Neural network surrogate for flow prediction and robust optimization in fractured reservoir systems

Abstract

Embedded discrete fracture models are widely used to model flow in naturally fractured systems. These models are, however, time-consuming to simulate, and this limits their use for computationally demanding applications such as optimization. In this work we present a deep-learning-based surrogate model for fast prediction of time-varying well flow rates over multiple fracture realizations, for given well bottom-hole pressure schedules. Our surrogate model applies convolutional and recurrent neural networks. The convolutional neural network is used to capture the spatial variability of fractures in different realizations, though the direct input of the fracture geometry is not feasible because structured data are required. We show, however, that the use of the single-phase steady-state pressure solution defined on the structured rock-matrix grid, for each realization, provides the requisite input to the convolutional neural network. The resulting proxy is shown to give accurate flow rate predictions for different discrete fracture realizations. The proxy is then applied for robust optimization (expected net present value computed over an ensemble of realizations is optimized) subject to nonlinear output constraints. Proxy-based optimization provides an 18% improvement in net present value, with an overall speedup of ∼500 relative to simulation-based optimization. The optimized solutions are validated through comparison to simulation results, and agreement is within 1%.