A Learning-Based Multiscale Model for Reactive Flow in Porous Media

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.