ISBN 9783868539516

978-3-86853-951-6, Reihe Mathematik

Isabel Ostermann
Modeling Heat Transport in Deep Geothermal Systems by Radial Basis Functions

195 Seiten, Dissertation Technische Universität Kaiserslautern (2011), Softcover, A5

Zusammenfassung / Abstract

The mathematical modeling and numerical simulation of the three-dimensional heat transport in a hydrothermal system, i.e., a water-bearing deep geothermal system, were discussed in this thesis. The hydrothermal reservoir was represented by the bounded, regular region B composed of a two-phase porous medium. For the heat transport, an initial boundary value problem in a space-time-domain was established. It consists of a transient advection-diffusion-equation for the temperature, an initial condition at time t = 0, and a Neumann boundary condition on the boundary of B (reflecting the possible inflow and outflow of heat to and from the reservoir). During the derivation of the above-mentioned partial differential equation, certain assumptions were imposed on the material parameters. These are a rigid and unmoving rock matrix, temporally and spatially constant solid as well as fluid heat capacities and densities, scalar heat conductivities (isotropic medium), the absence of heat sources/sinks in the solid phase, the thermodynamic equilibrium, and the linear coupling of the solid and the fluid phase via the porosity. Furthermore, the injection and extraction of heat into and from the reservoir is represented by a (fluid) source/sink term. Due to the complexity of the initial boundary value problem, the weak solution of the introduced problem was the focus of the subsequent considerations. Based on positivity, continuity, and integrability conditions for the material parameters, the continuity and modified coercivity of the quadratic form (occurring in the weak formulation) was proven. The existence of a linear, bounded operator corresponding to the quadratic form and the definition of a source- boundary-term imply that the initial boundary value problem can be rewritten as an initial value problem. Subsequently, the existence and uniqueness of the solution of the initial value problem and, consequently, the weak solution of the initial boundary value problem were verified under integrability assumptions for the initial condition and the source-boundary-term.