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European Journal of Applied Sciences – Vol. 12, No. 4
Publication Date: August 25, 2024
DOI:10.14738/aivp.124.17319.
Gareyev А. А. (2024). About the Heat Transfer Coefficient. European Journal of Applied Sciences, Vol - 12(4). 183-189.
Services for Science and Education – United Kingdom
About the Heat Transfer Coefficient
A. A. Gareyev
Ufa University of Science and Technology. Ufa, Russia
ABSTRACT
As an oil field is exploited, productive strata are depleted. This phenomenon is
typical for many oil and gas fields. The exploitation of depleted deposits leads to
complications during the operation of electric centrifugal pumps. The purpose of
this work is to investigate the causes of failures and develop technological
solutions.
Keywords: Oil field, operation of an oil field by installations of electric centrifugal
pumps, causes of pump failures.
When solving the problem of the centrifugal pump’s temperature, we assumed that the heat- transfer factors , the heat-conductivity factor of the gas blanket on the pump surface
из
, the
gas-layer thickness
из
and the dependency of the pump head on gas content h are known.
In the field, the heat transfer coefficient cannot be explored by experiment due to the high
pressure affecting the liquid-gas mixture inside the centrifugal pump. Therefore, a theoretical
modeling of this physical value is required with further use of the modeling results for solving
practical problems. The liquid-gas mixture is pumped by the centrifugal pump stage; inside
the pump stage, heat generation takes place, whereby this heat is transferred to the liquid-gas
mixture.
Figure 1: Schematic View of One Centrifugal Pump Stage. 1 - Diffuser; 2- Impeller; 3 – Pump
Shaft; 4 – Liquid-Gas Mixture Flow Channels; 5 – Slide Bearing; 6 – Direction of The Liquid-Gas
Flow.
Sectional view of a centrifugal pump
stage
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Services for Science and Education – United Kingdom 184
European Journal of Applied Sciences (EJAS) Vol. 12, Issue 4, August-2024
Figure 1 shows the sectional view of stage 1 of the centrifugal pump, 2 – impeller of the
centrifugal pump, permanently attached to the shaft 3 and rotating together with the latter; 4
– impeller pot, 5 – slide bearing, 6 – directions of the liquid-gas-mixture flow in the centrifugal
pump stage.
When the centrifugal pump impeller (2) is rotating inside the diffuser (1), the liquid-gas
mixture contacts the metal surfaces of the diffuser pot and the impeller. Due to the high
rotational speed of the impeller and the frequent change of the liquid-gas mixture’s flow
directions, it is impossible to identify any particular type of the mixture motion (laminar or
turbulent stream). Presumably, during skimming over the metal surfaces inside the pump
stage cavity, the gas phase does not contact these surfaces.
Figure 1.1: Sectional view of the ESP unit stage. R- impeller radius, d – thickness of the mixture
flowing from the impeller into the diffuser, Qv – quantity of heat generated by the slide bearing
friction.
Only the liquid phase contacts the metal surfaces inside the pump stage, thereby providing
heat transfer between the liquid and the pump stage (figure 1.1). Then, within the impeller- related coordinate system, the water-oil mixture flow can be roughly characterized as eddy
motion (permanent change of the flow speed and direction).
The kinetic energy of the liquid-gas mixture, acquired in the process of rotation, is converted
into potential compression energy. Friction (or heat generation) takes place between the slide
bearing and the impeller hub. Since the heat conductivity of the bearing (0.01 W
(m∗K)
) is
insignificant, the resulting amount of heat is partially transferred into the liquid-gas mixture,
whose thermal properties largely depend on the availability of free gas, associated
(formation) water and oil in the wellstream.
Impeller
Diffuser
Gas blanket
Liquid layer
Pump shaft
The slide bearing is
the source of heat
emission (Qv).
gas
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Gareyev А. А. (2024). About the Heat Transfer Coefficient. European Journal of Applied Sciences, Vol - 12(4). 183-189.
URL: http://dx.doi.org/10.14738/aivp.124.17319
The liquid-gas mixture flows out through the gap between the impeller rim and the diffuser
body cavity. The width of the diffuser is d=0.002 m, the impeller radius is Rr=0.037 m, the
liquid-gas mixture flow is Qg-l with gas concentration φ.
Dividing the volumetric flow rate by the area of the gap between the impeller and the diffuser
body cavity, we obtain the average linear travel of the liquid-gas mixture. To calculate the
average linear travel of the water-oil mixture, the gas concentration φ must be considered.
Then (say, with the flow rate
Qg−l
=18 m3/day= 0,00021 m3/s) we get:
R d
Q
g l
g l
−
− −
=
2
*(1 )
υ =
0.00021∗(1−φ)
2∗3.14∗0.037∗0.002
= 0.451 m
s
(1 − φ)
The gas content in the liquid-gas mixture may vary between 50 and 80 % (
0,5 0,8
).
Then the oil-and-gas mixture flow velocity may be within the range of:
0,104 0,261
m/s.
Then the Re value at the flow velocity of υ = 0,451 m
s
(when ν = 0,000001 m2
s
):
* d
Re = 33374
0.000001
0.451*0.074 Re = =
where: Re - Reynolds number; d – diameter; ν – kinematic viscosity.
When the Reynolds number Re is equal to 3374, the stream is turbulent (over 4200),
therefore the boundary-layer theory for turbulent liquid streams [15, 17, 19] must be applied
to estimate the heat transfer coefficient.
Indeed, according to the Prandtl hypothesis [2], the boundary layer thickness (liquid layer
thickness) ξ shall satisfy the inequality (1):
l пг
(1)
where
пг
thickness of the liquid boundary layer, l– typical size of the impeller (e.g. l=0.074 m
- impeller diameter).
Let’s estimate the boundary layer thickness
пг
of the liquid flow in the impeller. To do this,
let’s assume the rotation radius of 37 mm, the rotation rate of 50 rpm with the liquid flow rate
in the impeller-related coordinate system:
υ = 0.451
m
s
(1 − φ)
δпг ≈
Vс
2πR∇x
(1 − φ) =
0,451∗10−3
(1−0,7)
2∗3,14∗0.037∗0.005∗50
= 0,001 m (2)