Assessment of Uncertainty in Estimation of Stored and Recoverable Thermal Energy in Low-Temperature Geothermal Reservoirs by Volumetric Methods

Abstract

In this paper, we investigate the propagation of uncertainties in the input variables (used in the volumetric method) on to stored and recoverable thermal energy estimates calculated from volumetric methods. Effects of the different types of input distributions, correlation among input variables and cognitive biases are also investigated. Both Monte Carlo (MC) and the analytic uncertainty propagation (AUP) methods are considered and compared for uncertainty characterization. Analytic uncertainty propagation equations (AUPEs) are derived based on a Taylor-series expansion around the mean values of the input variables. The AUPEs are general in that correlation among the input variables, if it exists, can also be accounted for on the resulting uncertainty. Monte Carlo methods (MCMs) were used to verify the results obtained from the AUPEs.

A comparative study that we have conducted shows that the AUPM is as accurate as the MCM for the problem of interest. We show that AUPM can be used as a fast tool, without resorting to the MCM because the resulting distributions of stored and recoverable heat are always log-normal, which makes it possible for the results of the AUPM to accurately characterize the uncertainty. It is also shown that it is incorrect ƒ{ a commonly made mistake ƒ{ to add the ¡§proved¡¨ and ¡§probable¡¨ (which corresponds to P10 and P90 percentiles of the cumulative distribution function, respectively) thermal energy ¡§reserves¡¨ from individual wells (or fields) to get ¡§proved¡¨ field (or country) reserves. Applications on synthetic and field data cases are presented to demonstrate the methodology considered in this work.