Constant pressure well tests in infinite radial reservoirs

Sometimes it may be desired to conduct a well test, or part of a well test with the well-bore pressure kept at a constant level. The objective of this paper is to present solutions to the radial diffusivity equation for cases involving constant well-bore pressures. Of interest are expressions, written for flow rate at the well-bore as a function of time, which are suitable for graphical analysis of measured flow rates during a conducted test, very much similar to the method of analysis of the constant production rate case in draw-down well testing. Example applications of the derived expressions are presented for some constant pressure test cases including a case consisting of a constant rate period followed by a constant pressure period.