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Proceedings of the Mavlyutov Institute of Mechanics

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Topolnikov A.S. Argumentation of Application if Quasi-Stationary Model to Describe the Periodic Regime of Oil Well. Proceedings of the Mavlyutov Institute of Mechanics. 2017. 12(1). 15–26.
2017. Vol. 12. Issue 1, Pp. 15–26
DOI: 10.21662/uim2017.1.003
Argumentation of Application if Quasi-Stationary Model to Describe the Periodic Regime of Oil Well
Topolnikov A.S.
Mavlyutov Institute of Mechanics, Ufa


In the paper the argumentation of application of quasi-stationary model of gas-liquid flow is presented to describe periodic regime of oil well operating. It is shown that this simplification actually does not affect the solution accuracy, but allows to essentially diminish the calculating time. In view of the considered problem specification the transition from non-stationary model of media to the quasi-stationary model greatly increases the computational speed, which is the necessary condition for execution the optimization calculations.


multiphase flow,
mass transfer,
oil recovery

Article outline


Monitoring and optimization of periodical regime of oil wells, which are operated by sets of electrical submersible pump, by the help of mathematical modeling methods


To describe multiphase flow in the reservoir and well elements (casing, tubing, annulus) the quasi-stationary model is suggested to use as an alternative to non-stationary model. This enables to accelerate the duration of optimization calculations without losses in computational accuracy


1) The problem of spreading of disturbance in multiphase flow in round tube is studied. Three characteristic time stages of non-stationary solution are highlighted

2) The comparison of results of calculations of non-stationary and quasi-stationary models for describing of multiphase flow in well elements is done. It is obtained that the quasi-stationary model shows error of calculation of the main parameters of the problem (averaged and extreme during one periodic cycle of pumping/accumulation values of liquid rate, well flow pressure, dynamic level) of about 1% compared with non-stationary model


1) By the model examples (part of a tube and oil well) it is shown that the influence of non-stationary effects in multiphase flow in tubes with reference to the problem of periodic operating of oil well by electric submersible pump is minimum and non-stationary model of the well in such problems can be replaced by quasi-stationary without losses in solution accuracy

2) For practical use it is advisable to switch from the solution of partial differential equations to the simplified correlations like Beggs-Brill or Ansari to calculate the pressure drop in tubes, which is solved by explicit numerical methods