Power spectrum of hydraulic fractures with constricted opening

Arcady Dyskin,Elena Pasternak

doi:10.5194/egusphere-egu21-5724

Abstract

&lt;p&gt;Propagation of hydraulic fractures in rocks is often a non-smooth process, which leaves behind a number of rock bridges distributed all over the fracture. The bridges constrict the fracture opening and thus affect the determination of hydraulic fracture dimensions from the volume of pump-in fracturing fluid. This makes it necessary to detect the emergence of bridges and their concentration over the fracture surface.&lt;/p&gt;&lt;p&gt;Opening of hydraulic fractures in rocks is determined by a balance of pressure from the fracturing fluid and the normal component of the in-situ compressive stress. If an external excitation is applied (e.g. by a seismic wave), closure of the fracture is additionally resisted by the stiffness of fracturing fluid. Subsequently, a simple model of hydraulic fracture is presented by a bilinear spring with a certain stiffness in tension and a very high stiffness in compression. This constitutes so-called bilinear oscillator [1, 2] in which the compressive stiffness considerably exceeds the tensile one. The presence of bridges increases stiffness in tension thus reducing bilinearity of the modelling spring. Therefore the determination of the bilinearity is a first step in the reconstructing the effective stiffness of the bridges. &amp;#160;&lt;/p&gt;&lt;p&gt;We use the model of bilinear oscillator, identify multiple resonances and determine the first two harmonics (or first two peaks of in the power spectrum). The ratio of their amplitudes directly depends upon the bilinearity (ratio of compressive to tensile stiffnesses), hence the bilinearity is determinable from the amplitude ratio. Then the effective bridge stiffness can be estimated.&lt;/p&gt;&lt;p&gt;1. Dyskin, A.V., E. Pasternak and E. Pelinovsky, 2012. Periodic motions and resonances of impact oscillators. Journal of Sound and Vibration 331(12) 2856-2873. ISBN/ISSN 0022-460X, 04/06/2012.&lt;/p&gt;&lt;p&gt;2. Pasternak, E., A. Dyskin&lt;sup&gt;&lt;/sup&gt;and Ch. Qi, 2020. Impact oscillator with non-zero bouncing point. International Journal of Engineering Science, 103203.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Acknowledgement&lt;/strong&gt;. The authors acknowledge support from the Australian Research Council through project DP190103260.&lt;/p&gt;

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