We have developed continuous and discrete-time finite-element (FE) methods to solve an initial boundary-value problem for the thermo-poroelasticity wave equation based on the combined Biot/Lord-Shulman (LS) theories to describe the porous and thermal effects, respectively. In particular, the LS model, which includes a Maxwell-Vernotte-Cattaneo relaxation term, leads to a hyperbolic heat equation, thus avoiding infinite signal velocities. The FE methods are formulated on a bounded domain with absorbing boundary conditions at the artificial boundaries. The dynamical equations predict four propagation modes, a fast P (P1) wave, a Biot slow (P2) wave, a thermal (T) wave, and a shear (S) wave. The spatial discretization uses globally continuous bilinear polynomials to represent solid displacements and temperature, whereas the vector part of the Raviart-Thomas-Nedelec of zero order is used to represent fluid displacements. First, a priori optimal error estimates are derived for the continuous-time FE method, and then an explicit conditionally stable discrete-time FE method is defined and analyzed. The explicit FE algorithm is implemented in one dimension to analyze the behavior of the P1, P2, and T waves. The algorithms can be useful for a better understanding of seismic waves in hydrocarbon reservoirs and crustal rocks, whose description is mainly based on the assumption of isothermal wave propagation.

You do not have access to this content, please speak to your institutional administrator if you feel you should have access.