The 6th International Conference on Hydraulic Machinery and Hydrodynamics Timisoara, Romania, October 21 - 22, 2004
Scientific Bulletin of the Politehnica University of Timisoara Transactions on Mechanics Special issue
EXPERIMENTAL RESEARCH OF TWO PHASE PRESSURE DROP IN PACKED COLUMNS FOR GAS-LIQUID OPPERATIONS Dr Srbislav B. GENIC, Assist. Prof., PE, Dr Branislav M. JACIMOVIC, Prof., PE,* Department of Process Engineering Department of Process Engineering Faculty of Mechanical Engineering Faculty of Mechanical Engineering University of Belgrade University of Belgrade Mr Pavle I. ANDRIC, PE, Department of Process Engineering Faculty of Mechanical Engineering University of Belgrade
*Corresponding author: 27 marta 80, 11000 Belgrade, Serbia and Montenegro Tel.: +381-11-3302360, Fax: +381-11-3370364, Email:
[email protected]
ABSTRACT Subject of this paper is a research of pressure drop of gaseous phase in two-phase (gas-liquid) flow through packed columns. Experimentally obtained data for pressure drop in random bed of metal Pall rings diameter 25,4 mm (752 experimental runs were conducted with water-air system, where superficial air velocity based on empty column was in range 0,16÷4,6 m/s and liquid load per unit cross-sectional area of empty column 0, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 100, 110, 120, 130, 140, 150, 160, 170, 177 m3 /(m2 ⋅h)) were compared with the data and the equations from the available literature (Eckert, Billet, Kafarov, Teutsch and Ergun), and it was shown that there is a relatively good correlation between the measured and the calculated values, for wide range of water loads. Some procedures are recommended for pressure drop in bed of packing predictions. KEYWORDS Packed columns, pressure drop, Pall rings NOMENCLATURE d p [m], equivalent packing diameter d p = 6⋅
dp =
1− ε in equations (1), (3) sv
4 ⋅ε in equation (2) sv
Dc [m], column inside diameter f LG [-], factor of fluidodynamic state of two-phase
f s [-], wall correction factor 1 4 = 1+ fs s v ⋅ Dc FLG [-], two-phase kinetic energy parameter
ρG V ρL L = ⋅ FLG = L ⋅ VG ρG G ρ L F p [1/m], packing factor FrL , [-], Froude number for liquid FrL =
wL2 ⋅ s v in equation (17) g
g [m/s2], acceleration due to gravity G [kg/s], gas mass rate H [m], height of bed of packing L [kg/s], liquid mass rate Re G [-], Reynolds number for gas Re G = Re G = Re G = Re G =
wG ⋅ d p ⋅ ρ G
µG wG ⋅ d p ⋅ ρ G
ε ⋅ µG wG ⋅ d p ⋅ ρ G
(1 − ε ) ⋅ µ G
in equation (1) in equation (2) ⋅ f s in equation (3)
4 ⋅ wG ⋅ρ G in equation (17) sv ⋅ µ G
Re L [-], Reynolds number for liquid wL ⋅ ρ L in equation (9) sv ⋅ µ L 4 ⋅ w L ⋅ρ L Re L = in equation (17) sv ⋅ µ L
Re L =
flow 489
s v [m2/m3], specific surface area (surface area per unit
volume)
VG [m3/s], gas flow rate V L [m3/s], liquid flow rate wG [m/s], superficial gas velocity based on empty
