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Progress in design of random packing for gas–liquid systems
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Progress in design of random packing for gas–liquid systems Jerzy Ma´ckowiak ∗ ENVIMAC Engineering GmbH, Im Erlengrund 27, Oberhausen, 46149, Germany
a r t i c l e
i n f o
a b s t r a c t
Article history:
The following work presents a generally applicable model for the prediction of the separation
Received 17 October 2014
efficiency of random packing of different shape with size between 8 and 90 mm for gas–liquid
Received in revised form 19 May
systems in the entire operating range up to the flooding point. The new model was derived on
2015
the basis of the droplet flow model and that mass transfer in the gas phase occurs between
Accepted 26 May 2015
continuous gas phase and the swarm of droplets falling down in packed bed.
Available online 6 July 2015
The new model was validated with about 5000 experimental distillation, absorption and desorption data of ENVIMAC data bank (EDB) in a very wide range of changing operational
Keywords:
and constructive parameters; from low top pressure of 13 mbar up to 2 bar. Satisfactory con-
Random lattice-type packing
sistency for practical application was found between experimental values of the separation
Separation efficiency
efficiency for about 115 different types of random packings and calculated values based on
Mass transfer in the gas and liquid
the new model. © 2015 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
phase Distillation Absorption Desorption
1.
Introduction
During the last 5 decades, a lot of random packings have been developed, which can be divided into 4 generations, from classical Raschig rings, Berl and Intalox saddle of 1st generation to new modern random lattice type packings of 3rd and 4th generation. Fig. 1 shows examples of different packing types of all 1st–4th generation. Random packings are widely and successfully used not only in the distillation, absorption and stripping processes or for direct gas cooling and gas preheating, but also in environmental protection processes like waste gas and wastewater treatment. Their form has changed significantly during that time and the field and range of applications in industrial practice compared to the 1st generation packings also significantly increased. A big progress in the available design methods was observed during that period of time, especially in the modelling of fluid dynamics, which is presented
∗
´ in the recent literature, for example, (Mackowiak, 2010; Billet and Schultes, 1993, 1999). Nor-Pac packing was the first lattice type packing in ´ (1980). As a result Germany presented by Billet and Mackowiak ´ of this work (Billet and Mackowiak, 1980), after 1982 a number of new lattice-type packing elements of different types of 3rd and 4th generation were developed, mainly by leading German packing manufacturers, see Fig. 1. One of the first models for the design of random packing of 1st and 2nd generation was the model of Onda et al. (1968), followed by the improved Monsanto Model of Bolles and Fair (1979), the model of Zuiderweg (1978) and model presented by Zech and Mersmann (1978). The first model for the design of distillation columns not only for classical random packings but also for lattice type packings of the 3rd generation was ´ (1984) which the model developed by Billet and Mackowiak ´ 1990). This model was has been modified by (Mackowiak,
Tel.: +49 2089410440; fax: +49 208941044100. E-mail address: [email protected] http://dx.doi.org/10.1016/j.cherd.2015.05.038 0263-8762/© 2015 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
29
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Nomenclature Symbols a geometric surface area of packing per unit volume [m2 /m3 ] interfacial area per unit volume [m2 /m3 ] ae surface area of the perforated wall of a packing A0 element [m2 ] total non-perforated wall surface area of a A packing element A = dh [m2 ] dimensionless specific liquid load acc. to BL ´ Mackowiak (2010) [dimensionless] constant, Eqs. (13) and (18) [dimensionless] CV packing diameter [m] d hydraulic diameter; dh = 4ε/a [m] dh particle diameter; dP = 6 (1 − ε) /a [m] dP dS column inner diameter [m] dT mean droplet diameter acc. to Sauter, dT = CT L /g with CT = 1 valid for big deformed droplets with L ≥ 15 mN/m [m] DV , DL diffusion coefficient in the gas or liquid phase [m2 /s] FV gas load factor in relation to full column cross √ section, FV = uV V [Pa0.5 ] acceleration of gravity [m/s2 ] g h packing height [m] liquid hold-up in relation to total packing volhL ume VS , hL = VL /VS [m2 /m3 ] height of packed bed element unit [m] h HTUOV height of an overall transfer unit related to vapour phase [m] height of a transfer unit [m] HTU H height of packed bed [m] K l L˙ myx n nt /H NTUOV pT uL uR uV VL VS V˙
wall factor, K =
A ´ packing form factor P ≡ A0 (Mackowiak, 2010) [dimensionless] contact time [s] density, density difference = L − V [kg/m3 ] surface tension [N/m] kinematic viscosity [m2 /s]
ϕP
1+
4 dS a
−1
´ (Mackowiak, 2010)
[dimensionless] mean contact path [m] molar flow of liquid [kmol/h] slope of equilibrium line [dimensionless] number of differential packed bed layer with hi = 0.02–0.10 m [dimensionless] number of theoretical stages per 1 m packing height [1/m] number of overall transfer units, related to vapour phase [dimensionless] operating pressure [mbar, bar] specific liquid load in relation to full cross section of empty column [m/s] uV relative phase velocity uR = ε−h + uhL [m/s] L L linear gas velocity in relation to full cross section of empty column [m/s] liquid volume [m3 ] packing volume, VS = Hd2S /4 [m3 ] molar flow of gas or vapour [kmol/h]
Greek symbols mass transfer coefficient [m/s] ˇ volumetric mass transfer coefficient [1/s] ˇ·ae ıi (. . .), ı¯ (...) relative error, middle value of relative error [%] ˙ stripping factor = myx V˙ [dimensionless] L
, L Indices Fl i L m S
relating to operating point at flooding point individual value relating to liquid mean value relating to operating point at loading point; FV = 0.65FV,Fl relating to gas or vapour
V
Dimensionless numbers u2 a FrL = gL Froude number of liquid uL ReL = a Reynolds number of liquid L
ReT =
uR dT V
BL =
L L g2
Sc =
D
Reynolds number of droplet
1/3
uL 1−ε ε εdP
dimensionless liquid load
Schmidt number
uV dp K (1−ε) V ˇV,T dT ShV,T = D V
ReV =
Reynolds number of gas/vapour Sherwood number of droplet
developed for more than 60 different packings for systems with the main mass transfer resistance located in the vapour phase. Based on the assumption of film formation in the packed bed, Billet and Schultes (1993, 1999) derived on the base of about 2600 experimental data, mainly presented in (Billet ´ 1984, 1988, 1985; Billet et al., 1987, 1983), new and Mackowiak, dimensionless correlations for determining the effective interfacial area per unit volume ae and mass transfer coefficients in the gas and liquid phase for 55 different classical and latticetype packings and structured packings. The main aim of the present work is to develop a generally applicable method for determining the volumetric mass transfer coefficient in the gas phase and the separation efficiency nt /H or HTUOV not limited to certain packing types for distillation and absorption systems.
