Data-Driven Geothermal Reservoir Modeling: Estimating Permeability Distributions by Machine Learning

Numerical modeling for geothermal reservoir engineering is a crucial process to evaluate the performance of the reservoir and to develop strategies for the future development. The governing equations in the geothermal reservoir models consist of several constitutive parameters, and each parameter is given to a large number of simulation grids. Thus, the combinations of parameters we need to estimate are almost limitless. Although several inverse analysis algorithms have been developed, determining the constitutive parameters in the reservoir model is still a matter of trial-and-error estimation in actual practice, and is largely based on the experience of the analyst. There are several parameters which control the hydrothermal processes in the geothermal reservoir modeling. In this study, as an initial challenge, we focus on permeability, which is one of the most important parameters for the modeling. We propose a machine-learning-based method to estimate permeability distributions using measurable data. A large number of learning data were prepared by a geothermal reservoir simulator capable of calculating pressure and temperature distributions in the natural state with different permeability distributions. Several machine learning algorithms (i.e., linear regression, ridge regression, Lasso regression, support vector regression (SVR), multilayer perceptron (MLP), random forest, gradient boosting, and the k-nearest neighbor algorithm) were applied to learn the relationship between the permeability and the pressure and temperature distributions. By comparing the feature importance and the scores of estimations, random forest using pressure differences as feature variables provided the best estimation (the training score of 0.979 and the test score of 0.789). Since it was learned independently of the grids and locations, this model is expected to be generalized. It was also found that estimation is possible to some extent, even for different heat source conditions. This study is a successful demonstration of the first step in achieving the goal of new data-driven geothermal reservoir engineering, which will be developed and enhanced with the knowledge of information science.