Chap. 11] 



GEOPHYSICAL WELL TESTING 



851 



applied on one side, the wax will melt along a broken line which makes 

 the angles ^i and ipi respectively, with the diagonal. Then C\ = 

 C2 tan ^i/tan ^2 , where the subscripts 2 refer to the standard material. 

 Another convenient relative method,^^ shown in Fig. ll-20c, places the 

 specimen, of the conductivity C\ and thickness d\ , in series with a standard 

 of the conductivity Ci and thickness di , with a copper plate between them. 

 If a thermal gradient is now produced by heating one side and cooling the 

 other, the conductivity of the specimen follows from that of the standard 

 ajid from the respective thermal gradients : 



Cl = C2 



rfi 62 — 63 

 di 61 — 62' 



(11-7) 



Anisotropy of heat conduc- 

 tion may be determined by 

 covering the surface of a 

 specimen with wax, apply- 

 ing heat at one point, and 

 measuring the axes of the 

 melting ellipse. 



Variations in thermal 

 conductivity of rocks and 

 formations are of profound 

 influence upon the thermal 

 gradient. Since the heat 

 current, that is, the quan- 

 tity of heat transferred in 

 the unit of time through a 

 plate of section S and thick- 

 ness d, is given by 



fOOO' 



ZOOO' 



3000' 



Depth 



Q = 



C(62 - 61) S 

 d 



(ll-8a) 



Fig. 11-21. Depth-temperature curve, showing 

 effect of change in thermal conductivity (15 miles 

 southeast of Thompsons, Grand County, Utah). 

 (After Van Orstrand.) 



and since c?/(62 — 61) is the 



reciprocal temperature gradient, or 1/b (see page 844), it is seen that 



1 _ S 



b " q''' 



(11-86) 



Hence, the reciprocal gradient is directly proportional to the heat con- 

 ductivity of a formation. This is well illustrated in Fig. 11-19 and par- 

 ticularly in Fig. 11-21, where a reduced slope (large reciprocal gradient) 

 corresponds to the increased conductivity of the salt. With the value of 



"^C. Christiansen, Ann. Physik., 14, 23-33 (1881). 