2.
Mass transfer in the liquid phase
Two models are in common use for predicting the height of the packed bed of random packing H: static HETP × nt model, Eq. (1), and kinetic HTUOV × NTUOV model, Eq. (2). H nt nt
[m]
(1)
H = HTUOV NTUOV
[m]
(2)
H = HETPnt =
In kinetic model, according to Chilton and Colburn (1935), the knowledge of both the liquid phase and gas phase volumetric mass transfer coefficients ˇL ·ae and ˇV ·ae , Eqs. (3), (4) and (5), is required. HTUOV = HTUV + HTUL
[m]
(3)
30
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 1 – Overview of investigated different random packing elements of 1st–4th generation. HTUV =
uV (ˇV ae )
[m]
(4)
HTUL =
uL (ˇL ae )
[m]
(5)
A new, generally valid model for the calculation of ˇL ·ae ´ (2011). Based on values has been presented by Mackowiak observations and measurements of droplet proportions in packed beds with different packings carried out by Bornhütter and Mersmann (1993), the new method for predicting the mass transfer in the liquid phase was developed on the assumption ´ of droplet flow in the packed bed (Mackowiak, 2011). Thus interfacial area per unit volume ae can be determined for ´ gas–liquid systems with the fundamental Eq. (6) (Mackowiak, 2011):
hL ae = 6 dT
3
2
m /m
ˇL ae = (6)
,
valid for disperse systems. According to the model, mass transfer is interrupted during the formation of rivulets and only recommences when new droplets are formed. The process therefore is non-stationary, as has been described by the well-known model of Higbie (Higbie, 1935), Eq. (7): 2 ˇL = √
DL
l lhL ⇒ u¯ L uL
1/3 1/4 (1 − P ) dh
u¯ L =
uL hL
(8)
[s]
1/3
= 0.57
(ˇL ae )S =
1/3 1/4 (1 − P ) dh
0.35 +
FV FV,Fl
[1/s]
(11)
L
g
5/6
uL
[1/s]
(12)
uL =const
Eqs. (11) and (12) allow to predict the volumetric mass transfer coefficient in the liquid phase ˇL ·ae of random packings up to flooding point for studied modern and classical packing types of d = 0.012–0.090 m with accurate good enough for practical applications with a mean error of ±12.5% ´ 2011), Fig. 2. (Mackowiak,
au2L g
1/3
m3 /m3 .
(9)
Mass transfer in the gas phase
The new droplet flow model is based on the assumption, that mass transfer is taking place from the continuous gas or vapour phase into the individual droplets falling down in packed bed acc. to the Frössling equation acc. to Eq. (13) presented by Hughmark (1967). 1/3
The correlations for predicting the hold-up of liquid for ReL < 2 and ReL > 200 and in the range above the loading point ´ are presented in the literature (Mackowiak, 2010). The contact paths l in Eq. (8) for the random packing was determined on ´ the basis of the following empirical correlation (Mackowiak, 2011): 1/2
5/6
uL
D g 1/2 a 1/6 L
15.1
ShV,T = 2 + CV RenT ScV
l = 0.115(1 − P )2/3 dh
g
For the operating range above the loading line up to flooding line 0.65 FV,Fl < FV < FV,Fl the following Eq. (12) is valid:
3. ´ Acc. to Mackowiak (2010), the liquid hold-up hL in random packings for turbulent liquid flow ReL ≥ 2 in the range below the loading point FV ≤ 0.65 FV,Fl can be described by Eq. (9) ´ (Mackowiak, 2010):
hL = 0.57FrL
L
(7)
[m/s]
for
D g 1/2 a 1/6 L
15.1
×
The contact time in Eq. (7) is described by the time that a droplet needs to cover the distance 1 between two contact points within the packing. Hence:
=
where, dh is the hydraulic diameter of packed beds ´ 2010) and the form factor ϕP is a geometrical (Mackowiak, parameter of the individual packing. The numerical value of the form factor represents the proportion of the perforated ´ surface area of a packing element (Mackowiak, 2010) and amounts e.g., ϕP = 0 for ceramic Raschig rings (no perforated surface), ϕP = 0.28 for metallic Pall rings and ϕP = 0.5–0.8 for ´ 2010). metallic modern lattice type packings (Mackowiak, Substitution of the relations of Eq. (8) into Eq. (7) and of Eq. (9) into Eq. (6) leads to the Eq. (11) for the prediction of the volumetric mass transfer coefficient ˇL ·ae in columns with random packing in the operating range below the loading line ´ FV ≤ 0.65 FV,Fl and for turbulent liquid flow ReL ≥ 2 (Mackowiak, 2011):
[m] ,
(10)
(13)
hL →0
where, ShV,T =
ˇV,ThL →0 dT
hL →0
ReT =
uR dT V
DV
(14)
(15)
31
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 2 – Comparison between evaluated volumetric mass transfer coefficient ˇL ·ae in the liquid phase acc. to eqn. 11, 12 and experimental data of EDB for investigated random packings of 1st–4th generation for dS = 0.15–1.2 m (Ma´ckowiak, 2011) for system no. 25, according to Table 1. ScL =
L DL
(16)
For a falling swarm of droplet in random packings, the mass transfer intensity decreases in comparison to single droplet flow and mass transfer can be described with the following relation Eq. (17):
ˇVhL >0 = ˇV,ThL →0 1 −
hL ε
m (17)
[m/s]
the volumetric mass transfer coefficient in the vapour phase ˇV ·ae will be estimated acc. to Eq. (18) (ˇV ae ) = ˇV,hL >0 ae =
DV hL 1/3 2 + CV RenT ScV 1− dT ε
m h L 6
dT
[1/s] (18)
as the product of Eqs.(6) and (17), in which the constants CV and exponents “n” and “m” must be evaluated from the experimental data.
4.
