A physical model for porosity reduction in sandstones

The experimental elastic moduli-porosity trends for clean sandstones can be described by the modified upper Hashin-Shtrikman (MUHS) bound. One geometrical (but not necessarily geological) realization is: as porosity decreases, the number of the pens stays the same and each pore shrinks while maintaining its shape. This concept of uniform porosity reduction implies that permeability is proportional to the effective porosity squared, and that formation factor is proportional to the inverse of the effective porosity. The effective porosity here refers to the part of the pore-space that dominates fluid flow. The proposed relations for permeability and formation factor agree well with the experimentally observed values. These laws an different from the often used forms of the Kozeny-Carman equation and Archie's law, where permeability is proportional to the total porosity cubed and formation factor is proportional to the inverse of the total porosity squared, respectively. We suggest that the uniform porosity reduction concept be used in consolidated rocks with porosities below 0.3. The transition from high-porosity unconsolidated sands to consolidated sandstones can be described by the cementation theory: the MUHS moduli-porosity curves connect with those predicted by the cementation theory at the porosity of about 0.3. This scheme is not appropriate for modeling other porosity reduction mechanisms such as glass bead sintering because, during sintering, the pores do not maintain their shapes, rather they gradually evolve to rounder, stiffer pores.