Waterflood, or other forms of immiscible displacement, have been the most widely used mechanism for secondary recovery and the determination of individual phase's relative permeability has been crucial for many reservoir engineering applications. Traditionally there are two ways of determining the relative permeability from laboratory experiments: the steady state experiment and the unsteady state experiment. The steady state experiment has the disadvantages of being time-consuming, obtaining few points on the relative permeability curves, as well as not being identical to the true reservoir displcacement process. On the other hand, the Johnson-Bossler-Naumann (JBN) method, based on Buckley-Leverett (B-L) immiscible displacement theory, is the standard procedure used to determine relative permeability from unsteady state experiments. However, the neglect of capillary pressure effect in the Buckley-Leverett theory has placed limitations on the method, such as requiring high flow rates. In order to remove the limitations of the displacement experiments and give more flexibility to the experiment configuration, an analytic model with capillary corrections is presented in the context of viscous dominated flow to study the impact caused by capillarity. The solution shows a fixed water-oil saturation bank at the outlet whose magnitude depends upon the wettability of the system. The analytic model is able to predict the saturation profile, considering capillarity, under various rock and fluid properties and experimental configurations. Therefore, the model could be used to calculate accurate relative permeability by matching experimental pressure drop and production reponses, correcting for capillarity. Also, through this method, a dimensionless parameter could be provided to quantify the effect caused by capillary end effect based on the length scale affected. It reflects the influence from a variety of aspects, not only from the experimental settings.

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