Model evaluation
The ENVIMAC data bank (EDB) was used to check the model presented here for 25 different test systems, 115 random packing types of 1st–4th generation with size of d = 8–100 mm made of metal, ceramic and plastic. The total number of experimental data evaluated within this work was about 1050 for distillation systems and 3100 data points for absorption and 1000 data points for desorption systems. The list of the systems and the physical properties of used systems is presented in Table 1. Physical properties were calculated local for each vapour and liquid from the top to the bottom according to recommendations of Poling et al. (Poling et al., 2007). ´ 1980, 1984, 1985, Literature data (Billet and Mackowiak, ´ 1988; Mackowiak, 1990, 2011; Bornhütter and Mersmann, 1993; Billet, 1979; Billet et al., 1987, 1983, 1986) including experiments with packing height of H = 1.3–4 m and column diameter of dS = 0.15/0.5/0.8 m were taken into account for model evaluation. The test plants with diameter of 150–1400 mm used in investigations are described in the literature (Billet and ´ ´ Mackowiak, 1980, 1984, 1988, 1985; Mackowiak, 1990, 2011; Billet et al., 1987, 1983, 1986). For each distillation run, all operating parameters as temperature of the vapour on the bottom and top, top pressure, cooling water flows for heat balance of the plant, packed
bed pressure drop and liquid reflux flow, were measured and recorded. The steady state was indicated through measurement of temperature and concentration profile of the lighter component on the top in liquid xD and at the bottom in the vapour yB . The vapour flow capacity factor FV in the column was evaluated even from the heat balance of the condenser on the top of column, where the vapour from the column was condensed using cooling water and additional verified with the measurement of flow meter. The samples of vapour after condensation and cooling down to 20 ◦ C were analysed with the density techniques acc. to recommendation of EFCE for test systems (Zuiderweg, 1969). The study of the kinetics of the mass transfer in the gas phase for absorption systems was carried out using the test systems: NH3 –air/water, NH3 –air/1 M H2 SO4 , SO2 –air/water and SO2 –air/1 M NaOH under atmospheric conditions and for mass transfer resistance in the liquid phase into the gas phase was investigated by using the system CO2 –water/air also under atmospheric conditions in columns with diameters of 150–1000 mm for packing height of H ≤ 2.5 m. A two types of liquid distributor with approximately B = 250/450/600 drip points/m2 was installed directly above the packing layer to distribute uniformly the liquid at the column top. The experimental distillation data were evaluated using the differential method based on the evaluation of mean local separation efficiency (nt /H)i or (HTUOV )i -values in each differential packing height unit hi .
n nt
n t
H
m
i=1
=
n
(HTUOV )m =
n t
H
m
=
H
i
n
[1/m]
(19)
(HTUOV )i
i=1
n
+1 1 (HTUOV )m 2
[m]
(20)
[1/m]
(21)
From the measured concentration of lighter component in the liquid on the top xD and vapour in the bottom yB the overall number of height units HTUOV and number of theoretical stages nt was calculated using the rigorous model ´ (Mackowiak, 1990). The schema of the evaluation procedure of experimental data is as follows: the packed bed height was divided into “n” differential packed bed heights of hi = 0.020 to 0.10 m. For each column height hi , all physical properties,
32
Table 1 – The physical properties of investigated systems for distillation and absorption, low and normal pressure range. System
pT mbar
TS K
V kg/m3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Chlorobenzene/ethylbenzene (n) Chlorobenzene/ethylbenzene (n) Chlorobenzene/ethylbenzene (n) Chlorobenzene/ethylbenzene (n) Chlorobenzene/ethylbenzene (n) Chlorobenzene/ethylbenzene Toluene/n-octane (n) Toluene/n-octane (n) Toluene/n-octane (n) Ethanol/water (p) Ethylbenzene/styrene Ethylbenzene/styrene Trans-decaline/cis-decaline (p) Methanol/ethanol (n) 1,2-dichlorethane/toluene (n) 1,2-propylene/ethylene glycol Methanol/water Methanol/water P-xylene/m-xylene NH3 –air/water NH3 –air/1 M H2 SO4 SO2 –air/water SO2 –air/1 n NaOH Cyclohexane/n-heptane CO2 –water/air
33 67 133 267 533 1000 80 133 267 1000 66.7 133 13 1000 1000 13.3 466.7 1000 66.7 1000 1000 1000 1000 1620 1000
314 329 345 364 385 407 321 327 345 352 335 350 336 343 365 381 338 338 411 293 293 303 293 378 293
0.140 0.268 0.510 0.967 1.827 3.241 0.373 0.473/0.525 0.90 0.8–1.294 0.30 0.483 0.066–0.095 1.2–1.4 3.20 0.076 0.54 1.10 0.25 1.183 1.18 1.150 1.19 4.97 1.183
n = negative system; p = positive system.
V × 106 m2 /s 52.4 28.7 15.8 8.8 4.9 2.9 19.1 15.3 8.5 8.2 25.6 15.9 105.8 8.4 3.2 281.3 21.9 10.5 29.1 15.1 15.2 15.9 15.1 1.65 15.1
DV × 106 m2 /s 64.8 35.8 19.9 11.1 6.3 3.7 21.0 17.0 9.5 14.5 34.0 19.9 120.0 9.1 4.0 336.5 34.4 18.0 3.62 23.9 24.0 13.1 12.3 2.18
ScV 0.809 0.803 0.793 0.791 0.785 0.780 0.908 0.96 0.894 0.4–1.25 0.752 0.798 0.881 0.929 0.806 0.836 0.724 0.728 0.685 0.633 0.632 1.220 1.224 0.756
L kg/m3
L × 106 m2 /s
956 941 926 908 887 866 779 774/780 758 787 837 835 846 739 968 1020 778 760 830 998 1033 989 1039 641 998
0.59 0.52 0.45 0.39 0.34 0.30 0.53 0.50 0.43 0.53 0.53 0.45 1.24 0.54 0.35 3.92 0.53 0.43 0.46 1.03 1.05 0.99 1.15 0.35 1.03
L × 103 kg/s2 28.5 26.9 25.1 23.2 21.1 19.0 23.1 22.5/24 20.7 25.7/40 25.0 21.0 26.0 17.2/16.5 22.3 35 21.7 19.8 24.2 72.7 59.4 70.0 54.6 13 72.7
DL ×109 m2 /s 2.33 2.85 3.50 4.33 5.41 6.67 2.33 2.53 3.18 3.42 3.06 3.64 1.04 4.75 4.86 0.98 2.5 3.39 3.25 2.13
ScL 255/270 125/255/270 128 89 62 45 195 171/190 118 82/105 173 123 850–1020 113/150 64 4000–10000 200 119 148 483
1.87
530
6.19 1.80
57.2 572
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
No.
