Theoretical study of micropolar fluid flow in porous media

Abstract

In this paper, a mathematical model of Hele-Shaw flow was developed on the basis of the field equation of micropolar fluid. The motion equation of micropolar fluid was extended to flow in porous media, contributing to the mathematical model of the unsteady radial flow of micropolar fluid in an infinite reservoir. The relations between flow velocity, pressure gradient and flow rate were obtained by solving the mathematical model under fixed production internal boundary and fixed-pressure external boundary conditions. In addition, the effect of the physical properties of micropolar fluid on its flow was analyzed. The results indicated a significant dependence between the apparent permeability and physical properties of micropolar fluid, which clearly deviated from the Newtonian fluid. The results showed that, as the ratio of rotational viscous force to Newtonian viscous force in the micropolar parameter and the characteristic length of the micropolar metamaterial increase, the non-Newtonian characteristics of the fluid become gradually more significant. The non-Newtonian behavior of micropolar fluid consequently becomes unneglected, leading to a decreasing apparent permeability. Compared with a Newtonian fluid, a micropolar fluid causes obvious flow resistance, resulting in larger energy consumption and lower flow rate. This study can provide an academic reference for nonlinear rheology and the flow of heterogeneous fluids in the fields of petroleum engineering and biofluid flow.