Mathematical models for heat and mass transport in geothermal systems

Abstract

Geothermal systems are an important energy source in many countries, both for direct use of hot groundwater for cooking, bathing, heating, and chemical processes as well as in usage of higher-enthalpy fluids for electricity generation. The sets of partial differential equations which describe the principles of conservation of mass, momentum, and energy of such multi-phase multicomponent systems are complicated by complex dependence of the various formation and fluid parameters on thermodynamic variables. While little has been described about the related disciplines of geology, geophysics, geochemistry, and reservoir engineering; these use scientific methods to deduce the formation parameters for geothermal reservoirs and also provide information about reservoir extent and likely boundary conditions for simulations. Without such a multidisciplinary approach, interaction and feedback about conceptual and mathematical models would not be possible. There are few analytical solution methods that produce useful results, although some provide insights on a local scale. Numerical procedures are successful in producing solutions to the governing equations, but require sophisticated discretisation and matrix inversion methods. Recent efforts are focused more on deeper heat and mass flows in regions below geothermal reservoirs, to provide understanding of the processes that transfer heat and chemicals from deep magmatic sources to the base of reservoirs and to surface discharge features.