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Abstract: Several parameter estimation problems (or “inverse” problems) such as those that occur in hydrology and geophysics are solved using partial differential equation (PDE)-based models of the physical system in question. Likewise, these problems are usually underdetermined due to the lack of enough data to constrain a unique solution. In this paper, we present a framework for the solution of underdetermined inverse problems using COMSOL Multiphysics (formerly FEMLAB) that is applicable to a broad range of physical systems governed by PDEs. We present a general adjoint state formulation which may be used in this framework and allows for faster calculation of sensitivity matrices in a variety of commonly encountered underdetermined problems. The aim of this approach is to provide a platform for the solution of inverse problems that is efficient, flexible, and not restricted to one particular scientific application. We present an example application of this framework on a synthetic underdetermined inverse problem in aquifer characterization, and present numerical results on the accuracy and efficiency of this method. Our results indicate that our COMSOL-based routines provide an accurate, flexible, and scalable method for the solution of PDE-based inverse problems. [Copyright &y& Elsevier]

• A combination of simple analytical models and optimization under uncertainty produces reasonable profit forecasts and highlights key sensitive parameters. • Increasing the surface area for heat transfer increases the thermal and financial sustainability of a geothermal reservoir. • Sensitivity analysis shows that effective reservoir transmissivity and well spacing exert the largest controls on the financial performance of the reservoir. Geothermal energy resources are highly available but under-utilized throughout the world. Previous studies have sought to understand reservoir response to geothermal production and optimize production rates to maximize lifetime profits of geothermal reservoirs; however, these studies largely overlook the uncertainty in subsurface structure, such as the number of preferential flow pathways (e.g., fractures) that are available for fluid and heat transport. We present a combination of simple analytical models that maximize the profits of an idealized synthetic geothermal reservoir, while considering reservoir structural uncertainty, using expected net present value. For a typical case, we find that effective reservoir transmissivity and inter-well spacing exert the largest controls on the lifetime profitability of an idealized geothermal reservoir, and for a given reservoir there exists a critical number of hydraulically active fractures beyond which additional fractures provide no increase in lifetime profits. Given initial reservoir characterization data, our model simulates reservoir performance that predicts financial outcomes, which operators can use during initial exploration stage. These predictions are also useful during normal operations to consider strategies, such as drilling make-up wells, to mitigate the effects of production-induced thermal drawdown. [ABSTRACT FROM AUTHOR]