About the book series |
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vii | |
Editorial board of the book series |
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Foreword |
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xvii | |
About the editors |
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xix | |
Acknowledgements |
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xxi | |
1 Mathematical modeling of thermo-hydro-mechanical behavior for reservoir formation under elevated temperature |
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1 | (18) |
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1 | (1) |
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1.2 General conservation equations of heat and mass transfer within a deformable porous medium |
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2 | (3) |
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1.2.1 Macroscopic mass conservation equations |
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2 | (1) |
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1.2.2 Linear momentum conservation equations |
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3 | (1) |
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1.2.3 Energy (enthalpy) conservation equations |
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4 | (1) |
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5 | (2) |
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1.3.1 Constitutive equations for mass transfer |
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5 | (1) |
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1.3.1.1 Advective flow of gas |
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5 | (1) |
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1.3.1.2 Advective mass flow of liquid |
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5 | (1) |
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1.3.2 Constitutive equations for heat transfer |
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6 | (1) |
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1.3.2.1 Conductive heat transfer within the domain Ω |
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6 | (1) |
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1.3.2.2 Heat transferred in radiation at boundary partialdifferenceΩ |
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6 | (1) |
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1.3.3 Constitutive equations for the mechanical response of the solid phase |
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6 | (1) |
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1.4 Some empirical expressions |
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7 | (1) |
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1.4.1 The expression of total porosity n |
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7 | (1) |
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1.4.2 The expression of mdesorp |
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7 | (1) |
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1.4.3 Effective thermal conductivity of the three-phase medium |
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8 | (1) |
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1.5 Resultant governing equations |
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8 | (1) |
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1.6 Equivalent integral of the governing differential equation and its weak form |
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9 | (4) |
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1.7 Approximate solution and spatial discretization |
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13 | (3) |
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16 | (3) |
2 Damage model for rock-like materials and its application |
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19 | (22) |
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19 | (1) |
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2.2 The Barcelona model: Scalar damage with different behaviors for tension and compression |
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20 | (3) |
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2.2.1 Uniaxial behavior of the Barcelona model |
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20 | (1) |
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21 | (1) |
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22 | (1) |
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22 | (1) |
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2.3 Calibration for the size of damage process zone |
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23 | (18) |
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2.3.1 Experiments performed with the white-light speckle method and four-point shear beam |
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24 | (1) |
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24 | (1) |
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2.3.1.2 Experimental results |
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24 | (1) |
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2.3.2 Numerical results obtained with finite-element analysis |
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25 | (9) |
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2.3.2.1 Discretization of the double-notched, four-point shear beam |
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27 | (1) |
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2.3.2.2 Numerical results obtained with double notched beam |
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28 | (6) |
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2.3.3 Numerical results obtained with single-notched beam |
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34 | (4) |
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2.3.4 Comparisons of the experimental results with the numerical results |
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38 | (1) |
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38 | (3) |
3 Trajectory optimization for offshore wells and numerical prediction of casing failure due to production-induced compaction |
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41 | (16) |
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41 | (1) |
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3.2 Geotechnical casing design and optimal trajectories |
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41 | (2) |
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43 | (1) |
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44 | (4) |
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44 | (1) |
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45 | (2) |
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3.4.3 Loads and boundary conditions of the global model |
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47 | (1) |
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3.5 Numerical results of the global model |
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48 | (2) |
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3.6 General principle of submodeling techniques |
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50 | (1) |
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51 | (2) |
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3.7.1 Local model results |
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53 | (1) |
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3.8 Secondary submodel and casing integrity estimate |
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53 | (1) |
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54 | (3) |
4 Numerical scheme for calculation of shear failure gradient of wellbore and its applications |
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57 | (24) |
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57 | (1) |
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4.2 Scheme for calculation of SFG with 3D FEM |
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58 | (1) |
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4.3 Numerical solution of SFG and its comparison with results obtained by Drillworks |
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59 | (8) |
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4.3.1 The model geometry of the benchmark and its FEM mesh |
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59 | (3) |
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4.3.2 Loads and parameters of material properties |
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62 | (1) |
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4.3.3 Abaqus submodel calculation and results with Mohr-Coulomb model |
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62 | (3) |
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4.3.4 Results comparison with Drucker-Prager criterion between Abaqus and Drillworks |
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65 | (2) |
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67 | (1) |
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4.4 Comparison of accuracy of stress solution of a cylinder obtained by Abaqus and its analytical solution |
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67 | (1) |
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68 | (10) |
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4.5.1 Pore pressure analysis with Drillworks |
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69 | (1) |
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4.5.2 The 3D computational model |
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70 | (13) |
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4.5.2.1 Global model: Geometry, boundary condition, and loads |
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70 | (3) |
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4.5.2.2 Numerical results of the global model |
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73 | (1) |
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4.5.2.3 Vector-distribution of principal stresses |
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74 | (1) |
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4.5.2.4 Submodel: Geometry, boundary condition, and loads |
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74 | (1) |
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4.5.2.5 Numerical results of the submodel |
