Parameter Inversion in Geothermal Reservoir Using Markov Chain Monte Carlo and Deep Learning

Traditional history-matching process suffers from non-uniqueness solutions, subsurface uncertainties, and high computational cost. This work proposes a robust history-matching workflow utilizing the Bayesian Markov Chain Monte Carlo (MCMC) and Bidirectional Long-Short Term Memory (BiLSTM) network to perform history matching under uncertainties for geothermal resource development efficiently. There are mainly four steps. Step 1: Identifying uncertainty parameters. Step 2: The BiLSTM is built to map the nonlinear relationship between the key uncertainty parameters (e.g., injection rates, reservoir temperature, etc.) and time series outputs (temperature of producer). Bayesian optimization is used to automate the tuning process of the hyper-parameters. Step 3: The Bayesian MCMC is performed to inverse the uncertainty parameters. The BiLSTM is served as the forward model to reduce the computational expense. Step 4: If the errors of the predicted response between the high-fidelity model and Bayesian MCMC are high, we need to revisit the accuracy of the BiLSTM and the prior information on the uncertainty parameters. We demonstrate the proposed method using a 3D fractured geothermal reservoir, where the cold water is injected into a geothermal reservoir, and the energy is extracted by producing hot water in a producer. Results show that the proposed Bayesian MCMC and BiLSTM method can successfully inverse the uncertainty parameters with narrow uncertainties by comparing the inversed parameters and the ground truth. We then compare its superiority with models like PCE, Kriging, and SVR, and our method achieves the highest accuracy. We propose a Bayesian MCMC and BiLSTM-based history matching method for uncertainty parameters inversion and demonstrate its accuracy and robustness compared with other models. This approach provides an efficient and practical history-matching method for geothermal extraction with significant uncertainties.