Abstract A two-phase model and its application to wavefields numerical simulation are discussed in the context of modeling of compressible fluid flows in elastic porous media. The derivation of the model is based on a theory of thermodynamically compatible systems and on a model of nonlinear elastoplasticity combined with a two-phase compressible fluid flow model. The governing equations of the model include phase mass conservation laws, a total momentum conservation law, an equation for the relative velocities of the phases, an equation for mixture distortion, and a balance equation for porosity. They form a hyperbolic system of conservation equations that satisfy the fundamental laws of thermodynamics. Two types of phase interaction are introduced in the model: phase pressure relaxation to a common value and interfacial friction. Inelastic deformations also can be accounted for by source terms in the equation for distortion. The thus formulated model can be used for studying general compressible fluid flows in a deformable elastoplastic porous medium, and for modeling wave propagation in a saturated porous medium. Governing equations for small-amplitude wave propagation in a uniform porous medium saturated with a single fluid are derived. They form a first-order hyperbolic PDE system written in terms of stress and velocities and, like in Biot’s model, predict three type of waves existing in real fluid-saturated porous media: fast and slow longitudinal waves and shear waves. For the numerical solution of these equations, an efficient numerical method based on a staggered-grid finite difference scheme is used. The results of solving some numerical test problems are presented and discussed.

中文翻译：

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基于热力学相容系统理论的饱和弹性多孔介质波场建模

摘要 在弹性多孔介质中可压缩流体流动建模的背景下，讨论了两相模型及其在波场数值模拟中的应用。该模型的推导基于热力学兼容系统理论和非线性弹塑性模型与两相可压缩流体流动模型相结合。该模型的控制方程包括相质量守恒定律、总动量守恒定律、相相对速度方程、混合畸变方程和孔隙度平衡方程。它们形成了满足热力学基本定律的守恒方程的双曲系统。模型中引入了两种类型的相相互作用：相压力松弛到共同值和界面摩擦。非弹性变形也可以通过变形方程中的源项来解释。如此建立的模型可用于研究可变形弹塑性多孔介质中的一般可压缩流体流动，以及用于模拟饱和多孔介质中的波传播。导出了在单一流体饱和的均匀多孔介质中小振幅波传播的控制方程。它们形成了一个用应力和速度写成的一阶双曲线 PDE 系统，并且与 Biot 的模型一样，预测了真实流体饱和多孔介质中存在的三种类型的波：快、慢纵波和横波。对于这些方程的数值解，使用了一种基于交错网格有限差分格式的有效数值方法。