Case II: 5 ^ 0, the measured D.R. including skin damage. 



(D.R.)„, = - -i— £i ( - — ) + — S (15) 



or (D.R.)» = (D.R.) + — S. (16) 



Furthermore, the pressure drop over the damaged region will be 



(D.R.) m - (D.R.),! (17) 



q S - qih 



D.R.),, 



kh 



Since we are normally interested in what percentage qS is of the total: 

 ,5x100 = ffD-R.) - rp.R., 1 



APtotal (D.R.)™ 



If (D.R.) can be determined, Equation 18 may be solved, since (D.R. ) „, 

 is measurable. 



From Equation 14, (D.R.) can be evaluated if the data are available. 



Using reasonable values, it appears that (D.R.) = 1 is not an unreasonable 

 upper limit for DST curves. 



Therefore, if (D.R.)„ is assumed to equal 1 as an arbitrary reference, 



* s = J iraj7 Up «- (19) 



AP form = Tf -L— AP tota , (20) 



(DR)m 



_?=(D.R.) m -JL— (21) 



Ar f o,- m A F total 



P.I. = (D.R.) TO x (P.I.)« f22 ) 



As the result in Equation 22 shows, the theoretically maximum (P.I.) should 

 be at least (D.R.) m times the measured (P.I.),„. 



In relating this factor to the published work of van Everdingen, Hurst, 

 Miller, Dyes, Hutchinson, and Arps, it is evident that they are all equivalent 

 It is noteworthy that the assumption (D.R.) = 1 is equivalent to an assign- 

 ment of N zrL 5.5 cycles in the Arps' graphical plotting method. The field 



759 



