Sequential Methods for Coupled Geomechanics and Multiphase Flow

A.3. NUMERICAL EXAMPLES 219
Table A.1: Input data for Case A.1
Property Value
Permeability (kp) 100 md
Porosity (φ0) 0.3
Drained modulus (Kdr) 6 GPa
Bulk density (ρb) 2400 kg m −3
Fluid density (ρf,0) 1000 kg m −3
Fluid viscosity (µ) 1.0 cp
Initial pressure (Pi) 2.125 MPa
Boundary pressure (Pbc) 2.125 MPa
Overburden (¯σ) 2×2.125 MPa
Grid spacing (∆z) 2 m
is clear that the instability propagates from the drainage boundary to the interior domain.
However, the combined finite-volume for flow and finite-elements for mechanics provide
stable and accurate pressures at early time that match the analytical solution, as shown
in the bottom of Figure A.2. For the combined finite-volume and finite-element method,
Figure 4.4 shows that the fully coupled method yields first-order accuracy in time.
A.3.2 Case A.2—Two dimensional plain strain strip footing consolidation
problem
At the top layer, the left part has an overburden, ¯σ = 2 × 2.125 MPa, and the right part
is a the drainage boundary. The domain is 160 m × 70 m with 16 × 7 grid blocks with
a plane strain mechanical problem. The domain is homogeneous. The overburden at the
drainage boundary is ¯σ = 2.125 MPa. No-horizontal displacement boundary conditions are
used on both sides and no-vertical displacement boundary condition is used at the bottom
for mechanics. The bulk density of the porous medium is ρb = 2400 kg m −1 . Initial fluid
pressure is Pi = 2.125 MPa. The fluid density and viscosity are ρf,0 = 1000 kg m −1 and
µ = 1.0 cp, respectively. The fluid compressibility is cf = 3.5 × 10 −8 Pa −1 . Permeability
is kp = 50 md, and porosity is φ0 = 0.3. Young’s modulus is E = 300 MPa, and Poisson’s
ratio is ν = 0.0. The Biot coefficient is b = 1.0. A no-flow boundary condition is applied to
the both sides, the bottom, and the left side of the top. No gravity is applied. The values