Reappraisal of the G Time Concept in Mini-Frac Analysis

Abstract

Industry is currently using mini-frac analysis for the determination of fracture closure stress and after-closure reservoir properties. The foundation of all mini-frac analysis is the one dimensional Carter leak-off model, which leads directly to the concept of G Time. For 30+ years, G Time (or the G function) has played the dominant role for the determination of closure stress. The current norm uses combination G function and combination square root Δt plots for closure pressure determination. Each combination plot has three plotting functions associated with it. These combination plots also allow the identification of non-ideal behavior. Additionally, various log-log derivative techniques based on pressure transient analysis concepts have been developed to act as a guide for determining flow regimes and closure pressure. These PTA based techniques also allow the determination of after-closure flow regimes and properties. Concurrently, various specialized afterclosure plotting techniques have been developed for fracture/reservoir property determination. Despite all these techniques, there remains ambiguity in performing mini-frac analysis. Part of the problem is that the recommended plots do not rigorously identify the various flow regimes that occur during a mini-frac fall-off. Mini-frac analysis requires a general theory that accounts for all of the actual observed flow regimes. A systematic approach based on pressure transient analysis (PTA) concepts has been developed to identify the various flow regimes (Carter leak-off being only one of them). The starting point is the Bourdet log-log derivative plot, accompanied by the primary pressure derivative (PPD) function. It will be shown that the PPD on its own has independent flow regime identification capabilities. Once specific flow regimes have been identified, specialized log-log plots can be constructed for further flow regime verification. New combination plots are then developed for each flow regime to further assist in closure pressure determination. The theory will first be developed and illustrated with various example problems.

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