Proposed Model to Match the Experimental Results for Oil Displaced by Externally Generated Foam

Abstract

Abstract A mathematical model was developed to predict the performance of the oil displaced by water foam in porous media. In this model, the diffusivity equations of both water foam (the displacing phase) and oil (the displaced phase) were combined in a single equation, which was solved numerically by a finite difference method, using the implicit-explicit method. The proposed model was compared with Poiseueille's model which represents the porous media by straight capillary tubes. It was found that the proposed model is superior to that of Poiseueille, because the Poiseueille model does not take into account the variations in foam properties along the sand pack. The production data used for the proposed model were obtained experimentally from the displacement of oil by water foam of different qualities (externally generated foam). The plastic viscosity of the water foam was measured experimentally for four foam quality ranges using capillary tubes of different sizes. The effective viscosity of the water foam determined from the plastic viscosity was used in the proposed model. Foam viscosity was found to increase as the quality increases, and the water foam obeys a Bingham plastic fluid model. The porous medium was represented by a sand pack whose length was 36 cm and diameter was 6.3 cm. Its absolute permeability was 341 md and porosity was 22.8%. The foam consisted of tap water, surfactant, and nitrogen gas.