Assessing Relative Permeabilities of Two Phase Flows of Water and Steam in Geothermal Reservoirs: State of the Art Relations

Abstract

A basic understanding of two phase flow of water and steam in geothermal reservoirs is essential to predict the performance of high temperature geothermal wells and reservoirs. Current simulation tools for liquid dominated reservoirs base flow calculations on the traditional Darcy equation, where flow is a function of fluid parameters such as density and viscosity, as well as the intrinsic permeability of the surrounding media to transmit fluid. For two phase flow of water and steam, this approach is based on the relative permeability of each phase, which is the effective portion of the intrinsic permeability for the phase. The traditional flow relation neglects interfacial shear forces and buoyancy effects acting between the two phases, introducing errors unless the two phases are flowing in completely separated channels. Thus, this formulation predicts that relative permeability is linearly dependant on the water saturation, since it should only account for the portion occupied by that phase in the cross sectional area of the flow channel. Experiments, generally with one dimensional flow, have shown this not to be the case, indicating that the relative permeability scales with the water saturation with an exponent greater than one (Eliasson et al. 1980, Verma 1986, Piquemal 1994, Satik 1998, Mahiya 1999). In this paper a literature review is presented together with a theoretical analysis of one dimensional two phase flow, using the concept of relative permeabilities as variable functions of water saturation. It is shown that relative permeabilities cannot be material constants but must also depend on flow configuration, thus relationship between water saturation and relative permeabilities must be developed in order to generate predictions more in accordance with observed experimental results. This paper states the theoretical groundwork for a large scale experimental study of the relative permeabilities of two phase flow of water and steam. The goal of the experimental work is to develop empirical relationships for two phase flow, using relative permeabilities, that describe the flow more accurately than existing formulations do.