33
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 3 – Local concentration (above) and separation efficiency (below) profile along the column height from the top to the bottom, for non-ideal system ethanol/water for 50 mm ceramic Pall rings.
Fig. 4 – Local concentration (above) and separation efficiency (below) profile along the column height from the top to the bottom, for ideal system ethylbenzene/styrene for 50 mm metal Pall rings; experimental data acc. to Billet (Billet, 1979). correlation, Eq. (22): (ˇV ae ) = 6
concentrations and vapour and liquid flows were evaluated acc. to correlation presented by Poling et al. (2007). These parameters change very much with column height for non ideal systems and were calculated as described above. The physical and diffusion properties of non ideal system methanol/water and ethanol/water change extremely from the top to the bottom of column, what influences strongly values of gas load factor (FV )i , specific liquid load (uL )i and also Reynolds numbers (ReV )i and (ReL )i , Schmidt numbers (ScV )i and (ScL )i and the slope of the equilibrium line myx,i and thereby have important influence on the calculation of the mass transfer efficiency and also on the concentration profile along packed bed. This procedure is essential for the evaluation of the experimental data for non-ideal systems, such as ethanol/water, Fig. 3, where the local separation efficiency (HTUOV )i or (nt /H)i declines with increasing packing bed height, because of change of the individual mass-transfer resistances due to the change of the mixture composition and change of the mxy value. Whereas for ideal system ethylbenzene/styrene, Fig. 4, the local separation efficiency (HTUOV )i or (nt /H)i is approximately constant and does not change along the height of packed bed H. Evaluation of all experimental distillation and absorption data of the data bank (EDB) allows the determination of model parameter CV , n and m in Eq. (18) what leads to the following
hL
DV d2T
2 + 0.0285
uR dT V
1/3 V
DV
1−
hL ε
6 [1/s] (22)
The model parameters in Eq. (22) were found according to optimisation of middle value of relative error ı¯ (ˇV ae ). The relative mean error for evaluated volumetric mass transfer coefficients ˇV ·ae in the gas phase for absorption systems was found to be 17.3% for the operating range below the loading line and also 17.3% for the entire range up to about 90% of the flooding point, Fig. 5.
Fig. 5 – Comparison between evaluated volumetric mass transfer coefficient ˇV ·ae in the gas phase acc. to eq. 22 for absorption systems and experimental data of EDB for investigated random packings of 1st–4th generation.
34
The presented model based on the droplet flow model in packed columns filled with random packing allows the prediction of the separation efficiency for all investigated types of packings of 1st–4th generation in the entire operation range up to 90–95% of the flooding point with a satisfactory accuracy for practical applications. For the determination of the
14.33 400 19.24 226 31.06 400 49.45 78.8 214
400
14.73 14.80 2084 1684 15.26 14.34 1203 977 23.44 21.63 2084 1684
ı (HTUOV )m [%] ı (HTUOV )m [%] No. of exp. data ı (HTUOV )m [%] No. of exp. data ı (HTUOV )m [%]
30.84 26.42 2084 1684 69.9 67.11 973 759
Total Loading range FV < 0.65 FV,Fl Below flooding 0.65 ≤ FV /FV,Fl < 1
Final remarks
No. of exp. data
The results of the evaluation of the absorption and desorption data from the EDB-data bank for gas–liquid systems with different correlations from literature is shown in Table 2. The model presented in this work allows prediction of the separation efficiency HTUOV below the loading line with similar accuracy to the model of Billet and Schultes (1993, 1999), but with a higher accuracy above the loading line and for twice more different packing types and systems. A generally better prediction of the separation efficiency is achieved compared to classical correlations like that of Onda et al. (1968), Zuiderweg (1978) and Zech and Mersmann (1978), which were developed for classical packings of 1st and 2nd generation only. This can be confirmed by the data listed in Table 3 which shows a comparison of calculated separation efficiencies to experimental distillation data of Billet (Billet, 1979). It becomes apparent that previous correlations of Onda et al. (Onda et al., 1968), Zuiderweg (Zuiderweg, 1978), Zech and Mersmann (Zech and ´ ´ (Mackowiak, 1990) are useful Mersmann, 1978) and Mackowiak for calculation of separation efficiency for classical packings of 1st/2nd generation in the range below loading line, but correlation presented in this work leads to best accuracy.
ı (HTUOV )m [%]
6. Comparison of the presented model with correlations from literature for gas-liquid systems
No. of exp. data
Figs. 12–14 present the comparison of the experimentally determined separation efficiency HTUOV with calculated values acc. to model presented here. Figures are valid for the absorption system ammonia–air/water for different packings type in the operating range up to the flooding line, see Table 4.
7.
Billet and Schultes (1993, 1999)
Absorption data
Table 2 – Results of exp. data evaluation for gas/liquid systems – comparison with correlation from literature.
5.2.
No. of exp. data
Figs. 6 and 7 present the comparison between the experimentally determined separation efficiency nt /H for 25 and 50 mm metallic Pall rings, calculated nt /H values acc. to model presented here valid for different distillation systems and experimental data of Billet (Billet, 1979) in the operating range up to 90–95% of flooding point. The Fig. 8 shows the comparison of the model with experimental data for lattice type Nor-Pac packing of the 3rd generation. The Figs. 9–11 show the parity plots for different packing types of 1st, 2nd, 3rd and 4th generation for experimental distillation data in the operating range up to 90–95% of the flooding point. The estimated mean relative error of all data evaluated for packings of 2–4th generation in the Figs. 10 and 11 is in the range between 3.15% and 15.5% and for different packing of 1st generation in the Fig. 9 between 11.2% and 27.5%.
Zech and Mersmann (1978)
Distillation data
Zuiderweg (1978)
5.1.
Onda et al. (1968)
Model validation
Author
5.
