Volume 02 Issue 06-2022
91
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
06
Pages:
91-99
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
A
BSTRACT
The article proposes a formula for calculating the flow rate of a heavy liquid supplied to the mixing zones
of the apparatus. The experimental setup presents the results and analysis of experimental studies carried
out to determine the flow rate of heavy liquid in the mixing zone of the bubbling extractor. The analysis
confirmed the accuracy of the theoretical equation proposed for calculating the heavy liquid flow rate.
According to the results of the study, it was possible to determine the flow rate of heavy liquid depending
on the size and coefficient of resistance of the holes.
K
EYWORDS
Heavy phase, flow, velocity, pressure, gas content, gas velocity, drag coefficient, flow rate, density, fluid
velocity.
I
NTRODUCTION
Journal
Website:
http://sciencebring.co
m/index.php/ijasr
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Research Article
HYDRODYNAMICS OF HEAVY LIQUIDS IN A BUBBLING
EXTRACTOR
Submission Date:
June 10, 2022,
Accepted Date:
June 20, 2022,
Published Date:
June 30, 2022
Crossref doi:
https://doi.org/10.37547/ijasr-02-06-13
Karimov Ikromali Tojimatovich
Doctor Of Technical Sciences, Professor, Fergana Polytechnic Institute, Fergana, Republic Of Uzbekistan
Rakhmanov Abdukhalim Toshpulat Ugli
Assistant, Fergana Polytechnic Institute, Fergana, Republic Of Uzbekistan
Volume 02 Issue 06-2022
92
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
06
Pages:
91-99
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
All over the world, scientific research is being
carried out to create new designs of highly
efficient extractors for liquid extraction
processes, increase the surface area of contact of
liquid phases and accelerate the mixing process.
In this regard, the use of the energy of
compressed gas, which is chemically inert to
liquids, the improvement of models for crushing
drops and mass transfer in terms of the
physicochemical properties of liquid phases,
reducing the consumption of extractant and
stability in the stages of the apparatus, reducing
the number of stages, high-performance metal
and energy-saving, compact, special attention is
paid to the creation of a new series of extractors
capable of extracting various liquids.
Object of study
Following the above requirements, we have
developed a new design of a bubbling extractor
using inert gases [1]. The light liquid is supplied
from the bottom of the apparatus to several
contact mixing elements located on the steps of
this multistage bubbling extractor, depending on
the performance of the apparatus [1,2].
The heavy liquid is supplied from the top of the
apparatus through holes drilled in special pipes.
The rate at which this liquid flows out of the hole
depends on the size of the hole, and the
physicochemical properties of the liquid, i.e. the
difference in density of the liquids, surface
tension, and amount of gas content. It is
recommended to choose the diameter of the pipe
that discharges the heavy liquid into the mixing
zone of the apparatus in the range dt = (3÷5) mm,
depending on the diameter of the hole drilled in
it.
The velocity of a heavy liquid flowing through a
pipe also depends on φ the amount of gas content
generated from the gas and liquid velocities.
Approximating the maximum amount of gas
content in the mixing zones of the apparatus to
the maximum value in the given limit φ → 0.3, it is
possible to achieve the maximum decrease in the
geometric pressure in the inner bubble tube
[3,4,5,6,7,8].
This, in turn, accelerates the flow of the heavy
fluid. As a result, the performance of the device is
improved. Let's analyze it theoretically (Fig.1).
Volume 02 Issue 06-2022
93
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
06
Pages:
91-99
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
Figure 1. Calculation scheme and experimental setup
The total pressure in the centre of the drain holes
is [4,7]
0
1
,
об
ж
P
р
р
р Па
(1)
where P
0
– is the pressure of the light liquid in the
inner bubble tube entering the centre of the heavy
liquid drain hole, which is determined by the
following formula.
0
0
(1
)
,
см
о
P
g
H Па
(2)
where ρ
ар
- the density of mixtures of light and
heavy liquids, which is determined as follows.
ρ
ар
= ρ
о
а + ρ
c
(1-a), кг / м
3
; (3)
where φ
0
– the amount of gas content in the inner
mixing zone, H
0
is the height of the mixing zone,
m; a - the proportion of heavy and light liquids in
the mixture,%;
Р
1
- the static pressure of the heavy liquid in the
bubble pipe falling towards the centre of the hole,
defined as follows.
1
2
,
т
P
gH Па
(4)
Where Н
2
- the height of the heavy liquid branch
pipe to the centre of the hole, m; ρm is the density
of the heavy liquid, kg/m
3
.
