This paper presents new type curves and type curve plotting functions which use integration rather than differentiation of well test data. These functions provide more unique type curve matches for noisy data because the integral of these data yields a much smoother function. The type curves presented in this work were generated from analytical solutions and are applied in exactly the same manner as in conventional type curve analysis.
The purpose of this paper is to introduce new type curves and type curve plotting functions that allow unique analysis of noisy well test data. These new type curves are based on the integral of the pressure drop function. The motivation for these new plotting functions and type curve solutions was our discouraging experiences with poor (non-unique) type curve matches of noisy data. poor (non-unique) type curve matches of noisy data. The solutions plotted on conventional pressure drop type curves and data analysis techniques have been reported by several authors for homogeneous and vertically-fractured reservoirs. The corresponding pressure derivatives and matching techniques have been discussed extensively in the petroleum literature. petroleum literature. This paper discusses development of the new type curve plotting functions and the corresponding analytical solutions used to generate type curves for homogeneous and vertically-fractured reservoirs. We demonstrate the advantages of these new type curves with examples of noisy test data. We conclude with a suggested procedure and example application of these new type curves to field data.
DEVELOPMENT OF THE NEW PLOTTING FUNCTIONS
Definition of Dimensionless Plotting Functions
The new type curves require a number of dimensionless variables, some of which are not in common use. To facilitate our later discussion of the curves, we define these dimensionless variables in this section. Their origin and their utility is discussed in later sections.
The dimensionless wellbore pressure, p is D defined as
The dimensionless time, t , based on the wellbore D radius is defined as
and the dimensionless time, t , based on fracture LfD half-length, L , is defined as f
The dimensionless pressure derivative function, p , is defined in two forms, which are Dd identical mathematically. The first form is
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