A porosity-gradient replacement approach for computational simulation of chemical-dissolution front propagation in fluid-saturated porous media including pore-fluid compressibility
A porosity-gradient replacement approach for computational simulation of chemical-dissolution front propagation in fluid-saturated porous media including pore-fluid compressibility
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DOI：
10.1007/s10596-012-9285-3
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发表时间：
2012-02
影响因子：
2.5
通讯作者：
Chong-bin Zhao;L. Reid;K. Regenauer‐Lieb;T. Poulet
中科院分区：
文献类型：
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作者：
Chong-bin Zhao;L. Reid;K. Regenauer‐Lieb;T. Poulet
在处理流体饱和多孔介质中的化学溶解前沿传播问题时，由介质的孔隙度表示的化学溶解前沿可能具有非常陡的斜率（即，非常大的孔隙度梯度），这取决于矿物溶解比，该矿物溶解比被定义为孔隙流体中溶解矿物的平衡浓度与固体基质中可溶解矿物的固体摩尔密度之比。当矿物溶解率趋于零时，孔隙度梯度的理论值在化学溶解前沿趋于无穷大。当用常规有限元法求解流体饱和多孔介质中的化学溶解问题时，即使对于地球化学系统中常见的矿物溶解率很小的情况，孔隙度梯度也会大到使解难以收敛。为了提高解的收敛速度，孔隙度梯度替换方法，其中涉及孔隙度梯度计算的术语被替换为一个新的术语组成的孔隙流体密度梯度和压力梯度计算，然后将其纳入有限元方法在这项研究中。通过对一个基准问题的数值计算结果与理论解的比较，证明了该方法在求解含孔隙流体可压缩性的饱和多孔介质中化学溶解前沿传播问题时，不仅可以避免解的发散，而且可以得到精确的模拟结果.
In dealing with chemical-dissolution-front propagation problems in fluid-saturated porous media, the chemical dissolution front represented by the porosity of the medium may have a very steep slope (i.e., a very large porosity gradient) at the dissolution front, depending on the mineral dissolution ratio that is defined as the equilibrium concentration of the dissolved minerals in the pore-fluid to the solid molar density of the dissolvable minerals in the solid matrix. When the mineral dissolution ratio approaches zero, the theoretical value of the porosity gradient tends to infinity at the chemical dissolution front. Even for a very small value of the mineral dissolution ratio, which is very common in geochemical systems, the porosity gradient can be large enough to cause the solution hard to converge when the conventional finite element method is used to solve a chemical dissolution problem in a fluid-saturated porous medium where the pore-fluid is compressible. To improve the convergent speed of solution, a porosity-gradient replacement approach, in which the term involving porosity-gradient computation is replaced by a new term consisting of pore-fluid density-gradient and pressure-gradient computation, is first proposed and then incorporated into the finite element method in this study. Through comparing the numerical results obtained from the proposed approach with the theoretical solutions for a benchmark problem, it has been demonstrated that not only can the solution divergence be avoid, but also the accurate simulation results can be obtained when the proposed porosity-gradient replacement approach is used to solve chemical-dissolution-front propagation problems in fluid-saturated porous media including pore-fluid compressibility.