∆P
ж
– Pressure loss due to the outflow of heavy
liquid from the hole of the drain pipe, which is
determined as follows.
2
0
,
2
о
m
ж
P
Па
(5)
where
0
- the coefficient of resistance of the
heavy liquid flowing out of the hole, ωо is the
velocity of the heavy liquid flowing out of the hole,
m/s.
Now we substitute equations 2, 4, and 5 into
equation 1.
0
0
0
2
0
(1
)
2
т
cм
т
p
g
H
g H
(6)
From expression 6 we find the speed of the
outflow of a heavy liquid.
Volume 02 Issue 06-2022
94
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
06
Pages:
91-99
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
2
0
0
0
2 (
)
(1
)
m
cм
с
m
g
H
H
w
(7)
Depending on this speed, one can find the flow
rate of a heavy liquid flowing through a single
hole.
2
3
3600,
/
o
Q
R
м соат
;
(8)
With the effective implementation of mass
transfer processes in the apparatus, the ratio of
light and heavy liquids should be correct from the
point of view of inversion [9]. It is very important
to take this ratio into account when designing
equipment. Depending on this, the number of
holes in the heavy liquid drain is determined.
As a result of the above theoretical studies, an
equation was proposed for determining the flow
rate of a heavy liquid into the internal mixing zone
of the apparatus.
As a result, we will be able to find the volume of
the heavy liquid supplied to the apparatus.
Depending on this value, conditions were created
for the correct selection of the ratio of light and
heavy liquids, i.e. conditions for the correct choice
of inversion.
R
ESULTS
At the first stage of the experiment, δ/d = 0,275;
0,475; 0,675; to the size of the hole opened in the
heavy liquid drain pipe; 1 Depending on and
selection of liquids with three different values of
surface tension, the drag coefficients of the holes
were determined. The ratio of the hole wall
thickness to the hole diameter δ/d and the surface
tension of the liquids were plotted graphically.
(Figure 3).
The next task was to test the proposed equation 7
by determining the flow rate of the experimental
device in the internal mixing zone depending on
the change in the gas content φ and the density of
the heavy liquid ρo, the density of the mixture ρar.
Water was chosen as a light liquid, and a mixture
of carbon tetrachloride with benzene was chosen
as a heavy liquid. The densities of a mixture of
light and heavy liquids were determined by
equation (9). To better distinguish between heavy
and light liquids in experimental processes, the
heavy liquid was stained with a powder called
Dithizone.
The size of the hole for draining the heavy liquid
was chosen d = 2 and 1 mm. The densities of a
mixture of light and heavy liquids were
determined by the following formula [9].
3
0
(1
),
/
ар
с
а
а кг м
(9)
where: ρ
ар
- mixture density, kg/m3; ρ0 is the
density of the heavy liquid, kg/m
3
;
а - the percentage of liquid density, %;
In the experiments, the proportion of heavy
liquids was 33%, and the proportion of light
liquids was 67%. As a result, the densities of the
mixture were determined.
1. ρ
ар
= 1200 ∙ 0,33 + 1000 (1 - 0,33) = 1066, кг /
м
3
;
2. ρ
ар
= 1100 ∙ 0,33 + 1000 (1 - 0,33) = 1033, кг /
м
3
;
Volume 02 Issue 06-2022
95
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
06
Pages:
91-99
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
Initially, a hole with a diameter of 2 mm was
drilled into the internal mixing zone of the
apparatus in the heavy liquid drain pipe, and the
heavy liquid was supplied. The velocity of the
liquid mixture supplied to the mixing zone of the
apparatus was transferred unchanged at the
value w0 = 0,07 m/s. The gas velocities at
constant liquid velocities varied by wг =0.051,
0,086, 0,012 m/s, and the experimental values of
the gas content in the internal mixing zones of the
apparatus were determined. To determine this
value, the internal mixing zone of the apparatus
was connected to a glass tube in the form of a
communicating vessel, and the change in the
height of the liquid mixture level H1 was recorded
(Fig. 1).
a-hole 2mm
b-hole 1mm
Figure 2. Determination of the heavy liquid flow rate in the
sedimentation zone.
According to these gas velocities, the
experimental values of the amount of gas content
changed up to φ = 0.1, 0.2, 0.3. Based on the
established regimes, the flow rate of the heavy
liquid entering the mixing zone of the apparatus
was experimentally determined. To do this,
depending on time and layer height h, the volume
of heavy liquid formed as a result of settling in the
apparatus zone was determined (Fig. 2-a and b),
and the time set in the experiment was 0.25
hours. The sequence of experiments was carried
out separately for each of the holes with
dimensions d = 2 and 1 mm, with gas content
values φ = 0.1, 0.2 0.3.
