Deep-Neural-Network-Based Workflow Increases Efficacy in Solving Complex Problems

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 220876, “Efficacy Gain From a Deep-Neural-Network-Based History-Matching Workflow,” by Bicheng Yan, SPE, and Yanjui Zhang, King Abdullah University of Science and Technology. The paper has not been peer reviewed. _ Reservoir history-matching is essential for understanding subsurface uncertainty in rock properties. However, conventional history-matching methods usually require numerous forward model evaluations and rely heavily on the previous estimation of uncertain model parameters. To resolve these issues, the authors write that they resort to cutting-edge deep-learning (DL) technologies for their universal approximation capability in forward and inverse modeling based on automatic differentiation. In the complete paper, the authors develop a deep neural network-based history-matching (DNN-HM) workflow with enhanced efficiency and scalability for solving complex history-matching problems. Methodology The developed DNN-HM workflow consists of a forward modeling part for two-phase waterflooding reservoir simulations and the inverse modeling part for history-matching tasks. The complete paper includes detailed descriptions of this workflow, including associated equations. Forward Reservoir Simulation. The forward problem consists of a two-phase waterflooding process in a 2D heterogeneous reservoir. The reservoir is saturated initially with water and oil phases, where oil is the primary phase. The edges of the reservoir domain are bounded by a no-flowing boundary condition. Five water-injection wells and one oil-production well are drilled in the reservoir. The fluid flow in the porous reservoir follows Darcy’s law and the mass conservation of each fluid phase. In this study, the authors ignore the effect of capillary pressure on two-phase flow in the porous reservoir. The partial differential equation (PDE) system is spatially discretized through the cell-centered finite-difference method and temporally discretized by the backward-Euler scheme. Therefore, the PDE system is solved using the conventional fully implicit method to ensure numerical stability. Because conventional numerical reservoir simulators typically are implemented in a black-box fashion, it is usually difficult to obtain the derivatives of reservoir or well responses with regard to reservoir model parameters from such simulators. Nevertheless, these derivatives are critical to perform a gradient-based history-matching workflow. Conventional reservoir simulators are first run to generate synthetic simulation data for the example of the two-phase waterflooding problem, and, further, such data are used to train a DL-based forward surrogate model capable of executing automatic differentiation to provide the relevant derivatives for the considered history-matching problem. Therefore, the forward model ultimately can be written as an abstract described in the complete paper. In the waterflooding process described in this study, the injection wells are operated with a constant water volumetric injection rate at surface condition, while the production wells are scheduled at constant bottomhole pressure (BHP). The observational data from well locations include the injection flowing BHP and the water and oil volumetric production rates at surface conditions. Furthermore, two Fourier neural operators (FNO) are used to separately predict the pressure of the well gridblocks and water saturation to achieve the nonlinear mapping of function G, which is denoted as NNf. The pretrained NNf ultimately is used to obtain the prediction of the observational data. The forward model G or NNf is trained based on the training data generated from a high-fidelity reservoir simulator.