Determining Longitudinal Dispersion Coefficients in Micro-Fractured Porous Media Via an Inverse Physics-Informed Neural Network

Abstract Component diffusion plays a critical role in various engineering applications, including CO2 miscible flooding for shale oil recovery, CO2 sequestration and migration in saline aquifers, and subsurface contaminant transport. However, despite the widespread presence of micro-fractures in natural reservoir systems, their impact on the longitudinal dispersion coefficient (De) has received relatively little attention in research. In this work, we generated a two-dimensional porous medium model using an unconsolidated granular packing algorithm, incorporating different micro-fracture systems to investigate their impact on the diffusion process. First, direct numerical simulations, coupling the Navier-Stokes and advection-diffusion equations, were conducted to generate training data. We then used an adaptive inverse Physics-Informed Neural Networks (PINN) to determine the De by fitting the component concentrations and incorporating the governing transport equations. After validating the effectiveness of the method, we further determined and analyzed the influence of micro-fracture characteristics on De during stable miscible displacement processes. The results indicate that adaptively adjusting the weights of different loss function components during the training process ensures the convergence of the inverse problem to the correct solution. During stable miscible displacement, both micro-fractures and operational parameters jointly influence the instability of the displacement front. This leads to a faster breakthrough and a larger contact area for molecular diffusion. In the absence of advection, De maintains a fixed relationship with the molecular diffusion coefficient as a function of porosity. Longer micro-fracture along the injection direction and lower micro-fracture density perpendicular to the injection direction result in a higher De. This work combines the capability of direct numerical simulations to accurately describe physical problems and the ability of neural networks to solve inverse problems, providing a novel framework for the scale-up of the numerical simulation from the pore-scale to the field-scale during CO2 miscible flooding in unconventional reservoirs and CO2 storage in saline aquifers.