Sequential Methods for Coupled Geomechanics and Multiphase Flow

66 CHAPTER 3. STABILITY OF THE DRAINED AND UNDRAINED SPLITS
Dimensionless pressure (P/P i )
Dimensionless pressure (P/P i )
0.8
0.75
0.7
0.65
Case 3.2, τ=0.95
Drained ∆ t d =4.4 × 10 −5
Drained ∆ 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 3.2, τ=1.05
Drained ∆ t d =4.4 × 10 −5
Drained ∆ t d =4.4 × 10 −2
0.6
0 0.2 0.4 0.6 0.8 1
Dimensionless time (pore volume produced)
Figure 3.11: Case 3.2 (1D injection–production problem). Results are shown for the drained
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 drained split is independent of the time
step size. The drained split is stable if τ < 1 and unstable if τ > 1, regardless of the time
step size.