Klinkenberg (or slip) effect

The Klinkenberg effect is a gas flow phenomenon and occurs if the mean free path is of the same magnitude as the pore diameter. Gas then no longer “sticks” to the walls of the pore channels but slips along them. The mean free path of Brownian motion depends on pressure, temperature and the type of gas. It decreases with increasing pressure. According to Klinkenberg (1941) the apparent permeability (falsified by the slip effect) k_a is a function of the true permeability k₀, the mean, absolute gas pressure within the specimen p and a the Klinkenberg factor b_k:

k_a = k₀*(1 + b_k/p)

Plotting k_a vs. 1/p gives b_k as the gradient of the regression line of the individual data points and k₀ as the intersection point of this regression line with the ordinate at 1/p = 0 bar^-1. The Klinkenberg effect increases with decreasing permeability, decreasing gas pressure and decreasing gas viscosity. For practical considerations it can be assumed that the Klinkenberg effect plays an important role for k < 0.1µm². In case of sandstone and dolomite the Klinkenberg factor b_k can be assumed to follow the empirical relation:

b_k = 4.84*10-3k_a^-0.35 (Häfner et al. 2009).