column cross-sectional area wL [m/s], superficial liquid velocity based on empty column cross-sectional area y i , measured value in the i-th experimental run y , correlated value in the i-th experimental run y av , average value of y for the complete set of the experimental data n
∑ yi
y av = i =1 n ∆ av [-], standard deviation
1 n ⎛ yi − ⋅ ∑⎜ n i =1 ⎜⎝ yi
∆ av =
y⎞ ⎟ ⎟ ⎠
2
∆pG [Pa], pressure drop in unwetted bed of packing ∆p LG [Pa], pressure drop in wetted bed of packing
ε [m3/m3], void fraction of packing ϕ L [m3/m3], liquid holdup λ [-], friction coefficient µ G [Pa⋅s], dynamic viscosity of gas µ H 2O [Pa⋅s], dynamic viscosity of water µ L [Pa⋅s], dynamic viscosity of liquid θ [-], correlation ratio n
θ = 1−
∑ ( yi − y )
1. INTRODUCTION Packed columns are apparatuses with continual contact between the phases, widely used in process industry for mass transfer operations such as distillation, absorption, desorption, etc. Because of theirs simple design and high mass transfer efficiency they are widely accepted in refineries, chemical, petrochemical, pharmacology industry and in environmental protection engineering (gas scrubbing processes and water treatment). There are several procedures in literature for calculation of fluidodynamic parameters of packed columns, and according to some authors, most of them give results that can be satisfactorily in practice. In order to confirm the validity of the existing literature data and calculation procedures, the research program was carried out in the following manner: • experimental research; • analysis and generalization of the experimental results based on the existing procedures. Hereby we will compare experimentally obtained pressure drop with values calculated by Eckert (in this paper were done some modifications of original Eckert chart in order to obtain explicit equation for pressure drop), Billet, Kafarov, Teutsch and Ergun estimation procedures. 2. PRESSURE DROP IN BED OF PACKING 2.1 Pressure drop of unwetted packing
• Ergun procedure [10]: ∆pG = ξ G ⋅
1− ε
2
i =1 n
∑ ( yi − y sr )2 i =1
Re G
ζG =
16 ,5 ReG0 ,2
, Re G > 400 in equation (2)
⎛ 64 1,8 ⎞⎟ + ζG = Cp ⋅⎜ , ⎜ Re G Re 0,08 ⎟ in equation (3) G ⎠ ⎝ C p = 0,957 for metal Pall 2′′ ring
Subscripts and Superscripts G , gas L , liquid lp , loading point fl , flooding point r , correlated values inv , phase inversion point 490
⋅
H ⋅ ρ G ⋅ wG2 dp
(1)
• Kafarov procedure [14]: ∆pG = ξ G ⋅
3
ρ G [kg/m ], gas density ρ L [kg/m3], liquid density ζ G [-], resistance coefficient 1− ε ζ G = 150 ⋅ + 1,75 in equation (1)
ε
3
H ρ G ⋅ wG2 ⋅ dp 2⋅ε 2
(2)
• Billet procedure [5]: ∆p G s ρ ⋅ w2 1 = ξG ⋅ v ⋅ G G ⋅ H fs 2 ε3
(3)
2.2 Pressure drop in wetted bed of packing
• Kafarov procedure [14] for Raschig rings: ∆pLG = (1+ f LG ) ⋅ ∆pG
(4)
