Simulating wormhole propagation during reactive dissolution of carbonates is often significantly challenging, because of the high nonlinearity of the governing equations with complex fluid physics. High resolution grids are often required to represent the complex geological heterogeneity, which demands massively parallel computers with a large number of processors. Herein, we present a parallel and scalable simulator on parallel computers for the fully implicit solution of the wormhole propagation model. Our approach is based on a family of mixed finite element methods for the spatial discretization and the implicit Backward Euler scheme for the temporal integration, to handle the combination of complicated flow physics and high resolution grids in their full complexity. Moreover, the active-set reduced-space method, as a class of bound-preserving inexact Newton algorithms, is proposed for the resultant nonlinear system of equations, to guarantee the nonlinear consistency of the fully implicit discretization in a monolithic way and to ensure the boundedness requirement of the solution. Numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed simulator for a set of heterogeneous medium problems. Large-scale results are provided to show the scalability for reservoir simulation with hundreds of millions of unknowns by using several thousand processors.

由于具有复杂流体物理的控制方程的高度非线性，模拟碳酸盐反应溶解过程中的虫洞传播通常具有很大的挑战性。通常需要高分辨率网格来表示复杂的地质异质性，这需要具有大量处理器的大规模并行计算机。在这里，我们在并行计算机上提出了一个并行且可扩展的模拟器，用于虫洞传播模型的完全隐式解。我们的方法基于一系列用于空间离散化的混合有限元方法和用于时间积分的隐式 Backward Euler 方案，以处理复杂的流体物理和高分辨率网格的完全复杂性的组合。此外，活动集缩减空间方法，作为一类保界不精确牛顿算法，被提出用于合成非线性方程组，以整体方式保证全隐式离散化的非线性一致性，并保证解的有界性要求。提出了数值实验来证明所提出的模拟器对一组异构介质问题的有效性和效率。提供了大规模结果，以显示使用数千个处理器对数亿个未知数进行储层模拟的可扩展性。提出了数值实验来证明所提出的模拟器对一组异构介质问题的有效性和效率。提供了大规模结果，以显示使用数千个处理器对数亿个未知数进行储层模拟的可扩展性。提出了数值实验来证明所提出的模拟器对一组异构介质问题的有效性和效率。提供了大规模结果，以显示使用数千个处理器对数亿个未知数进行储层模拟的可扩展性。