Rate Normalization of Buildup Pressure By Using Afterflow Data
Authors: Fetkovich M.J. , Vienot M.E. 
Published: December 2007

Summary
Field data indicate that in some instances signify cant after flow occurs after a well is considered shut in. Analysis method for after flow-dominated pressure buildup data is presented whereby the PD-TD model describing the transient behavior of the well can be directly obtained by matching a log-log plot of the rate-normalized pressure vs. time data to published type curves. The PD-TD model thus obtained allows a rigorous mathematical superposition analysis to be performed on the same data with results equivalent to those obtained from the normalizedtype-curve analysis. The work demonstrates that rate normalization must be based on total after flow rates, confirming with field data Perrine's assumption that total rate should he used in multiphase flow analyses. Dramatic changes in character are seen between the rate-normalized pressure vs. time and the conventional pressure vs. time log-log data plots for low permeability stimulated wells. Several field examples demonstrate the application of this simple and effective technique.

Introduction
Currently, wellbore storage type curves based on the assumption of a constant wellbore storage coefficient are used to evaluate after flow-dominated data from pressure alone. For pumping wells, the ability to calculate reliable buildup pressures and corresponding after flow rates, along with the wellbore storage coefficient variation with time, has been reported in several papers. More direct bottom hole measurements of after flow and pressure using production logging tools during pressure buildup tests production logging tools during pressure buildup tests have been reported recently by Meunier et al. In the U. S., wellbore storage effects often characterize pressure buildup tests because the majority of domestic wells are produced by rod pumps where after flow dominates during produced by rod pumps where after flow dominates during the buildup. This type of completion can result in long periods of wellbore storage during test situations even for periods of wellbore storage during test situations even for stimulated wells. The first attempt to use both pressure and after flow rate data was presented by Gladfelter et al in 1955. They suggested that the pressure rise after shut-in divided by the instantaneous change in rate caused by after flow should be plotted vs. the logarithm of shut-in time. This resulted in a modified Miller-Dyes-Hutchinson (MDH)buildup plot. The validity of this approach was confirmed by Ramey" in 1965, and extended by him to include wellbore unloading effects during drawdown testing. About this same time Wine stock and Colpitts proposed a similar rate normalization of pressure for proposed a similar rate normalization of pressure for drawdown analysis of gas wells when rates were monotonically declining during drawdown tests. Rate variations were not a result of wellbore storage effects but were more a result of a nearly constant wellbore pressure test condition. Their rate normalization of the pressure test condition. Their rate normalization of the pressure data was simply an attempt to make a constant pressure data was simply an attempt to make a constant rate analysis from essentially constant wellbore pressure data. A computer study by Lee et al. basically confirmed the validity of the Wine stock and Colpitts rate normalization analysis procedure. Additional discussion of the Gladfelter et al. and the Wine stock and Colpitts normalization methods was given by Ramey in 1976. Rate-normalized type-curve plots of the Gladfelter etal. and Wine stock and Colpitts example data show that after normalization virtually all the data were on the semilog straight line. Rate normalization linearized all the data in both instances. However, tests on low-permeabilityoil and gas wells with large negative skins often cannot be analyzed using their suggested rate-normalized pressurevs. logarithm of time plotting approach because the data may not reach the semilog straight line even after normalization. A simple method of analyzing after flow-dominated pressure buildup data is presented. The PD-TD model pressure buildup data is presented. The PD-TD model describing the transient behavior of the well may be obtained directly by matching a log-log plot of the rate-normalized pressure vs. time data to published type curves. The PD-TD model thus obtained allows a rigorous mathematical superposition analysis to be performed on the same data with results equivalent to those obtained from the normalized type-curve analysis.

Drawdown Rate Normalization Equations
Rate normalization techniques and procedures are best illustrated by first examining their application to drawdown data. Although the nature of the rate variation of drawdown data with time is different than that of after flow rate variation, the end result is the same. Also, draw down rate variations generally last much longer than after flow rate variations. The rate normalization equation given by Wine stock and Colpitts for a gas well drawdown analysis can be written as
(1)
JPT
p. 2211