Lee P.J. Statistical methods for estimating petroleum resources. - Oxford: Oxford University Press, 2008. - xxi, 234 p.: ill. - (Studies in mathematical geology; 8). - International Association for Mathematical Geology. - Ref.: p.213-220. - Ind.: p.221-234. - ISBN 978-0-19-533190-5  Место хранения:   018 | Институт нефтегазовой геологии и геофизики им. А.А.Трофимука | Новосибирск | Библиотека

Оглавление / Contents

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