Paper: Simplified Graphical Solutions of Equations Relating Well Productivity To Wellbore Damage and Stimulation

This paper presents simplified methods of relating the following terms commonly used by the petroleum engineer in evaluating wellbore problem conditions of damage and of stimulation: 1. Well productivity 2. van Everdingen's skin factor, s 3. Permeability change-radial extent of change Mathematical relationships between these concepts were originally defined and applied by Muskat, l van Everdingen,2 Matthews and Russell," Hawkins,4 and Grubb and Martin.5 Since a well is generally considered to drain a reservoir by radial-type flow, each of the equations involve logarithms, and the usual graphical plots yield exponential-type curves which are difficult to extrapolate or to interpolate for intermediate values of interest. Straight-line forms of the three equations relating (1) well productivity, (2) van Everdingen's skin factor, s, and (3) permeability change-radial extent of change-were obtained by rearranging and regrouping of terms in the original equations. The straight-line graph of each equation is also presented in Figs. 1, 2 and 3. The practicing engineer and others interested in interpreting well production problems will find that the straight-line graphical representation is more accurately extrapolated and interpolated for intermediate values and also is considerably more easily drawn than the typical exponential curves usually given, for the relationships presented here. These should greatly assist the operations engineer in planning and designing completion, workover and stimulation procedures.