Physics-informed machine learning for reservoir management of enhanced geothermal systems

Abstract

With the energy demand arising globally, geothermal recovery by Enhanced Geothermal Systems (EGS) becomes a promising option to bring sustainable energy supply along with mitigating CO2 emission. However, reservoir management of EGS primarily relies on reservoir simulation, which is quite expensive due to the reservoir heterogeneity, the interaction of matrix and fractures, and the intrinsic multi-physics coupled nature. Therefore, a robust optimization framework is critical for the management of EGS. We develop a general Physics-Informed Machine Learning (PIML) framework for reservoir management with multiple optimization options. A robust forward surrogate model fl is developed based on a convolutional neural network, and it successfully learns the nonlinear relationship between input reservoir model parameters (e.g., fracture permeability field) and interested state variables (e.g., temperature field and produced fluid temperature). fl is trained using simulation data from the EGS coupled thermal-hydro simulation model by sampling reservoir model parameters. As fl is accurate, efficient and fully differentiable, EGS thermal efficiency can be optimized following two schemes: (1) training a control network fc to map reservoir geological parameters to reservoir decision parameters by coupling it with fl; (2) directly optimizing the reservoir decision parameters based on coupling the existing optimizers with fl. We evaluate the impact of reservoir model parameters on the thermal recovery based on simulation datasets through sensitivity analyses, and demonstrated that injection mass rate dominates thermal recovery. Further, the forward model fl performs accurate and stable predictions of evolving temperature fields (relative error 1.27 ± 0.89%) in EGS and the time series of produced fluid temperature (relative error 0.26 ± 0.46%), and its speedup to the counterpart high-fidelity simulator is 4564 times. When optimizing with fc, we achieve thermal recovery with a reasonable accuracy but significantly low CPU time during inference, 0.11 seconds/task. When optimizing with Adam optimizer, we achieve the objective perfectly with relatively high CPU time, 4.58 seconds/task. This is because the former optimization scheme requires a training stage for fc but its inference is non-iterative, while the latter scheme requires an iterative inference without training. We also investigate the option to use fc inference as an initial guess for Adam optimizer, which decreases Adam’s CPU time but achieves excellent convergence in the objective function. This is the highest recommended option among the three evaluated. The efficiency, scalability and accuracy observed in our reservoir management framework makes it highly applicable to near real-time reservoir management in EGS as well as other similar system management processes.