Extending Darcy's law to the flow of yield stress fluids in packed beds: Method and experiments

A large number of complex fluids commonly used in industry exhibit yield stress, e.g., concentrated polymer solutions, waxy crude oils, emulsions, colloid suspensions and foams. Yield stress fluids are frequently injected through unconsolidated porous media in many fields such as soil remediation and reservoir engineering, so modelling their flow through this type of media is of great economic importance. However, obtaining macroscopic laws to model non-Newtonian flow poses a considerable challenge given the dependence of the viscosity of the fluid on pore velocity. For this reason, no macroscopic equation is currently available to predict the relationship between injection flow rate and the pressure drop generated during the flow of a yield stress fluid without using any adjustable parameter. In this work, a method to extend Darcy's equation to the flow of yield stress fluids through model unconsolidated porous media consisting of packs of spherical beads is presented. Then, the method is experimentally validated through comparison with a total of 572 experimental measurements obtained during the flow of a concentrated aqueous polymer solution through different packs of glass spheres with uniform size. An improved prediction of the pressure drop-flow rate relationship is achieved by taking into account the non-linear relationship between apparent shear rate and average pore velocity.