7. Concluding remarks

mesh consists of 7985 points and 15,539 elements. The domain lengths are 1 m�0.5 m. The

Figure 13 shows temperature field snapshots for different times increasing from top to bottom. The example simulates 0.1 s with a fully implicit approach. It is observed that a heating front quickly travels from left to right as expected due to the temperature gradient. The temperature scale in the color maps is from 0 to 1000�K. As a qualitative benchmark, the temperature

The example finalizes with a simple loosely coupled thermal and mechanics computation. It takes the temperature variation that the arch problem experiences as driving force for the mechanical problem. It assumes linear isotropic elasticity with E ¼ 30 Ksi and ν ¼ 0:3 and the coefficient of thermal dilatation <sup>β</sup> <sup>¼</sup> <sup>1</sup> � <sup>10</sup>�<sup>5</sup>K�<sup>1</sup> and the bulk modulus. The bottommost edges are clamped while the remainders are traction free. The right column in Figure 13 includes three snapshots that depict the mean stress. Dilatation grows from the upper-right corner

profile reported by Winget and Hughes [9] accords very well with the results herein.

erfc <sup>x</sup> 2 ffiffiffiffiffiffi κt <sup>∗</sup> p � �˚

<sup>∗</sup> <sup>¼</sup> <sup>0</sup>:0005 s in the calculation of the initial conditions.

K, (36)

<sup>∗</sup> for a plane semi-infinite medium. In the

initial temperature distribution was taken to be [9]:

240 Finite Element Method - Simulation, Numerical Analysis and Solution Techniques

which is the short-time linear solution at a time t

analysis, it is assumed κ ¼ 1 and t

Figure 12. The mesh for the arch-problem.

Figure 13. Temperature, Th, (left) and mean stress, Sm, snapshots (right).

T x; y; t <sup>∗</sup> ð Þ¼ 103

> This chapter introduced how to estimate stress-induced changes using elasticity simulations that are often performed through FE computations. It thus presented a formulation for linear thermo-poroelasticity. It covered the nonlinear energy equation as well. It also implemented a comprehensive MFEM on curved interfaces where the classical DN-DDM was employed to decouple the global SPP for elasticity, and steady single-phase flow. The coupled flow and geomechanics computation that utilizes the reconstructed model showed that this workflow is valuable to tackle realistic reservoir compaction and subsidence simulations. The research presented herein unfolds new prospects to further parallel codes for reservoir simulation coupled with geomechanics.
