Formation Testing – Low Mobility Pressure Transient Analysis

<p>Preface xi</p>
<p>Acknowledgements xiii</p>
<p>1 Basic Ideas, Interpretation Issues and Modeling Hierarchies 1</p>
<p>1.1 Background and Approaches 1</p>
<p>1.2 Modeling Hierarchies 5</p>
<p>1.3 Experimental Methods and Tool Calibration 13</p>
<p>1.4 References 24</p>
<p>2 Single–Phase Flow Forward and Inverse Algorithms 25</p>
<p>2.1 Overview 25</p>
<p>2.2 Basic Model Summaries 27</p>
<p>2.2.1 Module FT–00 28</p>
<p>2.2.2 Module FT–01 30</p>
<p>2.2.3 Module FT–03 30</p>
<p>2.2.4 Forward Model Application, Module FT–00 31</p>
<p>2.2.5 Inverse Model Application, Module FT–01 33</p>
<p>2.2.6 Eff ects of Dip Angle 35</p>
<p>2.2.7 Inverse Pulse Interaction Approach Using FT–00 37</p>
<p>2.2.8 Computational Notes 40</p>
<p>2.2.9 Source Model Limitations and More Complete Model 41</p>
<p>2.2.10 Phase Delay Analysis, Module FT–04 43</p>
<p>2.2.11 Drawdown–Buildup, Module FT–PTA–DDBU 45</p>
<p>2.2.12 Real Pumping, Module FT–06 48</p>
<p>2.2.13 Closing Remarks 50</p>
<p>2.2.14 References 50</p>
<p>3 Advanced Drawdown and Buildup Interpretation in Low Mobility Environments 51</p>
<p>3.1 Basic Steady Flow Model 51</p>
<p>3.2 Transient Spherical Flow Models 53</p>
<p>3.2.1 Forward or Direct Analysis 53</p>
<p>3.2.2 Dimensionless Formulation 54</p>
<p>3.2.3 Exact Solutions for Direct Problem 55</p>
<p>3.2.4 Special Limit Solutions 56</p>
<p>3.2.5 New Inverse Approach for Mobility and Pore Pressure Prediction 58</p>
<p>3.3 Multiple–Drawdown Pressure Analysis (Patent Pending) 59</p>
<p>3.3.1 Background on Existing Models 59</p>
<p>3.3.2 Extension to Anisotropic, No–Skin Applications 60</p>
<p>3.3.2.1 Method 1 – Drawdown–Alone Test 61</p>
<p>3.3.2.2 Method 2 – Single–Drawdown–Single–Buildup Test 62</p>
<p>3.3.2.3 Method 3 – Double–Drawdown–Single–Buildup Test 62</p>
<p>3.4 Forward Analysis with Illustrative Calibration 64</p>
<p>3.5 Mobility and Pore Pressure Using First Drawdown Data 66</p>
<p>3.5.1 Run No. 1, Flowline Volume 200 Cc 66</p>
<p>3.5.2 Run No. 2, Flowline Volume 500 Cc 69</p>
<p>3.5.3 Run No. 3, Flowline Volume 1,000 Cc 71</p>
<p>3.5.4 Run No. 4, Flowline Volume 2,000 Cc 73</p>
<p>3.6 Mobility and Pore Pressure from Last Buildup Data 74</p>
<p>3.6.1 Run No. 5, Flowline Volume 200 Cc 74</p>
<p>3.6.2 Run No. 6, Flowline Volume 500 Cc 76</p>
<p>3.6.3 Run No. 7, Flowline Volume 1,000 Cc 77</p>
<p>3.6.4 Run No. 8, Flowline Volume 2,000 Cc 78</p>
<p>3.6.5 Run No. 9, Time–Varying Flowline Volume 79</p>
<p>3.7 Tool Calibration in Low Mobility Applications 81</p>
<p>3.7.1 Steady Flow Model 81</p>
<p>3.7.2 Example 1, Calibration Using Early–Time Buildup Data 81</p>
<p>3.7.3 Example 2, Calibration Using Early–Time Buildup Data 86</p>
<p>3.7.4 Example 3, Example 1 Using Drawdown Data 89</p>
<p>3.7.5 Example 4, Example 2 Using Drawdown Data 91</p>
<p>3.8 Closing Remarks 93</p>
<p>3.9 References 94</p>
<p>4 Phase Delay and Amplitude Attenuation for Mobility Prediction in Anisotropic Media with Dip (Patent Pending) 95</p>
<p>4.1 Basic Mathematical Results 96</p>
<p>4.1.1 Isotropic Model 96</p>
<p>4.1.2 Anisotropic Equations 98</p>
<p>4.1.3 Vertical Well Solution 99</p>
<p>4.1.4 Horizontal Well Solution 100</p>
<p>4.1.5 Formulas for Vertical and Horizontal Wells 101</p>
<p>4.1.6 Deviated Well Equations 101</p>
<p>4.1.7 Deviated Well Interpretation for Both Kh and Kv 103</p>
<p>4.1.8 Two–Observation–Probe Models 105</p>
<p>4.2 Numerical Examples and Typical Results 107</p>
<p>4.2.1 Example 1, Parameter Estimates 108</p>
<p>4.2.2 Example 2, Surface Plots 109</p>
<p>4.2.3 Example 3, Sinusoidal Excitation 110</p>
<p>4.2.4 Example 4, Rectangular Wave Excitation 113</p>
<p>4.2.5 Example 5, Permeability Prediction at General Dip Angles 115</p>
<p>4.2.6 Example 6, Solution for a Random Input 117</p>
<p>4.3 Layered Model Formulation 118</p>
<p>4.3.1 Homogeneous Medium, Basic Mathematical Ideas 118</p>
<p>4.3.2 Boundary Value Problem for Complex Pressure 120</p>
<p>4.3.3 Iiterative Numerical Solution to General Formulation 120</p>
<p>4.3.4 Successive Line Over Relaxation Procedure 121</p>
