A PHYSICAL MODEL FOR POROSITY REDUCTION IN SANDSTONES

The experimental elastic moduli-porosity trends for clean sandstones c an be described by the modified upper Hashin-Shtrikman (MUHS) bound. O ne geometrical (but not necessarily geological) realization is: as por osity decreases, the number of the pens stays the same and each pore s hrinks while maintaining its shape. This concept of uniform porosity r eduction implies that permeability is proportional to the effective po rosity squared, and that formation factor is proportional to the inver se of the effective porosity. The effective porosity here refers to th e part of the pore-space that dominates fluid flow. The proposed relat ions for permeability and formation factor agree well with the experim entally observed values. These laws an different from the often used f orms of the Kozeny-Carman equation and Archie's law, where permeabilit y is proportional to the total porosity cubed and formation factor is proportional to the inverse of the total porosity squared, respectivel y. We suggest that the uniform porosity reduction concept be used in c onsolidated rocks with porosities below 0.3. The transition from high- porosity unconsolidated sands to consolidated sandstones can be descri bed by the cementation theory: the MUHS moduli-porosity curves connect with those predicted by the cementation theory at the porosity of abo ut 0.3. This scheme is not appropriate for modeling other porosity red uction mechanisms such as glass bead sintering because, during sinteri ng, the pores do not maintain their shapes, rather they gradually evol ve to rounder, stiffer pores.