POROSITY DOMAIN THEORY: IMPLICATIONS AND APPLICATIONS

Porosity Domain Theory (PDT) explains how the full possible range in intrinsic total porosity values in a granular material can be divided into three distinct domains.  Each total porosity domain in PDT can physically be defined by limits on the amount of pore space that is available for the transport of free fluids.  The amount of this pore space is defined herein as effective porosity n_e.  The effective porosity does not include pore space occupied by bound liquid or trapped gases, which together define ineffective porosity n_ie. The intrinsic total porosity n is the sum of effective and ineffective porosities.

 

In PDT, the three total porosity domains are separated by a granular material’s porous percolation threshold n_p, the porosity below which all pores are disconnected, and it’s critical porosity n_c, the porosity above which all grains are disconnected.  In total porosity Domain I, total porosity is less than the material’s percolation threshold (0 < n < n_p); all of the pore space is disconnected (n = n_ie) so that no pore space is available for fluid flow (n_e = 0).  In Domain III, total porosity is greater than the material’s critical porosity (n_c < n < 1); the grains are in suspension so that all pore space is available for fluid flow (n = n_e and n_ie » 0). Rarely in natural settings do total porosities fall within Domains I or III, however their limits set limits for Domain II (n_c < n < n_p), the domain of most natural granular porous materials.  In Domain II, the grains and pores are connected, and the amounts of the effective and ineffective porosities depend on surface tensions and viscosities of the bounding liquids.   The effective – total porosity relationship in porosity Domain II is defined by the material’s characteristic percolation threshold, critical porosity, and pore characteristic parameter.

 

PDT is simple and intuitive, yet the implications are rather significant.  Each total porosity domain is not only physically distinct, but also hydraulically, elastically and electrically distinct.  Therefore, PDT should be used when modeling fluid and electrical flows and when employing rock physics relationships to define the intrinsic pore space of granular materials.