Factor of fluidodynamic state of two-phase flow is given by equation: ⎛L⎞ f LG = (C k − 0,175 ) ⋅ ⎜ ⎟ ⎝G⎠ ⎛µ ⋅ ⎜⎜ L ⎝ µG
⎞ ⎟ ⎟ ⎠
0, 045
⎛L⎞ ,⎜ ⎟ ⎝G⎠
1,8
0, 405
⎛ρ ⋅ ⎜⎜ G ⎝ ρL
⎛ρ ⋅ ⎜⎜ G ⎝ ρL
⎞ ⎛ µL ⎟⎟ ⋅ ⎜⎜ ⎠ ⎝ µG
⎞ ⎟ ⎟ ⎠
⎞ ⎟⎟ ⎠
0, 225
⋅
(5)
0, 2
≤ 0,5
⎛L⎞ f LG = (C k + 1,39 ) ⋅ ⎜ ⎟ ⎝G⎠ ⎛µ ⋅ ⎜⎜ L ⎝ µG
⎞ ⎟ ⎟ ⎠
0,105
1,8
0,945
⎛ρ ⋅ ⎜⎜ G ⎝ ρL
⎛L⎞ ,⎜ ⎟ ⎝G⎠
⎛ρ ⋅ ⎜⎜ G ⎝ ρL
⎞ ⎛ µL ⎟⎟ ⋅ ⎜⎜ ⎠ ⎝ µG
⎞ ⎟ ⎟ ⎠
⎞ ⎟⎟ ⎠
• Eckert procedure [8] – In this paper some modi-
0,525
⋅
fications of original Eckert chart is done in order to obtain explicit equation for pressure drop for air-water system:
0, 2
> 0,5
⎛ρ ∆p LG = 3006,5 ⋅ w1G,85 ⋅ ⎜⎜ G ⎝ ρL
where ⎛ ⎞ wG − 0,853 ⎟ C k = exp ⎜ 3,0 ⋅ ⎜ ⎟ wG ,inv ⎝ ⎠
(6)
Gas velocity in phase inversion point is defined by equation: ⎡ 2 wG ,inv ⋅ s v ρ G ln ⎢ ⋅ ⎢ g ⋅ε 3 ρL ⎣⎢
⎛ µ ⋅⎜ L ⎜ µH O 2 ⎝
0,16 ⎤
⎞ ⎟ ⎟ ⎠
⎥= ⎥ ⎦⎥
(7)
1,5
⎞ ⎟⎟ ⎠
(8)
where ⎧⎡ ⎛ Re L ⎪⎢exp ⎜ ⎝ 200 ⎪⎪⎣ W =⎨ ⎪⎡ ⎛ Re L ⎪⎢exp ⎜ ⎝ 200 ⎪⎩⎣
⎞⎤ ⎟⎥, ϕ L ≤ ϕ L,lp ⎠⎦ ⎞ ⎟ ⎟ ⎠
⎞⎤ ⎛⎜ ϕ L ⎟⎥ ⋅ ⎠⎦ ⎜⎝ ϕ L,rt
(9)
0,3
, ϕ L > ϕ L,lp
Liquid holdup is: ⎡
⎛ wG ⎜ wG ,inv ⎝
ϕ L = ϕ L,lp ⋅ ⎢1 + 1,2 ⋅ ⎜ ⎢ ⎣⎢
⎞ ⎟ ⎟ ⎠
⎛ ⎜ ⎝
µ L ⋅ s v2 ⋅ wL ρL ⋅ g
(15)
−3,7
, F p = 158, metal 2′′ Pall
wetted and unwetted bed of packing is given as a function of parameter K T on diagram in [23]:
∆p LG / ∆pG = f ( K T )
(16)
(
)
The experimental installation, shown on Figure 1, has been designed for the research on fluidodinamic parameters of the columns with random bed of packing. The experimental work was carried out on the semiindustrial glass column 314 mm in diameter, under atmospheric pressure. Random bed of metal Pall rings diameter 25.4 mm were dumped in height of 1 m. All measurements (752 experimental runs were conducted) was ran with water-air system, where superficial air velocity based on empty column was in
3⎤
17
⎥ ⎥ ⎦⎥
1/ 3
⎞ ⎟ ⎟ ⎠
(10)
⎛ s v ,h ⋅ ⎜⎜ ⎝ sv
⎞ ⎟ ⎟ ⎠
(11)
0,15 0,1 s v ,h ⎧⎪C h ⋅ Re L ⋅ Fr L , Re L < 5 =⎨ 0, 25 0,1 sv ⎪⎩0,85 ⋅ C h ⋅ Re L ⋅ Fr L , Re L ≥ 5 C h = 0,719 for metal Pall 2 ′′ ring
water
24 14 23
(12) 4
Gas velocity in phase inversion point for air-water systems is defined as follows:
=
⎛µ ⋅ ⎜⎜ G ⎝ µL
⎞ ⎟⎟ ⎠
21
13
12
2/3
16
15
The ratio of wetted and unwetted packing surface is:
wG2 ,inv ⋅ s v ρ G ⋅ ρL g ⋅ε 3
(17)
3. EXPERIMENTAL INSTALLATION
Liquid holdup in loading point is: ϕ L,lp = ⎜12 ⋅
⋅
K T = FrL ⋅ Re −L0,8 ⋅ 1,2 ⋅ 10 5 + 7,5 ⋅ Re G
• Billet procedure [5]: ⎛ ε ⋅ ⎜⎜ ⎝ ε − ϕL
0,925
• Teutsch procedure [23] – Ratio of pressure drop in
where
1/ 4 = 0,057 − 4,03 ⋅ FLG
∆p LG =W ∆pG
⎡ g ⎤ ⋅ ⎢4 − 1,4 ⋅ wL ⎥ ⎢⎣ F p ⎥⎦
⎞ ⎟⎟ ⎠
11
3
22 20
0,4⋅qinv
5
6
10
8
19
=
2⋅q 2 ⋅ FLG inv 0,0187 ⋅ Cinv
(13)
2
18
Cinv = 2,083 for metal Pall 2′′ ring 1
where qinv = −0,194, FLG ≤ 0,4 qinv = −0,708, FLG > 0,4
(14)
air
7
9
Figure 1 The experimental installation 491