This work
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Table 3 – Comparison of the model prediction of the separation efficiency acc. to Eqn. (12,22,21) with literature correlations and experimental data of Billet (Billet, 1979); below ˙ V˙ = 1. loading line FV /FV,Fl ≤ 0.65 for various low and normal pressure distillation systems for random 15–50 mm metallic Pall rings, dS = 0.5 m, L/ Packing type and system
pT [mbar] dS [m]
Ethylbenzene/styrene
Methanol/ethanol 35 mm Pall ring, metal Ethylbenzene/styrene
Methanol/ethanol 25 mm Pall ring, metal Ethylbenzene/styrene
Methanol/ethanol 15 mm Pall ring, metal Ethylbenzene/styrene
Methanol/ethanol Mean absolute deviation [%] a
FV [Pa0.5 ]
nt /H [1/m]
Onda et al. (1968)
nt /H [1/m]
ı(nt /H) [%]
Zuiderweg (1978)
nt /H [1/m]
ı(nt /H) [%]
Zech and Mersmann (1978)a nt /H [1/m]
ı(nt /H) [%]
´ Mackowiak (1990)
nt /H [1/m]
13 0.5
2.2
1.25
1.17
−6.4
1.22
−2.2
1.25
0.4
1.4
133 0.5
1.93
1.95
1.68
−13.7
1.64
−16.1
2.66
36.6
1000 0.5
1.95
2.01
1.73
−13.9
1.97
−1.8
3.3
133 0.5
1.77
2.15
2.53
17.8
1.83
−14.7
1000 0.5
1.50
2.60
2.73
5.0
2.10
133 0.5
1.7
2.40
3.54
47.4
1000 0.5
1.67
3.15
3.52
133 0.5
1.7
3.36
3.75
1.2 1000 0.5 9 measuring points
ı(nt /H) [%]
Billet and Schultes (1993) nt /H [1/m]
´ Mackowiak (this work)
ı(nt /H) [%]
nt /H [1/m]
ı(nt /H) [%]
12.4
2.03
62.7
1.24
−0.5
1.66
−14.8
2.73
40.1
1.82
−6.8
64.4
1.74
−13.3
3.26
62.0
2.26
12.2
2.73
27.0
1.97
−8.3
2.44
13.5
2.05
−4.7
−19.2
3.38
30.0
2.02
−22.3
2.87
10.3
2.46
−5.5
2.07
−13.6
2.73
13.9
2.32
−3.4
2.79
16.2
2.32
−3.5
11.7
2.56
−18.9
3.21
1.8
2.13
−32.5
3.11
−1.3
2.62
−16.8
2.65
−21.2
2.63
−21.6
2.86
−14.8
3.22
−4.2
3.32
−1.1
3.02
−10.2
2.58
−31.1
2.66
−29.1
3.10
−17.2
2.47
−34.2
3.41
−9.0
3.10
−17.4
18.7
15.2
22.9
16.2
24.0
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
50 mm Pall ring, metal Trans-/cis-decaline
Exp. data Billet (1979)
8.6
Method not generated for those packing types, for calculation mean constants have been used.
35
36
Table 4 – Comparison of the model prediction of the separation efficiency acc. to Eqn. (3,11,22) with literature correlations and experimental data of this work below loading line FV /FV,Fl ≤ 0.65 for absorption system NH3 -air/water for random 15–50 mm metallic Pall rings, 1 bar, 293 K, dS = 0.3–0.45 m. pT [mbar]
uL [m/h]
dS [m]
FV [Pa0.5 ]
Exp. data Billet (1979)
HTUOV,exp. [m]
Onda et al. (1968)
Zuiderweg (1978)
HTUOV [m]
ı(HTUOV ) [%]
HTUOV [m]
ı(HTUOV ) [%]
Zech and Mersmann (1978)a
´ Mackowiak (1990)
Billet and Schultes (1993, 1999)
´ Mackowiak (this work)
HTUOV [m]
HTUOV [m]
HTUOV [m]
ı(HTUOV ) [%]
HTUOV [m]
ı(HTUOV ) [%]
ı(HTUOV ) [%]
ı(HTUOV ) [%]
50 mm Pall ring, metal
1000 0.45
10.01 2.1
0.467
0.706
51.3
0.359
−23.1
0.448*
−4.2
0.472
1.0
0.442
−5.3
0.547
17.1
35 mm Pall ring. metal
1000 0.3
9.98 2.21
0.419
0.558
33.2
0.312
−25.6
0.442*
5.4
0.390
−6.9
0.484
15.4
0.476
13.6
25 mm Pall ring. metal
1000 0.3
9.98 1.99
0.369
0.361
-2.1
0.244
−33.9
0.422*
14.3
0.303
−18.0
0.388
5.3
0.387
4.9
15 mm Pall ring. metal Mean absolute deviation [%] Total mean deviation [%] for (a) and (b)
9.98 1000 0.3 1.71 4 measuring points
0.275
0.477
73.4
0.186
−32.4
0.319*
38.5
0.223
−19.0
0.311
13.0
0.297
7.9
∗
13 measuring points
40.0
28.8
15.6
11.2
9.8
10.9
25.3
19.4
20.7
14.7
19.7
9.3
Method not generated for those packing types, for calculation mean constants have been used.
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Packing type
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
37
Fig. 6 – Experimental verification of the model for distillation systems, valid for 25 mm metallic Pall rings for various column diameters; experimental data according to: (a) and (b) this work (A)/c) and (d) Billet (1973) (Billet, 1979).
Fig. 7 – Experimental verification of the model for distillation systems, valid for 50 mm metallic Pall rings for various systems, experimental data according to Billet (Billet, 1979). separation efficiency of random packing for given system only the physical properties of the systems, operating conditions and packing characteristic data related to the geometrical shape of the packing such as the specific packing area “a”, packing void fraction “ε” and packing form factor “ϕP ” are required. These data are also needed to determine the fluid
´ dynamics of random packings (Mackowiak, 2010). The characteristic packing data for about 150 different types and ´ size of random packing are listed in literature (Mackowiak, 2010). The use of individual packing specific constants for mass transfer prediction is not necessary anymore in the model
Fig. 8 – Experimental verification of the model for distillation systems for plastic 17–50 mm packing Nor-Pac.
38
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 9 – Parity plots for the model for distillation for packings of 1st generation.
Fig. 10 – Parity plots for the model for distillation for packings of 2nd generation.
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 11 – Parity plots for the model for distillation for packings of 3rd/4th generation.
Fig. 12 – Experimental verification of the model for gas-liquid systems for 25 and 50 mm metallic Pall rings.
