Abstract

Three different types of measurement:

  1. determination of formation factors,

  2. measuring the rate of capillary rise, and

  3. determination of "pseudo-dead-end-pore volumes" at different applied capillary pressures have been carried out.

"pseudo-dead-end-pore volumes" are measured by the volume of mercury, or some other non-wetting liquid, contained in the porous medium that is not flowing in a relative permeability test because the exits of the pores containing the non-flowing liquid are too narrow to penetrate at the prevailing capillary pressure. Pseudo-dead-end-pore volumes have been determined by penetrating the sample with mercury at increasing capillary pressures and miscible displacing the mobile part of the mercury with radioactive mercury at each capillary pressure.

A mathematical network model of porous media has been used to calculate, in addition to the permeabilities, the formation resistivity factors and the apparent diameters of capillary rise. The input data consisted of the mercury intrusion porosimetry curve and the photo micrographic pore size distribution of the sample.

Experimental determination of the "pseudo-dead-end-pore volumes" as a function of capillary pressure permits a correction of the mercury intrusion porosimetry curve such that it gives the relationship between the neck diameter and the pore volume, the flow through which is controlled by that diameter. This correction is very significant (about 50 volume %) near the threshold capillary pressure of penetration. Relative permeability calculations can be based, in the future, on the mobile volume instead of the total penetrated volume.

Introduction

Transport and capillary phenomena in porous media are strongly dependent on the pore structure of the medium and, therefore, it is important to search for a model of the pore structure which is both representative and sufficiently simple to permit numerical calculations of the phenomena of interest. Attempts to develop a model which is capable of characterizing single phase transport phenomena have been reported in series of papers by Dullien and coworkers (1–8).

The model proposed in these contributions contains some drastic simplifications of the actual three-dimensional interconnected pore network it is meant to simulate. In a first approximation it has been assumed that the real network can be characterized as a set of independent networks, while realizing that if these networks intersect with each other they will result in an increase in the conductivity over and above the sum of conductivities of the set of networks.

Each class I of the set consists of different representing capillary elements, shown in Figure 1, which form a cubic network (see Figure 2). The representing capillary elements in the different classes I have different pore diameter distributions Vi j ≡ (Dj, Dj) ΔDi ΔDj (see Figure 3), where Vi j is the (normalized) volume of a capillary segment of diameter Dj, the flow through which is controlled by diameter D1. It is evident that class I of the set is characterized by the controlling diameter Dj. The distribution function (Di, Dj) has been called "bivariate pore volume (or, pore size) distribution".

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