Enhanced Geothermal Site Characterization Using Generative Adversarial Network and Ensemble Method

Characterizing the subsurface properties such as permeability and thermal conductivity is important for stimulation planning and heat production in enhanced geothermal systems (EGS). Data assimilation methods, such as the Kalman-type methods, are widely used for characterization by assimilating observed dynamic data such as pressure and temperature. However, these approaches only perform well when the parameters follow a Gaussian distribution. The geothermal sites are usually highly heterogeneous with non-Gaussian distributed complex structures such as faults and fractures, which are difficult to characterize. Over the past few years, emerging deep generative models and their impressive applications in different tasks have provided a solution to produce images with complicated features. In this work, we use the Wasserstein Generative Adversarial Network (WGAN), a deep generative model, to generate fractured images from the low-dimensional and Gaussian distributed latent space. The ensemble method, a Kalman-type data assimilation method, is then applied to the latent variables to characterize the permeability fields of a fractured geothermal site using temperature data. A synthetic two-dimensional example is presented to show the performance of our approach. 1 INTRODUCTION Subsurface characterization is important for a geothermal system to conduct stimulation and heat production. For the subsurface inverse problem (Carrera et al., 2005; McLaughlin and Townley, 1996; Oliver et al., 2008), spatially distributed geologic parameters such as permeability are estimated from noisy and sparse data such as pressure and temperature. Due to ill-posedness in the inverse problem, it is hard to accurately characterize subsurface properties using limited measurements. Data assimilation (DA) methods can integrate dynamic data (e.g., time-series pressure and temperature) into numerical models to identify unknown model parameters and reduce the estimation uncertainty (Liu and Gupta, 2007; Liu et al., 2012). Among various DA methods, Kalman-type methods such as the ensemble method (Emerick and Reynolds, 2013) are widely used due to their optimality and efficiency. However, the traditional Kalman-type methods share a common problem, i.e., the limitation of Gaussian assumption (Ghorbanidehno et al., 2020). These Gaussian prior-based methods can provide optimal solutions if the unknown parameters follow a Gaussian distribution, but there are also many non-Gaussian situations that these methods cannot handle (Zhou et al., 2014).