39
40
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 13 – Experimental verification of the model for gas-liquid systems for plastic 50 mm Nor-Pac packing for various column diameters.
Fig. 14 – Experimental verification of the model for gas–liquid systems for modern lattice-type packings.
41
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
presented here, what distinguishes the presented model from other models in literature. Table 5 shows the validity range for physical properties of the investigated systems, investigated packings data and data of used column operating range. Application of presented model for predicting the separation efficiency nt /H of random 50 mm metallic Pall rings is demonstrated in the attached numerical example.
Solution: (1) Height of overall transfer unit acc. to Eq. (2): HTUOV = HTUV + HTUL =
(2) Calculation of the volumetric liquid phase mass transfer coefficient ˇL ·ae for FV ≤ 0.65 FV,Fl acc. to Eq. (11): dh = 4
ˇL ae = 15.1
=
(1 − 0.28)
1/3
× 0.03461/4
D g 1/2 a 1/6 L
15.1 (1 − P )
ε 0.952 =4 = 3.462 × 10−2 a 110
1/3 1/4 dh
L
g
The separation efficiency of 50 mm metal Pall rings in a column with diameter dS = 0.5 m should be calculated using the method presented in this paper for the system ethylbenzene/styrene operated under low pressure pT = 133 mbar and ˙ V˙ = 1. total reflux L/ ´ 2010): Technical data of metal 50 mm Pall rings (Mackowiak, a = 110 m2 /m3 ε = 0.952 m3 /m3 ϕP = 0.28 N = 6100 1/m3
1/6
1.61 × 10−3
5/6
=
[1/s]
hL = 0.57
au2L g
= 1.75 × 10−2
1/3
= 0.57
m3 /m3
110 1.61 × 10−3
2 1/3
=
9.81
(3.2) Relative vapour velocity uR uV uL = + hL (ε − hL )
uR =
+
1.61 × 10−3 1.75 × 10−2
2.777 0.952 − 1.75 × 10−2
= 3.064
[m/s]
(3.3) Droplet diameter dT
The conditions are as follows:
system: top pressure reflux ratio diameter ratio vapour capacity factor vapour velocity vapour capacity factor at flooding point specific liquid load
110 9.81
(3) Volumetric vapour phase mass transfer coefficient ˇV ·ae using the following equations (3.1) Liquid hold-up hL acc. to Eq. (9):
Example of calculation
specific packing area void fraction form factor packing density
[m]
uL 5/6 =
1/2
4.66 × 10−9 (833 − 0.483) 9.81 0.022 = 1.14 × 10−2
8.
myx uL uV + ˙ V˙ ˇL ae ˇV ae L/
ethylbenzene/styrene pT = 133 mbar ˙ V˙ = 1 L/ ϕ = dS /d = 10 √ FV = 1.93 Pa uV = 2.777 m/s √ FV,Fl = 2.975 Pa uL = 1.61 × 10−3 m3 /(m2 s)
Physical properties of the system: All properties refer to a mean mole fraction of the volatile component of ym = 0.60 kmol/kmol.
dT =
L = (L − V ) g
= 1.641 × 10−3
0.022 (833 − 0.483) 9.81
[m]
(3.4) Droplet Reynolds number ReT acc. to Eq. (15): ReT =
uR dT 3.064 × 1.641 × 10−3 = = 318.2 V 1.58 × 10−5
(3.5) Sherwood number ShV and vapour phase mass transfer coefficient ˇV acc. to Eq. for CV = 0.0285 and n = 1: 1/3
ShV,T = 2 + 0.0285Re1.0 T ScV = = 2 + 0.0285 × 318.21.0 × 0.7951/3 = 10.4
slope of equilibrium line density of vapour mixture density of liquid Schmidt number of vapour mixture Schmidt number of liquid vapour phase diffusion coefficient liquid phase diffusion coefficient kinematic viscosity of vapour kinematic viscosity of liquid surface tension of liquid
myx = 0.919 V = 0.483 kg/m3 L = 833 kg/m3 ScV = 0.795 ScL = 121 DV = 1.989 × 10−5 m2 /s DL = 4.66 × 10−9 m2 /s V = 1.58 × 10−5 m2 /s L = 5.64 × 10−7 m2 /s L = 22 mN/m
acc. to Eq. (14): ˇV,T =
ShV,T DV 10.4 × 1.989 × 10−5 = = 0.126 dT 1.641 × 10−3
acc. to Eq. (17):
ˇVhL >0
hL = ˇV,T · 1 − ε = 0.113
6
1.75 × 10−2 = 0.126 1 − 0.952
[m/s]
(3.6) Specific mass transfer area ae acc. to Eq. (6): The experimental data of Billet (Billet, 1979) was evaluated to (nt /H)exp. = 1.95 1/m.
ae = 6
[m/s]
hL 1.75 × 10−2 =6 = 64.0 dT 1.641 × 10−3
m2 /m3
6
42
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Table 5 – Validity range of presented model. V = 0.066–5 kg/m3 L = 641–1100 kg/m3 L = 13–72.7 mN/m ScL = 45–10,000 ScV = 0.4–1.25 V = 6.6–21.4 × 10−6 kg/(m s) L = 0.2–4 × 10−6 kg/(m s)
d = 0.008–0.090 m a = 54.2–550 m2 /m3 ε = 0.696–0.987 m3 /m3 dS = 0.10–1.4 m dS /d ≥ 6 H = 0.8–4 m
(3.7) Volumetric mass transfer coefficient ˇV ·ae : ˇV ae = 0.113 × 64.0 = 7.23
[1/s]
(4) By inserting obtained (ˇV ·ae )- and (ˇL ·ae )-values into the Eq. (3) we obtain: HTUOV = =
myx uL uV + = ˙ V˙ ˇL ae ˇV ae L/
2.777 0.919 1.61 × 10−3 = 0.384 + 0.9186 × 0.141 + × 7.23 1 1.14 × 10−2 = 0.514 [m]
(5) Therefore the separation efficiency nt /H comes acc. to Eq. (21) to: nt = H
1 HTUOV
= 1.87
×
( + 1) 2
=
1 (0.919 + 1) 0, 514
×
2
[1/m]
Calculation results for the separation efficiency of 50 mm Pall ring, metal √ System: ethylbenzene/styrene, FV = 1.93 Pa, dS = 0.5 m, ˙ V˙ = 1 pT = 133 mbar, L/ acc. to Billet (Billet, 1979): acc. to Author 100% = −4.1%
nt H
nt H
exp
= 1.95 1/m
= 1.87 1/m
⇒
ı
nt H
=
1.87−1.95 1.95
×
References ´ Mackowiak, J., 2010. Fluid Dynamic of Packed Columns. Springer, Heidelberg/New York.
