Moving Boundary Problem in a Geothermal Chamber

Abstract

In previous studies, unsteady free convection within a geothermal reservoir has been investigated by the finite element analysis. The problems of heat and mass transfer in a hot magma includes not only unsteady free convection but also phase changes after intrusion into the country rock. The consideration of phase changes is necessary to describe the mechanism of heat transfer in a magma body in a general mode. The problem under investigation can be defined as a two phase Stefan problem associated with moving boundaries. To study the effect of phase changes on the solidification of a magma, one dimensional, two phase Stefan formulation is developed by the finite element method after using the Duvaut's transformation to resolve the discontinuity of the temperature gradient on the solid liquid interface. The convection gradients in the upper portion of the magma are more steep than those in the lower by transporting the heat at the bottom upward.