Effect of Interfacial Tension on Water/Oil Relative Permeability and Remaining Saturation with Consideration of Capillary Pressure
Authors: Andrew Chukwudeme Edwin , Fjelde Ingebret , Abeysinghe Kumuduni , Lohne Arild 
Published: September 2011

Abstract
In surfactant flooding, a conventional assumption is to neglect the effect of capillary pressure on measured two-phase flow properties such as remaining saturations and relative permeabilities. This often leads to poor interpretation of laboratory data used as input in surfactant models. This paper describes the experimental and simulation work undertaken to study how the remaining saturation at different capillary number can depend on capillary end effects and production rate.
Three fluid systems of different interfacial tensions (IFTs) were prepared using a solvent system (CaCl2-brine/iso-octane/iso- propanol) rather than a surfactant system with the assumption that both systems have similar flood behaviour at reduced interfacial tension. Three core flood cycles, including multirate oil injection (drainage) followed by multirate water injection (imbibition), were carried out at each IFT in water-wet Berea cores. Relative permeability functions corrected for capillary end effects were derived by numerically history-matching of the experimental production and pressure drop history.
A typical capillary desaturation curve (CDC) is observed for the non-wetting phase oil, with a roughly constant plateau in residual oil saturation, Sor, below a critical capillary number (Ncc) and a declining slope above Ncc towards zero Sor. No influence of capillary pressure was found for the non-wetting phase CDC.
The results from displacement of the wetting phase formed an apparent CDC with declining slope and no critical capillary number. Analysing the wetting phase results, we find that the wetting phase CDC is not a true CDC. Firstly, it is a plot of the average remaining water saturation in the core which in all the experiments is higher than residual water saturation, Swr, obtained from capillary pressure measurements. Secondly, we find that the remaining water saturation is only partly a function of Nc. At low Nc, the water production is limited by capillary end effects. Rate dependent water production observed with the high IFT system is fully reproduced in simulations using constant relative permeability and capillary pressure. The remaining wetting-phase saturation at low Nc is a result of the core-scale balance between viscous and capillary forces and would e.g., depend on the core length. At higher Nc, the water production is found to be limited by the low relative permeability tail typical for wetting phases. However, we find that the relative permeability functions become rate dependent at higher Nc, and this rate dependency can assumingly be modelled as function of Nc. The remaining wetting phase saturation at higher Nc would then be a function of Nc and the number of pore volumes injected. The observed Nc dependency in the flow functions indicates a potential for accelerated production of the wetting phase by using surfactant.
Assuming that the results obtained here for the wetting phase also applies to oil in a mixed-wet system, it is strongly recommended to evaluate both the effect of capillary pressure and capillary number when designing a surfactant model for a mixed-wet field.