The Use of Pseudotime: Wellbore Storage and the Middle Time Region
- J.P. Spivey (SoftSearch Inc.,) | W.J. Lee (Texas A and M U.)
- Document ID
- Society of Petroleum Engineers
- SPE Unconventional Gas Technology Symposium, 18-21 May, Louisville, Kentucky
- Publication Date
- Document Type
- Conference Paper
- 1986. Society of Petroleum Engineers
- 5.2.1 Phase Behavior and PVT Measurements, 4.1.4 Gas Processing, 5.6.4 Drillstem/Well Testing, 4.3.4 Scale, 5.6.3 Pressure Transient Testing, 1.2.3 Rock properties
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The gas flow equation is often linearized to allow liquid type curves to be used to analyze transient tests of gas wells. In the absence of wellbore storage, drawdown tests are best analyzed using the pseudo pressure-time linearization. Buildup tests, however, require the pseudopressure-pseudotime linearization for best results. If wellbore storage is present, both time and pseudotime should be used in a combination analysis for drawdown. pseudotime should be used in a combination analysis for drawdown
The equation describing flow of slightly compressible liquids is easily linearized by neglecting terms involving the square of the pressure gradient. The resulting diffusivity equation has been solved analytically for a number of different boundary conditions. Since 1970, type curves based on these analytical solutions have been used to analyze pressure transient test data. In order to use the same type curves for analysis of gas well tests, the gas flow equation must be linearized to give it the form of the diffusivity equation.
The flow equation for real gases may be partially linearized by defining a real gas pseudopressure:
The equation for radial flow of real gases then becomes
The pseudopressure is then to be used instead of pressure in analyzing transient tests of gas wells. If the product ct is constant with pressure, the pseudopressure linerization is exact.
For large drawdowns, the product ct may vary by as much as two orders of magnitude. Thus Eq. 2 must be further linearized. This is achieved by the use of the real gas pseudotime, defined by Agarwal as
Agarwal recommended the use of pseudotime for buildup test analysis for both vertically fractured wells and with radial geometry and wellbore storage.
In this paper, the use of pseudotime for wells with radial symmetry is studied. The study is limited to drawdown at constant rate and the subsequent buildup. Particular attention is given to the effect of wellbore storage. In addition, an example is presented of the use of pseudotime for analysis of both drawdown and buildup when wellbore storage is present.
Pseudopressure Pseudopressure In 1976, Aziz, Mattar, Ko, and Brar used a finite difference simulator to generate drawdown data to evaluate the use of pressure, pressure-squared, and pseudopressure in transient test analysis. pressure-squared, and pseudopressure in transient test analysis. They concluded that "the use of pseudo-pressure is found to be the only reliable method when large drawdowns exist." Their investigation was restricted to constant rate production from infinite-acting reservoirs. They did not investigate the case of buildup following drawdown, nor did they consider the effects of skin and wellbore storage.
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