A Refined Methodology for Quantifying Estimates of Extractable Geothermal Energy: Experimental Design (ED) and Response Surface Methodology (RSM)

Abstract

Estimating power potential (MWe) of geothermal resources with higher accuracy remains both a necessity and a challenge confronting the geothermal industry. Reservoir models that underpin resource management and decision making can quantify uncertainties and provide a predictive likelihood of MWe capacity. However, uncertainty quantification of power (MWe) prediction from a geothermal numerical model is time-consuming, and reservoir models do not mesh well with the Monte Carlo simulation. The Monte Carlo method approximates the probability of different outcomes based on the probability distribution of the values of the uncertain parameters. The present study critically examined all existing resource assessment methodologies and practices for quantifying the power potential of geothermal fields with a particular focus on the volumetric method and reservoir simulation. This work provides more substantial evidence that these two methods are preferred for estimating resource potential and highlights the inevitable difficulty in obtaining accurate predictions. This study also investigated the use of the Experimental Design (ED) - Response Surface Methodology (RSM) framework as an alternative method for probabilistic resource assessment using a calibrated numerical model. The ED-RSM approach enables uncertainty to be modelled with multiple stochastic parameters, while requiring only a relatively small number of simulation runs. The steps involved are to build a polynomial equation of the numerical model, and apply a Monte Carlo simulation to this polynomial equation, thereby generating a probabilistic estimate expressed in generated power (MWe). In order to construct this polynomial model, it is first necessary to run several versions of the numerical model with key stochastic parameters set based on the chosen Experimental Design (ED) and parameters. The outputs of the model can be fitted to the input parameters by fitting a regression model. The ED-RSM framework using Full Factorial and Fractional designs were tested and implemented into four numerical models of the Rotorua, Ohaaki and Wairakei geothermal fields in New Zealand and the Leyte geothermal field in the Philippines. These designs are the three-level Full Factorial, two-level Full Factorial, three-level Box-Behnken and two-level Plackett-Burman. Overall, the ED-RSM framework using the Plackett-Burman fractional design proved to be a practical approach for estimating potential capacity from a calibrated natural-state model.