Future Performance Predictions by Lumped Parameter Models: A Field Application

Abstract

This paper deals with the application of lumped parameter models to a field case. The models are used to match the long-term observed pressure behavior of Hofsstadir geothermal field which is a typical low-temperature liquid dominated geothermal system, in West Iceland. Once the parameters of the models are determined by history matching, future performance predictions are made under given production/injection scenarios by using Randomized Maximum Likelihood method.

In the lumped models considered in this work, the geothermal system is assumed consist of reservoir, aquifer and recharge source, which are represented as different tanks having different properties. The models are used to match the long-term observed water level or pressure response of a field to a given production history. For history matching purposes, an optimization algorithm based on the Levenberg-Marquardt method is used to minimize an objective function based on weighted least-squares, to estimate relevant aquifer/reservoir parameters. In addition, we constrain the parameters during the nonlinear minimization process to keep them within physically meaningful limits and compute statistics (e.g., standard 95% confidence intervals) to assess uncertainty in the estimated parameters. Moreover, Root Mean Square errors (RMS) are also computed for each observed data set matched.

Once the parameters of the model are determined by history matching, the future performance of the reservoir is predicted for different production/injection scenarios to optimize the management of a given low-temperature geothermal field. However, throughout the modeling work, it is very important to assess the uncertainty that arises from "measurement" errors or noise in observed data, modeling errors, nonlinear relationship between model parameters and observed response, and non-uniqueness of the problem. Furthermore, it is crucial that this uncertainty be reflected to the future predictions. Hence instead of dealing with a single deterministic response, one can analyze various possible outcomes of the future predictions. Therefore, in this study the Randomized Maximum Likelihood (RML) is used for predicting the uncertainty in future flow behavior predicted by lumped parameter models.