Discrimination Between Reservoir Models in Well Test Analysis

3.1 Mathematical Model......Page 16
1.2 Previous Work......Page 18
1.4 Dissertation Outline......Page 24
2.1 Signal Analysis Problem......Page 25
2.2 Inwerse Problem......Page 28
3.2.1 Model Recognition......Page 39
3.2.2 Parameter Estimation......Page 42
3.2.3 Model Verification......Page 44
3.3 Nonlinear Regression......Page 45
3.3.1 Nonlinear Regression Algorithm......Page 46
3.3.2 Statistical Inference......Page 50
3.3.3 Least Absolute Value Method......Page 51
3.4 Bayesian Inference......Page 54
3.4.1 Bayes Theorem......Page 55
3.4.3 Bayesian Inference......Page 56
3.4.4 Important Probability Distributions......Page 58
Intervals......Page 61
1 Confidence Intervals......Page 59
2 Exact Confidence Intervals......Page 86
3 Ftest......Page 87
a1 Predictive Probability Method......Page 90
entia1 Predictive Probability Method......Page 91
retical Features......Page 102
Probability at the Starting Point......Page 115
Parameter Estimates at Each Time Step......Page 119
Joint Probability......Page 117
Comparison of Joint Probability......Page 118
Sequential Predictive Probability Method......Page 120
ime Step Sequences......Page 158
arting Point......Page 166
mber of Data Points......Page 170
5.1.4 Effect of the Magnitude of Errors......Page 174
fidence Interval Analysis and Graphical Analysis......Page 178
5.3.1 Commonly Encountered Situations......Page 185
5.3.2 Complex Reservoir Models......Page 197
5.4.1 Case 1: Multirate Pressure Data......Page 208
5.4.3 Case 3: Buildup Pressure Data......Page 214
6 Conclusions and Recommendations......Page 220
A Derivatives With Respect To Parameters......Page 36
A.2.4 Constant Pressure Outer Boundary Model......Page 242
A.2.5 Double Porosity Model......Page 245
A.2.6 Double Porosity and Sealing Fault Model......Page 251
Double Porosity and No Flow Outer Boundary Model......Page 256
Acceptable confidence intervals (from Horne......Page 73
Reservoir and fluid data......Page 74
model was used......Page 76
model was used......Page 176
Normalized joint probabilities step 61 to......Page 141
Modified sequential predictive probability method......Page 156
4.14 Estimated variance (g2)......Page 142
4.16 Overall predictive variance (02 + = (1 + gTH-'g) - a2)......Page 145
4.18 Probability associated with the model......Page 146
4.20 Relative confidence interval of permeability......Page 148
4.25 Distance to the boundary estimate......Page 149
and the corresponding normalized joint probability (lower)......Page 164
per) and the corresponding normalized joint probability (lower)......Page 161
corresponding normalized joint probability (lower)......Page 162
corresponding normalized joint probability (lower)......Page 163
and the corresponding normalized joint probability (lower)......Page 165
(lower)......Page 213
5.37 Field buildup pressure data from Vieira and Rosa......Page 215
malized joint probability associated with each model (lower)......Page 216
World Oil Oct. 1983b)......Page 110