Sequential Methods for Coupled Geomechanics and Multiphase Flow

62 CHAPTER 3. STABILITY OF THE DRAINED AND UNDRAINED SPLITS
Dimensionless pressure (P−P i )/∆p i
Dimensionless pressure (P−P i )/∆p i
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
Case 3.1 The Terzaghi Problem, τ=0.83
Analytic sol
Fully coupled
Undrained
Drained
0.2
0 0.1 0.2 0.3 0.4 0.5
1
0.9
0.8
0.7
0.6
0.5
Dimensionless time (t d =4c v t/(Lz) 2 )
Case 3.1 The Terzaghi Problem, τ=1.21
Analytic sol
Fully coupled
Undrained
Drained
0.4
0 0.1 0.2 0.3 0.4
Dimensionless time (t d =4c v t/(Lz) 2 )
Figure 3.9: Case 3.1 (the Terzaghi problem). Evolution of the dimensionless pressure as a
function of dimensionless time. ∆pi is the pressure rise at t = 0, Lz is the vertical extent
of the reservoir, t is the simulation time, and cv is the consolidation coefficient. The results
from the fully coupled, drained, and undrained methods are shown. Top: coupling strength
τ = 0.83. Bottom: coupling strength τ = 1.21.