Flow in porous media of variable permeability and novel effects

The flow of polymeric liquids in a porous medium of variable permeability represented by a cylindrical tube randomly packed with glass spheres is studied. The cylinder represents two porous media of different permeabilities and same porosity arranged in series. We show that the energy loss is higher if the polymeric solution flows first through the porous medium with the smaller permeability rather than through the section of the cylinder with the larger permeability. The difference in energy requirements increases with increasing Reynolds number and may be as high as 25-35 percent for Reynolds numbers of O(I). This is a novel effect not observed for Newtonian and highly shear thinning inelastic fluids flowing through the same configuration. Energy requirements for the same volume flow rate are much higher than a Newtonian fluid of the same zero shear viscosity as the polymeric solution. Energy loss increases with increasing Reynolds number at a fixed concentration to level off at a Reynolds number of O(I). At a fixed Reynolds number, the loss is a strong function of the concentration and shows large increases with increasing concentration. For shear-thinning oil field spacer fluids De similar to 0.1 represents a good criterion for the onset of elasticity effects. For solutions of polyacrylamide De similar to 0.1 corresponds approximately to the flow rate at which pressure drop starts becoming dependent on the flow direction. Expressions for the friction factor and the resistance coefficient as a function of the Reynolds number have been developed using the inelastic KPK (Kutateladze-Popov-Kapakhpasheva) and viscoelastic eight constant Oldroyd models, respectively. The behavior of inelastic shear-thinning and viscoelastic fluids as represented by oil field spacer fluids and aqueous solutions of polyacrylamide is predicted qualitatively except the difference in energy requirements when the flow direction is reversed in the case of the latter.