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Abstract
Since the introduction of the G-function derivative analysis, pre-frac diagnostic injection tests have become a valuable and commonly used technique. Unfortunately, the technique is frequently misapplied or misinterpreted leading to confusion and misdiagnosis of fracturing parameters. This paper presents a consistent method of analysis of the G-function, its derivatives, and its relationship to other diagnostic techniques including square-root(time) and log(Dpwf)-log(Dt) plots and their appropriate diagnostic derivatives. Actual field test examples are given for the most common diagnostic curve signatures.
 
Introduction
Pre-frac diagnostic injection test analysis provides critical input data for fracture design models, and reservoir characterization data used to predict post-fracture production. An accurate post-stimulation production forecast is necessary for economic optimization of the fracture treatment design. Reliable results require an accurate and consistent interpretation of the test data. In many cases closure is mistakenly identified through misapplication of one or more analysis techniques. In general, a single unique closure event will satisfy all diagnostic plots or methods. All available analysis methods should be used in concert to arrive at a consistent interpretation of fracture closure.

Relationship of the pre-closure analysis to after-closure analysis results must also be consistent. To correctly perform the after-closure analysis the transient flow regime must be correctly identified. Flow regime identification has been a consistent problem in many analyses. There remains no consensus regarding methods to identify reservoir transient flow regimes after fracture closure. The method presented here is not universally accepted but appears to fit the generally assumed model for leakoff used in most fracture simulators.

Four examples are presented to show the application of multiple diagnostic analysis methods. The first illustrates the expected behavior of normal fracture closure dominated by matrix leakoff with a constant fracture surface area after shut-in. The second example shows pressure dependent leakoff (PDL) in a reservoir with pressure-variable permeability or flow capacity, usually caused by natural or induced secondary fractures or fissures. The third example shows fracture tip extension after shut-in. These cases generally show definable fracture closure. The fourth example shows what has been commonly identified as fracture height recession during closure, but which can also indicate variable storage in a transverse fracture system.

For each example the analysis will be demonstrated using the G-function and its diagnostic derivatives, the sqrt(time) and its derivatives, and the log-log plot of pressure change after shut-in and its derivatives.1-4 When appropriate, the after-closure analysis is presented for each case, as is an empirical correlation for permeability from the identified G-function closure time.5 A critical part of the analysis is the realization that there is a common event indicating closure that should be consistently identified by all diagnostic methods. To reach a conclusion all analyses must give consistent results.

The goal of this paper is to provide a method for consistent identification of after-closure flow regimes, an unambiguous fracture closure time and stress, and a reasonable engineering estimate of reservoir flow capacity from the pressure falloff data, without requiring assumptions such as a known reservoir pressure. Other methods, based on sound transient test theory, require pressure difference curves based on the observed bottomhole pressure during falloff minus the “known” reservoir pressure.5,8 While these methods are technically correct they can lead to confusing results at times, especially in low permeability reservoirs when pore pressure is difficult to determine accurately prior to stimulation.

This is not a transient test analysis paper but is intended to present a practical approach to analysis of real, and frequently marginal-quality, pre-fracture field test data. The techniques applied are based on some transient test theory. Some of the results presented here are still under debate and development. The methods shown have been tested and, we believe, proven in the analysis of hundreds of tests. Application of these methods provides consistent analysis that helps to avoid misinterpretation of falloff data, and give the most useful information available from diagnostic injection tests.