Preface |
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xi | |
Acknowledgements |
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xiii | |
1 Basic Ideas, Interpretation Issues and Modeling Hierarchies |
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1 | (24) |
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1.1 Background and Approaches |
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1 | (4) |
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5 | (8) |
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1.3 Experimental Methods and Tool Calibration |
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13 | (11) |
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24 | (1) |
2 Single-Phase Flow Forward and Inverse Algorithms |
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25 | (26) |
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25 | (2) |
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2.2 Basic Model Summaries |
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27 | (24) |
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28 | (2) |
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30 | (1) |
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30 | (1) |
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2.2.4 Forward Model Application, Module FT-00 |
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31 | (2) |
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2.2.5 Inverse Model Application, Module FT-01 |
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33 | (2) |
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2.2.6 Effects of Dip Angle |
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35 | (2) |
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2.2.7 Inverse "Pulse Interaction" Approach Using FT-00 |
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37 | (3) |
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2.2.8 Computational Notes |
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40 | (1) |
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2.2.9 Source Model Limitations and More Complete Model |
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41 | (2) |
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2.2.10 Phase Delay Analysis, Module FT-04 |
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43 | (2) |
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2.2.11 Drawdown-Buildup, Module FT-PTA-DDBU |
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45 | (3) |
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2.2.12 Real Pumping, Module FT-06 |
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48 | (2) |
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50 | (1) |
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50 | (1) |
3 Advanced Drawdown and Buildup Interpretation in Low MobilityEnvironments |
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51 | (44) |
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3.1 Basic Steady Flow Model |
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51 | (2) |
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3.2 Transient Spherical Flow Models |
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53 | (6) |
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3.2.1 Forward or Direct Analysis |
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53 | (1) |
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3.2.2 Dimensionless Formulation |
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54 | (1) |
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3.2.3 Exact Solutions for Direct Problem |
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55 | (1) |
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3.2.4 Special Limit Solutions |
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56 | (2) |
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3.2.5 New Inverse Approach for Mobility and Pore Pressure Prediction |
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58 | (1) |
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3.3 Multiple-Drawdown Pressure Analysis (Patent Pending) |
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59 | (5) |
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3.3.1 Background on Existing Models |
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59 | (1) |
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3.3.2 Extension to Anisotropic, No-Skin Applications |
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60 | (6) |
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3.3.2.1 Method 1 - Drawdown-Alone Test |
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61 | (1) |
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3.3.2.2 Method 2 - Single-Drawdown- Single-Buildup Test |
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62 | (1) |
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3.3.2.3 Method 3 - Double-Drawdown- Single-Buildup Test |
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62 | (2) |
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3.4 Forward Analysis with Illustrative Calibration |
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64 | (2) |
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3.5 Mobility and Pore Pressure Using First Drawdown Data |
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66 | (8) |
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3.5.1 Run No. 1, Flowline Volume 200 Cc |
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66 | (3) |
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3.5.2 Run No. 2, Flowline Volume 500 Cc |
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69 | (2) |
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3.5.3 Run No. 3, Flowline Volume 1,000 Cc |
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71 | (2) |
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3.5.4 Run No. 4, Flowline Volume 2,000 Cc |
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73 | (1) |
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3.6 Mobility and Pore Pressure from Last Buildup Data |
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74 | (7) |
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3.6.1 Run No. 5, Flowline Volume 200 Cc |
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74 | (2) |
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3.6.2 Run No. 6, Flowline Volume 500 Cc |
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76 | (1) |
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3.6.3 Run No. 7, Flowline Volume 1,000 Cc |
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77 | (1) |
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3.6.4 Run No. 8, Flowline Volume 2,000 Cc |
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78 | (1) |
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3.6.5 Run No. 9, Time-Varying Flowline Volume |
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79 | (2) |
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3.7 Tool Calibration in Low Mobility Applications |
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81 | (12) |
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81 | (1) |
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3.7.2 Example 1, Calibration Using Early-Time Buildup Data |
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81 | (5) |
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3.7.3 Example 2, Calibration Using Early-Time Buildup Data |
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86 | (3) |
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3.7.4 Example 3, Example 1 Using Drawdown Data |
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89 | (2) |
