February 1, 2011
|| Dipl.-Math. Isabel Ostermann
Projektgruppe Geomathematik,Fraunhofer ITWM, Kaiserslautern
||Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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The need for alternative energy increases steadily - especially due to the climate change and the limited availability of fossil fuels. Geothermal power uses the intrinsic heat which is stored in the accessible part of the Earth's crust. Its importance among the renewable energy resources originates from the almost unlimited energy supply of the Earth and its independence from external influences such as seasonal or even daily climatic variability. Nevertheless, there are risks which have to be assessed.\\From a mathematical point of view - as realized in the Geomathematics Group, TU Kaiserslautern - there are four building blocks of the characterization of deep geothermal systems: seismic exploration, gravimetry, modeling transport processes, and modeling the stress field. In particular, local depletion poses a significant risk during the industrial utilization of geothermal reservoirs. In order to reduce this risk, reliable techniques to predict the heat transport and the production temperature are required. To this end, a 3D-model to simulate the heat transport in hydrothermal systems is developed which is based on a transient advection-diffusion-equation for a 2-phase porous medium. The existence, uniqueness, and continuity of the weak solution of the resulting initial boundary value problem is verified. For the numerical realization, a linear Galerkin scheme is introduced on the basis of scalar kernels. The convergence of the uniquely determined approximate (Galerkin) solution to the weak solution of the initial boundary value problem is proven. Moreover, numerical integration methods on geoscientifically relevant bounded regions in R³
are introduced and tested for appropriate geometric representations of a hydrothermal reservoir. Furthermore, exemplary applications of the Galerkin method are investigated for the biharmonic kernel as well as the considered geometries.