Abstract
ABSTRACT The fingering phenomenon arises during the secondary and tertiary oil recovery processes when injected fluid (water, gases, nano/biomaterials, or polymer particles) shoots through a porous medium at a relative speed. Oil recovery is influenced by various factors including the fluid type, capillary pressure, permeability, and porous material structure. All these elements play crucial roles in determining the success and efficiency of the oil recovery process. Many scientists have debated the fingering phenomenon from different perspectives. Here, we developed mathematical models with and without considering mass flow rates of oil and water for an inclined oil layer flowing through a homogenous porous medium to generate immiscible fingers. Furthermore, a mathematical model of miscible viscous finger formation with carbonated water injection (flooding) during the enhanced oil recovery process (EOR) has been analyzed in this paper. To solve each of these mathematical models, we used the recently developed approach known as the Method of Directly Defining the inverse Mapping (MDDiM). We found approximate solutions to the nonlinear partial differential equations (PDEs), which describe each modeling of the fingering phenomenon in a homogeneous porous medium by incorporating gravitational effects for several types of flooding and discussed the effects of the saturation rate.
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