We study solute-laden flow through permeable geological formations with a focus on advection-dominated transport and volume reactions. As the fluid flows through the permeable medium, it reacts with the medium, thereby changing the morphology and properties of the medium; this in turn, affects the flow conditions and chemistry. These phenomena occur at various lengths and time scales, and makes the problem extremely complex. Multiscale modeling addresses this complexity by dividing the problem into those at individual scales, and systematically passing information from one scale to another. However, accurate implementation of these multiscale methods are still prohibitively expensive. We present a methodology to overcome this challenge that is computationally efficient and quantitatively accurate. We introduce a surrogate for the solution operator of the lower scale problem in the form of a recurrent neural operator, train it using one-time off-line data generated by repeated solutions of the lower scale problem, and then use this surrogate in application-scale calculations. The result is the accuracy of concurrent multiscale methods, at a cost comparable to those of classical models. We study various examples, and show the efficacy of this method in understanding the evolution of the morphology, properties and flow conditions over time in geological formations.

翻译：我们研究了溶质在渗透性地质构造中的流动，重点关注对流主导的输运及体积反应。当流体流经渗透介质时，会与介质发生反应，从而改变介质的形态与属性，继而影响流动条件与化学过程。这些现象跨越多个时空尺度，使问题极为复杂。多尺度建模通过将问题分解为不同尺度的子问题，并系统性地在各尺度间传递信息来应对这一复杂性。然而，这些多尺度方法的精确实现仍面临高昂计算代价。我们提出了一种兼具计算效率与定量精度的方法来克服这一挑战。我们引入循环神经算子作为低尺度问题求解器的替代模型，利用低尺度问题重复求解生成的离线数据进行一次性预训练，然后将该替代模型应用于实际尺度计算。最终实现了与同步多尺度方法相当的精度，而计算成本仅与传统模型相近。通过多组算例验证，我们展示了该方法在理解地质构造中形态、属性及流动条件随时间演化规律方面的有效性。