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Prediction of Two‐phase Relative Permeability Using a Modified Carman‐Kozeny Relationship: Comparing Model Results with Laboratory Measurements

Bac Ho DANG, Hoang Minh Nguyen, Son Hai Pham - 2014

Australian School of Petroleum

University of Adelaide


Relative permeability relationships are used to study multiphase flow in porous media, and are typically used in reservoir simulation. These relationships are obtained from laboratory experiments or they may be derived from semi-analytical or theoretical considerations. The main model used is based on a modified Carman-Kozeny equation, where the derived two-phase formulation is based on a hydraulic flowzone unit description, assuming that the saturation changes during (water) flooding and changes in saturation of the porous medium mimics the changes of a rock under the diagnostic influence in geological time, i.e. both are perturbations of the original pore space. This two-phase formulation of the Carman-Kozeny (MCK) equation is used to predict relative permeability.

This study focuses on the prediction of relative permeability for validating laboratory results, including cases where only endpoints are available. Furthermore, the study also aims at identifying the differences in laboratory results based on alternative laboratory methods, i.e. steady state versus unsteady state. Thirdly, the study compares different two-phase flows: water‐oil (O-W) and gas-water (G-W).

Laboratory data from 12 fields were analysed during this study. Analysed results showed that in several cases, initial and final laboratory measurements appear abnormal, arising from initial instability of the water phase entering the plug and fines plugging or water channelling during the last part of an experiment. In more severe cases, a plug may fail catastrophically, in which case laboratory relationships exhibit a flat or concave downward profile for the water phase, instead of the normal concave upward profile. In comparing the modified Carman-Kozeny model (MCK) with the modified Brooks-Corey (MBC) model, it is evident that the MBC model can only be used for data fitting rather than prediction. The reason for this limitation is the dependency of the MBC method on endpoints.

In some other cases, both methods give similar results, indicating a high degree of confidence. For selected cases where micrographs are available, it can be shown how sorting and grain size of a pore structure has an influence on residual oil saturation and relative permeability. Other researchers have also found that relative permeability profiles (oil-water system) are a function of the degree of sand consolidation and other factors such as viscosity of the oil, connate water and an immobile third phase (Honarpour, Koedritz, Harvey, 1986).

The last study involves a comparison of unsteady state and steady state methods. It could be confirmed that the steady state method generally gives more realistic results and the unsteady state method usually shows initial instability as water enters the plug. None of the methods can cater for severe plug heterogeneity, such as layering or fractures, a potential area of future research.


Australian School of Petroleum



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