Pressure Derivative Enhances Use of Type Curves for the Analysis of Well Tests

Abstract

ABSTRACT Numerous type-curves of dimensionless pressure versus dimensionless time have been developed in the past. They all suffer from the fact that the log-log representation has poor resolution at late time, thus the uniqueness of the match is reduced. The semi-log representation enhances the character of the pressure response but, because of the cartesian pressure scaling, the type curve technique cannot be applied. This drawback is alleviated by plotting the slope of the semi-log curve (i.e. the pressure differentiated with respect to the logarithm of time) on a log-log grid. The pressure type-curves differentiated in the same manner can thus be matched to the derivative data. The matching procedure is further improved by combining on the same plot both pressure and derivative data. Field examples are presented showing how interpretation is enhanced by using the derivative. It is shown that the derivative sheds light on facets of pressure response that were imperceptible on pressure data alone. The derivative can also be used to deconvolve pressures during the afterflow period of a build up, to compensate for the wellbore storage effect. Provided the wellbore storage coefficient is reasonably constant, the true reservoir response, which is masked at early times by wellbore storage, can be restituted allowing interpretation of early time data. This proves especially useful in the case of heterogeneous formations with permeabilities on the high side, as demonstrated by the examples.