Reservoir simulation is the industry standard for prediction and characterization of processes in the subsurface. However, large gridblock counts simulation is computationally expensive and time-consuming. This study explores data-driven reduced-order models (ROMs) as an alternative to detailed physics-based simulations. ROMs that use neural networks (NNs) effectively capture nonlinear dependencies and only require available operational data as inputs. NNs are usually labeled black-box tools that are difficult to interpret. On the other hand, physics-informed NNs (PINNs) provide a potential solution to these shortcomings, but they have not yet been applied extensively in petroleum engineering.

In this study, a black-oil reservoir simulation model from Volve public data release was used to generate training data for an ROM leveraging long short-term memory (LSTM) NNs’ temporal modeling capacity. Network configurations were explored for their optimal configuration. Monthly oil production was forecast at the individual wells and full-field levels, and then validated against real field data for production history to compare its predictive accuracy against the simulation results. The governing equations for a capacitance resistance model (CRM) were then added to the reservoir-scale NN model as a physics-based constraint and to analyze parameter solutions for efficacy in characterization of the flow field.

Data-driven ROM results indicated that a stateless LSTM, with single time lag as input, generated the most accurate predictions. Using a walk-forward validation strategy, the single well ROM increased prediction accuracy by about 95% average when compared with the reservoir simulation and did so with much less computational resources in short time duration. Physical realism of reservoir-scale predictions was improved by the addition of CRM constraint, demonstrated by the removal of negative flow rates. Parameter solutions to the governing equation showed good agreement with the field-scale streamline plots and demonstrated the ROM ability to detect spatial irregularities. These results clearly demonstrate the ease with which ROMs can be built and used to meet or exceed the predictive capabilities of certain time-history production data using the reservoir simulation.

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