Rate of capillary rise in porous media with nonuniform pores

An equation for the rate of capillary rise in porous media with nonuniform pores has been derived on the basis of a three-dimensional network model of pore structure, consisting of a repeating capillary element with step changes in its diameter. The measured rates of capillary rise of water in a number of sandstone samples have been accurately predicted by the model. The apparent capillary diameter for the rate of the capillary rise has been found to be several orders of magnitude smaller than the pore diameter corresponding to the peak of the mercury intrusion porosimetry curve. The permeability of the sandstone samples has been found to be approximately directly proportional to the apparent diameter of the rate of capillary rise. This approximate proportionality has been shown to follow from the capillary network model of the pore structure used in this work.