We study solute-laden flow through permeable geological formations with a focus on surface reactions that lead to changes in flow and formation. 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 make 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 is 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.

中文翻译：

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基于学习的多孔介质反应流多尺度模型


我们研究穿过可渗透地质构造的溶质流动，重点关注导致流动和地层变化的表面反应。当流体流经可渗透介质时，它与介质发生反应，从而改变介质的形态和性质；这反过来又影响流动条件和化学性质。这些现象以不同的长度和时间尺度发生，使问题变得极其复杂。多尺度建模通过将问题划分为各个尺度的问题，并系统地将信息从一个尺度传递到另一个尺度来解决这种复杂性。然而，准确实施这些多尺度方法仍然非常昂贵。我们提出了一种方法来克服这一挑战，该方法计算高效且定量准确。我们以循环神经算子的形式引入一种较低规模问题的求解算子的代理，使用较低规模问题的重复解决方案生成的一次性离线数据对其进行训练，然后在应用中使用该代理：规模计算。结果是并发多尺度方法的准确性，其成本与经典模型的成本相当。我们研究了各种例子，并展示了该方法在理解地质构造中形态、性质和流动条件随时间的演变方面的有效性。