Ali R. Mohammed Jawad


      

Al-Khwarizmi 

Engineering   

Journal 

Al-Khwarizmi Engineering Journal,  Vol. 8, No. 1, PP 37 -47 (2012) 

 

 

Effect of Solid Properties on Axial Liquid Dispersion in  

Bubble Column 
 

Ali Raad Mohammed Jawad 
Department of Chemical Engineering /University of Technology 

Email: aliolimpic@yahoo.com 

 
(Received 30 June 2011; accepted 13 December 2011) 

 
 

Abstract 

 
Experiments were conducted to study axial liquid dispersion coefficient in slurry bubble column of 0.15 m inside 

diameter and 1.6 m height using perforated plate gas distributor of 54 holes of a size equal to 1 mm diameter and with a 

0.24 free area of holes to the cross sectional area of the column. The three phase system consists of air, water and PVC 

used as the solid phase. The effect of solid loading (0, 30 and 60 kg/m
3
) and solid diameter (0.7, 1.5 and 3 mm) on the 

axial liquid dispersion coefficient at different axial location (25, 50 and 75 cm) and superficial gas velocity covered 

homogeneous-heterogeneous flow regime (1-10 cm/s) were studied in the present work. The results show that the axial 
liquid dispersion coefficient increases with increasing superficial gas velocity, axial distance, solid concentration and an 

inverse relationship with particles diameter. 

 

Keywords: Axial liquid dispersion coefficient; Axial dispersion; Mixing; Liquid circulation; Backmixing; Slurry bubble 
column; Bubble column. 

 
 

1. Introduction 
 

Slurry Bubble column are multiphase contactors 

widely used as absorbers, strippers and reactors in 
chemical, biochemical and petro chemical industrial 

processes, because of their advantages as simple 

construction and excellent heat and mass transfer, 
as mixing is induced only by gas aeration [1,2]. 

Holdup and axial dispersion of liquid are two 

important parameters affecting the performance of 
the gas – liquid contacting devices. Wrong 

estimations of liquid holdup and axial dispersion 

lead to an unexpected low performance [1]. Flow 

distribution in different axial locations is an 
important aspect of study in gas-liquid-solid three 

phase fluidized beds   [3]. 

The main drawback is a severe degree back 
mixing in the liquid phase, which is due to the low 

liquid flow rate. Back mixing is known to increase 

drastically when local liquid circulation develops 
[4]. The dispersion coefficient is expressed in 

dimensionless form as Peclet number (Pe); its value 

denoting the degree of back mixing in the column. 

If Pe=0 back mixing is complete and if Pe=∞ plug 

flow prevails [1]. 
 Axial and radial mixing of the liquid phase in 

bubble columns is characterized by using dispersion 

coefficients that are analogous to the diffusion 
coefficient of Fick's law diffusion [1]. The 

estimation of the axial dispersion coefficient of the 

liquid phase is important for the design and scale up 
of bubble column reactors [2]. Dispersion 

coefficients are generally calculated using the 

measured concentration – time response to input of 

a nonreactive, nonabsorptive inter tracer in the 
reactor. The methodology is well established for 

calculating the axial dispersion coefficient only, as 

the one dimensional dispersion model that is 
typically used for the fitting contains axial 

dispersion coefficient as the only fitting parameter 

[5]. It is usually assumed that the dispersion 

coefficient does not depend on the column height 
[6]. 

Unlike diffusion, dispersion arises from 

convective motion of fluid caused by the following 
main factors : relative movement of the gas and 

liquid phase; bubble coalescence and break up; the 

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Ali Raad Mohammed                           Al-Khwarizmi Engineering Journal, Vol. 8, No. 1, PP 37 - 47 (2012)  

38 

 

carry forward of liquid in wakes behind the rising 
gas bubbles and the consequent return flow 

generated for maintaining mass balance; and 

turbulence generated by any superimposed flow of 
liquid [1,2]. 

