage Two – Testing Pattern External Similarity

3.3 APPLICATION

3.4 CHAPTER SUMMARY

CHAPTER 4 HIERARCHICAL SIMILARITY OF LOBES: SIMULATION AND

COMPARISON

4.1 INTRODUCTION

4.2 A LOBE MIGRATION MODEL WITH INPUT LOBE SEQUENCE

4.2.1 Root Mean Square Distances: The Scaling Factor for Stacking Patterns

4.2.2 The Bifactor Modeling Scheme

4.2.3 The Input Stacking Pattern Factor

4.2.4 The Modeling Algorithms

4.2.5 Example

4.3 HIERARCHICAL SIMILARITY

4.3.1 Quantitative Measure of Hierarchical Similarity

4.3.2 Implicit Hierarchical Control in the CRW-based Mechanism

4.3.3 Application of Hierarchical Similarity Control

4.4 CHAPTER SUMMARY

CHAPTER 5 CONCLUSIONS AND FUTURE WORK

5.1 CONCLUSIONS

5.2 RECOMMENDATIONS FOR FUTURE WORK

BIBLIOGRAPHY

xiLIST OF TABLES

Table 2.1: Three categories of patterns are interpreted from the sediment event plot 1) channels, where the width of erosion is equal or greater than that of deposition; 2) lobe with erosion, where the width of deposition is greater than that of erosion; 3) lobe without erosion.

Table 2.2: Dimensionless ratios are used to characterize the relationship between erosion-deposition geometries identified from the sediment event plot.

Two probability functions respectively for channel and for lobe with erosion are interpreted. The probability of erosion occurs with lobes is 0.29.

Table 2.3: Primary simulation parameters.

Table 3.1: P-values of hypothesis testing between samples.

Sample 1 and 2 are detected to be similar, which Sample 3 is different from 1 and 2

Table 4.1: Values of primary parameters in the simulation.

xiiLIST OF FIGURES

Figure 1.1: Various static reservoir modeling techniques.

Along with the improvement of geological realism from two-point statistics to process-based method, the difficulty of conditioning models increases. After Bertoncello 2011.

Figure 1.2: A combined modeling algorithm.

Different algorithms are used at proper stages to maximize their advantages. After Michael et al. 2010.

Figure 2.1: The demonstration of a deepwater turbidite system.



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