The mathematical structure of multiphase thermal models of flow in porous media
The mathematical structure of multiphase thermal models of flow in porous media
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多孔介质流动多相热模型的数学结构
DOI：
10.1098/rspa.2008.0268
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
N. Nikiforakis
中科院分区：
文献类型：
--
作者：
D. V. van Odyck;J. Bell;F. Monmont;N. Nikiforakis
本文讨论了多孔介质中多组分、两相热流体流动的数学模型方程的建立和数值解。流体模型由单个化学组分（物种）守恒方程、体积流速的达西定律和焓的能量方程组成。该模型是封闭的状态方程和相平衡条件，确定的化学成分到相的分布。结果表明，在扩散力的情况下，流动方程可以分裂成一个系统的双曲守恒定律的物种和焓和压力的抛物方程。这种分解形成了一个顺序制定的基础上，压力方程是隐式求解，然后明确解决的组件和焓守恒定律。一个数值方法的基础上，这个顺序制定的，并用于演示一些典型的流动行为，发生在流体注入到油藏。
This paper is concerned with the formulation and numerical solution of equations for modelling multicomponent, two-phase, thermal fluid flow in porous media. The fluid model consists of individual chemical component (species) conservation equations, Darcy's law for volumetric flow rates and an energy equation in terms of enthalpy. The model is closed with an equation of state and phase equilibrium conditions that determine the distribution of the chemical components into phases. It is shown that, in the absence of diffusive forces, the flow equations can be split into a system of hyperbolic conservation laws for the species and enthalpy and a parabolic equation for pressure. This decomposition forms the basis of a sequential formulation where the pressure equation is solved implicitly and then the component and enthalpy conservation laws are solved explicitly. A numerical method based on this sequential formulation is presented and used to demonstrate some typical flow behaviour that occurs during fluid injection into a reservoir.