As far as is known, in all previous dispersion 

studies in semi batch packed bubble columns 

performed, the tracer has been added directly to the 
top of the bed. In Co – or counter – current flow 

reactors, the tracer is generally injected to the liquid 

inlet stream whereas the response is measured at the 
outlet [7]. The mixing process involves a shuffling 

or redistribution of material either by slippage or 

eddies; this repeated a considerable number of 

times during the circulation in the reactor [5]. 
Ichikawa and Chen found a significant effect of 

superficial liquid velocity on axial liquid dispersion 

coefficient [8]. 
The effect of solid concentration and particle 

size on gas holdup has been investigated by a 

number of researchers. Several researches 
concluded that an increase in solids concentration 

generally reduces the gas holdup [9]. The influence 

of particle size on hydrodynamics of bubble column 

has been found to depend on a number of factors 
including flow regime, gas velocity, liquid 

properties and slurry concentration [10].  

Shawaqfeh [11] reported that the liquid 
superficial velocity had negligible effect on gas 

holdup, but had significant effect on the axial 

dispersion coefficient. The axial liquid dispersion 
coefficient was found to depend on both gas and 

liquid velocities. 

Shah et al., [1] stated that the increase in gas 

velocity generally increases the liquid dispersion 
coefficient. 

Therning and Rasmuson [12] using packed 

bubble column, reported that in both homogeneous 
and heterogeneous flow regime the one dimensional 

axial liquid dispersion coefficient increases with 

increasing gas velocity. 

Krishna et al., [13] measured the axial liquid 
dispersion coefficient at three Metrophm 

immersing-type conductivity cells which were 

placed near the wall. 
Rubia et al., [5] reported that the value of the 

radial dispersion coefficient was typically about 1% 

axial liquid dispersion coefficient value under any 
given condition. The larger bubbles in tap water 

underwent more frequent breakup and coalescence 

and this increased the axial liquid dispersion 

coefficient.  
The aim of the present work is to study the 

effect of solid concentration and particle size at 

different axial location and superficial gas velocity 

(covered homogeneous-heterogeneous flow regime) 
on the axial liquid dispersion coefficient. 

 

 

2. Experimental 
 

Experiments were carried out in a QVF 

cylindrical bubble column of (15 cm inside 

diameter and 1.6 m height) with static liquid height 

(100 cm). The system is operated in a semi-batch 
mode with stagnant liquid and continues gas flow. 

A schematic diagram is shown in Fig. (1). 

In all experiments, the liquid phase was tap 
water and the gas phase was air. The air flow rate 

was measured with a pre-calibrated rotameter. A 

compressed air was dispersed from the bottom of 

the column through perforated plate consisted of 54 
hole, 1 mm diameter and free surface area to cross 

sectional diameter of 0.24.  

PVC particles (1025 kg/m
3
 density) were used 

as the solid phase. Different particles size were 

used (0.7, 1.5 and 3 mm) and different loading solid 

particles (0, 30 and 60 kg/m
3
) were used in the 

experiments. 

For the tracer experiments, residence time 

distribution (RTD) of the liquid phase was 

measured using different amounts of saturated 
solution of NaCl as a tracer. Different volumes of 

tracer were used to obtain the optimal amount of 

tracer that corresponds to optimal signal within the 
operating range of conductivity cell. This optimal 

amount of a saturated solution of NaCl was found 

equal to 5 wt % .The probes were placed on three 
points (25, 50 and 75 cm) from the distributer 

axially. The signals from the electrodes were 

transmitted to conductance meter (Philips type). 

The meters were connected via an interface to a PC 
computer.  

Tracer was injected as a pulse input; local 

changes in tracer concentration were displayed and 
saved continuously on PC. 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 



Ali Raad Mohammed                           Al-Khwarizmi Engineering Journal, Vol. 8, No. 1, PP 37 - 47 (2012)  

39 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

Fig.1. Schematic Diagram of the Experimental Apparatus. 
 

 

 

3. Theoretical Analysis 
 

In order to characterize mixing in bubble 

column, a two dimensional dispersion model has 

been used. The dimensionless tracer concentration 
can be written as [14, 5]: 

 
                                                                  …(1) 

Where: 
 

                                                      …(2)               
 

                                                               …(3) 
 

                                                       …(4) 

 

Accordingly when CT in Eq. (1) is radially 

invariant  (i.e.  Dr=∞), υn, βand x become zero and 
J0t(υnβ)=J0(υnx) =1. In this case Eq. (1) reduces to: 

         …(5)   

The average axial liquid dispersion coefficient 

(Dax.L av) was calculated: 

                                            …(6) 

 

 



