Sequential Methods for Coupled Geomechanics and Multiphase Flow

108 CHAPTER 4. CONVERGENCE OF THE DRAINED AND UNDRAINED SPLITS
Dimensionless distance (z/Lz)
Dimensionless distance (z/Lz)
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
Undrained for incompressible fluid (1 iteration)
∆ t d =2.1×10 −2
∆ t d =4.2×10 −3
∆ t d =2.1×10 −3
∆ t d =4.3×10 −4
∆ t d =2.1×10 −4
∆ t d =1.07×10 −4
∆ t d =5.3×10 −5
True solution
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Dimensionless pressure P =(P−P )/∆p
d i i
Undrained for incompressible fluid (1 iteration)
∆ t d =2.1×10 −2
∆ t d =2.1×10 −3
∆ t d =2.1×10 −4
∆ t d =5.3×10 −5
True solution
0 5 10 15 20
x 10 −3
0
Dimensionless displacement (u =u/L )
d z
Figure 4.11: Spatial distributions of pressure (top) and displacement (bottom) for an incompressible
fluid. The undrained split does not converge to the true solutions. There is
no pressure jump and displacement by the overburden at early time.