Deep-Learning Accelerated Phase Equilibrium Calculations for Compositional Simulation in Shale Reservoir

Abstract In shale reservoirs, the prevalent tight porosity induces significant capillary pressure (Pc), markedly altering fluid behavior from bulk conditions. Numerical convergence and methodologicalissues were reported for phase equilibrium calculations (PECs) incorporating Pc in nano-pore media. Thus, it is imperative to develop an efficient and robust PECs algorithm that includes Pc to accuratelysimulate oil and gas production in shale reservoirs. We developed two independent artificial neural network (ANN)-basedmodels for stability testing and flash calculations incorporating Pc. Both models share the same inputs—pressure, feed composition, and pore radius—yet they feature distinct architectures. Additionally, weintroduced a novel method for generating training data, which utilizes the production properties of gasinjection for enhanced oil recovery (EOR). In this method, except for injected gas, all componentcompositions decrease, and the working pressure range spans from maximum injection to minimumproduction pressure. We boosted the phase boundary identification capability of the stability modelthrough intensified sampling. After training, we converted the models to the C++ platform using theFrugally-deep project to ensure better comparability with standard C++ based algorithms. Furthermore, to align with traditional methods, we made specific adjustments: 1) the stability modelemploys a probabilistic threshold to filter predictions; 2) the flash model provides initial estimates forconventional algorithms. These models, with their unique configurations, establish a new framework for PECs including Pc, which has been successfully integrated into Stanford's ADGPRS simulator for fasterand more accurate simulations of shale reservoirs. Standalone calculations for various fluids and compositionalsimulations of reservoirs characterized by low permeability and nanopores have been implemented. The stability model achieves over 99.9% accuracy in determining the phase status of unseen points intraining. Additionally, the convergence iterations required for flash calculations, initiated from the flashmodel, are significantly reduced. Our innovative framework facilitates a near 80% reduction incomputational time for PECs, consequently decreasing the overall simulation duration by 40%. Thisstudy presents a rapid and robust approach to PECs within shale oil reservoir simulations, critical foraccurately forecasting production and ultimate recovery. The novelty of this study resides in the development of two ANN-basedmodels to replace stability testing and flash calculation with Pc in compositional simulations in shalereservoirs. Additionally, a novel training point generation method was designed to cater to the production characteristics of EOR of gas injection. With specific configurations, the new frameworkachieves results equivalent to standard algorithms for PECs including Pc, and reduces the simulationtime over 40%.