Effects of different numerical algorithms on simulation of chemical dissolution-front instability in fluid-saturated porous rocks

不同数值算法对模拟饱水孔隙岩石中化学溶解面非稳定性的影响（英文）

Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them.The chemical dissolution-front instability problem in fluid-saturated porous rocks is no exception.Since this kind of instability problem has both the conventional(i.e.trivial)and the unconventional(i.e.nontrivial)solutions,it is necessary to examine the effects of different numerical algorithms,which are used to solve chemical dissolution-front instability problems in fluid-saturated porous rocks.Toward this goal,two different numerical algorithms associated with the commonly-used finite element method are considered in this paper.In the first numerical algorithm,the porosity,pore-fluid pressure and acid/solute concentration are selected as basic variables,while in the second numerical algorithm,the porosity,velocity of pore-fluid flow and acid/solute concentration are selected as basic variables.The particular attention is paid to the effects of these two numerical algorithms on the computational simulation results of unstable chemical dissolution-front propagation in fluid-saturated porous rocks.The related computational simulation results have demonstrated that:1)the first numerical algorithm associated with the porosity-pressure-concentration approach can realistically simulate the evolution processes of unstable chemical dissolution-front propagation in chemical dissolution systems.2)The second numerical algorithm associated with the porosity-velocity-concentration approach fails to simulate the evolution processes of unstable chemical dissolution-front propagation.3)The extra differential operation is the main source to result in the failure of the second numerical algorithm.

鉴于求得解析解的困难,需要采用数值方法和算法得到大量科学和工程问题的计算模拟结果。这对求解饱水孔隙岩石中化学溶解面非稳定性问题而言也不例外。由于这类非稳定性问题可具有常规解和非常规解,很有必要探讨不同数值算法对模拟饱水孔隙岩石中化学溶解面非稳定性的影响。因此,本文考虑了与常用有限元相关的2种不同数值算法。在第1种数值算法中,孔隙率、孔隙流体压力和酸液浓度被选为基本变量。在第2种数值算法中,孔隙率、孔隙流体流速和酸液浓度被选为基本变量。相关的计算模拟结果表明:(1)第1种数值算法可真实地模拟非稳定化学溶解面在化学溶解系统中传播时的演化过程;(2)第2种数值算法不能模拟非稳定化学溶解面在化学溶解系统中传播时的演化过程;(3)过度的数学微分运算是导致第2种数值算法失效的主要原因。