A pore-network model is adopted to simulate fluid flow in porous media. The model is examined for two different hydrophobic loadings. A new algorithm for displacing the fluid inside the porous medium is developed. The algorithm uses an effective pressure as a combination of capillary pressure and hydrodynamic pressure. The capillary pressure is a function of pore size distribution and the wettability characteristics of the medium while the hydrodynamic pressure is correlated to the local saturation of the pores. Thus, the algorithm automatically switches between the capillary driven and the viscous displacement mechanisms based on the value of the local capillary number. The results are compared with the available experimental and numerical data.

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