Preface |
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xv | |
1 Motivating Ideas - General Formulation and Results |
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1 | (36) |
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1 | (1) |
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2 | (2) |
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1.3 Physical Model and Numerical Formulation |
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4 | (9) |
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4 | (1) |
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1.3.2 New discretization approach |
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4 | (1) |
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1.3.3 Analytical formulation |
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5 | (1) |
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1.3.4 An alternative approach |
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6 | (4) |
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1.3.5 Solution philosophy |
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10 | (1) |
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1.3.6 Governing equations |
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11 | (1) |
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1.3.7 Finite difference methodology |
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11 | (2) |
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1.4 Validation Methodology |
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13 | (3) |
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1.4.1 Fundamental physics |
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14 | (1) |
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1.4.2 Biot-Savart finite coil validations |
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14 | (1) |
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1.4.3 Analytical dipole validations |
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15 | (1) |
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1.4.4 Fully three-dimensional solutions |
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15 | (1) |
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1.5 Practical Applications |
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16 | (18) |
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1.5.1 Example 1. Granularity transition to coil source |
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16 | (3) |
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1.5.2 Example 2. Magnetic field, coil alone |
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19 | (1) |
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1.5.3 Example 3. Steel mandrel at dip |
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20 | (2) |
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1.5.4 Example 4. Conductive mud effects in wireline and MWD logging |
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22 | (2) |
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1.5.5 Example 5. Longitudinal magnetic fields |
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24 | (4) |
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1.5.6 Example 6. Elliptical coils |
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28 | (2) |
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1.5.7 Example 7. Calculating electromotive force |
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30 | (2) |
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1.5.8 Example 8. Detailed incremental readings |
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32 | (1) |
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1.5.9 Example 9. Coil residing along bed interface |
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33 | (1) |
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34 | (1) |
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35 | (2) |
2 Detailed Theory and Numerical Analysis |
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37 | (105) |
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37 | (3) |
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40 | (7) |
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2.2.1 Physical and mathematical complications |
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40 | (1) |
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2.2.2 Numerical challenges |
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41 | (1) |
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2.2.3 Alternative approaches |
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42 | (1) |
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43 | (4) |
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2.3 Preliminary Mathematical Considerations |
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47 | (11) |
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2.3.1 General governing differential equations |
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48 | (1) |
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48 | (1) |
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2.3.3 Equivalent vector and scalar potential formulation |
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49 | (2) |
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2.3.4 Recapitulation and mathematical observations |
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51 | (1) |
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2.3.5 Matching conditions at bed interfaces |
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52 | (3) |
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2.3.6 Exact surface charge modeling |
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55 | (2) |
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2.3.7 Constant frequency analysis |
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57 | (1) |
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2.4 Boundary Value Problem Formulation |
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58 | (8) |
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2.4.1 Model for weak charge buildup |
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59 | (3) |
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2.4.2 Distributed surface charge |
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62 | (1) |
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2.4.3 Predictor-corrector model for strong polarization |
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63 | (1) |
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2.4.4 Fully coupled model for strong polarization |
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64 | (2) |
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2.5 Computational Issues and Strategies |
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66 | (14) |
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2.5.1 Alternative computational approaches |
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67 | (1) |
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2.5.2 Difference model at field points within layers |
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68 | (1) |
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2.5.3 Discontinuous functions and normal derivatives |
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69 | (2) |
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2.5.4 Scalar potential solution |
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71 | (1) |
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2.5.5 No limiting assumptions |
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72 | (1) |
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2.5.6 Logging tool mandrels |
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72 | (1) |
