Natural frequencies of longitudinal oscillations of a droplet in the constriction of the capillary tube

About the authors:

Amir A. Gubaidullin, Dr. Sci. (Phys.-Math.), Professor, Сhief Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; eLibrary AuthorID, ORCID, Web of Science ResearcherID, Scopus AuthorID, a.a.gubaidullin@yandex.ru

Aleksei Yu. Maksimov, Lead Engineer, CompMechLab® LLC, Peter the Great St. Petersburg Polytechnic University; eLibrary AuthorID, ORCID, maksimov@compmechlab.ru

Abstract:

The actual problem of improving wave technologies of enhanced oil recovery lies in challenges of fi nding the frequency of longitudinal oscillations of oil droplets (ganglion), jammed in the narrowing of pores. To determine the natural frequencies of droplets computer modeling can be used. As a mathematical model for the numerical study Navier – Stokes equations or Lattice-Boltzmann method can be used. However, to obtain preliminary estimates and solve engineering problems it is convenient to have a formula that allows, even approximately, getting the desired result. In this paper a formula is obtained for the natural frequencies of longitudinal oscillations of a droplet surrounded by immiscible with its fl uid in the narrowing of capillary conical shape.  Comparison of the results of calculations by the formula with the numerical solution of the problem has been carried out. The analysis of the frequency of the droplet oscillations in the static pressure difference, surface tension and contact angle of wetting has been carried out.

References:

1.  Gubaidullin, A. A., Maksimov, A. Y. Modeling of dynamics of oil droplet in a capillary with narrowing // Herald of the Tyumen State University. 2013. № 7. Pp. 71-77.

2.  Hilpert, M. Capillarity-induced resonance of blobs in porous media: Analytical solutions, Lattice-Boltzmann modeling, and blob mobilization // J. of Colloid and Interface Science. 2007. Vol. 309 (2). Pp. 493-504.

3.  Nikolaevski, V., Stepanova, G. S. Nonlinear seismic and acoustic impact on oil recovery // Acoustical Physics. 2005. Vol. 51. Pp. 150-159.

4. Maksimov, G. A, Radchenko A. V. Modeling of oil production intensification at acoustical impact on the formation of the well // Acoustical Physics. 2005. Vol. 51. Pp. 118-131.

5. Serdyukov, S. V., Kurlenya, M. V. The mechanism of stimulation of oil fields of low intensity seismic // Acoustical Physics. 2007. Vol. 53. № 5. Pp. 703-714.

 6.  Dyblenko, V. P., Kamalov, R. N., Sharifullin, R. J., Tufanov I. A. Increased productivity and resuscitation wells using vibration impact. M., 2000. 381 p.

7.  Surguchev, M. L., Kuznetsov, O. L., Simkin, E. M. Hydrodynamic, acoustic, thermal cyclic exposure to oil reservoirs. M.: Nedra, 1975.

8. Beresnev, I. A. Theory of vibratory mobilization of non-wetting fluids entrapped in pore constrictions // GEOPHYSICS. Vol. 71. № 6. 2006. Pр. 47-56.

 9.  Beresnev, I. A., and W. Deng. Viscosity effects in vibratory mobilization of residual oil // GEOPHYSICS. Vol. 75. № 4. 2010. Pр. 79-85.

10.  Beresnev, I., Gaul, W., Vigil, R. D. Direct pore-level observation of permeability increase in two-phase fl ow by shaking // GEOPHYSICAL RESEARCH LETTERS. Vol. 38. 2011. L20302.

11.Gubaidullin, D. A., Nikiforov, G. A. The simulation of two-phase fl uid flow in a layered oil reservoir under a nonliner fi ltration law // Bullettin of the Tyumen State University. Physical and mathematical modeling. Oil, Gas , Energy. № 1(1). Т. 1. 2015. Pp. 59-64.