Numerical simulation of seismic waves in porous media components

This work presents a mathematical algorithm for modeling the propagation of poroelastic waves. We have shown how the classical Biot equations can be put into Ursin’s form in a plane-layered 3D porous medium. Using this form, we have derived explicit for- mulas that can be used as the basis of an efficient computational algorithm. To validate the algorithm, numerical simulations were performed using both the poroelastic and equivalent elastic models. The results obtained confirmed the proposed algorithm’s reliability, identify- ing the main wave events in both low-frequency and high-frequency regimes in the reservoir and laboratory scales, respectively. We have also illustrated the influence of some physical parameters on the attenuation and dispersion of the slow wave.

A monolithic phase-field model of a fluid-driven fracture in a nonlinear poroelastic medium

In this paper, we present a full phase-field model for a fluid-driven fracture in a nonlinear poroelastic medium. The nonlinearity arises in the Biot equations when the permeability depends on porosity. This extends previous work (see Mikelić et al. Phase-field modeling of a fluid-driven fracture in a poroelastic medium. Comput Geosci 2015; 19: 1171–1195), where a fully coupled system is considered for the pressure, displacement, and phase field. For the extended system, we follow a similar approach: we introduce, for a given pressure, an energy functional, from which we derive the equations for the displacement and phase field. We establish the existence of a solution of the incremental problem through convergence of a finite-dimensional Galerkin approximation. Furthermore, we construct the corresponding Lyapunov functional, which is related to the free energy. Computational results are provided that demonstrate the effectiveness of this approach in treating fluid-driven fracture propagation. Specifically, our numerical findings confirm differences with test cases using the linear Biot equations.

The Biot Model for Anisotropic Poro-Elastic Media: The Viscoelastic Fluid Case

We show that an existence theorem for the completely anisotropic, time-harmonic poro-elastic boundary value problem can be established for the linear anisotropic Biot equations. Using the existence of these solutions, we present a scheme for solving the quasi-linear system for a nonlinear fluid–fluid viscosity such as the Carreau type.