The motivation for the work described in this paper arose from a need to analyze production decline data where the flowing bottomhole pressure varies significantly. The variance of the bottomhole pressure with time excludes the use of the exponential decline model for conventional decline curve analysis (semilog plots and type curves). Using pressure normalized flow rate rather than flow rate usually does not remedy this problem. The method we present uses a rigorous superposition function to account for the variance of rate and pressure during production. This function is the constant rate analog for variable-rate flow during post-transient conditions and can be used to develop a constant pressure analog for the decline curve analysis of field data.

The constant pressure analog time function is computed from the constant rate function using the identity that cumulative production for both cases must be equal. Using the cumulative production identity, we solve recursively for the time function using trapezoidal rule integration and, as an alternative, finite difference formulae. We have also developed a constant pressure analog time relation which is rigorous for boundary dominated flow and serves as an accurate approximation for transient flow.

We apply these relations to analytical solutions for verification and then use the boundary dominated flow relation on simulated and field cases. These simulation cases include large and small step changes in bottomhole flowing pressures, and periodic shut-ins. Finally, we apply these relations to a gas well field case.

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