Non-Darcy Flow and Wellbore Storage Effects in Pressure Build-Up and Drawdown of Gas Wells
Authors: Ramey H.J. 
Published: December 2007

Abstract
The wellbore acts as a storage tank during drawdown and build-up testing and causes the sand-face flow rate to approach the constant surface flow rate as a function of time. This effect is compounded if non-Darcy flow (turbulent flow) exists near a gas wellbore. Non-Darcy flow can be interpreted as a flow-rate dependent skin effect. A method for determining the non-Darcy flow constant using this concept and the usual skin effect equation is described. Field tests of this method have identified several cases where non-Darcy flow was severe enough that gas wells in a fractured region appeared to be moderately damaged. The combination of wellbore storage and non-Darcy flow can result in erroneous estimates of formation flow capacity for short-time gas well tests. Fortunately, the presence of the wellbore storage effect permits a new analysis which can provide a reasonable estimate of formation flow capacity and the non-Darcy flow constant from a single short-time test.
The basis of the Gladfelter, Tracy and Wilsey correction for wellbore storage in pressure build-up was investigated. Results led to extension of the method to drawdown testing. If non-Darcy flow is not important, the method can be used to correct short-time gas well drawdown or build-up data. A method for estimation of the duration of wellbore storage effects was developed.

INTRODUCTION
In 1953, van Everdingen1 and Hurst2 generalized results published in their previous paper3 concerning wellbore storage effects to include a "skin effect", or a region of altered permeability adjacent to the wellbore. Later, Gladfelter, Tracy and Wilsey4 presented a method for correcting observed oilwell pressure build-up data for wellbore storage in the presence of a skin effect The method depended upon measuring the change in the fluid storage in the well bore by measuring the rise in liquid level.
To the author's knowledge, application of the Gladfelter, Tracy and Wilsey storage correction to gas-well build-up has not been discussed in the literature. It is, however, a rather obvious application. Gas storage in the wellbore is a compressibility effect and can be estimated easily from the measured wellbore pressure as a function of time.
Several approaches to the wellbore storage problem have been suggested. As summarized by Matthews,5 it is possible to minimize annulus storage volume by using a packer, and to obtain a near sand-face shut-in by use of down-hole tubing plug devices. Matthews5 and Perrine6 have suggested criteria for determining the time when storage effects become negligible.
In 1962, Swift and Kiel7 presented a method for determination of the effect of non-Darcy flow (often called turbulent flow) upon gas-well behavior. This paper provided a theoretical basis for peculiar gas-well behavior described previously by Smith8.
Recently, Carter, Miller and Riley9 observed disagreement among flow capacity kgh data determined from gas-well drawdown tests conducted at different flow rates for short periods of time (less than six hours flowing time). In the original preprint of their paper, Carter et al.9 proposed that the discrepancy in flow capacity was possibly a result of wellbore storage effects, Results of an analytical study of unloading of the wellbore and nonDarcy flow were recorded by Carter.10 In the final text of their paper, Carter et al.9 stated that they no longer believed wellbore storage was the reason for discrepancy in their kgh estimates.
In view of the preceding, this study was performed to establish the importance of non-Darcy flow and wellbore storage for gas-well testing. In the course of the study, a reinspection of the previous work by van Everdingen1 and Hurst2 was made, and the basis for the Gladfelter, Tracy and Wilsey4 wellbore storage correction was investigated and extended to flow testing.

WELLBORE STORAGE THEORY
As has been shown by Aronofsky and Jenkins,11,12 Matthews,5 and others, flow of gas can often be approximated by an equivalent liquid flow system. The following development will use liquid flow nomenclature to simplify the presentation. Application to gas-well cases will be illustrated later. First, we will use the van Everdingen-Hurst3 treatment of wellbore storage in transient flow to establish (1) the duration of wellbore storage effects, and ( 2) a method to correct flow data for wellbore storage.