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Discontinuity, Nonlinearity, and Complexity 5(3) (2016) 199--207 | DOI:10.5890/DNC.2016.09.001

Rakiz M. Sattarov$^{1}$, Ilham R. Sattarzada$^{1}$, Sayavur I. Bakhtiyarov$^{2}$, and Ranis N. Ibragimov$^{3}$

$^{1}$ Azerbaijan Institute of Oil Industry, Baku, Azerbaijan

$^{2}$ FLOUR, Houston, TX, USA

$^{3}$ Department of Mathematics and Physics, University of Wisconsin-Parkside, Kenosha, WI, USA

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Abstract

An unsteady flow of rheological complex fluid with fractal structure in various pipe geometries was studied when the pressure is a harmonic function of time at a given frequency at the initial cross section of the pipe. An integral type rheological equation by fractional derivative is applied for the first time to model the thixotropic rheological type oils with a high content of wax, resins and asphaltene. The obtained results show that, the relaxation time and the fractal parameters can significantly influence the process of damping pressure along the pipe. It is shown that depending on these parameters the attenuation process may increase and decrease compared to the processes in a viscous damping fluid pressure. The results of simulations are compared to those for resin-asphalt-paraffin oils of two types.

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