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73 | (1) |
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74 | (1) |
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2.5.9 Validation procedures |
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74 | (6) |
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2.6 Typical Simulation Results |
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80 | (32) |
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2.6.1 Example 1. Vertical hole, 20 KHz |
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80 | (1) |
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2.6.2 Example 2. Vertical hole, 2 MHz |
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80 | (1) |
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2.6.3 Example 3. Vertical hole, 2 MHz, collar |
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80 | (4) |
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2.6.4 Example 4. Tilted beds, 45° dip, 20 KHz |
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84 | (4) |
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2.6.5 Example 5. Tilted beds, 45° dip, 2 MHz |
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88 | (4) |
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2.6.6 Example 6. Tilted beds, 60° dip, 2 MHz |
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92 | (1) |
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2.6.7 Example 7. Tilted beds, 75° dip, 2 MHz |
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93 | (2) |
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2.6.8 Example 8. Tilted beds, 90° dip, 2 MHz |
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95 | (3) |
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2.6.9 Example 9. 90° dip, 2 Hz, with collar |
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98 | (3) |
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2.6.10 Example 10. Anisotropic effects |
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101 | (2) |
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2.6.11 Example 11. More anisotropic effects |
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103 | (2) |
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2.6.12 Example 12. Transmitter placement |
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105 | (1) |
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2.6.13 Example 13. More, transmitter placement |
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106 | (2) |
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2.6.14 Example 14. Double bed intersections |
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108 | (4) |
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2.7 Post-Processing and Applications |
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112 | (14) |
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2.7.1 Amplitude and phase |
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112 | (4) |
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2.7.2 Effects of interfacial surface charge |
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116 | (2) |
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2.7.3 Cylindrical radial coordinates |
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118 | (3) |
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2.7.4 Coordinate system notes |
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121 | (3) |
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2.7.5 Magnetic field modeling |
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124 | (2) |
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2.8 Restrictions with Fast Multi-frequency Methods |
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126 | (2) |
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126 | (1) |
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127 | (1) |
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2.9 Receiver Design Philosophy |
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128 | (3) |
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2.10 Description of Output Files |
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131 | (7) |
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2.10.1 Output Answer.Dat files in rectangular coordinates |
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131 | (4) |
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2.10.2 Output 'Quiklook.Dat' files in rectangular coordinates |
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135 | (1) |
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2.10.3 Output functions in cylindrical coordinates |
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135 | (1) |
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2.10.4 Typical "Point Summary" output |
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135 | (2) |
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2.10.5 Additional simulation files |
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137 | (1) |
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2.10.6 Creating color plots in planes perpendicular to z coordinate surfaces |
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137 | (1) |
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2.11 Apparent Resistivity Using Classic Dipole Solution |
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138 | (1) |
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2.12 Coordinate Conventions for Mud and Invasion Modeling |
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139 | (1) |
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2.12.1 Modeling borehole mud and invaded zones |
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139 | (1) |
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2.13 Generalized Fourier Integral for Transient Sounding |
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140 | (1) |
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141 | (1) |
3 Validations - Qualitative Benchmarks |
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142 | (138) |
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142 | (6) |
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3.2 Introductory Problems |
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148 | (97) |
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3.2.1 Example 1. Horizontal "coil alone," vertical well in homogeneous un-layered medium |
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148 | (18) |
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3.2.1.1 Validation of results |
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152 | (1) |
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3.2.1.2 Understanding electric fields |
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153 | (3) |
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3.2.1.3 Understanding magnetic fields |
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156 | (7) |
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3.2.1.4 Understanding point summaries |
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163 | (3) |
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3.2.2 Example 2. Vertical "coil alone horizontal well in homogeneous unlayered medium |
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166 | (6) |
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3.2.3 Example 3. 45 degree "coil alone" problem in homogeneous unlayered medium |
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172 | (9) |
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3.2.4 Example 4. Ninety degree dip, three-layer problem, "coil alone" |
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181 | (15) |
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3.2.4.1 Understanding interfacial surface charge |
