Immiscible multiphase flow in ground water hydrology: a computer analysis of the well flow problem

Abstract

A mathematical analogue of immiscible multiphase flow in porous media is derived considering three compressible fluids -- two liquids and one gas. Isothermal conditions are assumed so that fluid properties such as compressibility, density, viscosity, and solubility of gas in the liquid are functions of fluid pressure only. A well flow computer simulator is developed by discretizing the mathematical analogue with fully implicit finite differences. A Newton iteration scheme is utilized to solve the system of non-linear difference equations. The problem solved in this study is that of free surface gravity well flow, including the effect of partial penetration. A theoretically accurate solution is obtained concluding that unconfined well flow is a multiphase flow phenomenon affecting aquifer response. The importance of capillarity, of air dissolved in water, or water compressibility, as well as the effect of the multiphase flow approach upon the shape of the free surface are discussed. Practically, it is concluded that confined well flow analyses do not apply to free surface gravity well flow problems.