Ali Raad Mohammed                           Al-Khwarizmi Engineering Journal, Vol. 8, No. 1, PP 37 - 47 (2012)  

40 

 

4. Results and Discussion 
 

4.1. Liquid Phase Dispersion in Bubble 
Column  

 
The conductivity data used for the calculation of 

dispersion coefficients are smoothed in order to 

remove the noise that already present due to 
occasional gas bubbles being in contact with the 

conductivity probes. A typical set of the pulse-

response data and the best fit model curve 

generated using Eq. (1) is shown in Fig. (2). the 
value of the radial dispersion coefficient influenced 

the height of the model generated peak, whereas the 

value of the axial dispersion coefficient influenced 
the width of the peak. The solution of Eq. (1) was 

found by using MATLAB R 2010b program. 

 

 
 

4.2. Radial Liquid Dispersion Coefficient 
(Dr,L ) 

 
This work takes into account only the axial 

(neglecting radial) liquid dispersion. Fig. (3-9) 

showed that its value does not exceed 1%. This is in 

agreement with the results obtained by Rubia et al., 

[5].  
The few measurements of radial dispersion 

coefficients cited by Deckwer [2], suggest that the 

radial dispersion coefficient is always less than one-
tenth of the value of the axial coefficient.  

Moreover, Joshi and Sharma [15] showed that 

the radial component of the velocity, i.e. the 
component that is relevant to radial mixing, is only 

about 36% of the axial component. This explains, 

that the relatively poor radial mixing in bubble 
columns compared to the axial mixing. 

 

 

4.3. Axial Liquid Dispersion Coefficient 
(Dax,L) 

 
The method of calculation of (Dax,L) carried out 

using equations (1) and (5) [i.e., using 
mathematical models with and without radial 

dispersion]. 

 
 

4.3.1.  Effect of Superficial Gas Velocity 

(Ug) and Axial Distance of Probe's Location 

(Z) on Axial Liquid Dispersion Coefficient 

(Dax,L) 
 

Fig. (3-9) show the effect of superficial gas 

velocity (Ug) on the axial dispersion coefficient for 
different axial distance (Z) from the distributor. It 

can be seen that, the axial dispersion coefficient 

increases with increase superficial gas velocity 
(Ug). This can be attributed to the decrease in 

mixing time which results from the increases of the 

average liquid circulation velocity (VC) which 

increases with the increase of (Ug). This result is in 
agreement with Therning and Rasmuson [12] and 

Shah et al., [1]. 

The axial dispersion coefficient increases 
slightly with increasing superficial gas velocity in 

the homogeneous regime (0-4 cm/sec) and then the 

increasing rate becomes faster in the heterogeneous 
regime (5-10 cm/sec). 

Moreover the axial liquid dispersion coefficient 

(Dax,L) increases with increase of the axial distance 

(Z). This increases in (Dax,L) due to a decrease in 
bubble rise velocity results from a decrease in 

bubble diameter and consequently increasing the 

liquid circulation velocity (VC),  then increase 
(Dax,L). These results are in agreement with Krishna 

et al., [13]. 

 
 

 

 

 
 

 

 
 

 

 

 
 

r/R=0, Ug=5 cm/s

0

1

2

3

4

0 10 20 30 40
Time (s)

C
T

/
C

0

Experimental

Model fitZ1 

Z2 
Z3 

C
T

 

 

Fig. 2. Typical Conductivity Responses of Different 

Probes. 

 



Ali Raad Mohammed                           Al-Khwarizmi Engineering Journal, Vol. 8, No. 1, PP 37 - 47 (2012)  

41 

 

  
 

 

 
 

 

 

 
 

 

 
 

 

 

 
 

Fig. 3. Effect of Superficial Gas Velocity on Axial Liquid Dispersion Coefficient at Different Z and CS=0. 

 

 

 

 

 

 
 

 

 
 

 

 
 

 

 

 
 

Fig. 4. Effect of Superficial Gas Velocity on Axial Liquid Dispersion Coefficient at Different Z, CS=30 and 

dp=3mm. 

 

 

 

Fig. 5. Effect of Superficial Gas Velocity on Axial Liquid Dispersion Coefficient at Different Z, CS=60 and  

dp= 3mm. 

