Gas Well Testing With Turbulence, Damage and Wellbore Storage
Authors: Wattenbarger Robert A. , Ramey H.J. 
Published: December 2007

Abstract
A systematic study has been made of the application of the real gas pseudo-pressure m(p) to short-time gas well testing. The m(p) function can be used in real gas flow problems to account for the variation of viscosity and z-factor with pressure. A mathematical model was solved numerically to generate solutions of various real gas flow problems. The erects of turbulence, formation damage and wellbore storage were included in the model.
The analysis of simulated well tests showed that the interpretation methods normally used for liquid flow are generally accurate when the m(p) is used. For practical rates without turbulence, the solutions are not rate-sensitive, and the flow capacity kh and skin effect can be determined accurately from either a buildup or a drawdown test. However, the kh calculated from a drawdown test can be significantly low when turbulence is present. A case was simulated in which this error was 36 percent. Turbulence does not affect the determination of kh from buildup tests.
The proper determination of kh from p and p2 buildup and drawdown plots is developed by analyzing their relationship to the m(p) method. A simple equation is given that can be used for long-range gas well performance forecasting. This expression is compared with a method presented by Russell et al.

Introduction
The formation flow capacity and wellbore damage condition can be determined for liquid-producing tests by means of buildup and drawdown tests. These tests make use of short-time pressure transient data rather than stabilized flow tests that are often used for gas well testing. Tracy presented a method of gas well testing that was based on ideal gas equations and utilized p buildup plots. This method was shown to be good for low pressure wells. Matthews suggested plotting p and using an average slope and average gas properties. This method was more successful on high pressure wells. Al-Hussainy, Ramey and Crawford showed that variation in gas properties could be simplified by using the real gas pseudo-pressure m(p). Some cases showed that the use of the m(p) function provided an accurate method of interpreting buildup and drawdown tests. Because the work of Al-Hussainy et al. included only a few actual cases, there was a need to explore the use of the m(p) method for a greater variety of flow conditions.
The occurrence of turbulent flow around the wellbore often is an important factor in gas well testing. Swift and Kiel, and Carter et al. treated turbulence in gas well testing, but did not consider the variation of viscosity and z-factor with pressure.
This paper presents the results of an investigation of the application of the m(p) method to buildup and drawdown testing. The investigation included the effects of turbulence, formation damage and wellbore storage.

Gas Flow Equations
To formulate the mathematical model, many of the assumptions usually used in well testing theory are applied. The system has radial geometry with a closed outer boundary and is composed of a horizontal porous formation that has uniform and isotropic rock properties and uniform thickness. Allowance is made, however, for a radial region of reduced permeability near the wellbore. This region represents formation damage. The geometry of the system is shown in Fig. 1.
Darcy's law does not always apply to gas flow.
JPT
P. 877ˆ