Combining the membrane potential E m with the corresponding ideal membrane potential E i and the liquid junction potential E lj , for the same activity ratio, givesEquationsigma w and sigma (sub + or -) are the reciprocal of the average of the reciprocal water conductivity and reciprocal of cation and anion conductivities, and sigma = sigma (sub +) + sigma (sub -) ; and <sigma w /sigma > is the average of the ratio of the water to the rock conductivity sigma w /sigma with respect to (1 - t) d ln ngamma + or -, where t is the transport number for the Na ion, n is the ionic concentration, and gamma (sub + or -) is the activity coefficient. This relationship is independent of any model and does not even refer to the value of clay counterion concentration. Combining sigma with E m gives the saturation dependent formation factor F, and thus the interpretation of shaly sands becomes no more difficult than for clean sands. Experimental data on 27 rocks for which both membrane potential and conductivity were measured by Smits (1968) and Waxman and Smits (1968) over a large salinity range are used to verify this relationship.

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