Foreword to the Series ........................................ vii
Foreword ....................................................... ix
1 Introduction ................................................. 3
Background ................................................... 3
Objectives ................................................... 4
An Outline of the Evaluation Procedure ....................... 5
Scope ........................................................ 5
2 Evaluation Models ............................................ 7
Geological Models and Play Definitions ....................... 7
Statistical Models .......................................... 11
Concepts Used ............................................... 14
The Nature of Geological Populations ........................ 18
The Beaverhill Lake Play ................................. 18
Outliers ................................................. 21
Correlation between Random Variables ..................... 22
Mixed Populations ........................................ 25
3 Estimating Mature Plays ..................................... 26
The Superpopulation Model ................................... 27
Lognormal Discovery Process Model ........................ 27
Nonparametric Discovery Process Model .................... 33
Estimating Pool-Size Distribution for the Beaverhill
Lake Play ................................................ 34
Lognormal/Nonparametric-Poisson Discovery Process
Model .................................................... 36
Previous Work ......................................... 36
The BDSCV Model ....................................... 38
The Keg River Shelf ................................... 39
Remarks ............................................... 39
Multivariate Discovery Process Model ..................... 40
Bivariate Lognormal Distribution for Oil and Gas
Pools ................................................. 43
Estimating the Covariance Matrix ...................... 44
Remarks .................................................. 45
Pool-Size-by-Rank by Order Statistics ....................... 45
Interpretations .......................................... 47
The Matching Process: Operation .......................... 51
The Beaverhill Lake Play ................................. 54
Pool Sizes Conditional on Pool Rank ...................... 55
Distribution of the Ratio of Two Pools ................... 56
Play Resource and Potential Distribution .................... 57
Play Resource Distribution ............................... 57
Play Potential Distribution .............................. 58
Expected Play Potential ............................... 58
Probable Play Potential Distribution .................. 59
The Beaverhill Lake Play .............................. 59
4 More about Discovery Process Models ......................... 61
Validation Study by Simulation .............................. 61
Validation Procedure ..................................... 61
Estimates for the N Value ................................ 63
Lognormal Population .................................. 63
Weibull Population .................................... 66
Pareto Population ..................................... 67
Mixed Population of Two Lognormal Populations ......... 68
Mixed Population of Lognormal, Weibull, and Pareto
Populations ........................................... 69
Estimation of Exploration Efficiency ..................... 72
Pool-Size-by-Rank ........................................ 74
Play Resource Distribution ............................... 74
Reduction of Uncertainty ................................. 11
Validation by Retrospective Study ........................... 80
Jumping Pound Rundle Gas Play ............................ 80
Swan Hills Shelf Margin Gas and Leduc Isolated Reef Oil
Plays .................................................... 82
Remarks .................................................. 83
Impact of Nonproductive and Noncommercial Pools ............. 85
Impact of a Nonproductive Trap ........................... 86
Impact of Missing Pools .................................. 87
Testing the Adequacy of Probability Distributions ........... 88
The Procedure ............................................ 89
Interpretation ........................................... 89
Outliers .............................................. 89
Long or Short Tails at Both Ends ...................... 90
Symmetry .............................................. 90
Plateaus .............................................. 90
The Beaverhill Lake Play ................................. 91
Plays from Worldwide Basins .............................. 91
Pool-Size Distribution of a Basin .......................... 100
Justifications for Using a Lognormal Distribution .......... 102
Evidence from the Q-Q Plots ............................. 102
Approximation of a Lognormal Distribution to
Geological Random Variables ............................. 102
Advantages of Using a Lognormal Distribution ............ 103
Estimation Error Resulting from Lognormal Distribution
Approximation ........................................... 105
5 Evaluating Conceptual Plays ................................ 106
Geological Factors ......................................... 106
