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Non-linear vibrations under slow kinetics of viscoelastic properties of oil
Drilling and development of hydrocarbon fields

Authors: Igor B. ESIPOV was born March 13, 1945. He graduated from Moscow Institute of Physics and Technology in 1968 specializing in Ultrasonic Engineering. He is Doctor of Physical and Mathematical Sciences, professor of the Department of Physics at Gubkin Russian State University of Oil and Gas since 1995. He is author of more than 89 scientific papers. Е-mail: igor.esipov@mail.ru
Oleg M. ZOZULYA is researcher at Schlumberger. E-mail: omzozulya@gmail.com
Michael A. MIRONOV is Candidate of Physical and Mathematical Sciences, Head of Laboratory at the Andreev Acoustics Institute. E-mail: mironov_ma@mail.ru

Abstract: We have previously identified slow evolution of the viscoelasticity modules of heavy crude oil. Shear modulus was measured during 72 hours at frequencies of 0,5, 5 and 50 Hz at different temperatures. The dependence of complex shear modulus on the deformation amplitude was studied with a rotational rheometer. The study showed a logarithmic growth of the nonlinearity parameter in time for this sample of oil. It was established experimentally that the complex shear modulus depends linearly on the amplitude of the shear perturbations, which is possible with the shear modulus linearly depending on the shear modulus of the medium deformation. Based on the Boltzmann statistical approach to the determination of the rate of transition to equilibrium , the model differential equation describing the slow kinetics of the changes in the internal parameters of the medium was obtained. It is shown that unlike the exponential time dependence, the slow kinetics leads to logarithmic time dependence of the perturbation decay.

Index UDK: 534.26; 542.34

Keywords: complex media, viscoelasticity, slow kinetics, nonlinearity parameter

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