D
a

x.
L 

(c
m

2
/s

)
 

Ug (cm/s) 

D
a

x.
L 

(c
m

2
/s

)
 

Ug (cm/s) 

D
a

x.
L 

(c
m

2
/s

)
 

Ug (cm/s) 



Ali Raad Mohammed                           Al-Khwarizmi Engineering Journal, Vol. 8, No. 1, PP 37 - 47 (2012)  

42 

 

 

 

Fig. 6. Effect of Superficial Gas Velocity on Axial Liquid Dispersion Coefficient at Different Z, CS=30 and  

dp= 1.5mm. 

 
 

 

 
 

 

 

 
 

 

 
 

 

 

 

 
Fig. 7. Effect of Superficial Gas Velocity no Axial Liquid Dispersion Coefficient at Different Z, CS=60 and  

dp= 1.5mm. 

 
 

 

 
 

 

 
 

 

 

 
 

 

 
 

 
 

Fig. 8. Effect of Superficial Gas Velocity no Axial Liquid Dispersion Coefficient at Different Z, CS=30 and  

dp= 0.7mm. 

 
 

D
a

x.
L 

(c
m

2
/s

)
 

Ug (cm/s) 

D
a

x.
L 

(c
m

2
/s

)
 

Ug (cm/s) 

D
a

x.
L 

(c
m

2
/s

)
 

Ug (cm/s) 



Ali Raad Mohammed                           Al-Khwarizmi Engineering Journal, Vol. 8, No. 1, PP 37 - 47 (2012)  

43 

 

 
 

 

 
 

 

 

 
 

 

 
 

 
 

 

Fig. 9. Effect of Superficial Gas Velocity no Axial Liquid Dispersion Coefficient at Different Z, CS=60 and 

 dp= 0.7mm 

 

 

4.3.2. Effect of Solid Concentration (Cs) 
on Axial Liquid Dispersion Coefficient 

(Dax,L) 

 
Fig. (10-12) show the effect of solid 

concentration on average axial dispersion 
coefficient. It can be seen that, the axial dispersion 

coefficient increases with the increase of solid 

concentration. This may be due to the fact that 

when the solid concentration increases lead to 

higher gas bubble concentration produced. Since 
the liquid envelopes the gas bubbles, therefore it 

will be entrained and dragged upwards and also 

part of gas – liquid dispersion will flow 
downwards again and consequently causing an 

increase in the liquid phase dispersion coefficient. 

These results are in agreement with Deckwer [2]. 

 

 

 

 
 

 

 

 
 

 

 
 

 

 
 

 

 

 

Fig.10. Effect of Superficial Gas Velocity and Solid Concentration on Average Axial Liquid Dispersion 

Coefficient at dp= 3mm. 

 
 

 

 
 

 

 

 
 

D
a

x.
L 

(c
m

2
/s

)
 

Ug (cm/s) 

D
a

x.
L 

a
v 

(c
m

2
/s

)
 

Ug (cm/s) 



Ali Raad Mohammed                           Al-Khwarizmi Engineering Journal, Vol. 8, No. 1, PP 37 - 47 (2012)  

44 

 

 
 

 

 
 

 

 

 
 

 

 
 

 

 
 

 

 

Fig. 11. Effect of Superficial Gas Velocity and Solid Concentration on Average Axial Liquid Dispersion 

Coefficient at dp= 1.5mm. 

 

 

 

 

 

 

 

 

 

 

Fig. 12. Effect of Superficial Gas Velocity and Solid Concentration on Average Axial Liquid Dispersion 

Coefficient at dp= 0.7mm. 

 

 

4.3.3. Effect of particle diameter (dp) on 
axial liquid dispersion coefficient (Dax,L) 
 

Fig. (13 and 14) show the effect of superficial 

gas velocity for various particle diameters. From 

these figures it can be noticed an inverse 

relationship between particles diameter and axial 
liquid dispersion coefficient. This can be 

attributed to the fact that the bubble rise velocity 

decreases lead to the rate of bubble coalescence 
increases as the particles diameter decreases. 

The larger bubbles which results from 
coalescence lead to an increase the axial liquid 

dispersion coefficient. This result is in agreement 

with Rubia et al., [5]. 

