Physics-informed machine learning for noniterative optimization in geothermal energy recovery

Geothermal energy is clean, renewable, and cost-effective and its efficient recovery management mandates optimizing engineering parameters while considering the underpinning physics, typically achieved through computationally intensive simulators. This study proposes a novel physics-informed machine learning (PIML) framework for geothermal reservoir optimization, integrating a data wrangler to process high-fidelity simulations, a forward network for forward predictions, and a control network to optimize engineering decision parameters while maximizing the objective function and satisfying various engineering constraints. The PIML incorporates an improved Hyperbolic-ReLU (HyperReLU) model to predict the produced geothermal fluid temperature robustly. The forward model uses a neural network to predict hyper-parameters of HyperReLU from reservoir model input and estimates the produced fluid temperature and energy. Further, the control network is trained with labels automatically generated by the forward model. During prediction, it can infer optimum decision parameters noniteratively by inputting uncertain reservoir parameters, ensuring it maximizes the objective function. Numerical experiments reveal that the HyperReLU enhances long-term predictive stability, and the forward network can achieve predictions of the produced temperature and energy within errors of 0.53±0.46% and 0.60±0.74%, respectively. We examine PIML to control the produced temperature drops or maximize the total energy recovery. Compared to the differential evolution (DE) optimizer, PIML closely matches DE with a 53.7% increase in total energy while running 5,465 times faster than DE. Moreover, PIML presents great efficiency and accuracy and is scalable for field-scale geothermal well-control design and other similar optimization problems.