The theoretical value of the amount of gas content
was determined by the following equation [3,4].
'
'
04
,
0
1
0
c
w
(10)
where
w'
с
- the reduced fluid velocity in the
mixing zone, m/s;
' - the amount of gas content in the liquid state
at rest, defined as follows.
'
0,97
2, 47
г
(11)
where:
ω
г
– the reduced gas velocity in the mixing
zone, m/s;
Using Equation 7, the theoretical heavy fluid flow
rates were determined. The flow rate of the heavy
Volume 02 Issue 06-2022
96
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
06
Pages:
91-99
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
liquid was determined by equation 8. Theoretical
and experimental values were compared and
analyzed. The analysis confirmed the correctness
of the proposed theoretical equation for
calculating the heavy liquid flow rate. The largest
difference between the theoretical and
experimental values was ±7%. Graphs of the
change in the heavy liquid flow rate depending on
the change in the volume of gas content are
plotted (Fig. 4 and 5). An empirical formula is
proposed for determining the hydraulic
resistance of holes based on the results of
experimental studies.
0,59
t
d
(12)
where σ - the surface tension of the heavy liquid,
N/m; δ - hole wall thickness, m; hole diameter, m.
1.σ
= 0,073 n/m,
2.σ
= 0,046 n/m,
3.σ
= 0,0245
n/m.
Figure 3. Graph of the change in the drag
coefficient depending on the change in wall
thickness and hole diameter.
The form of the resulting regression equations is
as follows:
y = -4,419x
2
+ 7,594x + 0,1297
R² =
0,974
y = -6,8454x
2
+ 11,806x + 0,1952
R²
=
0,9757
y = -13,019x
2
+ 22,183x + 0,4017
R²
=
0,9704
Volume 02 Issue 06-2022
97
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
06
Pages:
91-99
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
Figure 4. Q = ƒ (φ) Graph of the change in heavy
liquid consumption depending on the change in
gas volume (comparative graph).
Hole resistance coefficient
ξ = 2,7
; fluid velocity
w
c
= 0,07 m/s, (const).
1,2 - heavy liquid density ρ
0
= 1200 kg/m
3
,
mixture density ρ
ар
= 1066 kg/m
3
;
3,4 - heavy liquid density ρ
0
= 1100 kg/m
3
,
mixture density ρ
ар
= 1033 kg/m
3
;
The form of the obtained regression equations is
as follows
1.y = 0,0125x+0,0163
2
R = 1
(13)
2.y = 0,012x+0,0158
2
R = 1
(14)
Figure 5. Q = ƒ (φ) Graph of the change in heavy
liquid consumption depending on the change in
gas volume (comparative graph).
Hole resistance coefficient
ξ
= 3,7; fluid velocity
w
c
= 0,07 m/s, (const).
1,2 - heavy liquid density
ρ
0
= 1200 kg/m
3
,
mixture density
ρ
ар
= 1066
kg/m
3
;
Volume 02 Issue 06-2022
98
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
06
Pages:
91-99
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
3,4 - heavy liquid density
ρ
0
= 1100 kg/m
3
,
mixture density
ρ
ар
= 1033 kg/m
3
;
The form of the obtained regression equations is
as follows
1.y = 0,004x+0,0034
2
R = 0,9881
(15)
2.y = 0,004x+0,0036
2
R = 0,9776
(16)
C
ONCLUSION
As a result of the theoretical studies carried out
above, a formula was recommended for
calculating the flow rate of a heavy liquid supplied
to the mixing zones of the experimental
apparatus. To test this formula, experiments were
carried out and analyzed on the experimental
setup of a bubbling extractor to determine the
rate of outflow of a heavy liquid into the mixing
zones. The analysis confirmed the correctness of
the proposed theoretical equation for calculating
the heavy liquid flow rate. Based on the results of
the study, it was possible to determine the flow
rate of heavy liquid depending on the size and
number of holes and to choose the right ratio of
liquid phases.
R
EFERENCES
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Патент. № ИАП 06714 (Узбекистан)
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Алиматов Б.А., Соколов В.Н., Саъдуллаев
Х.М., Каримов И.Т. Многоступенчатый
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Сборник
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по
материалам XXX международной научно-
Volume 02 Issue 06-2022
99
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
02
I
SSUE
06
Pages:
91-99
SJIF
I
MPACT
FACTOR
(2021:
5.478
)
(2022:
5.636
)
METADATA
IF
–
7.356
практической конференции. Технические
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