Chap. 10] ELECTRICAL METHODS 631 



rosity measurements. They are produced by the contact of fresh-water 

 drilling mud with the saline connate water solutions in sandy or other 

 porous la3^ers. Theoretically, the e.m.f. generated between two solutions 

 of the ion concentrations Ci and C2 is given by 



(10-2) 



where Ic and I.4 are the mobilities of the cation and anion, and n is their 

 valency. For a NaCl solution, for instance, n = 1, lc/(lc + U) = 0.4 

 and Ia/O-c + h) = 0.6. Therefore, the diffusion potential at standard 

 temperature E = 11.6 logio C1/C2 millivolts. If Ci = IOC2 , the potential 

 difference is 11.6 millivolts. Inasmuch as the concentrations are inversely 

 proportional to the resistivities of the drilling mud (p2) and the formation 

 water (pi), p2/pi may be substituted for C1/C2 , and therefore AE = 

 11.6-logio P2/P1 millivolts. 



(c) Electrofiltration potentials are likewise important in the measurement 

 of porosities in wells. They occur when a solution of the conductivity a 

 and the viscosity w is forced with a difference in pressure P through a 

 porous medium (or a number of capillaries) with the adsorption potential p 

 (potential of double layer on wall of capillaries, depending on concentra- 

 tion) and the dielectric constant k, so that the potential difference 



AE = /^ . (10-3) 



4tw- fl- 

 it is seen that the potential increases with the fluidity of the liquid and 

 with pressure and, therefore, with the speed with which the ions can be 

 transported. In wells the diffusion potentials are due to the penetration 

 of drilling fluid into porous formations; and they are usually negative and 

 of the order of 0.1 to 0.2 volts. When the drilUng mud is of the same 

 composition as the formation solution, electrofiltration potentials are the 

 only ones giving rise to spontaneous polarization. If, however, the ion 

 concentrations of the two liquids are different, both effects are superim- 

 posed on each other, and it is possible that the diffusion potentials over- 

 shadow the electrofiltration potentials in such cases. 



2. Polarization potentials are produced by applying an electric field to an 

 electrolyte. They are of importance in some "Eltran" methods, in the 

 determination of rock resistivities with D.C., in some applications of the 

 D.C. equipotential-line method, and in connection with the corrosion of 

 pipes. 



If an electrical field is applied to an electrolyte or rock containing mole- 

 cules in dissociated form, the ions move to the electrodes of opposite 



