Correspondence between membrane potential and conductivity
Combining the membrane potential [Formula: see text] with the corresponding ideal membrane potential [Formula: see text] and the liquid junction potential [Formula: see text], for the same activity ratio, gives [Formula: see text]. [Formula: see text] and [Formula: see text] are the reciprocal of the average of the reciprocal water conductivity and reciprocal of cation and anion conductivities, and [Formula: see text]; and [Formula: see text] is the average of the ratio of the water to the rock conductivity [Formula: see text] with respect to [Formula: see text], where t is the transport number for the Na ion, [Formula: see text] is the ionic concentration, and [Formula: see text] is the activity coefficient. This relationship is independent of any model and does not even refer to the value of clay counterion concentration. Combining σ with [Formula: see text] 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.