Simulation of thermoporoelastic medium with damage

A. S. Meretin ; E. B. Savenkov

Matematičeskoe modelirovanie, Tome 32 (2020) no. 7, pp. 59-76.

Résumé

In this paper we consider a numerical simulation of thermoporoelastic medium with damage. The model generalizes the classical Biot model for poroelastic medium evolution to the case of thermoelastic effects. Damage of the medium is simulated within the framework of continuum damage mechanics, where state of the medium is described by scalar damage parameter, which affects on elastic and flow properties. The system of governing equations consists of fundamental mass, momentum and energy conservation laws and is closed by thermodynamically-consistent constitutive relations. Moreover, the energy expression takes into account its changing due to formation of damaged zones. The computational algorithm is based on the finite element method. The “monolithic” approach is used, which assumes that all groups of equations (mechanics, heat transfer and flow) are solved simultaneously without splitting on physical processes and / or iteration coupling between groups of equations. The model is approximated by a fully implicit scheme. Damage parameter evolution depending on the stress-strain state can be described within the framework of instant or finite-time kinetics. The paper briefly describes the mathematical model. The computational algorithm and its implementation features are described in detail. Significant part of the work is related to the application of the developed approaches for solving a number of model and realistic threedimensional problems. The main field of the model and algorithm application is the analysis of geomechanical problems of thermal enchanced oil recovery methods, which require a consistent description of the elastic, filtration and thermal fields dynamics coupled with medium damage evolution.

Détail

Keywords: thermoporoelasticity, Biot, damage, thermodynamic consistency, ColemanNoll procedure, finite element method.

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