This report gives an insight into basics of stress field simulations for geothermal reservoirs.
The quasistatic equations of poroelasticity are deduced from constitutive equations, balance
of mass and balance of momentum. Existence and uniqueness of a weak solution is shown.
In order of to find an approximate solution numerically, usage of the so–called method of
fundamental solutions is a promising way. The idea of this method as well as a sketch of
how convergence may be proven are given.
Insbesondere bei der industriellen Nutzung tiefer geothermischer Systeme gibt es Risiken, die im Hinblick auf eine zukunftsträchtige Rolle der Ressource "Geothermie" innerhalb der Energiebranche eingeschätzt und minimiert werden müssen. Zur Förderung und Unterstützung dieses Prozesses kann die Mathematik einen entscheidenden Beitrag leisten. Um dies voranzutreiben haben wir zur Charakterisierung tiefer geothermischer Systeme ein Säulenmodell entwickelt, das die Bereiche Exploration, Bau und Produktion näher beleuchtet. Im Speziellen beinhalten die Säulen: Seismische Erkundung, Gravimetrie/Geomagnetik, Transportprozesse, Spannungsfeld.
Due to the increasing demand of renewable energy production facilities, modeling geothermal reservoirs is a central issue in today's engineering practice. After over 40 years of study, many models have been proposed and applied to hundreds of sites worldwide. Nevertheless, with increasing computational capabilities new efficient methods are becoming available. The aim of this paper is to present recent progress on seismic processing as well as fluid and thermal flow simulations for porous and fractured subsurface systems. The commonly used methods in industrial energy exploration and production such as forward modeling, seismic migration, and inversion methods together with continuum and discrete flow models for reservoir monitoring and management are reviewed. Furthermore, for two specific features numerical examples are presented. Finally, future fields of studies are described.
The inverse problem of recovering the Earth's density distribution from data of the first or second derivative of the gravitational potential at satellite orbit height is discussed for a ball-shaped Earth. This problem is exponentially ill-posed. In this paper a multiscale regularization technique using scaling functions and wavelets constructed for the corresponding integro-differential equations is introduced and its numerical applications are discussed. In the numerical part the second radial derivative of the gravitational potential at 200 km orbitheight is calculated on a point grid out of the NASA/GSFC/NIMA Earth Geopotential Model (EGM96). Those simulated derived data out of SGG (satellite gravity gradiometry) satellite measurements are taken for convolutions with the introduced scaling functions yielding a multiresolution analysis of harmonic density variations in the Earth's crust. Moreover, the noise sensitivity of the regularization technique is analyzed numerically.