Surrogate and inverse modeling for two-phase flow in porous media via theory-guided convolutional neural network
This work addresses computational challenges in subsurface flow modeling for applications like oil recovery or groundwater management, representing an incremental improvement by adapting an existing framework to a specific domain.
The authors tackled the problem of modeling two-phase flow in porous media by extending a theory-guided convolutional neural network (TgCNN) framework to approximate pressure and saturation simultaneously, achieving better accuracy than ordinary CNNs and enabling efficient permeability field inversion with the iterative ensemble smoother algorithm.
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.