Relative permeability (kr) and capillary pressure (Pc) are the most important flow functions in numerical simulation of multiphase flow in porous media. The values of kr and Pc are conventionally measured in separate experiments often with different methods. kr curves are usually measured by performing corefloods in the laboratory using two methods namely, ‘steady state’ and ‘unsteady state’ experiments. Pc is normally measured by mercury porosimetry, the porous plate method or by centrifuge method. The drawback of determining relative permeability and capillary pressure separately is that they may not be consistent with each other and the measured Pc does not correspond to the kr which is measured from dynamic flow system. Therefore, simultaneous determination of Pc and kr for a given system would be preferred. History matching techniques have been applied in the past to estimate relative permeability and capillary pressure simultaneously from unsteady state core flood experiments. In previous attempts, two independent functions were used to generate these two flow functions in the process of the history matching. To reduce the associated non-uniqueness problem of history matching, some in-situ measurements such as saturation and pressure profiles may be included in the history matching data but this information is rarely available.

The objective of this study is to honor a known relationship between the core relative permeability and the Pc curve and improve the optimization process and the accuracy of the estimated Pc and kr. Making the kr function dependent on the Pc in the history matching process will reduce the number of tuning parameters and is expected to reduce the uncertainty associated with the history matching process. A Purcell type model, which is based on the physics of fluid displacement, is used as the basis for linking the permeability (or relative permeability) to Pc.

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