This article presents an accurate porosity-velocity-concentration approach, in which porosity, pore-fluid velocity and the concentration of dissolvable substances in the pore fluid are selected as four primary unknown variables for solving reactive mass transport problems involving chemical dissolution in fluid-saturated porous media with arbitrarily initial porosity distributions. The first advantage of using the proposed approach is that since pore-fluid velocity, instead of pore-fluid pressure, is selected as the primary unknown variable to describe the pore-fluid flow process, the pore-fluid velocity obtained from the proposed approach is more accurate than that obtained from the numerical simulation, in which pore-fluid pressure is selected as the primary unknown variable to describe the pore-fluid flow. The second advantage of using the proposed approach is that because the property matrices of a four-node rectangular element are precisely calculated in a purely mathematical way, the overall accuracy of numerical solutions can be ensured. After the proposed approach is verified by a benchmark problem, it has been applied for solving reactive mass transport problems involving chemical dissolution in fluid-saturated porous media with three different kinds of initial porosity distributions. It has been demonstrated that: (1) the proposed approach can produce highly-accurate numerical solutions for solving reactive mass transport problems involving chemical dissolution in fluid-saturated porous media with arbitrarily initial porosity distributions; (2) the initial porosity distribution in a porous medium can have remarkable effects on the reactive mass transport process in the porous medium; (3) the porosity and dimensionless concentration fronts propagate from the entrance to the exit of the problem domain, which is identical to the pore-fluid flow direction.

中文翻译：

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一种精确的孔隙度-速度-浓度方法，用于解决涉及具有任意初始孔隙度分布的流体饱和多孔介质中的化学溶解的反应性传质问题

本文提出了一种精确的孔隙度-速度-浓度方法，其中孔隙度、孔隙-流体速度和孔隙流体中可溶解物质的浓度被选为四个主要未知变量，用于解决涉及饱和流体中化学溶解的反应传质问题。具有任意初始孔隙率分布的多孔介质。使用该方法的第一个优点是，由于选择孔隙流体速度而不是孔隙流体压力作为主要未知变量来描述孔隙流体流动过程，因此从该方法获得的孔隙流体速度为比数值模拟更准确，其中选择孔隙流体压力作为主要未知变量来描述孔隙流体流动。使用该方法的第二个优点是，由于四节点矩形单元的属性矩阵是以纯数学方式精确计算的，因此可以保证数值解的整体精度。在通过基准问题验证所提出的方法后，它已被应用于解决涉及化学溶解在具有三种不同初始孔隙度分布的流体饱和多孔介质中的反应传质问题。已经证明：（1）所提出的方法可以产生高精度的数值解来解决反应性传质问题，该问题涉及具有任意初始孔隙率分布的流体饱和多孔介质中的化学溶解；(2) 多孔介质中的初始孔隙度分布对多孔介质中的反应传质过程有显着影响；(3) 孔隙度和无量纲浓度前沿从问题域的入口传播到出口，与孔隙流体流动方向相同。