Modelling Pore Structure By 2-D And 3-D Networks With ApplicationTo Sandstones
Authors: Chatzis I. , Dullien F.A.L. 
Published: March 2010

Abstract
The Present investigation is a study of the properties of 2-dimensional (2-D) and 3-D network models of capillary tubes generalized for any pore size distribution.
These properties include:the breakthrough condition subject to the step-by-step invasion of a non-wetting phase into an empty (evacuated) 2-D or 3-D "network;the accessibility of pores; andthe "pseudo' dead-end pore fractions, characteristic of the fractional amount of the non-conducting penetrated pore volume.
It was found that for infinitely deep networks the breakthrough condition is defined by the coordination number Z and the dimensionality of the network through the relations PrZ =2 and PrZ = 1.5 for 2-D and 3-D networks, respectively. 2-D networks do not allow the existence of bicontinua and, as such, they cannot simulate realistically 2-phase flow phenomena.
Generalized saturation plots for the accessibility of pores and the pseudo dead-end pore fractions have been established. It was found that the accessibility of pores and the pseudo dead-end pore fractions are determined by (i) the dimensionality of the network, (ii) the coordination numberof the network and (iii) the topology of pore interconnectedness at the microscopic level. The accessibility of pores found in the network analysis of the penetration process into 2-D and 3-D networks has been criticallytested by using:the experimentally known mercury porosimetry capillary pressure curves of two sandstone samples of known "complete" pore size distribution and the experimentally determined accessibility junctions; andthe saturation at breakthrough observed in mercury penetration experiments.
It was established that:the accessibility of pores predicted by the network Analysis of 2-D and 3-D network models of randomly distributed capillary tubes does not agree quantitatively with the quantities obtained experimentally;when the length of a capillary is of the same order of magnitude as its diameter, the saturation predicted at breakthrough is about 30% to 80%;with bulges present in the middle of capillary segments a lower-order relationship between the volume and the entry diameter of the segments could be assumed. Fairly good simulations of the experimental capillary pressure curve and the accessibility of pores have been obtained in the case of 3-D networks by assuming that the volume of a capillary segment is proportional to its entry diameter.

Introduction
EQUILIBRIUM AND TRANSPORT PHENOMENA in a porous medium are strongly dependent on the pore structure of the medium. As the macroscopic properties of a porous medium depend on the pore structure, a thorough understanding of this is important for the purpose of correlating various processes that involve porous media, The customary pore structure parameters, such as the porosity, the hydraulic diameter and the pore-of-entry size distribution, are insufficient for the interpretation of some important static phenomena (i.e. capillary pressure curves) and flow phenomena (i.e. relative permeabilities) in porous media, Permeable porous media contain 3-D networksconsisting of capillary segments or pores of various sizes.