Sequential Methods for Coupled Geomechanics and Multiphase Flow

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$Drilling-induced tensile wall-fractures - Stanford University$

220 APPENDIX A. STABILITY IN SPACE for the input parameters are also listed in Table A.2. Table A.2: Input data for Case A.2 Property Value Permeability (kp) 50 md Porosity (φ0) 0.3 Young modulus (E) 300 MPa Poisson ratio (ν) 0 Biot coefficient (b) 1.0 Bulk density (ρb) 2400 kgm −3 Fluid density (ρf,0) 1000 kgm −3 Fluid viscosity (µ) 1.0 cp Initial pressure (Pi) 2.125 MPa Boundary pressure (Pbc) 2.125 MPa Left overburden (¯σ) 2×2.125 MPa Overburden at the drainage boundary (¯σ) 2.125 MPa Grid spacing (∆x) 10 m Grid spacing (∆z) 10 m Grid 16 × 7 The top of Figure A.3 shows that the fluid pressure is high at the left part, whereas it is low at the right part at early time, td = 3.7 × 10−19 , where td = 4 cvt LxLz . High pressure gradients occur around the central area. Large subsidence occurs under the left part on the top, where subsidence is positive (the bottom of Figures A.3 and A.4). But, the subsidence decreases at the drainage boundary, and there is a rebound of the surface showing negative displacements at the right part of the top layer because of dilation. Figure A.5 shows the convergence behaviors of pressure and displacement with respect to time step size. These results confirm first-order accuracy in time for both pressure and displacement. The combined finite-volume and finite-element scheme yields stable and accurate solutions at early time.
A.3. NUMERICAL EXAMPLES 221 Vertical directionz z (m) 10 20 30 40 50 60 6 4 2 0 −2 0 x 10 −3 20 Pressure distribution (P d ) 20 40 60 80 100 120 140 Horizontal direction x (m) 40 z (m) Vertical diplacement distribution 60 80 0 Figure A.3: Case A.2 Dimensionless pressure (top) and vertical displacement distributions (bottom) at early time, td = 3.7 × 10 −19 . Note that subsidence is positive. 50 100 x (m) 150 200 1.2 1.15 1.1 1.05 1 x 10 −3 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0
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SEQUENTIAL METHODS FOR COUPLED GEOM
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splits, are, at best, conditionally
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deeply. There was deep discussion o
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3 Stability of the Drained and Undr
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6.2.3 Undrained split . . . . . . .
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3.7 Left: the Terzaghi problem in 1
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2 CHAPTER 1. INTRODUCTION Reservoir
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4 CHAPTER 1. INTRODUCTION problem (
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6 CHAPTER 1. INTRODUCTION undrained
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10 CHAPTER 1. INTRODUCTION Even whe
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14 CHAPTER 2. FORMULATION full form
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16 CHAPTER 2. FORMULATION dE dt =
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18 CHAPTER 2. FORMULATION where the
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20 CHAPTER 2. FORMULATION coupling
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22 CHAPTER 2. FORMULATION where Div
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28 CHAPTER 3. STABILITY OF THE DRAI
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118 CHAPTER 5. FIXED-STRAIN AND FIX
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164 CHAPTER 6. COUPLED MULTIPHASE F
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Sequential Methods for Coupled Geomechanics and Multiphase Flow

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