Sequential Methods for Coupled Geomechanics and Multiphase Flow

144 CHAPTER 5. FIXED-STRAIN AND FIXED-STRESS SPLITS
Dimensionless pressure (P/P i )
Dimensionless pressure (P/P i )
0.8
0.75
0.7
0.65
Case 5.2, τ=0.95
Fixed strain ∆ t d =4.4 × 10 −5
Fixed strain ∆ t d =4.4 × 10 −2
0.6
0 0.2 0.4 0.6 0.8 1
Dimensionless time (pore volume produced)
0.8
0.75
0.7
0.65
Case 5.2, τ=1.05
Fixed strain ∆ t d =4.4 × 10 −5
Fixed strain ∆ t d =4.4 × 10 −2
0.6
0 0.2 0.4 0.6 0.8 1
Dimensionless time (pore volume produced)
Figure 5.4: Case 5.2 (1D injection–production problem). Results are shown for the fixedstrain
split, with two different coupling strengths: τ = 0.95 (top), and τ = 1.05 (bottom),
and two very different time step sizes. The stability of the fixed-strain split is independent
of time step size. The fixed-strain split is stable if τ < 1 and unstable if τ > 1, regardless
of time step size.