When a low permeability well is hydraulically fractured, the test time required to acquire meaningful data and estimate both fracture and matrix parameters from a single test is often impractically long.
Using today's linear flow analysis techniques, the test can be designed to achieve more reservoir information in less time. The general success of the stimulation, and the fracture half-length can be evaluated from two short tests, one before and one after the frac.
It is necessary to obtain a pre-frac or other independent estimate of matrix permeability which can be combined with the linear flow data to yield an estimate of fracture parameters. By spending time on the pre-frac test, a greater amount of time can be saved by reducing the length of the post-frac portion of the test.
This paper was written by and for the practising reservoir engineer. It collects and summarizes several important developments in pressure transient analysis and emphasizes how to practically apply them to the design and analysis of fractured well tests.
It has been the authors' experience that quite often fractured wells are not tested properly, that the tests are long and expensive and fail to yield the desired practical evaluation of the success of the frac job. This is usually combined with the improper use of drawdown type curves and semi-log analysis. These well-known conventional techniques need to be supplemented with other techniques that have been specifically designed to account for the flow regimes found in fractured well tests.
This paper presents three main ideas; the TandemRoot-T plot, and the delta-t-equivalent-radial and delta-t-equivalent-linear type curves. These are all powerful and useful ideas which have been previously published but do not yet seem to be used and applied widely in the industry.
The use of these techniques is illustrated with a series of simple and practical examples.
Millheim and Cichowicz (1) originally demonstrated that for a buildup test dominated by linear flow, the pressure transient behavior could be modelled as: Equations (Available in full paper)
This equation is presented in United States field units and uses pressure to represent gas potential Converted into metric units and using real gas pseudo-pressure, the equation reads as follows: Equations (Available in full paper)
What this means is that, in a fractured gas well test where the pressure transient behavior can be adequately modelled by this equation, a plot of pseudo-pressure versus the tandem-root-t time function gives a straight line of slope (ml) which is directly proportional '[to the fracture half length (xf) and the square root of the formation permeability √k. The first step is to use a type curve to identify the linear flow dominated portion of the test and then draw a straight Line through that portion of the tandem-root-t plot.
In their paper, which is a useful reference for engineers dealing with fractured wells, Lee and Holdiech (2) examined the theory and application of the Millheim and Cichowicz (N-C) method and proposed some further modifications.