 

 

 

 

 

 

 

 

 

 

D
a

x.
L 

a
v 

(c
m

2
/s

) 

Ug (cm/s) 

D
a

x.
L 

a
v 

(c
m

2
/s

)
 

Ug (cm/s) 



Ali Raad Mohammed                           Al-Khwarizmi Engineering Journal, Vol. 8, No. 1, PP 37 - 47 (2012)  

45 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

Fig. 13. Effect of Superficial Gas Velocity and Solid Concentration on Average Axial Liquid Dispersion 

Coefficient at CS= 30kg/m3. 

 

 

 

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 

Fig. 14. Effect of Superficial Gas Velocity and Solid Diameter on Average Axial Liquid Dispersion Coefficient at 

CS= 60kg/m3

 

 

 

5. Conclusions 
 

The following major conclusions can be drawn 

from the present work. 

1. In homogeneous regime (0-4), axial liquid 
dispersion coefficient increases slightly with 
increasing superficial gas velocity while it 

increases rapidly in heterogeneous regime.  

2. Increases the axial distance of the probe's 
location led to increase the axial liquid 

dispersion coefficient. 

3. Increasing solid concentration the gas – liquid 
flow exhibit higher gas bubble concentration 
led to increase the axial liquid dispersion 

coefficient. 

4. Axial liquid dispersion coefficient decreases 
with increasing particle diameter. 

Nomenclature 

 
C   tracer concentration, kmol m

−3
 

CT Dimensionless tracer concentration 
defined by Eq. (4) 

C0   initial concentration of the  
tracer, kmol m

−3
 

C∞ final or equilibrium concentration of 
the tracer, kmol m

−3
 

Dax.L axial liquid dispersion coefficient., 

m
2
s

-1
 

Dr   radial liquid dispersion coefficient, 
m

2
s

-1
  

J0 zero-order Bessel function 
J1 first-order Bessel function 
L height of dispersion, m 
T time or instantaneous time, s 

D
a

x.
L 

a
v 

(c
m

2
/s

) 

Ug (cm/s) 

D
a

x.
L 

a
v 

(c
m

2
/s

) 

Ug (cm/s) 



Ali Raad Mohammed                           Al-Khwarizmi Engineering Journal, Vol. 8, No. 1, PP 37 - 47 (2012)  

46 

 

UG superficial gas velocity, ms
−1

 
y dimensionless axial position 

z axial distance, m 

Vc liquid circulation velocity 
Cs solid concentration, Kg/m

3
 

dp particle diameter 

n flow index 

 
                 

Greek symbols 

 
ʋn the nth root of the first-order 

 Bessel function 

Π the number pi 
ɵ dimensionless time 
β parameter in Eq. (1) 

m integer. 
 

               

6. Reference 
 

[1] Shah, Y.T., Godbole, S.P., Kelkar, B.G., 
Deckwer, W.D., "Design Parameters 

Estimation for Bubble Column Reactors", 
AICHEJ, 28(3); 353-379, (1982). 

[2] Deckwer, W.D., "Bubble Column Reactors", 
New York: Wiley (1992). 

[3] Zhu, J.-X., Zheng, Y., Karamanev, D., Bassi, 
A., "(Gas-) Liquid- Solid Circulating 

Fluidized Beds and Their Potential 

Applications to Bioreactor Engineering", 
Canadian Journal of Chemical Engineering, 

78, 82-94, (2000). (Cited in:- 

http://onlinelibrary.Wiley.com/athens). 
[4] Chisti, M.Y., Moo-Young, M., "Airlift 

Reactors: Characteristics, Applications and 

Design Considerations", Chemical 

Engineering Communications, 60, 195-242, 
(1987). (Cited in:- Changqing, C., Shuqin, 

D., Qijin, G., Qingie, G., "Hydrodynamics 

and Axial Dispersion in A Gas-Liquid-

(Solid) EL-AIR with Different Sparger 
Designs", Industrial and Engineering 

Chemistry Research, 47, 4008-4017, (2008). 

[5] Rubia, F.C., Miron, A.S., Ceron Garcia, 
M.C., Comacho, F.G., Grima, E.M., Chisti, 

Y., "Mixing in Bubble Columns: A New 

Approach for Characterizing Dispersion 
Coefficient", Chemical Engineering Science, 

59, 4369-4376, (2004). 

[6] Deckwer, W.D., Graeser, U., Longemann, H. 
and Serpemen, Y., "Zones of Different 

Mixing in the Liquid Phase of Bubble 

Columns", Chemical Engineering Science, 
28, 1223-1225, (1973). 