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3.7.5 Example 4, Example 2 Using Drawdown Data |
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91 | (2) |
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93 | (1) |
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94 | (1) |
4 Phase Delay and Amplitude Attenuation for Mobility Prediction in Anisotropic Media with Dip (Patent Pending) |
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95 | (45) |
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4.1 Basic Mathematical Results |
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96 | (11) |
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96 | (2) |
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4.1.2 Anisotropic Equations |
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98 | (1) |
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4.1.3 Vertical Well Solution |
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99 | (1) |
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4.1.4 Horizontal Well Solution |
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100 | (1) |
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4.1.5 Formulas for Vertical and Horizontal Wells |
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101 | (1) |
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4.1.6 Deviated Well Equations |
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101 | (2) |
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4.1.7 Deviated Well Interpretation for Both Kh and K |
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103 | (2) |
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4.1.8 Two-Observation-Probe Models |
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105 | (2) |
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4.2 Numerical Examples and Typical Results |
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107 | (11) |
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4.2.1 Example 1, Parameter Estimates |
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108 | (1) |
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4.2.2 Example 2, Surface Plots |
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109 | (1) |
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4.2.3 Example 3, Sinusoidal Excitation |
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110 | (3) |
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4.2.4 Example 4, Rectangular Wave Excitation |
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113 | (2) |
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4.2.5 Example 5, Permeability Prediction at General Dip Angles |
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115 | (2) |
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4.2.6 Example 6, Solution for a Random Input |
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117 | (1) |
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4.3 Layered Model Formulation |
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118 | (5) |
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4.3.1 Homogeneous Medium, Basic Mathematical Ideas |
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118 | (2) |
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4.3.2 Boundary Value Problem for Complex Pressure |
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120 | (1) |
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4.3.3 literative Numerical Solution to General Formulation |
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120 | (1) |
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4.3.4 Successive Line Over Relaxation Procedure |
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121 | (1) |
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4.3.5 Advantages of the Scheme |
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122 | (1) |
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4.3.6 Extensions to Multiple Layers |
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122 | (1) |
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4.3.7 Extensions to Complete Formation Heterogeneity |
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123 | (1) |
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4.4 Phase Delay Software Interface |
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123 | (4) |
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126 | (1) |
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4.4.2 Special User Features |
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126 | (1) |
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4.5 Detailed Phase Delay Results in Layered Anisotropic Media |
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127 | (13) |
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4.6 Typical Experimental Results |
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134 | (4) |
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4.7 Closing Remarks - Extensions and Additional Applications |
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138 | (1) |
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139 | (1) |
5 Four Permeability Prediction Methods |
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140 | (11) |
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5.1 Steady-State Drawdown Example |
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142 | (2) |
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5.2 Early-Time, Low-Mobility Drawdown-Buildup |
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144 | (3) |
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5.3 Early-Time, Low-Mobility Drawdown Approach |
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147 | (1) |
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5.4 Phase Delay, Non-Ideal Rectangular Flow Excitation |
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148 | (3) |
6 Multiphase Flow with Inertial Effects |
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151 | (24) |
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6.1 Physical Problem Description |
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152 | (7) |
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6.1.1 The Physical Problem |
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152 | (2) |
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6.1.2 Job Planning Considerations |
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154 | (1) |
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6.1.3 Modeling Challenges |
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155 | (1) |
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6.1.4 Simulation Objectives |
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156 | (1) |
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157 | (2) |
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6.2 Immiscible Flow Formulation |
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159 | (9) |
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6.2.1 Finite Difference Solution |
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160 | (1) |
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6.2.2 Formation Tester Application |
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161 | (2) |
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6.2.3 Mudcake Growth and Formation Coupling at Sandface |
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163 | (2) |
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6.2.4 Pumpout Model for Single-Probe Pad Nozzles |
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165 | (1) |
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6.2.5 Dual Probe and Packer Surface Logic |
