To develop the inflow performance relationship in terms of pressure, we assumed that the group, , was relatively constant in the pressure range of interest, and we removed the entire group from the pressure integral in Equation 5.10. In the pressure-squared formulation, we assume that the product is relatively constant with pressure and remove it from Equation 5.10, leaving:
Again, we will see that the product can be safely assumed to be relatively constant over a particular pressure range. Performing both integrations in Equation 5.16 results in:
Rearranging Equation 5.17 results in:
or, after substituting the normal U.S. definitions of and :
In this equation, we evaluate and at the arithmetic mean average pressure, Equation 5.15. Again, we can add a skin factor to account for well damage or stimulation and write similar equations in terms of average pressure for the pseudo-steady state flow regime. Equation 5.18c is the Inflow Performance Relationship for Gas in Terms of Pressure-Squared.