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A new approach for phase transitions in miscible multi-phase flow in porous media

机译：多孔介质中混相多相流相变的新方法

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摘要

The tightly coupled, strongly nonlinear nature of non-isothermal multi-phase flow in porous media poses a tough challenge for numerical simulation. This trait is even more pronounced, if miscibility is also considered. A primary reason why inclusion of miscibility tends to be problematic are the difficulties stemming from phase transitions: on the one hand, phase transitions need to be included since the presence or absence of fluid phases has a major impact on the flow behavior; on the other hand, convergence of the nonlinear solver may be severely affected if they are not handled robustly. In this work, we present a mathematically sound approach to include phase transitions in the nonlinear system of equations: first, the transition conditions are formulated as a set of local inequality constraints, which are then directly integrated into the nonlinear solver using a nonlinear complementarity function. Under this scheme, Newton-Raphson solvers exhibit considerably more robust convergence behaviour compared to some previous approaches, which is then illustrated by several numerical examples.
机译：多孔介质中非等温多相流的紧密耦合，强非线性性质对数值模拟提出了严峻挑战。如果还考虑互溶性，则该特征更加明显。相混性趋于成问题的一个主要原因是由于相变带来的困难：一方面，由于流体相的存在或不存在都会对流动特性产生重大影响，因此必须包括相变。另一方面，如果非线性求解器的收敛性不强，可能会严重影响其收敛性。在这项工作中，我们提出一种数学上合理的方法，将方程组的相变包括在非线性系统中：首先，将转换条件公式化为一组局部不等式约束，然后使用非线性互补函数将其直接集成到非线性求解器中。在这种方案下，与以前的方法相比，牛顿-拉夫森求解器表现出了更强健的收敛性能，然后通过几个数值示例进行说明。

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  • 来源
    《Advances in Water Resources》 |2011年第8期|p.957-966|共10页
  • 作者

    A. Lauser; C. Hager; R. Helmig; B. Wohlmuth;

  • 作者单位

    Institute of Hydraulic Engineering (MS), Universitat Stuttgart, Pfaffenwaldring 61, 70569 Stuttgart, Germany;

    Institute of Applied Analysis and Numerical Simulation (IANS), Universitat Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany;

    Institute of Hydraulic Engineering (MS), Universitat Stuttgart, Pfaffenwaldring 61, 70569 Stuttgart, Germany;

    Institute of Applied Analysis and Numerical Simulation (IANS), Universitat Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany;

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  • 正文语种 eng
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  • 关键词

    phase transition; phase state; multi-phase flow; semismooth newton; porous media;

    机译：相变;相态;多相流;半光滑牛顿;多孔介质;

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