Sequential Methods for Coupled Geomechanics and Multiphase Flow

List of Figures
1.1 Schematics of the fully coupled (top) and the iteratively coupled (bottom)
methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Ωt and Ω f
t
are the geometrical volumes of the solid and fluid at time t,
respectively. Even though the elementary solid system has the same fluid
mass content at time t, Ωt = Ω f
t , the solid system does not have the same
fluid mass content after time dt, Ωt+dt = Ω f
t+dt . wJ is the mass flux of fluid
phase J relative to the solid skeleton (Coussy, 1995). . . . . . . . . . . . . . 15
3.1 Element shape functions for displacement (left) and pressure (right) in 2-D 31
3.2 Sequential methods for flow and geomechanics. Left: drained split. Right:
undrained split. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 One-dimensional element with the finite-volume and finite-element methods.
h is the grid spacing, and j is the element index . . . . . . . . . . . . . . . . 38
3.4 The characteristic equations for the drained split when α = 1 (top), and
when α = 0.5 (bottom) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5 The characteristic equations for the undrained split when C0 ≤ 0 and C0 > 0. 45
3.6 Top: the associative flow rule under the assumption of maximum plastic
work (Coussy, 1995). Bottom: geometric interpretation of the algorithmic
plastic dissipation, which corresponds to the associative flow rule (Simo and
Hughes, 1998). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
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