Verification of the Gladfelter-Tracy-Wilsey Concept For Wellbore Storage-Dominated Transient Pressures During Production

Abstract

Introduction The fact that real wells have finite volumes leads to inertia in the sandface response of a well to a production rate change at the surface. The duration of wellbore storage (sometimes called "afterflow" for buildup or "annulus unloading" for production tests) rate changes is not often more than a few days. It may be as short as a few minutes. Perhaps for this reason, and also because it usually impossible to determine the sandface production rate with much accuracy, the Gladfelter-Tracy-Wilsey(2) afterflow correction for pressure buildup tests received minimal application. Actually, the Gladfelter et al. idea has a broad and important application in handling production rate change effects in general – rather than the specific production rate changes during pressure buildup. In 1965(1), the Gladfelter et al. pressure buildup afterflow correction was extended to production testing for the special case of an exponential production rate (starting from a zero producing rate and increasing toward the constant rate, q). Because of publication of both production pressure drops and sandface production rates(3, 4) for the classic wellbore storage boundary conditions(5, 3), it is possible to test the Gladfelter et al. idea for the wellbore storage case as well. Winestock and Colpitts(6) Carter(7), Aron and Scotts(9, 10), and others have also noticed that the reciprocal productivity index, (Δp/q), is often a linear function of the logarithm of producing time. This is a simple alternative to superposition to match production rate changes.