The capillary pressure J-function is a dimensionless measure of the capillary pressure of a fluid in a porous medium. The function was derived based on a capillary bundle model. However, the dependence of the J-function on the saturation Sw is not well understood. A prediction model for it is presented based on capillary pressure model, and the J-function prediction model is a power function instead of an exponential or polynomial function. Relative permeability is calculated with the J-function prediction model, resulting in an easier calculation and results that are more representative.
Xu, W. S., Luo, P. Y., Sun, L., & Lin, N. (2016). A prediction model of the capillary pressure j-function. PLoS ONE, 11(9). https://doi.org/10.1371/journal.pone.0162123