This paper presents theoretical and practical aspects of methods used to determine formation permeability, fracture length, and fracture conductivity permeability, fracture length, and fracture conductivity in low-permeability, hydraulically fractured gas reservoirs. Methods examined include Horner analysis, linear flow analysis, type curves, and finite-difference reservoir simulators.
The purpose of this paper is to summarize the theoretical background of methods that we have attempted to use to determine formation permeability, fracture length, and fracture conductivity 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, in some cases, have remained obscure to the practicing engineer. The paper also includes examples from 13 wells in which postfracture-treatment pressure buildup surveys have been analyzed in detail.
Test analysis methods discussed in the paper include (1) a method applicable only after a pseudoradial flow pattern is developed in the pseudoradial 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 that 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.
Pseudoradial Flow Pseudoradial Flow Russell and Truitt pioneered application of methods based on the assumption of pseudoradial flow in a fractured reservoir for determination of formation permeability and fracture length. A working permeability and fracture length. A working definition of pseudoradial flow is that sufficient time has elapsed in a buildup or drawdown test so that bottomhole pressure (BHP) varies linearly with the logarithm of flow time (drawdown) or the Horner time group (tp + delta t)/ delta 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
and the observation that, for infinitely conductive vertical fractures,
Eqs. 1 and 2 can be combined to avoid the intermediate step of calculating s:
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 qgBga mu a/mh) and determine fracture half-length, Lf from Eq. 3 (see Fig. 1).