Application of the Pressure Derivative Function in the Pressure Transient Testing of Fractured Wells

Abstract

Summary A new technique is presented for the analysis of wells with a finite-conductivity fracture. The technique simultaneously uses the pressure and pressure derivative for cases with no fracture skin and no wellbore storage and for cases with fracture skin and wellbore storage during the bilinear-flow period. New type curves are presented and applied to three field cases. The paper concludes that use of the pressure derivative with pressure-behavior type curves reduces the uniqueness problem in type-curve pressure-behavior type curves reduces the uniqueness problem in type-curve matching and gives greater confidence in the results. Introduction Increased production has been achieved by the introduction of massive hydraulic fractures to tight reservoirs. This has led to the need for pressure-transient analysis techniques to determine reservoir parameters and, ultimately, to forecast well production. Because conventional radial-flow analysis methods are not valid for prepseudoradial flow in wells with finite-conductivity vertical fractures, most methods use either type-curve shape of transitional flow regime pressure behavior or the pressure behavior of a single flow regime. In addition, both wellbore and other reservoir effects - e.g. wellbore storage fracture damage, turbulence and fracture height - have been accounted for. The use of derivative type curves to improve flow regime detection and to enhance analysis confidence is not new. Bourdet et al. developed pressure-derivative type curves for radial-flow wells, and Suresh and Tiab applied pressure-derivative solutions to infinite-conductivity pressure-derivative solutions to infinite-conductivity and uniform-flux vertically fractured wells. The purpose of this paper is to develop simultaneous pressure and pressure-derivative type curves for finite-conductivity pressure-derivative type curves for finite-conductivity fractures and to apply them to three field cases. Pressure Behavior of a Fractured Well Pressure Behavior of a Fractured Well Consider a well intercepting a horizontal, isotropic, homogeneous, infinite reservoir containing a slightly compressible fluid and totally penetrated by a finite-conductivity vertical fracture (see Fig. 1). It has been shown that PWD=f1 (tDxf, CfD),........................(1) where PwD=dimensionless pressure tDxf=dimensionless time, and CfD=dimensionless fracture conductivity. From this relationship, the type curve illustrated in Fig. 2 was created. Bourdet et al. determined that the pressure derivative with respect to time is convenient to use and is proportional to the semilog slope. For the case of a finite-conductivity vertical fracture, the pressure derivative was calculated with the central difference approach and is shown in Fig. 3. Characteristics of the Pressure-Derivative Type CurveThe bilinear-flow regime has a single line of one-quarter slope.The recently defined pseudolinear-flow has a one-half slope.There is a short transition between the bilinear and pseudolinear flow regimes. pseudolinear flow regimes.Pseudoradial flow occurs as a horizontal line. (See Fig. 3.) Damaged Vertical Fracture With Wellbore Storage Under Bilinear-Flow Conditions It has been shown that PwD=F2(tDxf, CfD, SfD, SD),.......................(2) PwD=F2(tDxf, CfD, SfD, SD),.......................(2) where SfD=dimensionless fracture storage and Sfs=dimensionless fracture skin. For bilinear-flow conditions, the pressure behavior for a well with wellbore storage and a damaged vertical fracture is derived in the Appendix is given by ........................................(3) SPEFE p. 470