698 Subsurface Geologic Methods 



the subscript e refers to the extreme outward radius of drainage 



and the pressure at that point, and 



the subscript w designates the radius of the well bore and the pressure 



at that point. 

 Likewise equation (8) becomes, for the inward radial isothermal flow of 

 a perfect gas to a central well-bore, the following 



Q _ 2Trkt{pe — Pw) 



J rvr~ (11) 



ixln — 



Q 



in which — is the volume rate of flow of gas in cubic centimeters per 

 second at the temperature of flow and the pressure 



Pe + Pv 



If units of barrels per day, darcys, centipoises, pounds per square inch, 

 and feet are employed, the right-hand side of equation (10) should be 

 multiplied by the conversion factor 7.07. Similarly, insertion of the 

 conversion factor, 39.7 in the right-hand side of equation (11) is required 

 for units of cubic feet per day, darcys, centipoises, pounds per square 

 inch, and feet. 



If the structure of the rock differs from pore to pore, A; is a variable 

 which must be expressed as a function of geometry, and the function 

 must be employed in the integration of equation (8) . The expression of 

 the variation in permeability as a function of distance or of geometry is 

 required for the integration of equation (8) and seldom can be accomp- 

 lished from a practical point of view with any degree of accuracy, al- 

 though qualitatively it can be seen to depend upon the unhomogeneity 

 of the rock. Furthermore, this requirement can be fulfilled only to the 

 extent that the student of geology can decipher the intricate process of 

 sedimentation and subsequent lithification for a given rock body and 

 translate this story into the necessary mathematical relationships. Syste- 

 matic variation of permeability can be expressed mathematically, but 

 haphazard variation virtually defies analysis. Sometimes a sufficient 

 number of core samples are available so that statistical data can be ob- 

 tained from measurements of permeability in the laboratory, which will 

 enable the student to work out an expression for systematic variations of 

 permeability with some parameter. For example, the coarser grained 

 components of a sandstone deposited offshore should be found closest to 

 the shore line, and the finest grained shales and slates farthest from the 

 shore. Consequently, sometimes under these conditions a linear variation 