range 0,16÷4,6 m/s. Liquid load was 0, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 100, 110, 120, 130, 140, 150, 160, 170, 177 m3/(m2⋅h). In the glass column (19) a sieve (20) was installed to enable the uniform profile of the air stream velocity. Air is driven by the fan (1) through the pipe (4 and 6) into the column, while the water is introduced into the column directly from the city water piping network. Regulation of the air and water flow is accomplished by the butterfly valves (3, 5) and valve (12), while the orifices (8, 13) have been installed to measure the flow rates. Pressure drop in bed of packing (23) was measured with U-tube manometer with water.
Experimentally obtained results were compared to values calculated by using equations (1-17). Results of statistic analyses are presented in Table 1 for unwetted and in Table 2 for wetted packing. Table 1 Statistical parameters – unwetted packing Θ Eq. no. Author (1) Ergun 0,9515 (2) Kafarov 0,9928 (3) Billet 0,9965
5.0 4.5 4.0 3.5
wG, m/s
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0
20
40
60
80
100 3
120
140
160
180
2
wL, m /(m h)
30,85 8,90 9,69
Table 2 Statistical parameters – wetted packing Θ Eq. no. Author (4) Kafarov 0,8932 (8) Billet 0,6291 (15) Eckert 0,7657 (17) Teutsch 0,9249
4. RESULTS AND ANALYSIS There were 752 experimental runs, 50 for research on pressure drop in unwetted and 702 for pressure drop in wetted bed of packing. The range of air and liquid flow rate in measurements is shown in Figure 2. Measured values of pressure drop are shown in Figure 3. It should be noted that pressure drop in phase inversion point reaches 1600 Pa/m for every liquid load (one of the definitions of the phase inversion point which is given in [15] is “The pressure drop reaches 2 in of water per foot of packing”).
∆ av ,%
∆ av ,%
52,91 62,80 44,69 53,29
Measured and correlated values of pressure drop in unwetted bed of packing are shown in Figure 4 Kafarov and Billet correlation gave good and nearly the same predictions (correlation ratio higher then 0.99 and standard deviation less then 10%). Ergun prediction for pressure drop on unwetted packing gave relatively good statistical parameters (correlation ratio 0.9515 and standard deviation 30.85%). Measured and correlated values of pressure drop in wetted bed of packing are shown in Figures 5-8. The best predictions for two-phase pressure drop give Eckert’s procedure, with correlation ratio 0.7657 and standard deviation 44.69%. Other procedures gave predictions in range of this statistical parameters 0.6291÷0.9249 (higher correlation ratio was for Kafarov and Teutsch procedures) and 52.91÷62.80%. These statistical parameters are valid for mentioned range of water and air loads. Eckert and Billet procedures give better predictions for smaller liquid loads (10÷90 m3/(m2⋅h)), Kafarov for liquid loads in range 10÷120 m3/(m2⋅h), and Teutsch for 100÷177 m3/(m2⋅h).