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166 | (2) |
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6.3 Miscible Flow Formulation |
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168 | (1) |
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6.4 Inertial Effects With Forchheimer Corrections |
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169 | (4) |
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6.4.1 Governing Differential Equations |
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169 | (2) |
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6.4.2 Pumpout Boundary Condition |
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171 | (1) |
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6.4.3 Boundary Value Problem Summary |
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172 | (1) |
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173 | (2) |
7 Multiphase Flow - Miscible Mixing Clean-Up Examples |
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175 | (54) |
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7.1 Overview Capabilities |
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175 | (16) |
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7.1.1 Example 1, Single Probe, Infinite Anisotropic Media |
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176 | (5) |
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7.1.2 Example 2, Single Probe, Three Layer Medium |
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181 | (2) |
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7.1.3 Example 3, Dual Probe Pumping, Three Layer Medium |
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183 | (2) |
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7.1.4 Example 4, Straddle Packer Pumping |
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185 | (2) |
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7.1.5 Example 5, Formation Fluid Viscosity Imaging |
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187 | (1) |
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7.1.6 Example 6, Contamination Modeling |
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188 | (1) |
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7.1.7 Example 7, Multi-Rate Pumping Simulation |
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189 | (2) |
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7.2 Source Code and User Interface Improvements |
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191 | (9) |
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7.2.1 User Data Input Panel |
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191 | (2) |
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7.2.2 Source Code Engine Changes |
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193 | (2) |
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7.2.3 Output Color Graphics |
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195 | (5) |
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7.3 Detailed Applications |
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200 | (29) |
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7.3.1 Run No. 1, Clean-Up, Single-Probe, Uniform Medium |
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200 | (9) |
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7.3.2 Run No. 2, Clean-Up, Dual-Probe, Uniform Medium |
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209 | (4) |
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7.3.3 Run No. 3, Clean-Up, Elongated Pad, Uniform Medium |
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213 | (5) |
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7.3.4 Run No. 4, A Minimal Invasion Example |
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218 | (4) |
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7.3.5 Run No. 5, A Single-Phase Fluid, Constant Viscosity example |
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222 | (2) |
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7.3.6 Run No. 6, A Low-Permeability "Supercharging" Example |
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224 | (2) |
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7.3.7 Run No. 7, A Three-Layer Simulation |
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226 | (3) |
8 Time-Varying Flowline Volume |
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229 | (41) |
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8.1 Transient Anisotropic Formulation for Ellipsoidal Source |
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230 | (8) |
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8.1.1 Formulation for Liquids and Gases |
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230 | (2) |
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8.1.2 Similarity Transform |
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232 | (1) |
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8.1.3 Transient Flow Numerical Modeling |
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233 | (1) |
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8.1.4 Finite Difference Equation |
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234 | (1) |
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8.1.5 Boundary Condition - Flowline Storage With and Without Skin Effects |
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235 | (1) |
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8.1.6 Detailed Time Integration Scheme |
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236 | (1) |
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8.1.7 Observation Probe Response |
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237 | (1) |
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8.2 FT-06 Software Interface and Example Calculations |
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238 | (6) |
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8.3 Time-Varying Flowline Volume Model |
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244 | (26) |
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8.3.1 Example 1, Software Calibration |
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245 | (7) |
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8.3.2 Example 2, Simple Interpretation Using Numerical Pressure Data |
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252 | (3) |
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8.3.3 Example 3, Simple Interpretation Using Numerical Pressure Data |
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255 | (2) |
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8.3.4 Example 4, Simple Interpretation Using Low Permeability Data |
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257 | (1) |
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8.3.5 Example 5, Simple Interpretation Using Numerical Pressure Data |
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258 | (4) |
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8.3.6 Example 6, Simple Interpretation Using Numerical Pressure Data |
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262 | (2) |
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8.3.7 Example 7, Enhancing Phase Delay Detection In Very Low Permeability Environments |
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264 | (6) |
9 Closing Remarks |
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270 | (11) |
References |
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281 | (6) |
Index |
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287 | (6) |
About the Authors |
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293 | |