Problems in the Use of Lumped Parameter Reservoir Models for Low-Temperature Geothermal Fields

Abstract

Lumped-parameter modeling is commonly used at the beginning of the life of a field, when field data are scarce. Generally, in lumped-parameter models, the reservoir is described as a single homogeneous block with the production/reinjection rates and recharge flow specified. Pressure (and/or water level) changes in the reservoir are modeled by using mass and energy balances and therefore, the potential of the field can be predicted under various production/reinjection scenarios.
The main objective of this paper is to discuss the problems involved in modeling the low-temperature liquid-dominated geothermal reservoirs by using lumped-parameter models. 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. Model solutions for constant production/reinjection flow rates are given in the form of analytical expressions. The variable flow rate case is modeled by Duhamel's Principle. 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.
Three field examples (Laugarnes and Glerardalur geothermal fields located in Iceland and Balcova-Narlidere geothermal field located in Turkey) and a hypothetical field case are considered to show the use of the models and the optimization algorithm. The observed and simulated water level changes obtained from the models are discussed. The modeling results indicate that the accuracy, continuity, and duration of the input data such as the production/reinjection flow rates and the water level measurements greatly affect the confidence intervals and RMS values computed from the matching analysis of the model. They cause major problems in choosing the appropriate model. Our results also suggest that the additional data, such as geological, geophysical, and hydrological, are required to identify the proper lumped-parameter model.