Unsteady Flow of Bingham Fluid Between Two Permeable Beds

As the application of chemical industry and oil and gas industry, fluid flow in the pipeline
is governed by Navier-Stokes equations. Darcy’s law is to express the fluid flow behaves
in the porous medium. As the oil and gas industry interested on the heavy oil, the study
focus on the heavy oil behaves in between permeable beds. The combination of Navier-
Stokes and Darcy explain the behavior of heavy oil in between permeable beds. Pressure
is assumed to vary exponentially with respect to time. Bingham fluid was deduced for
velocity field between beds and between rigid walls, shear stress and mass flow rate for
lower zones, upper zones and plug flow region. Findings have shown that permeable beds
increases the velocity of the fluid flow compared to the rigid wall condition. It also found
out low σ increases the fractional increase drastically after σ<6.