The purpose of this paper is to summarize the theoretical background of methods which we have attempted to use to determine formation permeability, fracture length, and fracture conductivity in low-permeability, hydraulically fractured gas reservoirs. This summary is intended to emphasize the major strengths and weaknesses of the methods studied. These characteristics have not always been emphasized in the original literature and have, in some cases, remained obscure to the practicing engineer. This pape is a companion paper to SPE 79301, in which our experience in application of these techniques to problems arising in practice is discussed. Test analysis methods discussed in the paper include (1) a method applicable only after a 'pseudo-radial' flow pattern is developed in the reservoir, (2) a method applicable when linear flow dominates in the reservoir, (3) published type curves, with emphasis on those which include finite-conductivity fractures, (4) a modification of linear-flow techniques useful for finite-conductivity fractures, and (5) use of finite-difference reservoir simulators in a history-matching mode.

Pseudo-Radial Flow

Russell and Truitt2 pioneered application of methods based on the assumption of 'pseudo-radial flow' in a fractured reservoir for determination of formation permeability and fracture length. A working definition of pseudo-radial flow is that sufficient time has elapsed in a buildup or drawdown test so that bottom-hole pressure varies linearly with flow time (drawdown) or the Horner time group, (tp+Î"t)/Î"t (buildup), as expected for radial flow in an unfractured reservoir.

In an infinite-acting (unbounded) reservoir, the analysis technique is based on the use of skin factor, s, which can be calculated from

  • Equation 1*

and the observation tat, for infinitely-conductive vertical fractures,

  • Equation 2

Eqs. (1) and (2) can be combined to avoid the need for the intermediate step of calculating skin factor, s,

  • Equation 3

In principle, we can plot buildup test data on a conventional Horner graph, determine the slope, m, and thus estimate formation permeability (k=162.6 qgBgiμi/mh) and determine fracture half-length, Lf, from Eq. (3). (See Figure 1.) In practice, there are three serious problems with this method:

  1. The time required to reach the required straight line where the slope is related to formation permeability can be impractically long (months or years) in low permeability gas reservoirs with long fractures, as demonstrated by Gringarten, et al.4 and Cinco5 et al.;

  2. Implicit in the method is the assumption of infinite fracture conductivity, which is not always valid6; and,

  3. By the time the pressure transient has moved beyond the region of the reservoir influenced by the fracture, effects of the reservoir boundary may have already become important, preventing development of the proper slope, m.

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