Surrogate and inverse modeling for two-phase flow in porous media via theory-guided convolutional neural network

TL;DR

This paper extends the theory-guided CNN framework to two-phase flow in porous media, improving surrogate modeling and enabling efficient permeability field inversion with better accuracy and computational efficiency.

Contribution

The work introduces a coupled, theory-guided CNN approach for two-phase flow modeling and proposes a piecewise training strategy for variable well controls.

Findings

TgCNN outperforms ordinary CNN in accuracy for two-phase flow.

The piecewise training strategy effectively handles varying well controls.

TgCNN enables efficient permeability field inversion with high accuracy.

Abstract

The theory-guided convolutional neural network (TgCNN) framework, which can incorporate discretized governing equation residuals into the training of convolutional neural networks (CNNs), is extended to two-phase porous media flow problems in this work. The two principal variables of the considered problem, pressure and saturation, are approximated simultaneously with two CNNs, respectively. Pressure and saturation are coupled with each other in the governing equations, and thus the two networks are also mutually conditioned in the training process by the discretized governing equations, which also increases the difficulty of model training. The coupled and discretized equations can provide valuable information in the training process. With the assistance of theory-guidance, the TgCNN surrogates can achieve better accuracy than ordinary CNN surrogates in two-phase flow problems. Moreover, a piecewise training strategy is proposed for the scenario with varying well controls, in which the TgCNN surrogates are constructed for different segments on the time dimension and stacked together to predict solutions for the whole time-span. For scenarios with larger variance of the formation property field, the TgCNN surrogates can also achieve satisfactory performance. The constructed TgCNN surrogates are further used for inversion of permeability fields by combining them with the iterative ensemble smoother (IES) algorithm, and sufficient inversion accuracy is obtained with improved efficiency.