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75 | (3) |
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78 | (3) |
5 Mud weight design for horizontal wells in shallow loose sand reservoir with the finite element method |
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81 | (14) |
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81 | (1) |
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5.2 Geological setting and geological factors affecting geomechanics |
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82 | (1) |
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5.3 Pore pressure and initial geostress field: Prediction made with logging data and one-dimensional software |
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83 | (1) |
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83 | (1) |
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5.3.2 Stress field orientation |
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83 | (1) |
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5.3.3 Overburden gradient (vertical in-situ stress) |
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84 | (1) |
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5.3.4 Minimum in-situ stress |
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84 | (1) |
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5.3.5 Maximum in-situ horizontal stress |
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84 | (1) |
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5.4 Formation strength and geomechanical properties |
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84 | (3) |
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87 | (1) |
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5.6 Numerical results with finite elemenfmodeling |
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88 | (4) |
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92 | (3) |
6 A case study of mud weight design with finite element method for subsalt wells |
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95 | (24) |
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95 | (2) |
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6.2 Brief review of concepts of MWW and numerical procedure for its 3D solution |
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97 | (2) |
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6.2.1 Brief review of mud weight window concepts |
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97 | (2) |
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6.2.2 Numerical procedure for calculating MWW with 3D FEM |
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99 | (1) |
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6.3 Global model description and numerical results |
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99 | (8) |
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99 | (7) |
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6.3.2 Numerical results of the global model |
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106 | (1) |
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6.4 Submodel description and numerical results |
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107 | (2) |
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107 | (2) |
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6.4.2 Numerical results of SFG and FG obtained with the secondary submodel |
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109 | (1) |
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6.5 Stress pattern analysis for saltbase formation |
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109 | (6) |
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6.6 Alternative validation on stress pattern within saltbase formation |
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115 | (1) |
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6.7 A solution with 1D tool Drillworks and its comparison with 3D solution |
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115 | (2) |
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117 | (2) |
7 Numerical calculation of stress rotation caused by salt creep and pore pressure depletion |
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119 | (20) |
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119 | (2) |
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7.2 Stress analysis for a subsalt well |
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121 | (4) |
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7.2.1 Computational model |
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121 | (1) |
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122 | (3) |
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7.3 Variation of stress orientation caused by injection and production |
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125 | (5) |
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7.3.1 The model used in the computation |
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125 | (1) |
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125 | (5) |
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7.3.2.1 Numerical results of stress rotation with isotropic permeability and injection |
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125 | (1) |
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7.3.2.2 Numerical results on stress rotation with isotropic permeability and production |
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125 | (2) |
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7.3.2.3 Numerical results on stress rotation with orthotropic permeability and injection |
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127 | (2) |
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7.3.2.4 Numerical results on stress rotation with orthotropic permeability and production |
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129 | (1) |
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130 | (1) |
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7.4 Variation of stress orientation caused by pore pressure depletion: Case study in Ekofisk field |
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130 | (6) |
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7.4.1 The numerical model |
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130 | (2) |
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132 | (4) |
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136 | (3) |
8 Numerical analysis of casing failure under non-uniform loading in subsalt wells |
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139 | (16) |
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139 | (2) |
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8.2 Finite element model and analysis of casing integrity |
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141 | (8) |
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8.2.1 Numerical analysis of global model at field scale |
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142 | (2) |
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142 | (1) |
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142 | (2) |
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8.2.1.3 Loads and boundary conditions of the global model |
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144 | (1) |
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8.2.1.4 Numerical results of global model |
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144 | (1) |
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8.2.2 Submodel and casing integrity estimate |
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144 | (12) |
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144 | (1) |
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145 | (1) |
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8.2.2.3 Loads specific to the submodel |
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146 | (1) |
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8.2.2.4 Numerical results of the submodel: Stress distribution around the borehole before cementing |
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146 | (1) |
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8.2.2.5 Numerical results of submodel: Stress distribution within the concrete ring and casing |
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147 | (2) |
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8.3 Numerical results of enhancement measure |
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149 | (2) |
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151 | (4) |
9 Numerical predictions on critical pressure drawdown and sand production for wells in weak formations |
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155 | (20) |
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155 | (1) |
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9.2 Model description and numerical calculation |
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156 | (3) |
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9.2.1 Numerical calculation with global model |
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156 | (3) |
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9.2.1.1 Values of material parameters |
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157 | (1) |
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9.2.1.2 Loads and boundary conditions of the global model |
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157 | (1) |
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158 | (1) |
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9.2.1.4 Numerical results of global model |
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159 | (1) |
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9.3 Case 1: Prediction of CVPDD for a well with openhole completion |
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159 | (4) |
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9.3.1 Submodel 1: Geometry of the submodel |
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159 | (1) |
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9.3.2 Submodel 1: Boundary condition and loads |
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159 | (1) |
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9.3.3 Numerical scheme of the calculation |
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159 | (1) |
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160 | (3) |
