636 



ELECTRICAL METHODS 



(Chap. 10 



r' • TT • n. Since the resistance in the direction of the tube is inversely propor- 

 tional to its area, — = — — , so that 

 irr^n. 



pi 



Px 



pi 



3 



Vi' 





(10-7e) 



The relation (10-7d) is 

 shown graphically in Fig. 

 10-2. Resistivities deter- 

 mined by this diagram 

 are in good agreement 

 with resistivities actually 

 observed. 



Table 60 gives some 

 values for the porosities of 

 various types of rocks, for- 

 mations, and soils, and for 

 the corresponding values 

 for the resistivity ratio 

 Px/pi. 



In the derivation of pre- 

 ceding equations, no as- 

 sumption was made in 

 regard to the spacing of 

 the mineral grains or pore 

 spaces, respectively. For 

 definite ratios of spacing to 

 size of the grains, it is possi- 

 ble to determine the pore volume and therefore the resistivity ratio 

 Px/pi ■ Table 61 (largely from Sundberg) gives these values for various 

 grain arrangements. This tabulation brings out the fact that the re- 

 sistivity may in certain cases depend on the direction of current with 

 respect to the arrangement of the particles. Materials of such nature are 

 called anisotropic. Anisotropy of resistivity plays an important part in 

 all stratified formations where resistivities in the bedding planes are 

 generally quite different from those at right angles thereto. 



It was shown before that the resistivity of a rock can be found if the 

 pore volume, the pore arrangement, and the resistivity of the water filling 

 the pores is known. The latter may be determined by experiment if 

 specimens of well or formation water have been taken. If the specimen 

 itself is not available, but only its analysis is, the conductivity can still 

 be calculated. For this purpose it is first necessary to recalculate the 



Fig. 10-2. Relation between resistivity ratio pi/pi 

 and porosity (after Sundberg). 



