A stochastic analysis of the flow of two immiscible fluids in porous media: The case when the viscosities of the fluids are equal

A new stochastic theory is developed to explain the flow of two immiscible fluids in porous medium when the viscosity difference between two fluids is zero. In an individual micropore the radius of curvature of the interface separating the fluids is assumed constant and flow is modeled by the random jumping of microscopic interfaces. A one dimensional model composed of an array of parallel capillary tubes of constant radius is analyzed in detail. For the case in which two fluids have equal viscosity an analytical solution is obtained. The fluid displacement process is Fickian and dispersion is described in terms of a diffusion or spreading constant.