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193 | (3) |
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3.2.5 Example 5. Ninety degree dip, three-layer problem, "steel mandrel" |
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196 | (3) |
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3.2.6 Example 6. Forty-five degree dip, three-layer problem, "coil alone" |
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199 | (23) |
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3.2.7 Example 7. Fully 3D, anisotropic, three-layer problem, with non-dipolar transmitter coil residing across three thin beds |
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222 | (23) |
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245 | (32) |
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3.3.1 Example 1. Vertical hole, 20 KHz |
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245 | (2) |
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3.3.2 Example 2. Vertical hole, 2 MHz |
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247 | (1) |
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3.3.3 Example 3. Vertical hole, 2 MHz, collar |
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248 | (1) |
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3.3.4 Example 4. Titled beds, 45° dip, 20 KHz |
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249 | (4) |
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3.3.5 Example 5. Tilted beds, 45° dip, 2 MHz |
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253 | (4) |
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3.3.6 Example 6. Tilted beds, 60° dip, 2 MHz |
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257 | (1) |
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3.3.7 Example 7. Tilted beds, 75° dip, 2 MHz |
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258 | (2) |
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3.3.8 Example 8. Tilted beds, 90° dip, 2 MHz |
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260 | (3) |
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3.3.9 Example 9. 90° dip, 2 MHz, with collar |
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263 | (2) |
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3.3.10 Example 10. Anisotropic effects |
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265 | (2) |
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3.3.11 Example 11. More anisotropic effects |
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267 | (2) |
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3.3.12 Example 12. Transmitter placement |
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269 | (2) |
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3.3.13 Example 13. More, transmitter placement |
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271 | (2) |
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3.3.14 Example 14. Double bed intersections |
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273 | (4) |
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3.4 Sign Conventions and Validation Methodology |
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277 | (2) |
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279 | (1) |
4 Validations - Quantitative Benchmarks at 0° and 90° |
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280 | (76) |
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280 | (1) |
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4.2 Wireline Validations in Homogeneous Media |
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281 | (23) |
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4.2.1 Simplified analytical models and comparison objectives |
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281 | (6) |
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4.2.1.1 Classical dipole model |
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281 | (2) |
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4.2.1.2 Nonconductive Biot-Savart model |
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283 | (1) |
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4.2.1.3 Electromagnetic versus simulation parameters |
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284 | (2) |
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4.2.1.4 Reiteration of basic ideas |
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286 | (1) |
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4.2.2 Inverse dependence of magnetic field source strength on coil diameter |
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287 | (4) |
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4.2.3 Calculating transmitter magnetic field source strength |
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291 | (1) |
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4.2.4 Validating receiver Bimag/Breal ratio on a wide range of variable grids |
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292 | (7) |
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4.2.4.1 Stretching Simulation Set No. 1 |
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294 | (1) |
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4.2.4.2 Stretching Simulation Set No. 2 |
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295 | (1) |
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4.2.4.3 Stretching Simulation Set No. 3 |
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296 | (1) |
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4.2.4.4 Stretching Simulation Set No. 4 |
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297 | (2) |
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4.2.5 Simulations holding resistivity fixed, with frequency varying |
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299 | (3) |
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4.2.6 Simulations holding frequency fixed, with resistivity varying |
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302 | (2) |
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4.3 Wireline Validations in Two-Layer Inhomogeneous Media |
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304 | (24) |
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4.3.1 Remarks and observations |
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304 | (4) |
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4.3.1.1 Detailed simulation results |
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306 | (1) |
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4.3.1.2 Simulation differences explained |
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306 | (2) |
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4.3.2 One inch diameter transmitter, vertical well |
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308 | (6) |
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4.3.2.1 Run 22a highlights |
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309 | (3) |
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4.3.2.2 Run 22b highlights |
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312 | (1) |
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4.3.2.3 Run 22c highlights |
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313 | (1) |
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4.3.3 Six inch diameter transmitter, vertical well |
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314 | (3) |
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4.3.3.1 Run 23a highlights |
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314 | (1) |
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4.3.3.2 Run 23b highlights |
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315 | (1) |
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4.3.3.3 Run 23c highlights |
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316 | (1) |
