Inverse modelling of geothermal reservoirs - a hierarchical bayesian approach

Abstract

The proper management of geothermal resources relies heavily on computational and mathematical modelling. Given a sufficiently complete description of the physical processes governing a geothermal field we can, in principle, predict future values of the field's measurable outputs. This is typically called the 'forward problem'. All models, especially complex simulation models, are subject to uncertainty, errors and under-determination, however. This naturally leads to the so-called 'inverse problem' - using those (typically few) quantities that can be reliably measured to determine and quantify the uncertainty in other model parameters and predictions. While inverse modelling techniques are common in many fields of engineering and physics, geothermal reservoir engineering presents a particularly difficult area of application since it involves nonlinear, coupled multiphase flows, along with possible phase transitions. Here we present preliminary results from our work on developing a unified Bayesian inverse modelling approach for computational models of geothermal fields. To address the multi-scale and coupled nature of geothermal problems we further advocate a so-called 'hierarchical' Bayesian approach; in this approach any assumptions on the separation, composition and reduction of different model components can be naturally expressed using standard conditional probability calculations. We illustrate how, after formulating a geothermal simulation as a hierarchical Bayesian model, statistical sampling procedures such as Markov Chain Monte Carlo (MCMC) can be used to carry out calibration, prediction and/or uncertainty quantification. The only distinction between these tasks in our framework lies in which particular conditional probability distribution is of interest. We briefly discuss how further extensions, such as the use of reduced-order stochastic process approximations to speed up computation, relate to the hierarchical framework. This commonality further illustrates the benefits of adopting an explicit, unified inverse modelling approach to geothermal reservoir simulation.