<p>4.3.5 Advantages of the Scheme 122</p>
<p>4.3.6 Extensions to Multiple Layers 122</p>
<p>4.3.7 Extensions to Complete Formation Heterogeneity 123</p>
<p>4.4 Phase Delay Software Interface 123</p>
<p>4.4.1 Output File Notes 126</p>
<p>4.4.2 Special User Features 126</p>
<p>4.5 Detailed Phase Delay Results in Layered Anisotropic Media 127</p>
<p>4.6 Typical Experimental Results 134</p>
<p>4.7 Closing Remarks – Extensions and Additional Applications 138</p>
<p>4.8 References 139</p>
<p>5 Four Permeability Prediction Methods 140</p>
<p>5.1 Steady–State Drawdown Example 142</p>
<p>5.2 Early–Time, Low–Mobility Drawdown–Buildup 144</p>
<p>5.3 Early–Time, Low–Mobility Drawdown Approach 147</p>
<p>5.4 Phase Delay, Non–Ideal Rectangular Flow Excitation 148</p>
<p>6 Multiphase Flow with Inertial Effects 151</p>
<p>6.1 Physical Problem Description 152</p>
<p>6.1.1 The Physical Problem 152</p>
<p>6.1.2 Job Planning Considerations 154</p>
<p>6.1.3 Modeling Challenges 155</p>
<p>6.1.4 Simulation Objectives 156</p>
<p>6.1.5 Modeling Overview 157</p>
<p>6.2 Immiscible Flow Formulation 159</p>
<p>6.2.1 Finite Difference Solution 160</p>
<p>6.2.2 Formation Tester Application 161</p>
<p>6.2.3 Mudcake Growth and Formation Coupling at Sandface 163</p>
<p>6.2.4 Pumpout Model for Single–Probe Pad Nozzles 165</p>
<p>6.2.5 Dual Probe and Packer Surface Logic 166</p>
<p>6.3 Miscible Flow Formulation 168</p>
<p>6.4 Inertial Effects With Forchheimer Corrections 169</p>
<p>6.4.1 Governing Differential Equations 169</p>
<p>6.4.2 Pumpout Boundary Condition 171</p>
<p>6.4.3 Boundary Value Problem Summary 172</p>
<p>6.5 References 173</p>
<p>7 Multiphase Flow – Miscible Mixing Clean–Up Examples 175</p>
<p>7.1 Overview Capabilities 175</p>
<p>7.1.1 Example 1, Single Probe, Infinite Anisotropic Media 176</p>
<p>7.1.2 Example 2, Single Probe, Three Layer Medium 181</p>
<p>7.1.3 Example 3, Dual Probe Pumping, Three Layer Medium 183</p>
<p>7.1.4 Example 4, Straddle Packer Pumping 185</p>
<p>7.1.5 Example 5, Formation Fluid Viscosity Imaging 187</p>
<p>7.1.6 Example 6, Contamination Modeling 188</p>
<p>7.1.7 Example 7, Multi–Rate Pumping Simulation 189</p>
<p>7.2 Source Code and User Interface Improvements 191</p>
<p>7.2.1 User Data Input Panel 191</p>
<p>7.2.2 Source Code Engine Changes 193</p>
<p>7.2.3 Output Color Graphics 195</p>
<p>7.3 Detailed Applications 200</p>
<p>7.3.1 Run No. 1, Clean–Up, Single–Probe, Uniform Medium 200</p>
<p>7.3.2 Run No. 2, Clean–Up, Dual–Probe, Uniform Medium 209</p>
<p>7.3.3 Run No. 3, Clean–Up, Elongated Pad, Uniform Medium 213</p>
<p>7.3.4 Run No. 4, A Minimal Invasion Example 218</p>
<p>7.3.5 Run No. 5, A Single–Phase Fluid, Constant Viscosity example 222</p>
<p>7.3.6 Run No. 6, A Low–Permeability Supercharging Example 224</p>
<p>7.3.7 Run No. 7, A Three–Layer Simulation 226</p>
<p>8 Time–Varying Flowline Volume 229</p>
<p>8.1 Transient Anisotropic Formulation for Ellipsoidal Source 230</p>
<p>8.1.1 Formulation for Liquids and Gases 230</p>
<p>8.1.2 Similarity Transform 232</p>
<p>8.1.3 Transient Flow Numerical Modeling 233</p>
<p>8.1.4 Finite Difference Equation 234</p>
<p>8.1.5 Boundary Condition – Flowline Storage With and Without Skin Effects 235</p>
<p>8.1.6 Detailed Time Integration Scheme 236</p>
<p>8.1.7 Observation Probe Response 237</p>
<p>8.2 FT–06 Software Interface and Example Calculations 238</p>
<p>8.3 Time–Varying Flowline Volume Model 244</p>
<p>8.3.1 Example 1, Software Calibration 245</p>
<p>8.3.2 Example 2, Simple Interpretation Using Numerical Pressure Data 252</p>
<p>8.3.3 Example 3, Simple Interpretation Using Numerical Pressure Data 255</p>
<p>8.3.4 Example 4, Simple Interpretation Using Low Permeability Data 257</p>
<p>8.3.5 Example 5, Simple Interpretation Using Numerical Pressure Data 258</p>
<p>8.3.6 Example 6, Simple Interpretation Using Numerical Pressure Data 262</p>
<p>8.3.7 Example 7, Enhancing Phase Delay Detection In Very Low Permeability Environments 264</p>
<p>9 Closing Remarks 270</p>
<p>References 281</p>
<p>Index 287</p>
<p>About the Authors 293</p>