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4.3.4 One inch diameter transmitter, horizontal well |
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317 | (8) |
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4.3.4.1 Run 25a highlights |
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318 | (2) |
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4.3.4.2 Run 25b highlights |
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320 | (4) |
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4.3.4.3 Run 25c highlights |
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324 | (1) |
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4.3.5 Six inch diameter transmitter, horizontal well |
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325 | (3) |
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4.3.5.1 Run 26a highlights |
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325 | (1) |
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4.3.5.2 Run 26b highlights |
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326 | (1) |
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4.3.5.3 Run 26c highlights |
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327 | (1) |
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4.4 Electric and Magnetic Field Sensitive Volume Analysis for Resistivity and NMR Applications |
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328 | (12) |
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4.4.1 Depth of electromagnetic investigation in layered media with dip |
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328 | (1) |
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4.4.2 Typical layered media simulations (Cases 1-5) |
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329 | (11) |
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4.5 MWD "Steel Collar" and Wireline Computations in Homogeneous and Nonuniform Layered Dipping Media |
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340 | (7) |
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4.5.1 Wireline vs MWD logging scenarios |
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340 | (1) |
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4.5.2 Wireline "coil alone" simulation in uniform media |
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341 | (1) |
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4.5.3 MWD "steel drill collar" simulation in uniform media |
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342 | (2) |
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4.5.4 Wireline "coil alone" simulation in layered media |
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344 | (1) |
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4.5.5 MWD "steel drill collar" simulation in layered media |
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345 | (2) |
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4.6 Exact Drill Collar Validation Using Shen Analytical Solution |
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347 | (2) |
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4.7 Dipole Interpolation Formula Validation in Farfield |
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349 | (3) |
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4.8 Magnetic Dipole Validation in Two-Layer Formation |
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352 | (3) |
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355 | (1) |
5 Quantitative Benchmarks at Deviated Angles |
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356 | (26) |
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356 | (1) |
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5.2 Limit 1. No Collar, No Mud |
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356 | (7) |
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5.2.1 Observations on variable mesh system |
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357 | (1) |
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5.2.2 Review of results for 0° and 90° |
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358 | (1) |
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5.2.3 Validation for general dip angles |
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359 | (4) |
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5.3 Limit 2. Collar Only, No Mud |
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363 | (8) |
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5.4 Limit 3. Mud Only, No Collar |
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371 | (6) |
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5.5 Limit 4. Collar and Mud |
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377 | (5) |
6 Validations - Quantitative Benchmarks at Deviated Angles with Borehole Mud and Eccentricity |
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382 | (58) |
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382 | (1) |
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382 | (57) |
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6.2.1 Simulation Set 1. Objective, validate steel drill collar logic for 6 inch transmitter coil in homogeneous medium, with borehole radius of "0" meaning "no mud" first. Later on, add mud effects |
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382 | (1) |
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6.2.2 Simulation Set 2. Objective, borehole modeling at 0 deg dip, vertical well application. Here, 1 ωm formation runs next, model the borehole with 0.01ωm if there is a hole, so we can "see" 0.02 its attenuative effects quickly |
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383 | (1) |
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6.2.3 Simulation Set 3. Objective, repeat calculations immediately above, but for 90 deg dip, horizontal well application. Intention is to duplicate above results with differently oriented logic loop |
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383 | (1) |
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6.2.4 Simulation Set 4. Objective, repeat work just above, but for 45° dip deviated well. Intention to duplicate prior results with differently oriented logic loop |
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383 | (1) |
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6.2.5 Simulation Set 5. Objective, next test eccentering of borehole relative to coil center, using our vertical well logic |
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384 | (35) |
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6.2.6 Simulation Set 6. Objective, test a 45° deviated well run with color reporting |
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419 | (7) |
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6.2.7 Simulation Set 7. Objective, consider magnetic fields with color reporting and validation, i.e., depth of investigation in layered media with dip |
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426 | (14) |
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6.2.7.1 Advanced electromagnetic modeling |
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426 | (2) |
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6.2.7.2 Layered media simulations |
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428 | (7) |
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435 | (2) |
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6.2.7.4 Concluding remarks |
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437 | (2) |
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439 | (1) |
7 Validations - Receiver Voltage Response and Apparent Resistivity |
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440 | (51) |
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440 | (1) |
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440 | (45) |
