Mathematical modeling and inverse mapping to find the saturation of carbonate-water in the fingering phenomenon

Abstract

The fingering phenomenon occurs during the secondary oil recovery process when the water is injected at a relative speed through the porous media. Water injection (water flooding) is a cheap and very effective method that depends on the oil-water viscosity ratio. Carbon Dioxide is a miscible gas with both oil and water, and it can reduce the viscosity of oil in a process called swelling. That led scientists to study water injection together with CO2 gas in the oil recovery process to recover important potion of oil. For the first time, in this study we build up a mathematical model to find the saturation of carbonate-water of the fingering phenomenon and, also discussed the effect of the inclination angle of the oil layer. To determine the parameters of this model we used the Method of Directly Defining the inverse Mapping (MDDiM) which is a novel technique to solve nonlinear differential equations.