On the role of poroelasticity for modeling of stress fields in geothermal reservoirs

Abstract

With growing interest in the safety and environment of our planet, geomathematics as the mathematics related to the “system Earth” finds itself challenged by new problems nearly every day. Some of these problems come from the field of renewable energy resources. Especially geothermics which is concerned with extracting the heat of the Earth’s crust and making it usable for the heat and energy market needs sophisticated mathematical methods to model geothermal reservoirs (see Ilyasov et al. 2010 and the references therein for an overview). One of the quantities which are essential for successful modeling is the stress field of the geothermal reservoir. Changes in the stress field influence the opening and growth of fractures and can also lead to seismic events. For an accurate model, we have to consider the interactions between the pressure of a fluid (water) which is injected into the Earth and the stresses of the rock and soil strata into which this pressurized fluid is pumped. In 1966, J. Geertsma introduced the term poroelasticity for the description of these interactions (Wang 2000). In this paper, we will give a short geomathematical introduction and survey into the field of poroelasticity. After the derivation of the basic partial differential equations for consolidation processes, we will discuss existence and uniqueness of weak solutions. Moreover, we will establish boundary integral equations and introduce a numerical solution scheme based on these boundary integral equations.