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7.2.1 Pitfalls in calculating receiver voltage response using classical formula |
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440 | (10) |
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7.2.2 Operating the "custom receiver design" interface |
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450 | (3) |
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7.2.3 Validating receiver voltage calculations at different dip angles |
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453 | (21) |
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7.2.4 Apparent resistivity predictions can be dangerous |
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474 | (2) |
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7.2.5 Receiver voltage response in deviated wells without collars |
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476 | (6) |
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7.2.6 Apparent resistivity calculations, classical dipole versus 3D finite difference method for small 1 inch diameter coil shows consistent agreement |
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482 | (3) |
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7.3 General Transmitter Design Philosophy |
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485 | (2) |
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7.4 General Receiver Design Philosophy |
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487 | (3) |
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7.5 Apparent Resistivity Estimation from Classic Dipole Model |
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490 | (1) |
8 Simulator Overview and Feature Summary |
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491 | (28) |
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491 | (2) |
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8.2 Simulator Comparisons |
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493 | (3) |
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8.3 Technical Specifications |
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496 | (2) |
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8.4 Advanced Logging Applications |
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498 | (1) |
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8.4.1 Constant frequency electromagnetic tool operation |
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498 | (1) |
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8.4.2 Nuclear magnetic imaging |
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498 | (1) |
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8.4.3 Pulsed resistivity logging |
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499 | (1) |
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8.4.4 Downhole hardware design |
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499 | (1) |
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499 | (4) |
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8.5.1 Partial differential equations |
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499 | (1) |
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8.5.2 Transmitter coil modeling |
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500 | (1) |
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8.5.3 Boundary conditions |
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501 | (1) |
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8.5.4 Finite difference grid system |
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501 | (1) |
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8.5.5 Electromagnetic properties |
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502 | (1) |
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8.6 Computational Technology |
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503 | (1) |
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504 | (1) |
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8.8 Integrated Utility Programs |
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505 | (1) |
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8.9 Detailed Output and Integrated Graphics |
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506 | (1) |
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507 | (1) |
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508 | (2) |
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8.11.1 Fundamental physical validations |
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508 | (1) |
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8.11.2 Biot-Savart finite coil validations |
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509 | (1) |
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8.11.3 Analytical dipole validations |
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509 | (1) |
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8.11.4 More demanding validations |
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510 | (1) |
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8.12 Simulator Speed Analysis |
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510 | (1) |
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8.13 Sample User Interface Screens |
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511 | (6) |
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8.14 Transmitter and Receiver Design Interface |
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517 | (2) |
9 Simulator Tutorials and Validation Problems |
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519 | (64) |
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9.1 Problem Set 1. Dipole and Biot-Savart Model Consistency - Validating Magnetic Fields |
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520 | (8) |
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9.2 Problem Set 2. Validating Farfield Phase Predictions |
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528 | (4) |
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9.3 Problem Set 3. Drill Collar Model Consistency - Exact Drill Collar Validation Using Shen Analytical Solution |
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532 | (2) |
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9.4 Problem Set 4. Magnetic Dipole in Two-Layer Formation |
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534 | (4) |
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9.5 Problem Set 5. Effects of Eccentricity and Invasion |
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538 | (4) |
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9.6 Problem Set 6. A Complicated Horizontal Well Geology |
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542 | (4) |
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9.7 Problem Set 7. Effects of Layering, Anisotropy and Dip |
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546 | (8) |
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9.8 Problem Set 8. Transmitter and Receiver Design |
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554 | (6) |
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9.9 Problem Set 9. Apparent Anisotropic Resistivities for Electromagnetic Logging Tools in Horizontal Wells |
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560 | (17) |
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9.10 Problem Set 10. Apparent Anisotropic Resistivities for Borehole Effects - Invasion and Eccentricity |
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577 | (6) |
Cumulative References |
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583 | (2) |
Index |
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585 | (6) |
About the Author |
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591 | |