Modeling Heat Transport in DeepGeothermal Systems by Radial
Ba-sis Functions
Isabel Ostermann,Fraunhofer ITWM Kaiserslautern / TU
Kaiserslautern, Ger-many
[email protected] |advisor(s) : Prof. Dr.Willi Freeden
& Prof. Dr.-Ing. Rainer Helmig
The need for alternative energy increases steadily -especially
due to the climate change and the limitedavailability of fossil
fuels. Geothermal power usesthe intrinsic heat which is stored in
the accessiblepart of the Earths crust. Its importance among
therenewable energy resources originates from the al-most unlimited
energy supply of the Earth and itsindependence from external
influences such as sea-sonal or even daily climatic variability.
Nevertheless,there are risks which have to be assessed.From a
mathematical point of view - as realizedin the Geomathematics
Group, TU Kaiserslautern -there are four building blocks of the
characterizationof deep geothermal systems : seismic
exploration,gravimetry, modeling transport processes, and mo-deling
the stress field. In particular, local depletionposes a significant
risk during the industrial utiliza-tion of geothermal reservoirs.
In order to reduce thisrisk, reliable techniques to predict the
heat transportand the production temperature are required. To
thisend, a 3D-model to simulate the heat transport in hy-drothermal
systems is developed which is based on atransient
advection-diffusion-equation for a 2-phaseporous medium.The
existence, uniqueness, and continuity of theweak solution of the
resulting initial boundary va-lue problem is verified. For the
numerical realiza-tion, a linear Galerkin scheme is introduced on
thebasis of scalar kernels. The convergence of the uni-quely
determined approximate (Galerkin) solutionto the weak solution of
the initial boundary valueproblem is proven. Furthermore, exemplary
appli-cations of this method are investigated for the bi-harmonic
kernel as well as appropriate geometric re-presentations of a
hydrothermal reservoir. Moreover,numerical integration methods on
geoscientificallyrelevant bounded regions in R3 are introduced
andtested for the considered geometries.
