In this paper, we present the fracture-compliance method, a technique for estimating the closure pressure from diagnostic fracture-injection tests (DFITs). The method is based on the observation that fractures retain a finite aperture after asperities come into contact (mechanical closure). An empirical, nonlinear joint-closure law is used to relate the after-closure fracture aperture and stiffness (the reciprocal of compliance) to effective normal stress. Fracture closure increases fracture stiffness, which, in low-permeability formations, causes an increase in the pressure derivative. On the basis of these insights, we propose the fracture-compliance method, which consists of picking closure at the first point of deviation from linearity on a plot of pressure or G×dP/dG vs. G-time (after the end of the very-early-time transient associated with wellbore and near-wellbore friction and fracture tip-extension). The contribution of this paper is to provide theoretical justification for why closure is best picked with the fracture-compliance method, and not with other widely used methods. We provide a series of numerical DFIT simulations to demonstrate the sensitivity of the pressure transient to input parameters. Governing equations are derived and used to demonstrate the effect of changing fracture aperture after closure. A field DFIT data set is analyzed with the new method. Finally, a field example is presented in which downhole tiltmeter measurements provide an independent estimate of the minimum principal stress.

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