FV /FV,Fl ≤ 0.90–0.95 pT = 0.013–2 bar ReL ∈ 1 − 220 ReV ∈ 400 − 17500
Billet, R., Schultes, M., 1993. Chem. Eng. Technol. 16, 1. ´ Billet, R., Mackowiak, J., 1980. Chem. Technol. (Heidelberg) 9, 219–226. Onda, K., Takeuchi, H., Okumoto, Y., 1968. J. Chem. Eng. 1, 56–62. Bolles, W.L., Fair, J.R., Proceedings of the 3rd International Symposium on Distillation (1979), London,;1; p.3.3/35-89. and Chemical Engineering, 12 (1982) p. 109–116. Zuiderweg, F.J., 1978. vt Verfahrenstechnik 12, 674–677. Zech, J.B., Mersmann, A., 1978. Chem. Eng. Technol. 50 (7) (MS 604/78). ´ Billet, R., Mackowiak, J., 1984. Fette. Seifen. Anstrichmittel 86, 349–358. ´ Mackowiak, J., Paper presented on AICHE-Meeting, Chicago (1990), ´ ´ 16. Nov., partly published in J. Mackowiak, J.F. Mackowiak, Random Packings in: Górak A, Olujic´ Zˇ (Eds.), Distillation: Equipment and Processes, Academic Press (Elsevier), 2014. Billet, R., Schultes, M., 1999. Trans. IChemE. 77, 498–504. Chilton, T.H., Colburn, A.P., 1935. Ind. Eng. Chem. 27 (3), 255–260. ´ Mackowiak, J., 2011. Chem. Eng. Res. Des. 89, 1308–1320. Bornhütter, K., Mersmann, A., 1993. Chem. Eng. Technol. 16, 46–57. Higbie, R.R., 1935. AIChE J., 365–389. Hughmark, G.A., 1967. I&EC Fundam. 6, 408–413. Billet, R., 1979. Distillation Engineering. Chemical Publishing Company, New York (or R. Billet, Industrielle Destillation, Chemie Verlag, Weinheim (1973)). Poling, B.E., Prausnitz, J.M., O’Connell, J.P., 2007. The Properties of Gases and Liquids. McGraw-Hill, Boston. ´ Billet, R., Chromik, R., Mackowiak, J., 1987. Chem. Tech. 16 (5), 79–87. ´ Billet, R., Mackowiak, J., 1988. Chem. Eng. Technol. 11, 213–227. ´ Billet, R., Filip, S., Lugowski, Z., Mackowiak, J., 1983. Fette, Seifen, Anstrichmittel 85, 383–391. ´ Billet, R., Mackowiak, J., 1985. Fette, Seifen, Anstrichmittel 87, 201–205. ´ Billet, R., Koziol, A., Mackowiak, J., Suder, S., 1986. Chem.-Ing.-Tech. 58, 897–900. Zuiderweg, F.J., 1969. Recommended Test Mixtures for Distillation Columns. Institute of Chemical Engineering, London.
Contents lists available at ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Progress in design of random packing for gas–liquid systems Jerzy Ma´ckowiak ∗ ENVIMAC Engineering GmbH, Im Erlengrund 27, Oberhausen, 46149, Germany
a r t i c l e
i n f o
a b s t r a c t
Article history:
The following work presents a generally applicable model for the prediction of the separation
Received 17 October 2014
efficiency of random packing of different shape with size between 8 and 90 mm for gas–liquid
Received in revised form 19 May
systems in the entire operating range up to the flooding point. The new model was derived on
2015
the basis of the droplet flow model and that mass transfer in the gas phase occurs between
Accepted 26 May 2015
continuous gas phase and the swarm of droplets falling down in packed bed.
Available online 6 July 2015
The new model was validated with about 5000 experimental distillation, absorption and desorption data of ENVIMAC data bank (EDB) in a very wide range of changing operational
Keywords:
and constructive parameters; from low top pressure of 13 mbar up to 2 bar. Satisfactory con-
Random lattice-type packing
sistency for practical application was found between experimental values of the separation
Separation efficiency
efficiency for about 115 different types of random packings and calculated values based on
Mass transfer in the gas and liquid
the new model. © 2015 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
phase Distillation Absorption Desorption
1.