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9.4 Case 2: Numerical prediction of CVPDD for well with casing completion |
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163 | (5) |
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164 | (1) |
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9.4.2 Case 2A: Casing with perforation of 8 shots per 0.3048 m |
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165 | (1) |
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9.4.2.1 Description of the model: Case 2A |
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165 | (1) |
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9.4.2.2 Numerical results of Case 2A |
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166 | (1) |
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9.4.3 Case 2B: Casing with perforation of 4 shots per 0.348 m (per ft) |
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166 | (2) |
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9.4.3.1 Geometry of the model: Case 2B |
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166 | (1) |
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9.4.3.2 Numerical results of Case 2B |
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167 | (1) |
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168 | (1) |
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9.5 Numerical prediction of sanding production |
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168 | (4) |
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9.5.1 Model description and simplifications |
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168 | (1) |
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9.5.2 Numerical procedure for prediction of sand production |
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169 | (1) |
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9.5.3 An example of prediction of sand production |
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170 | (2) |
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172 | (3) |
10 Cohesive crack for quasi-brittle fracture and numerical simulation of hydraulic fracture |
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175 | (18) |
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175 | (1) |
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10.2 Cohesive crack for quasi-brittle materials |
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175 | (6) |
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10.2.1 Concepts of cohesive crack |
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175 | (1) |
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10.2.2 Influence of hydraulic pressure on yielding conditions |
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176 | (1) |
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10.2.3 Cohesive models for mixed-mode fracture |
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177 | (1) |
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10.2.4 Cohesive model of effective opening for mixed-mode crack |
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177 | (2) |
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10.2.5 Cohesive law formulated in standard dissipative system |
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179 | (2) |
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10.2.5.1 Elastoplastic damage interface model |
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180 | (1) |
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10.2.5.2 Viscoplastic interface crack model |
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181 | (1) |
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10.3 Cohesive element coupled with pore pressure for simulation of hydraulic fracture of rock |
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181 | (3) |
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10.3.1 Nodal sequence and stress components of cohesive element |
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181 | (1) |
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10.3.2 Fluid flow model of the cohesive element |
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182 | (2) |
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10.3.2.1 Defining pore fluid flow properties |
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182 | (1) |
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182 | (1) |
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183 | (1) |
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183 | (1) |
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10.3.2.5 Normal flow across gap surfaces |
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183 | (1) |
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10.4 Numerical simulation of hydraulic fracturing with 3-dimensional finite element method |
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184 | (5) |
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10.4.1 Numerical procedure for the numerical simulation of hydraulic fracturing |
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184 | (1) |
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10.4.2 Finite element model |
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184 | (3) |
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10.4.2.1 Geometry and mesh |
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184 | (1) |
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10.4.2.2 Initial conditions |
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184 | (1) |
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10.4.2.3 Boundary condition |
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185 | (1) |
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185 | (1) |
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10.4.2.5 Values of material parameter |
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185 | (2) |
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187 | (2) |
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189 | (4) |
11 Special applications in formation stimulation and injection modeling |
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193 | (28) |
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193 | (1) |
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194 | (2) |
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11.3 Special applications |
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196 | (1) |
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11.4 Unconventional shale gas reservoirs |
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196 | (4) |
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11.4.1 Theoretical basis in simulation |
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196 | (1) |
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11.4.2 An equivalent shale gas hydraulic fracturing model |
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197 | (2) |
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11.4.3 Leakoff effect for a contained fracture |
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199 | (1) |
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11.4.4 Concluding remarks |
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199 | (1) |
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11.5 Cuttings re-injection |
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200 | (6) |
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11.5.1 Theoretical basis in simulation |
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200 | (1) |
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11.5.2 An equivalent cuttings re-injection model |
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200 | (1) |
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11.5.3 Key input parameters for cuttings re-injection modeling |
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201 | (1) |
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11.5.4 Multiple fracture modeling |
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202 | (2) |
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11.5.5 Net pressure responses in cyclic injection |
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204 | (2) |
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11.5.6 Concluding remarks |
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206 | (1) |
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11.6 Fracture packing in unconsolidated formation |
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206 | (6) |
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11.6.1 Theoretical basis in simulation |
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206 | (1) |
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11.6.2 An equivalent frac-pack model |
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206 | (2) |
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11.6.3 Key input parameters for frac-pack modeling |
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208 | (1) |
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11.6.4 Fracture re-growth during the frac-pack process |
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208 | (3) |
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11.6.5 Concluding remarks |
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211 | (1) |
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11.7 Produced water re-injection |
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212 | (9) |
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11.7.1 Theoretical basis in simulation |
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212 | (1) |
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11.7.2 An equivalent produced water re-injection model |
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212 | (1) |
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11.7.3 Numerical modeling of cross flow in produced water transport |
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213 | (5) |
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11.7.4 Analytical modeling of cross flow and its effect on produced water transport |
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218 | (1) |
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11.7.5 Concluding remarks |
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219 | (2) |
Subject index |
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221 | (12) |
Book series page |
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233 | |