Exploration Risk ........................................ 106
Methods for Estimating Marginal Probability ............. 107
Play-Level Geological Factor ......................... 108
Prospect-Level Geological Factor ..................... 111
Marginal Probability Distribution .................... 112
Dependence in Prospect-Level Geological Factors ......... 114
The East Coast Play ..................................... 115
Pool-Size Distribution ..................................... 116
The Monte Carlo Method .................................. 116
The Lognormal Approximation ............................. 119
Examples ................................................ 120
The Beaverhill Lake Play ............................. 120
The East Coast Play .................................. 124
Estimating Resources ....................................... 127
Number-of Prospects Distribution ........................ 127
Number-of-Pools Distribution ............................ 127
Play Resource Distribution .............................. 131
Pool-Size-by-Rank ....................................... 133
Generation of Reservoir Parameters ...................... 135
Constructing Probability Distributions ..................... 136
6 Estimation Update and Feedback Procedures .................. 140
Procedure for Estimating Mature Plays ...................... 143
Step 1: Formulating a Play Definition and Its
Geographic Boundary ..................................... 143
Step 2: Compiling Play Data ............................. 143
Step 3: Validating Mixed Populations or Lognormal
Assumptions ..................................... 144
Step 4: Estimating Pool-Size Distribution ............... 145
Step 5: Determining an Appropriate Probability
Distribution .................................... 145
Step 6: Estimating Pool-Size-by-Rank .................... 145
Step 7: Estimating Expected and Probable Play
Potential ....................................... 145
Step 8: Computing Play Resource Distribution ............ 146
Procedure for Estimating Conceptual Plays .................. 146
Conceptual Plays from a Mature Basin .................... 146
Conceptual Plays from a Frontier Basin .................. 146
Step 1: Formulating Play Definitions ................. 146
Step 2: Estimating Pool-Size Distribution ............ 147
Step 3: Estimating Number-of-Pools Distribution ...... 147
Step 4: Estimating Individual Pool-Size
Distribution ................................. 148
Step 5: Estimating Play Resource Distribution ........ 148
Step 6: Estimating Other Reservoir Parameters ........ 149
Update Procedure ........................................... 149
Feedback Procedure ......................................... 149
Can We Predict the Current Situation? ................... 149
Has the Largest Pool Been Discovered? ................... 150
Pool Size Conditional on Play Resource .................. 151
7 Other Assessment Methods—An Overview ....................... 152
Geological Approach ........................................ 153
Volumetric Yield by Analogous Basin Method .............. 153
Basin Classification Method ............................. 154
Geochemical Approaches 154
Petroleum System or Geochemical Mass Balance Method ..... 154
Burial and Thermal History Modeling ..................... 158
Statistical Approaches ..................................... 161
Finite Population Methods ............................... 161
The Arps and Roberts Method .......................... 161
Bickel, Nair, and Wang's Method ...................... 163
Kaufman's Anchored Method ............................ 164
Chen and Sinding-Larsen's Geo-Anchored Method ........ 166
Superpopulation Methods ................................. 166
USGS Log-Geometric Method ............................ 166
The Creaming Method .................................. 169
The Long Method ...................................... 170
The Regression Method ................................... 170
The Fractal Method ...................................... 171
8 Concluding Remarks ......................................... 174
Appendix A: Estimation of Superpopulation Parameters
from a Successively Sampled Finite Population ........... 176
The Likelihood Function ................................. 178
Maximum-Likelihood Estimation ........................... 183
Inference for в and N ................................... 192
Inference for the Weight Function ....................... 197
Appendix B: Nonparametric Procedure for Estimating
Distributions ........................................... 200
Appendix C: The Largest Pool Size and Its Distribution ..... 203
The rth Largest Pool-Size Distribution .................. 203
Generation of Reservoir Parameters for a Given Pool
Size .................................................... 205
Appendix D: Pool Size Conditional on Pool Ranks ............ 208
Theorem 1 ............................................... 208
Corollary ............................................ 209
Theorem 2 ............................................... 210
References .................................................... 213
Index ......................................................... 221
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