Simulator‐Based Bayesian Inference of Enhanced Geothermal Reservoir Properties

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Abstract
Inversions of dynamic multi‐scale multi‐physics subsurface system properties rely on the effective sampling of high‐dimensional parameter spaces and are thus notoriously difficult to perform. The associated models are defined by complex nonlinear relationships with potentially stochastic components, which lead to analytically intractable likelihoods that require challenging forward simulations of the system response. This paper presents the application of the Bayesian optimization for likelihood‐free inference (BOLFI) algorithm to invert the properties of a geothermal reservoir. We use the viscoelastic damage rheology simulator HydroPED to model an enhanced geothermal system (EGS) with controlled reservoir properties. Our results demonstrate the effectiveness of combining BOLFI and the computationally expensive simulator HydroPED to estimate an informative posterior distribution from a comparatively small number of forward evaluations. In this pilot, we use BOLFI to invert for ambient principal stress values using synthetic target data. We parameterize the 2‐km scale reservoir with ∼16′000 elements and perform tests with 200 and 500 HydroPED forward simulations that each take a wall‐clock time of 1.5 hr using an 8‐core CPU node to simulate one day of a hydraulic stimulation. Using potency, which encodes the spatial distribution of energy release within the simulator reservoir as a target function for the inversion, yields better results compared to a simpler event count target function. The approach we use in this study can be extended to a wide range of seismic and hydraulic target observations to constrain ambient stress and local EGS model parameters.

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