A New Set of Type Curves for Well-Test Interpretation With the Pressure/Pressure-Derivative Ratio

Abstract

Summary This paper presents a new set of type curves used in well-test analysis forhomogeneous reservoirs with wellbore storage and skin effects. When thepressure/pressure-derivative ratio (PDR)is used as a parameter in constructingthe type curves, the vertical scales on both type-curve and field-data plotsare identical. This automatic alignment of the vertical scale makes the newtype curves easier to match and, subsequently, easier to use in thecomputer-aided analysis. The paper concludes that use of the new type curvesreduces the uniqueness problem in pressure-transient type-curve matching, identifies the flow regimes effectively, and gives greater confidence in theresults. A new method to correct the pressure buildup when drawdown type curvesare used in radial-flow wells is also proposed. Two example applications, onewith a long producing time and one with a short producing time before shut-in, are included to demonstrate the use of these type curves. Introduction The first pressure-transient type curve was introduced by Agarwal et al. in1970 for analyzing pressure data from wells with wellbore storage and skineffects. In the same year, Ramey demonstrated that log-log graphs can be usedto identify wellbore effects, acidized wells, and fractured wells. This typecurve was constructed by plotting dimensionless pressure vs. dimensionless timeon a log-log graph for various values of wellbore storage and skin factor. Gringarten et al. improved the type curves of Ref. 1 to reduce the uniquenessproblem by plotting log(pD) vs. log(tD/CD) for various wellbore-storage/skinvalues, CDe2s. In recent years, the interpretation of pressure-transient tests bytype-curve matching has been made easier and more accurate by use of pressurederivatives and the development of new software for computer-aided analysis. The derivative type curves allow the simultaneous analysis of the pressurederivative and pressure response. This paper uses the same theoretical model as the pressure and derivativetype curves of Refs. 3 and 4 and combines them into a single set of typecurves. This set of type curves was constructed by plotting dimensionless PDRvs. dimensionless time. By doing this, the match is constrained on the verticalaxis. The proposed type curves are also easier to use in the computer-aidedanalysis and the PDR can be used to identify the flow regimes-i.e., wellbore-storage, radial, linear, bilinear, and pseudo-steady-state flows. A new technique to correct the pressure-buildup changes for radial-flowwells is also proposed for when drawdown type curves are used. Preview The type curves published by Gringarten et al. for wells with wellborestorage and skin effects are shown in Fig. 1 as the dashed lines. Thedimensionless pressure is plotted vs. the dimensionless time group on a log-loggraph. The resulting curves, characterized by the dimensionless group, CDe2s, correspond to well conditions ranging from damaged wells to acidized andfractured wells. One interesting feature of these type curves is that all curves merge to anasymptote at a slope equal to unity at early times because of the wellborestorage equation: (1) For infinite-acting radial flow, we have (2) Infinite-acting radial flow does not show any characteristic shapes on alog-log scale. Approximate starting times for radial flow are thereforesketched on the type curves as shown in Ref. 3. Bourdet et al. developed a set of pressure-derivative type curves. Thepressure response is plotted in terms of the pressure-derivative group, pDtD'/CD, on the v axis vs. the dimensionless time group on the × axis (solidlines in Fig. 1). From Eqs. 1 and 2, the pressure-derivative group, pDtD'/CD, will be (3) for wellbore storage flow and (4) for infinite-acting radial flow. Two straight lines can be observed on the derivative type curves in Fig. 1. The first straight line, which has a slope of unity, indicates wellbore-storageflow regime. The second straight line, which is the one-half straight line, corresponds to the infinite-acting radial flow regime. Fig. 1 shows that the pressure differences between the pressure responsesand the pressure derivatives have different characteristics for differentvalues of wellbore storage and skin factors and can be used to present the wellflow conditions. The dimensionless pressure and pressure-derivative group, respectively, aregiven a (5) (6) (7) (8) New Wellbore-Storage and Skin Type Curve Drawdown Analysis. Figs. 2 and 3 present the same pressure responses andpressure derivatives as in Fig. 1 but are plotted in terms of the PDR, pD/(pDtD'/CD), on the y axis against the usual dimensionless time group, tD/CD, on the × axis as a log-log plot and as a semilog plot, respectively. With thePDR used as a parameter in constructing the type curves, the vertical scales onboth type curves and field data plots are identical. This can be demonstratedby Eq. 9: (9) Eq. 9 was obtained by dividing Eq. 5 by Eq. 6. To complete the type curves for evaluation of the model parameters, 2pDcurves are also included as the dashed lines, as shown in Fig. 4. For the sakeof simplicity and brevity, let us define the PDR as Fpd. Thus, (10) and the new set of type curves is referred to as the PDR type curvesthroughout this text. Characteristics of the PDR Type Curves (Fig. 4). 1. All PDR curves are asymptotic to Fpd = 1 at early times forwellbore-storage-dominated flow.