Figure 2 Range of air and liquid flow
4000
(1) (2) (3)
4000 3000
2000
2000
1000
∆p G, Pa
∆pLG, Pa
800 1000 900 800 700 600 500
r
600 400
400
200
300 200
100 80 60 60
100 90 80 0.2
0.4
0.6
0.8
1
2
4
wG, m/s
Figure 3 Measured values of pressure drop 492
6
80 100
200
400
600
∆pG, Pa
800 1000
2000
4000
Figure 4 Measured and correlated (1-3) values of pressure drop
4000
According to our analysis value for packing factor for metal 2″ Pall rings in equation (15) F p = 232 give better fit to measured values:
⎡ g ⎤ ⋅ ⎢4 − 1,4 ⋅ w L ⎥ ⎢⎣ F p ⎥⎦
0,925
1000
⋅
(18)
−3,7
, F p = 232 , metal 2 ′′ Pall 200
3
2
3
2
100 100
r
∆p LG, Pa
600 400
⎛L⎞ f LG = (C k − 0,175) ⋅ ⎜ ⎟ ⎝G⎠
200
100 80 100
200
400
600
800 1000
2000
4000
∆ pLG, Pa
Figure 5 Measured and correlated (4) values of pressure drop 10000 8000 6000
wL = 10 m /m h
4000
wL = 35 m /m h
3
2
wL = 15 m /m h
3
2
wL = 25 m /m h
3
2
wL = 30 m /m h
3
2
wL = 40 m /m h
3
2
wL = 50 m /m h
3
2
wL = 60 m /m h
3
2
wL = 70 m /m h
3
2
wL = 20 m /m h wL = 30 m /m h wL = 45 m /m h
2000
wL = 55 m /m h wL = 65 m /m h
1000 800 600 400
wL = 75 m /m h 3
r
2
3
2
3
2
3
2
3
2
3
2
3
2
3
2
3
2
3
2
3
2
3
wL = 130 m /m h
2
3
2
wL = 150 m /m h
3
2
wL = 170 m /m h
3
2
3
2
3
2
wL = 110 m /m h
wL = 120 m /m h wL = 160 m /m h
2000
4000
⎞ ⎟ ⎟ ⎠
0,045
1,8
⎛L⎞ ,⎜ ⎟ ⎝G⎠
⎛ρ ⋅ ⎜⎜ G ⎝ ρL
⎛L⎞ f LG = (C k + 1,39 ) ⋅ ⎜ ⎟ ⎝G⎠ ⎞ ⎟ ⎟ ⎠
0,105
1,8
⎛L⎞ ,⎜ ⎟ ⎝G⎠
0, 405
⎞ ⎛ µL ⎟⎟ ⋅ ⎜⎜ ⎠ ⎝ µG
0,945
⎛ρ ⋅ ⎜⎜ G ⎝ ρL
⎛ρ ⋅ ⎜⎜ G ⎝ ρL ⎞ ⎟ ⎟ ⎠
⎛ρ ⋅ ⎜⎜ G ⎝ ρL
⎞ ⎛ µL ⎟⎟ ⋅ ⎜⎜ ⎠ ⎝ µG
⎞ ⎟ ⎟ ⎠
⎞ ⎟⎟ ⎠
0,315
⋅
0, 2
⎞ ⎟⎟ ⎠
≤ 0,5
(19)
0,505
⋅
0, 2
> 0,5
Results of statistic analyses of these transformed equations are presented in Table 3. Measured and correlated ((18) and (19), (4), (6, 7)) values of pressure drop in unwetted bed of packing are shown in Figure 9 and Figure 10.
