A theoretical and experimental study of the steady state capillary end effect

Abstract

Formulas are derived for calculating the steady state saturation profile and pressure profile resulting from the end effect. A numerical integration is required to obtain the results. Two dimensionless numbers containing various parameters of the system are introduced, which, along with the viscosity ratio and the fractional flow of one component, characterize the system. It is suggested that the magnitude of the end effect can be estimated just knowing these numbers. Sample calculations are carried out showing the influence of the various parameters on the end effect. A discussion is given to show that in the measurement of relative permeability curves by the dynamic method, the end effect has a large influence on the preferentially nonwetting phase relative permeability curve if the pressure drop is measured in the wetting phase. If the pressure drop is measured in the nonwetting phase, the largest error appears in the wetting phase curve. If the pressures are measured in both phases, the errors tend to be self-correcting for each relative permeability curve. End effects were measured experimentally on a Boise core for water-oil and gas-oil systems. Three different rates were used in each series. There was satisfactory agreement between the theory and experimental results.