Augmenting a pure and hybrid vertical equilibrium scheme via data-driven surrogate modelling

Abstract

Vertical equilibrium (VE) models have been introduced as computationally efficient alternatives to traditional mass and momentum balance equations for fluid flow in porous media. Since VE models are only accurate in regions where phase equilibrium holds and traditional simulations are computationally demanding, hybrid methods have been proposed to combine the accuracy of the full-dimensional approach with the efficiency of VE model. However, coupling both models introduces computational overhead that can make hybrid simulations slower than fully traditional ones. To address the computational overhead introduced by coupling interfaces in hybrid models, we utilize data-driven surrogates to accelerate the overall scheme. To this end, we predict the gas plume distance and coarse-level mobilities in the VE model, and also enhance the computation of the coupling scheme via surrogates. We focus on surrogate models with short inference times to minimize computational overhead during frequent function calls. The proposed approach preserves key physical properties, such as mass conservation, despite the deployment of data-driven models, while substantially reducing simulation runtimes. Overall, combining data-driven methods with the hybrid VE scheme yields an enhanced model that outperforms traditional simulations in speed while introducing only negligible errors.