2
wL = 90 m /m h
3
wL = 100 m /m h
⎛µ ⋅ ⎜⎜ L ⎝ µG
⎛µ ⋅ ⎜⎜ L ⎝ µG
wL = 80 m /m h
2
wL = 85 m /m h
wL = 140 m /m h
200
3
800 1000
Pressure drop in bed of packing prediction on that way is simpler then other procedures. Also we have done some modifications of Kafarov factor of fluidodynamic state of two-phase flow for metal 2″ Pall rings:
800
80
600
2
w L = (90-177) m /m h
1000
∆p LG, Pa
400
Figure 8 Measured and correlated (17) values of pressure drop
w L = (30-85) m /m h 3
200
∆ pLG, Pa
w L = (10-30) m /m h
2000
600 400
Equation (18) enables explicit pressure drop calculations, and there is no need for knowing gas velocity in phase inversion point. 4000
800
r
⎞ ⎟⎟ ⎠
∆p LG, Pa
⎛ρ ∆p LG = 3006 ,5 ⋅ w1G,85 ⋅ ⎜⎜ G ⎝ ρL
2000
wL = 177 m /m h
100 80 60
Table 3 Statistical parameters – transformed equations
40
Θ Eq. no. (18) 0,9242 (19) and (4), (6,7) 0,9432
20 100
1000
∆pLG, Pa
10000
Figure 6 Measured and correlated (8) values of pressure drop 4000
3
2
3
2
∆ av ,%
48,07 32,01
4000
wL = (10-30) m /m h wL = (30-85) m /m h 3
2
wL = (90-177) m /m h
2000
2000
1000
800
∆p LG, Pa
800
600
600
r
r
∆p LG, Pa
1000
400
200
400
200
100
100
80
80
80 100
200
400
600
∆ pLG, Pa
800 1000
2000
4000
Figure 7 Measured and correlated (15) values of pressure drop
80 100
200
400
600
∆ pLG, Pa
800 1000
2000
4000
Figure 9 Measured and correlated (18) values of pressure drop 493
control calculations for the existing columns (for variable working conditions).
4000
2000
ACKNOWLEDGMENTS 1000
The present work has been supported from the Molipak S.r.l. KOCH – GLITCH COMPANY (Italy) and PROING (Serbia and Montenegro). The authors wish to acknowledge and thank specially to Ing. Carlo Perugini and Ing. Ilija Andric, PE.
600
r
∆p LG, Pa
800
400
200
REFERENCES
100 80 80 100
200
400
600
∆ pLG, Pa
800 1000
2000
4000
Figure 10 Measured and correlated (19), (4), (6, 7) values of pressure drop 5 CONCLUSIONS The paper deals with gas side pressure drop, which is one of important fluidodynamic parameters of packed columns. Experimental research of pressure drop on bed of packing was conducted on layer 1 m high, using metal Pall 2″ rings, with air-water system under atmospheric pressure. There were 752 experimental runs. Three equations from the available literature were tested for the pressure drop on unwetted bed of packing, and four procedures for pressure drop on wetted bed of packing procedures. Experimental research has shown that literature sources, especially pressure drop on unwetted bed procedures, should be taken with certain safety factor. Kafarov and Billet predictions for pressure drop on unwetted packing gave very well and nearly the same predictions, while Ergun correlation gave unsatisfactory statistical parameters. In paper it was shown that the best predictions for two-phase pressure drop are obtained using Eckert’s procedure, while procedures of Billet, Kafarov and Teutsch gave slightly worse predictions. Eckert and Billet procedures are better suited for lower liquid loads (10÷90 m3/(m2⋅h)), Kafarov for liquid loads in range 10÷120 m3/(m2⋅h), and Teutsch for 100÷177 m3/(m2⋅h). On the basis of research presented in this paper, the packing factor value for metal 2″ Pall ring in Eckert procedure can be corrected (in [15] it was shown that, for a few packings, the packing factors gave poor fit to experimental pressure drop data) and some modifications of Kafarov procedure (original Kafarov procedure is for Raschig rings only) can be done. Also it was shown that pressure drop in phase inversion point has value of about 1600 Pa/m and in flooding point about 3200 Pa/m for all liquid loads, which means that we can control the fluidodynamic state in column with pressure regulation. Based on this research the recommended design procedures (18) and (4), (6, 7) and (19) can be used in the field of new column design, as well as for 494
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