[7] Campos, J.B.L.M., Guedes de Carvalho, 
J.R.F., "A New Experimental Technique to 

Study Backmixing in Packed Bubble 
Columns", Chemical Engineering Science, 

47, 4063-4067, (1992). (Cited in:- Therning 

and Rasmuson [12]). 
[8] Chen, B.H. and Yang, N.S., "Characteristics 

of a Co-current Multistage Bubble Column", 

Industrial and Engineering Chemistry 

Research, 28, 1405-1410, (1989). 
[9] Smith, D.N., Ruether, J., Shah, Y.T. and 

Badgnjar, M.N., "Modified Sedimentation-

Dispersion Model for Solid in A Three-Phase 
Slurry Column", AICHEJ, 32(3); 426, 

(1986). 

[10] Viswanathan, S., Kakar, A., Murti, S., 
"Proceedings Symposium on the Interaction 

between Fluid and Particles", Chemical 

Engineering Science, 20, 903, (1965). 

[11] Ahmad, T., Shawaqfeh, "Gas Holdup and 
Axial Dispersion under Slug Flow 

Conditions in Gas-Liquid Bubble Column", 

Chemical Engineering and Processing, 42, 
767-775, (2003). 

[12] Therning, P., Rasmuson, A., "Liquid 
Dispersion and Gas Holdup in Packed 
Bubble Columns at Atmospheric Pressure", 

Chemical Engineering Journal, 81, 69-81, 

(2001). 

[13] Krishna, R., Urseanu, M.I., Van Boten, 
J.M., Ellenberger, J., "Liquid Dispersion in 

Bubble Columns Operating in the Churn-

Turbulent Flow Regime, Chemical 
Engineering Journal, 78, 43-51, (2000). 

[14] Chen, W., Yang, W., Wang, J., Jin, Y., 
Tsutsumi, A., "Characterization of Axial 

and Radial Liquid Mixing in A Liquid-
Solid Circulation Fluidized Bed", Industrial 

and Engineering Chemistry Research, 40, 

5431-5435, (2001). 
[15] Joshi, J.B., Sharma, M.M., "A Circulation 

Cell Model for Bubble Columns", 

Transactions of the Institution of Chemical 
Engineering", 67, 244-251, (1979). (Cited 

in:- Rubia et al., [5]). 

 

 

 

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 ((2012 37 - 47  ، صفحة1، العذد 8مجلة الخوارزمي الهنذسية المجلذعلي رعذ محمذ                                                                

47 

 

 

 

 تأثير خواص الصلب على التشتت الطولي للسوائل في ابراج التفقيع
 

علي رعذ محمذ جواد 
  الداهؼح الركٌىلىخٍح /قسن الهٌذسح الكٍوٍاوٌح

aliolimpic@yahoo.com :الثرٌذ االلكرروًً  

 

 
 

 الخالصة

 
م تأسرخذام صفٍحح هثقثح 1.6م وارذفاع 0.15رو قطر داخلً  (للسىائل الؼالقح)اخرٌد الردارب الؼولٍح لذراسح هؼاهل الرشرد الطىلً فً اتراج الرفقٍغ 

– الواء – تأسرخذام ًظام ثالثً هركىى هي الهىاء .  ًسثح هساحح حرج للفرحاخ الى الوساحح الوقطؼٍح0.24هلن هغ 1 فرحح تقطر 54لرىزٌغ الهىاء ذحىي ػلى 

م/  كغن 60 ,30 , 0)أسرخذهد ذراكٍس هخرلفح هي الوادج الصلثح . (تىلً فٌٍٍل كلىراٌذ)الصلة 
3

لذراسح ذأثٍرها ػلى  ( هلن3 , 1.5 , 0.7)واقطار للصلة  (

اظهرخ الٌرائح . لرغطً الوٌطقح الورداًسح والغٍر هرداًسح (ثا/ سن10 – 1)وسرػح غاز  ( سن75 , 50 , 25)هؼاهل الرشرد الطىلً واتؼاد طىلٍح هخرلفح 

 .زٌادج هؼاهل الرشرد الطىلً للسائل هغ ازدٌاد سرػح الغاز والثؼذ الطىلً وذركٍس الصلة وًقصاى الوؼاهل هغ قطر الصلة
 

 

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