BORE-HOLE INVESTIGATIONS 1039 



E = B±P (7) 



V 



where E = electromotive force ; m = a constant which depends on the 

 porous medium ; p = resistivity of the fluid ; p = the differential hydro- 

 static pressure ; v = viscosity of the flowing electrolyte. 



According to Poiseuille'sf law, the quantity Q of fluid which flows 

 through a given capillary tube at a pressure p is : 



e=^ (8) 



where m' is a constant. 



On combining Equations 7 and 8 one obtains 



^_ wp_Q 



or 



E = constant • pQ (9) 



Equation 9 states that the electromotive force of filtration for a given elec- 

 trolyte and pervious medium is proportional to the product of the amount 

 of liquid which is filtered and the electrical resistivity of the liquid. 



Generally, the potential opposite a surface of ingress will be negative 

 with respect to that opposite a surface of egress. That is, in the usual case, 

 a potential measured opposite a porous formation will be relatively negative 

 if the bore-hole fluid is flowing into the formation, and relatively positive 

 if the formation fluid is flowing into the hole. 



The electrofiltration potentials are a minimum at the boundaries of the 

 porous zone and a maximum in the most permeable section. The mag- 

 nitude of the electrofiltration potential differences may be of the order of 

 100 to 200 millivolts over a length of a few meters. 



It has been suggested that formation pressures may be determined from electro- 

 filtration potential measurements by using Equation 7 twice.f To develop the relevant 

 mathematical theory, it is convenient to write Equation 7 in the form : 



E=kiH-P) (10) 



where k is a constant for a given porous medium and electrolyte; H is the pressure 

 of the well fluid; P is the pressure of the formation fluid. If the fluid level in the 

 well is lowered, by bailing for example, then for the new hydrostatic pressure H' 



E' = k(H' — P) 

 Hence, 



-g-r. ^~^ (11) 



£' H'-P ^ ^ 



Theoretically, therefore, it is possible to determine the pressure P of the forma- 

 tion fluid by altering the fluid level and observing the quantities : E/E', H/H', and 

 H or H'. 



t Poiseuille, Comptes Rendus (1842), 18, 1167. 



t C. and M. Schlumberger and Leonardon, loc. cit., p. 262. 



