VOLUME-AVERAGING ISSUES ILLUSTRATED FOR POROUS-MEDIA THERMO-FLUID TRANSPORT

This paper discusses the various issues causing errors in the formulation of volume-averaged equations for porous-media thermo-fluid transport. Proper implementation of the ground rules of porous-media volume averaging of the microscopic transport equations is demonstrated for formulation of the macroscopic mass, momentum, and energy equations. Because the ground rules of conventional (standard) porous-media volume averaging have been defined based on a constant representative elementary volume of bulk porous media, first the formulation of the porous-media macroscopic transport equations are carried out in terms of the bulk-volume averages of the various quantities and their divergence or gradient before converting the resulting superficial bulk-volume average quantities to intrinsic phase-volume average quantities. An important error concerning the bulk-volume averaging of fluid-volume averages is corrected and other errors involved in the formulation of the porous conservation equations are explained. The present implementation of the volume-averaging rules is shown to lead to consistent formulations. The properly formulated macroscopic equations are applied for a single-phase incompressible fluid that is saturating a rigid porous-solid material under thermal equilibrium conditions, both having constant physical properties. The improved formulation reveals the significant implications of the errors in a previous approach.