The ratio Rj/R is sometimes designated as the resistivity index I (accord- 

 ingly, S w = I" 1 '"). 



Furthermore, by definition F = R /R,„. 



F = formation factor 



R w — water resistivity 



Hence, equation 3 can also be written: 



s w = (R /R t yi n = I _Lf ' 



/ F x R w \ 



V R / 



The exponent n varies approximately between 1.7 and 2.2, depending on 

 the type of formation. Experience shows that taking n = 2 should give a 

 sufficiently good approximation in most instances for all practical purposes. 



Equation 4 would, therefore, read: 



1/2 



(5) 



/ F x R w X 



V R / 



Again, the relation between formation resistivity and water saturation is 

 more complex in shaly sands because of the additional conductance due to the 

 shale network. 



Schematic Representation of a Permeable Bed Invaded by Mud Filtrate 



Usually, the hydrostatic pressure of the mud is greater than the 

 natural pressure of the formations. Under these conditions, the mud nitrate 

 tends to filter into the permeable beds. 



Figure 14-5A represents a schematic cross section of a permeable bed 

 penetrated by the borehole. For the sake of simplicity, the formation is 

 supposed to be homogeneous, isotropic, and free of shaly material. 



The diagram of radial distribution of resistivities is shown on Figure 

 14-5B, where the distances from the axis of the hole are in abscissae and the 

 resistivities are in ordinates. 



Starting from the axis, one encounters the following media: 



Drilling Mud: Resistivity R m 



Mud Cake: Resistivity R mc 



The thickness and the nature of the mud cake depend on the nature of the 

 mud and on the drilling conditions rather than on the formations. The thick- 

 ness usually varies between }/ 8 and 1 inch. In water-base mud, the resistivity 

 of the mud cake (R mc ) is about equal to one or two times the resistivity of the 



273 



