The nature of flows through porous media

Abstract

The present paper points out that the pressure drop of a porous media flow is only due to a small extent to the shear force term usually employed to derive the Kozeny—Darcy law. For a more correct derivation, additional shear terms have to be taken into account since the fluid is also exposed to elongational forces when it passes through the porous media matrix. These are usually not taken into account in the conventional theoretical treatment of flow through porous media as is explained in the literature. This explains why the available theoretical derivations of the Kozeny—Darcy relationship, which are based on one part of the shear-caused pressure drop only, require an adjustment of the constant in the theoretically derived equation to be applicable to experimental results. Details of this derivation are given in this paper and existing derivations are extended to yield better agreement with experiments. To verify experimentally some of the results of the theoretical derivation provided, porous media flows of dilute polymer solutions are studied experimentally. It is shown that the addition of small amounts of high molecular weight polymers to a solvent with Newtonian flow properties causes drastic pressure drop increases if the flow rate exceeds an onset flow rate corresponding to a critical Deborah number of the porous matrix-polymer solution system. This can only be explained if the flow field in the porous medium is exposed to shear and elongational strain. The extent of this interaction is deduced from experimental findings.