Mercury porosimetry in random sphere packings: Breakthrough pressure and pore structure determination

Abstract Previous investigators of mercury porosimetry and/or capillary condensation in random packings of spheres have stated that these pore analysis techniques can only extract size/structure information on a small fraction of the total number of pores as the result of network effects. These investigators have assumed that a central pore cavity is completely filled when sufficient pressure is obtained to force mercury through the largest pore throat to the cavity. However, this assumption neglects the fact that the other pore throats connecting the cavity will not fill at that pressure. In an effort to demonstrate that this continued filling of all pore throats will provide additional pore size/structure information, we have developed a model to describe filling of both the central cavity (or core) and the throats associated with the various faces of the core. Using a modified form of Mason's random sphere packing model, we have calculated pore filling/drainage as a function of dimensionless radius (r/R) and accounted for filling in all pore throats. Of the total pore volume, ≈ 11% was found to be associated with face filling. The dimensionless curvature was related to the actual intrusion pressure using both the Mayer—Stowe—Princen method and an inscribed sphere approximation. In addition to mercury porosimetry, application of this work can be extended to the behavior of both wetting and non-wetting fluids in random sphere packings. Mercury porosimetry experiments were conducted on three different porous solids over the pressure range of 12 to 33 000 psia. These solids were fabricated by pelleting monodisperse silica microspheres with average sphere diameters of 160, 206 and 410 nm. Pellet porosity ranged between 0.362 and 0.372, which is in excellent agreement to the accepted range for a close random packing of spheres. Two peaks in the pore volume distribution are noted with the smaller peak corresponding to intrusion in a pore formed by three close-packed spheres. Measured pore volume distributions ( d V/ d r versus r) are compared with the calculated pore volume distribution. Agreement between theory and experiment is good in terms of locating the two major ( d V/ d r)-r peaks and the respective heights of the two peaks. However, the experimental peak corresponding to initial breakthrough is sharper than the theoretical curve obtained using either the Mayer—Stowe—Princen (MSP) theory or inscribed sphere approximation. This is presumably a result of neglecting network effects in the model. A comparison of the actual pressure—volume intrusion curves with those calculated from the model do not show the same level of agreement. The predicted breakthrough pressure for the MSP approach is lower than that which is observed. This is the result of both network effects and approximations associated with our application of the MSP theory. By accounting for mercury intrusion in all pore throats, we have demonstrated that porosimetry does indeed yield significant pore size information for the smaller pore sizes and that network effects, while playing a major role during the initial breakthrough process, do not disguise pore structure information to the degree suggested by previous investigators.