Development of Reduced Order Models Using Reservoir Simulation and Physics Informed Machine Learning Techniques

Abstract

Reservoir simulation is the industry standard for prediction and characterization of processes in the subsurface. However, simulation is computationally expensive and time consuming. This study explores reduced order models (ROMs) as an appropriate alternative. ROMs that use neural networks effectively capture nonlinear dependencies, and only require available operational data as inputs. Neural networks are a black box and difficult to interpret, however. Physics informed neural networks (PINNs) provide a potential solution to these shortcomings, but have not yet been applied extensively in petroleum engineering. A mature black-oil simulation model from Volve public data release was used to generate training data for a ROM leveraging long short term memory (LSTM) neural networks' temporal capacity. Network configurations were explored for the optimum configuration. Monthly oil production was forecasted at the individual well and full field levels, and then validated against real history to compare predictive accuracy with simulation results. The governing equation for a capacitance resistance model (CRM) was then added to the reservoir scale model as a physics based constraint, and to analyze parameter solutions for efficacy in characterization of the flow field. Data driven results indicated that a stateless LSTM, with single time lag as input, generated the most accurate prediction. Using a walk-forward validation strategy, the single well ROM increased prediction accuracy by a 95% average when compared to the simulation, and did so with less computational resources in less time. Physical realism of reservoir scale predictions was improved by the addition of a CRM constraint, demonstrated by the removal of negative rates. Parameter solutions to the governing equation showed good agreement with streamline plots, and demonstrated ability to detect spatial irregularities. The results of this research clearly demonstrate the ease of which ROMs can be built and used to meet or exceed individual capabilities of reservoir simulation. Furthermore, the potential for application of PINN methodology in petroleum engineering research was established and proven effective.