Productivity Ratio (PR)

In evaluating well performance, the standard usually referred to is the productivity index of an open hole that completely penetrates a circular formation normal to the strata and in which no alteration in permeability has occurred in the vicinity of the wellbore. Substituting Eq. (8.47) into Eq. (8.49), we get

The productivity ratio (PR) then is the ratio of the PI of a well in any condition to the PI of this standard well:

Thus, the productivity ratio may be less than one, greater than one, or equal to one. Although the productivity index of the standard well is generally unknown, the relative effect of certain changes in the well system may be evaluated from theoretical considerations, laboratory models, or well tests. For example, the theoretical productivity ratio of a well reamed from an 8-in. borehole diameter to 16 in. is derived by Eq. (8.52):

Assuming r_e = 660 ft,

Thus, doubling the borehole diameter should increase the PI approximately 11%. An inspection of Eq. (8.50) indicates that the PI can be improved by increasing the average permeability k, decreasing the viscosity μ, or increasing the wellbore radius r_w. Another name for the productivity ratio is the flow efficiency (FE).