Complexity Analysis Of Lumped Parameter Models

Lumped parameter models have been shown to be a useful tool for geothermal reservoir analysis and production planning.Tank model is a common form of lumped parameter model,incorporating tanks of given capacitance partially filled with fluid.Between the tanks are connections with given conductance,that allow fluid to flow between connected tanks with different fluid levels.With the development of generalized lumped parameter models,the number of models available increased drastically.Thus,determining the proper model one by one becomes impractical.In this thesis,tank models of varying complexity are compared in terms of accuracy and utility.An algorithm called Complexity Reduction Algorithm(CRA)is developed that automatically finds models which are likely to be the best by choosing a certain path through the model space.In general,it is reasonable to expect that a complex model is able to give an accurate fitting result and the optimum model indicated by CRA only has a medium complexity,thus,switch-back method is developed to decrease the training error of the complex models.In addition,in some cases,there is a large number of production wells that are producing hot water,which will lead to a situation where a large amount of parameters are needed to be estimated,since the number of parameters grows quadratically in terms of the number of tanks.The K-means clustering algorithm is shown to be suitable for finding an initial production tank configuration under such situations.Real data from the Laugarnes geothermal field and Reykir geothermal area in Iceland are shown in the thesis.The results show that the newly developed algorithm provides insights into model selection for lumped parameter models.Coupled with switch-back method,the model indicated by CRA shows an improvement in both fitting accuracy and prediction capacity.The accuracy of both history-matched and predicted drawdown for lumped parameter models of varying complexity and the results by using the Akaike Information Criterion(AIC)and Bayesian Information Criterion(BIC)as an indicator for model selection have been shown.