Neural Operators for Hydrodynamic Modeling of Underground Gas Storages

Abstract

Hydrodynamic modeling via numerical simulators of underground gas storages (UGSs) is an integral part of planning and decision-making in various aspects of UGS operation. Although numerical simulators can provide accurate predictions of numerous parameters in UGS reservoirs, in many cases this process can be computationally expensive. In particular, calculation time is one of the major constraints affecting decisions related to optimal well control and distribution of gas injection or withdrawal over the reservoir area. Novel deep learning methods that can provide a faster alternative to traditional numerical reservoir simulators with acceptable loss of accuracy are investigated in this paper. Hydrodynamic processes of gas flow in UGS reservoirs are described by partial differential equations (PDEs). Since PDEs involve approximating solutions in infinite-dimensional function spaces, this distinguishes such problems from traditional ones. Currently, one of the most promising machine learning approaches in scientific computing (scientific machine learning) is the training of neural operators that represent mappings between function spaces. In this paper, a deep learning method for hydrodynamic modeling of UGS is proposed. A modified Fourier neural operator for hydrodynamic modeling of UGS is developed, in which the model parameters in the spectral domain are represented as factorized low-rank tensors. We trained the model on data obtained from a numerical model of UGS with nonuniform discretization grid, more than 100 wells and complex geometry. Our method demonstrates superior performance compared to the original Fourier neural operator (FNO), with an order of magnitude (50 times) fewer parameters. Tensor decomposition not only greatly reduced the number of parameters, but also increased the generalization ability of the model. Developed neural operator simulates a given scenario in a fraction of a second, which is at least \(10^{6}\) times faster than a traditional numerical solver.