846 



GEOPHYSICAL WELL TESTING 



[Chap. 11 



in which e is temperature, d is depth, % is initial temperature, t is time 

 smce beginning of cooling, and k is thermal diffusivity. Therefore, for 

 the earth's surface, da/dd = %/y/^. Substituting a value of T F. per 

 50 feet for the temperature gradient and a value of 64 10"* C.G.S. fork, 

 and assuming further a temperature of 7000° F. for the initial condition, 

 it follows that the time elapsed since the beginning of the cooling is about 

 175 million years. This is generally considered too low for the age of the 

 earth, yet it is nearly of the right order of magnitude. An earth with 

 the temperature distribution postulated by the Kelvin theorem has been 

 claimed to be unstable against tidal and similar forces. Therefore, the 

 assumption has been made that the cooling process is partly compensated 



Shale, limestone, sandstone 



Granite 



Depth 



Feet 



Fig. 11-19. Trends of temperature depth curves {1) near basement rocks, and 

 in sedimentary areas (after Van Orstrand). 



by the heat generated at moderate depth by a layer of constant or expo- 

 nentially decreasing radioactivity. 



Whatever the cause of the earth's heat, the amount of heat transmitted 

 to the surface is exceedingly small and barely sufl&cient to melt a layer 

 of ice T^ of an inch thick in one year. The heat quantity Q transmitted 

 in the time t between the faces of surface S and distance Z of a slab of the 

 conductivity c is given by 



Ae 



Q = cS< 



(11-3) 



If for Z/Ae the normal reciprocal gradient, or 50 feet for 1° F., is substi- 

 tuted, it follows that the amount transmitted is onlj'^ 200 B.t.u.'s per 

 square foot in one year. 



