Ensemble Kalman Inversion for Geothermal Reservoir Modelling

TL;DR

This paper explores the use of ensemble Kalman inversion (EKI) as an efficient, robust alternative to traditional methods like MCMC for estimating parameters in complex geothermal reservoir models, demonstrating its effectiveness through case studies.

Contribution

It introduces EKI as a derivative-free, parallelisable method suitable for large-scale geothermal models, showing its advantages over conventional techniques in accuracy and computational efficiency.

Findings

EKI requires fewer simulations than MCMC for accurate uncertainty quantification.

EKI is robust to simulation failures and can incorporate geological constraints.

Case studies confirm EKI's effectiveness in real-world geothermal reservoir modeling.

Abstract

Numerical models of geothermal reservoirs typically depend on hundreds or thousands of unknown parameters, which must be estimated using sparse, noisy data. However, these models capture complex physical processes, which frequently results in long run-times and simulation failures, making the process of estimating the unknown parameters a challenging task. Conventional techniques for parameter estimation and uncertainty quantification, such as Markov chain Monte Carlo (MCMC), can require tens of thousands of simulations to provide accurate results and are therefore challenging to apply in this context. In this paper, we study the ensemble Kalman inversion (EKI) algorithm as an alternative technique for approximate parameter estimation and uncertainty quantification for geothermal reservoir models. EKI possesses several characteristics that make it well-suited to a geothermal setting; it is derivative-free, parallelisable, robust to simulation failures, and in many cases requires far fewer simulations to provide an accurate characterisation of the posterior than conventional uncertainty quantification techniques such as MCMC. We illustrate the use of EKI in a reservoir modelling context using a combination of synthetic and real-world case studies. Through these case studies, we also demonstrate how EKI can be paired with flexible parametrisation techniques capable of accurately representing prior knowledge of the characteristics of a reservoir and adhering to geological constraints, and how the algorithm can be made robust to simulation failures. Our results demonstrate that EKI provides a reliable and efficient means of obtaining accurate parameter estimates for large-scale, two-phase geothermal reservoir models, with appropriate characterisation of uncertainty.