Changing Wellbore Storage

Changing wellbore storage occurs when one of the following conditions exists within the wellbore:

  • Changing wellbore fluid compressibility
  • Phase redistribution
  • Change in the type of storage from a changing liquid level to a liquid filled wellbore

The phenomenon of phase redistribution occurs in a well that is shut in at the surface with gas and liquid flowing simultaneously into the tubing. In these situations, the gravity effects cause the liquid to fall and the gas to rise to the surface. Because of the very low compressibility of liquid and no extra room for gas to expand in a closed chamber, the redistribution of phases causes a net increase in the wellbore pressure. When the phenomenon is present in a buildup test, the extra pressure surge in the wellbore is relieved through the formation. Eventually, equilibrium will be attained between the wellbore pressure and the formation pressure adjacent to the wellbore. However, at early times, the wellbore pressure may exceed the formation pressure causing an anomalous hump in the buildup pressure, which cannot be analyzed in a conventional way with only the dimensionless wellbore storage constant (CD). In order to deal with phase redistribution, two models have been proposed by Fair (1981) and Hegeman et al. (1993), which introduces two additional dimensionless wellbore constants, apparent storage (CaD) and the pressure parameter (CpD).

Fair considered the exponential expression for the dimensionless anomalous pressure (ppD) rise as:

 

Later, Hegeman et al. showed that the negative CpD values in the Fair model can be used for buildup data that has an anomalous pressure decrease. Therefore, for these wells, they argued that using an error function to model the anomalous pressure may allow for better modeling of field data with increasing or decreasing storage. Thus, Hegeman et al. proposed that:

 

However, it has been found in practice that the models of Fair and Hegeman et al. are not substantially different.

The following plots illustrate the effects of the three dimensionless storage parameters on the dimensionless type curves.

References

"How Wellbore Dynamics Affect Pressure Transient Analysis", L. Mattar and M. Santo, JCPT (February 1992) Volume 31, No. 2, 32 - 40.

"The Primary Pressure Derivative (PPD) – A New Diagnostic Tool in Well Test Interpretation", L. Mattar and K. Zaoral, JCPT (April 1992) Volume 31, No. 4, 63 - 70.

"Pressure Buildup Analysis with Wellbore Phase Redistribution", W.B. Fair Jr., SPEJ (April 1981) 259 - 270.

"Well-Test Analysis with Changing Wellbore Storage", P.S. Hegeman, D.L. Hallford, and J.A. Joseph, SPEFE (September 1993) 201 - 207.