| Title | Probabilistic Resource Estimation of Stored and Recoverable Thermal Energy for Geothermal Systems by Volumetric Methods |
|---|---|
| Authors | Mustafa Onur, Hülya Sarak, and Ö. İnanç Türeyen |
| Year | 2010 |
| Conference | World Geothermal Congress |
| Keywords | Resource Estimation, Volumetric Methods, Probabilistic, Uncertainty Characterization, Adding Field Resources |
| Abstract | This paper investigates the propagation of uncertainties in the input variables (used in the volumetric method) on to stored and recoverable thermal energy resources calculated from volumetric methods. 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. Hence, it can be used as a fast tool eliminating the need for MCM because the resulting distributions of thermal resources always tend to be log-normal. We also discuss the problem of aggregating thermal resources for projects involving more than one field. Should one use an arithmetic or probabilistic addition to determine “proved,” “probable,” and “possible” (which corresponds to P10, P50, and P90 percentiles of the cumulative distribution function, respectively) corresponding a geothermal project or a country which may involve many diverse fields, each with its estimated values of P10, P50, and P90? We show that the arithmetic sum underestimates the P10 value, compared to probabilistic sum which is the statistically proper method for adding resources or reserves. Applications on synthetic and field data cases are presented to demonstrate the methodology considered in this work. |