A new method is proposed to estimate the compliance and conductivity of induced unpropped fractures as a function of the effective stress acting on the fracture from DFIT data. A hydraulic fracture's resistance to displacement and closure is described by its compliance (or stiffness). Fracture compliance is closely related to theelastic, failure and hydraulic properties of the rock. Quantifying fracture compliance and fracture conductivity under in-situ conditions is crucial in many earth science and engineering applications but very difficult to achieve. Even though laboratory experiments are often used to measure fracture compliance and conductivity, the measurement results are strongly influenced by how the fracture is created, the specific rock sample obtained andthe degree to which it is preserved. As such the results may not be representative of field scale fractures

Over the past two decades, Diagnostic Fracture Injection Tests (DFIT) has evolved into a commonly used and reliable technique to obtain in-situ stresses, fluid leak-off parameters and formation permeability. The pressure decline response across the entire duration of a DFIT test reflects the process of fracture closure and reservoir flow capacity. As such it is possible to use this data to quantify changes in fracture conductivity as a function of stress. In this paper we presenta single, coherent mathematical framework to accomplish this. We show how each factor impacts the pressure decline response and the effects of previous overlooked coupled mechanisms are examined and discussed. Synthetic and field case studies are presented to illustrate the method. Most importantly,a new specialized plot (normalized system stiffness plot) is proposed, which not only providesclear evidence of the existence of a residual fracture width as afracture is closing during a DFIT, but also allows us to estimate fracture compliance (or stiffness) evolution and infer un-propped fracture conductivity using only DFIT pressure and time data based on a time-convolution solution. It is recommended that the normalized system stiffness plot be used as a standard practice to complement the G-function or square root of time plotbecause it provides veryvaluable information on the properties of fracture surface roughness at a field-scale, information that cannot be obtained by any other means.

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