Representation of Unknown Parameters in Geothermal Model Calibration

Abstract

Computational reservoir models are commonly used to inform management decisions in the geothermal energy sector. With a well-calibrated model, a range of future scenarios can be simulated and informed decisions can be made. However, the task of calibrating large-scale geothermal models is challenging, both from a conceptual standpoint and in terms of computational cost. Furthermore, decision-makers typically desire the quantification of uncertainty and confidence in any calibration results. These problems have been addressed quite successfully in related fields, such as petroleum engineering, by using so-called ensemble-based uncertainty quantification methods.
Ensemble-based methods use a small collection (ensemble) of models, with each ensemble member having different values for the model parameters (such as deep mass and heat sources or subsurface permeabilities). The associated calibration methods guide this ensemble of different models to regions in parameter space which provide adequate matches to the measured field data, while ensuring an appropriate diversity of models to characterise uncertainty. In the Bayesian framework, ideally, the distribution of the ensemble should converge to the posterior probability distribution representing this uncertainty, i.e., the probability distribution of the unknown parameters given the measured field data.
A crucial task in ensemble methods, as well as in uncertainty quantification in general, is to simultaneously allow the parameters of interest to be uncertain and variable, while also being physically sensible (i.e., realistic). Careful parameterisations of the unknown parameters can fulfil these two objectives. In the context of ensemble-based methods, such parameterisations should also correspond to easy-to-evaluate prior terms. Here we propose a variety of possible parameterisations for deep mass and heat sources and subsurface permeabilities for use in the calibration of geothermal reservoir models. Each of the parameterisations presented can easily be implemented within an ensemble-based framework for model calibration.