Analytical Investigation of the Effect of the Vertical Component of Water Oil Interfacial Tension on Capillary Number

Many definitions of the capillary number currently used in petroleum science neglect the contact angle or set it equal to zero by assuming strongly water-wet reservoir conditions. Nonetheless mixed-wet and oil-wet reservoirs are more common than water-wet ones. In those studies in which the contact angle or its cosine, respectively, is considered, wettability alterations are often treated independent of the water-oil interfacial tension. However, drastic reductions of the latter, which have been in the focus of studies on surfactant flooding for several years, should not be thought to leave the contact angle unchanged. Also, to the knowledge of the authors, the vertical component of water-oil interfacial tension and its effect on the capillary number have not been discussed in petroleum science by now. This value, described extensively by Kern and Müller (1991), is considered to be of some relevance in the mathematical treatment of microscopic wetting phenomena. Taking the vertical component of the interfacial tension into account, a new expression of the capillary number was derived to explain the connection between contact angle, oil-rock surface tension, water-rock surface tension and water-oil interfacial tension.