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Simulation of a Thermoporoelastic Medium Taking the Damage into Consideration
Mathematical Models and Computer Simulations Pub Date : 2021-04-23 , DOI: 10.1134/s2070048221020113
A. C. Meretin , E. B. Savenkov

Abstract—

The issues of the mathematical modeling of a thermoporoelastic medium taking its damage into account are considered. The employed model generalizes the classical Biot model simulating the behavior of a poroelastic medium taking the thermoelastic effects into account. In order to describe the damage of the medium, the approach of continual damage mechanics is used, in which the state of the medium is described by the scalar damage parameter, which affects the elastic and poroperm characteristics of the medium. The system of the governing equations for the model consists of the fundamental mass, momentum, and energy conservation laws and is closed by thermodynamically consistent constitutive relations. Moreover, the medium’s energy expression takes into account its changes due to the formation of damaged zones. The computational algorithm is based on the finite-element method. A monolithic approach is used, which assumes that all groups of equations (mechanics, heat transfer, and flow) are solved simultaneously without being split into physical processes and/or iterations between groups of equations. The system of equations of thermoporoelasticity is approximated by a fully implicit scheme. The damage parameter’s evolution depending on the stress-strain state of the medium can be described in terms of both instant and finite-time kinetics. This paper briefly describes the mathematical model and presents a detailed description of the computational algorithm and its implementation. A significant part of the study is devoted to the application of the developed approaches for solving several model and realistic three-dimensional problems. The analysis of the geomechanical problems of thermal enhanced oil recovery methods, which require a consistent description of the elastic, filtration, and thermal fields’ dynamics taking into account the evolution of the medium’s fracture, is considered to be the main field of the application of the model and algorithm.



中文翻译:

考虑损伤的热多孔弹性介质的模拟

摘要-

考虑了考虑到其损害的热多孔弹性介质的数学建模问题。所采用的模型推广了经典的Biot模型,并考虑了热弹性效应,从而模拟了多孔弹性介质的行为。为了描述介质的损坏,使用连续损伤力学的方法,其中介质的状态由标量损伤参数来描述,这会影响介质的弹性和多孔性。该模型的控制方程组由基本质量,动量和能量守恒定律组成,并由热力学一致的本构关系封闭。此外,介质的能量表达考虑了由于损坏区域的形成而引起的变化。该计算算法基于有限元方法。使用一种整体方法,该方法假设所有方程组(力学,传热和流动)都可以同时求解,而无需拆分为物理过程和/或方程组之间的迭代。热孔隙弹性方程组由一个完全隐式的方案近似。可以根据瞬时和有限时间动力学来描述取决于介质的应力-应变状态的损伤参数的演变。本文简要介绍了数学模型,并对计算算法及其实现进行了详细描述。该研究的重要部分致力于解决某些模型和实际的三维问题的已开发方法的应用。

更新日期:2021-04-23
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