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A numerical simulation method for dissolution in porous and fractured media

机译：多孔介质和压裂介质中溶解的数值模拟方法

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We describe an algorithm for simulating reactive flows in porous media, in which the pore space is mapped explicitly. Chemical reactions at the solid-fluid boundaries lead to dissolution (or precipitation), which makes it necessary to track the movement of the solid-fluid interface during the course of the simulation. We have developed a robust algorithm for constructing a piecewise continuous (C_1) surface, which enables a rapid remapping of the surface to the grid lines. The key components of the physics are the Navier-Stokes equations for fluid flow in the pore space, the convection-diffusion equation to describe the transport of chemical species, and rate equations to model the chemical kinetics at the solid surfaces. A lattice-Boltzmann model was used to simulate fluid flow in the pore space, with linear interpolation at the solid boundaries. A finite-difference scheme for the concentration field was developed, taking derivatives along the direction of the local fluid velocity. When the flow is not aligned with the grid this leads to much more accurate convective fluxes and surface concentrations than a standard Cartesian template. A robust algorithm for the surface reaction rates has been implemented, avoiding instabilities when the surface is close to a grid point. We report numerical tests of different aspects of the algorithm and assess the overall convergence of the method.
机译：我们描述了一种模拟多孔介质中反应流的算法，其中显式映射了孔隙空间。固-液边界处的化学反应导致溶解（或沉淀），这使得有必要在模拟过程中跟踪固-液界面的运动。我们已经开发了一种健壮的算法来构造分段连续（C_1）曲面，该曲面能够将曲面快速重新映射到网格线。物理学的主要组成部分是用于在孔隙空间中流动的Navier-Stokes方程，用于描述化学物质迁移的对流扩散方程以及用于模拟固体表面化学动力学的速率方程。使用格-玻尔兹曼模型来模拟孔空间中的流体流动，并在固体边界处进行线性插值。建立了浓度场的有限差分方案，沿局部流体速度的方向求导数。当流体不与网格对齐时，这将导致比标准笛卡尔模板更精确的对流通量和表面浓度。已经实施了一种针对表面反应速率的鲁棒算法，避免了当表面靠近网格点时的不稳定性。我们报告了算法不同方面的数值测试，并评估了该方法的总体收敛性。

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