Determination of Pore Accessibilities - An Approach
Authors: Dullien F.A.L. 
Published: December 2007

It seems to be a generally held view at present that the pore structure of most porous media is better represented by a model consisting of voids separated from each other by constrictions than one consisting of capillary tubes. The geometrical quantities - pore volume, surface area, and pore size distribution - that have been used in the past to describe the structure of porous materials do not yield any information on the accessibility of pores. Mercury porosimetry measures the equivalent pore entry radii re' in relation to the volume of voids of equivalent radii r, such that re &gt;re'. The analysis of adsorption and desorption isotherms must contend with difficulties similar to those of mercury porosimetry. We feel that a more accurate geometrical characterization of pore structure would benefit the petroleum industry as well as other industries. petroleum industry as well as other industries. Assuming that the pore structure consists of voids separated from each other by constrictions, it is proposed that each void be characterized by its proposed that each void be characterized by its equivalent radius re and by the equivalent radius re' of its pore of entry. This information can be condensed in pore of entry. This information can be condensed in a bivariate distribution function alpha(re, re') dre dre', giving the frequency of voids with radii in the range between re and re + dre and With pore entry radii in the range between re' and re' + dre'. The following is a brief outline of the experimental procedure that is being used in the Petroleum procedure that is being used in the Petroleum Engineering Dept. of the U. of Waterloo for experimental determination of alpha(re, re') dre dre' in some sandstone samples. Mercury porosimetry permits measurement of re' through the equation
(1)
If the mercury in the pores at a particular Deltap were frozen and the size distribution of the mercury "particles" in the voids were determined by some particles" in the voids were determined by some independent method, we would obtain the distribution function alpha(re, re') dre giving the frequency of voids with radii in the range between re and re + dre, and with pore entry radii equal to or greater than re'. For reasons of convenience, low melting Wood's metal alloy is being used in this work instead of mercury. Performing similar experiments on a series of identical samples (core samples were cut into a number of shorter pieces) at different pressure differentials deltap2 We obtain alpha(re, re') dr, as a function of re'. From this information the accessibility distribution function is calculated as
(2)
Assuming that the voids may be regarded as distinct particles alpha(re, re') dre is determined by micrographic analysis of polished sections of the sample using methods developed by metallographers (among others) for the determination of grain size distributions. We have tested these methods recently in computer simulation studies. The immediate purpose of this work is to determine to what extent alpha(re, re') dre dre' can be used as a measure of the "structural difficulty" of recovering oil by water and water additive floods. The underlying assumption is that oil in voids with narrow necks tends to get cut off by the water and it can be recovered only by squeezing the oil drops through the necks under the influence of the pressure differential
(3)