Annulus Unloading Rates as Influenced by Wellbore Storage and Skin Effect

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Abstract
The modern trend in well testing (buildup or drawdown) bas been toward acquisition and analysis of short-time data. Pressure data early in a test are usually distorted by several factors that mask the conventional straight line. Some of the factors are wellbore storage and various skin effects such as those due to perforations, partial penetration, non-Darcy flow, or well stimulation effects. Recently, Agarwal et al. presented a fundamental study of the importance of wellbore storage with a skin effect to short-time transient flow. This paper further extends the concept of analyzing short-time well test data to include solutions of certain drillstem test problems and of cases wherein the storage constant, CD, undergoes an abrupt change from one constant value to another. An example of the latter case is change in storage type from compression to liquid level variations when tubinghead pressure drops to atmospheric Arks production. The purpose of the present paper is to: production. The purpose of the present paper is to: - present tabular and graphical results for the sandface flow rate, qsf, and the annulus unloading rate, qa, as a fraction of the constant surface rate, q, and - illustrate several practical well test situations that require such a solution. Results include a range of values of the storage constant, CD, and the skin effect, s, useful for well test problems. problems. Annulus unloading or storage bas been shown to be an important physical effect that often controls early well test behavior. As a result of this study, it appears that interpretations of short-time well test data can be made with a greater reliability, and solutions to other storage-dominated problems can be obtained easily. Techniques presented in this paper should enable the users to analyze certain short-time well test data that could otherwise be regarded as useless. Introduction: In a recent paper, Agarwal et al. presented a study of the importance of wellbore storage with a skin effect to short-time transient flow. They also presented an analytical expression for the fraction presented an analytical expression for the fraction of the constant surface rate, q, produced from the annulus Although the rigorous solution (inversion integral) and long- and short-time approximate forms were discussed, neither tabular nor graphical results ofdpwD the annulus unloading rate, CD, were given.dtD It now appears that such solutions are useful in certain drillstem test problems and in cases wherein the storage constant, CD, changes during a well test. An example is change in storage type from compression to liquid level change when tubinghead pressure drops to atmospheric during production. pressure drops to atmospheric during production. The purpose of this study is to (1) present tabular and graphical results for the sandface flow rate and the annulus unloading rate and (2) illustrate several practical well test situations that require the practical well test situations that require the solutions.

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