Introduction
During the last 5 decades, a lot of random packings have been developed, which can be divided into 4 generations, from classical Raschig rings, Berl and Intalox saddle of 1st generation to new modern random lattice type packings of 3rd and 4th generation. Fig. 1 shows examples of different packing types of all 1st–4th generation. Random packings are widely and successfully used not only in the distillation, absorption and stripping processes or for direct gas cooling and gas preheating, but also in environmental protection processes like waste gas and wastewater treatment. Their form has changed significantly during that time and the field and range of applications in industrial practice compared to the 1st generation packings also significantly increased. A big progress in the available design methods was observed during that period of time, especially in the modelling of fluid dynamics, which is presented
∗
´ in the recent literature, for example, (Mackowiak, 2010; Billet and Schultes, 1993, 1999). Nor-Pac packing was the first lattice type packing in ´ (1980). As a result Germany presented by Billet and Mackowiak ´ of this work (Billet and Mackowiak, 1980), after 1982 a number of new lattice-type packing elements of different types of 3rd and 4th generation were developed, mainly by leading German packing manufacturers, see Fig. 1. One of the first models for the design of random packing of 1st and 2nd generation was the model of Onda et al. (1968), followed by the improved Monsanto Model of Bolles and Fair (1979), the model of Zuiderweg (1978) and model presented by Zech and Mersmann (1978). The first model for the design of distillation columns not only for classical random packings but also for lattice type packings of the 3rd generation was ´ (1984) which the model developed by Billet and Mackowiak ´ 1990). This model was has been modified by (Mackowiak,
Tel.: +49 2089410440; fax: +49 208941044100. E-mail address: [email protected] http://dx.doi.org/10.1016/j.cherd.2015.05.038 0263-8762/© 2015 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
29
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Nomenclature Symbols a geometric surface area of packing per unit volume [m2 /m3 ] interfacial area per unit volume [m2 /m3 ] ae surface area of the perforated wall of a packing A0 element [m2 ] total non-perforated wall surface area of a A packing element A = dh [m2 ] dimensionless specific liquid load acc. to BL ´ Mackowiak (2010) [dimensionless] constant, Eqs. (13) and (18) [dimensionless] CV packing diameter [m] d hydraulic diameter; dh = 4ε/a [m] dh particle diameter; dP = 6 (1 − ε) /a [m] dP dS column inner diameter [m] dT mean droplet diameter acc. to Sauter, dT = CT L /g with CT = 1 valid for big deformed droplets with L ≥ 15 mN/m [m] DV , DL diffusion coefficient in the gas or liquid phase [m2 /s] FV gas load factor in relation to full column cross √ section, FV = uV V [Pa0.5 ] acceleration of gravity [m/s2 ] g h packing height [m] liquid hold-up in relation to total packing volhL ume VS , hL = VL /VS [m2 /m3 ] height of packed bed element unit [m] h HTUOV height of an overall transfer unit related to vapour phase [m] height of a transfer unit [m] HTU H height of packed bed [m] K l L˙ myx n nt /H NTUOV pT uL uR uV VL VS V˙
wall factor, K =
A ´ packing form factor P ≡ A0 (Mackowiak, 2010) [dimensionless] contact time [s] density, density difference = L − V [kg/m3 ] surface tension [N/m] kinematic viscosity [m2 /s]
ϕP
1+
4 dS a
−1
´ (Mackowiak, 2010)
[dimensionless] mean contact path [m] molar flow of liquid [kmol/h] slope of equilibrium line [dimensionless] number of differential packed bed layer with hi = 0.02–0.10 m [dimensionless] number of theoretical stages per 1 m packing height [1/m] number of overall transfer units, related to vapour phase [dimensionless] operating pressure [mbar, bar] specific liquid load in relation to full cross section of empty column [m/s] uV relative phase velocity uR = ε−h + uhL [m/s] L L linear gas velocity in relation to full cross section of empty column [m/s] liquid volume [m3 ] packing volume, VS = Hd2S /4 [m3 ] molar flow of gas or vapour [kmol/h]
Greek symbols mass transfer coefficient [m/s] ˇ volumetric mass transfer coefficient [1/s] ˇ·ae ıi (. . .), ı¯ (...) relative error, middle value of relative error [%] ˙ stripping factor = myx V˙ [dimensionless] L
, L Indices Fl i L m S
relating to operating point at flooding point individual value relating to liquid mean value relating to operating point at loading point; FV = 0.65FV,Fl relating to gas or vapour
V
Dimensionless numbers u2 a FrL = gL Froude number of liquid uL ReL = a Reynolds number of liquid L
ReT =
uR dT V
BL =
L L g2
Sc =
D
Reynolds number of droplet
1/3
uL 1−ε ε εdP
dimensionless liquid load
Schmidt number
uV dp K (1−ε) V ˇV,T dT ShV,T = D V
ReV =
Reynolds number of gas/vapour Sherwood number of droplet
developed for more than 60 different packings for systems with the main mass transfer resistance located in the vapour phase. Based on the assumption of film formation in the packed bed, Billet and Schultes (1993, 1999) derived on the base of about 2600 experimental data, mainly presented in (Billet ´ 1984, 1988, 1985; Billet et al., 1987, 1983), new and Mackowiak, dimensionless correlations for determining the effective interfacial area per unit volume ae and mass transfer coefficients in the gas and liquid phase for 55 different classical and latticetype packings and structured packings. The main aim of the present work is to develop a generally applicable method for determining the volumetric mass transfer coefficient in the gas phase and the separation efficiency nt /H or HTUOV not limited to certain packing types for distillation and absorption systems.
2.
Mass transfer in the liquid phase
Two models are in common use for predicting the height of the packed bed of random packing H: static HETP × nt model, Eq. (1), and kinetic HTUOV × NTUOV model, Eq. (2). H nt nt
[m]
(1)
H = HTUOV NTUOV
[m]
(2)
H = HETPnt =
In kinetic model, according to Chilton and Colburn (1935), the knowledge of both the liquid phase and gas phase volumetric mass transfer coefficients ˇL ·ae and ˇV ·ae , Eqs. (3), (4) and (5), is required. HTUOV = HTUV + HTUL
[m]
(3)
30
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 1 – Overview of investigated different random packing elements of 1st–4th generation. HTUV =
uV (ˇV ae )
[m]
(4)
HTUL =
uL (ˇL ae )
[m]
(5)
A new, generally valid model for the calculation of ˇL ·ae ´ (2011). Based on values has been presented by Mackowiak observations and measurements of droplet proportions in packed beds with different packings carried out by Bornhütter and Mersmann (1993), the new method for predicting the mass transfer in the liquid phase was developed on the assumption ´ of droplet flow in the packed bed (Mackowiak, 2011). Thus interfacial area per unit volume ae can be determined for ´ gas–liquid systems with the fundamental Eq. (6) (Mackowiak, 2011):
hL ae = 6 dT
3
2
m /m
ˇL ae = (6)
,
valid for disperse systems. According to the model, mass transfer is interrupted during the formation of rivulets and only recommences when new droplets are formed. The process therefore is non-stationary, as has been described by the well-known model of Higbie (Higbie, 1935), Eq. (7): 2 ˇL = √
DL
l lhL ⇒ u¯ L uL
1/3 1/4 (1 − P ) dh
u¯ L =
uL hL
(8)
[s]
1/3
= 0.57
(ˇL ae )S =
1/3 1/4 (1 − P ) dh
0.35 +
FV FV,Fl
[1/s]
(11)
L
g
5/6
uL
[1/s]
(12)
uL =const
Eqs. (11) and (12) allow to predict the volumetric mass transfer coefficient in the liquid phase ˇL ·ae of random packings up to flooding point for studied modern and classical packing types of d = 0.012–0.090 m with accurate good enough for practical applications with a mean error of ±12.5% ´ 2011), Fig. 2. (Mackowiak,
au2L g
1/3
m3 /m3 .
(9)
Mass transfer in the gas phase
The new droplet flow model is based on the assumption, that mass transfer is taking place from the continuous gas or vapour phase into the individual droplets falling down in packed bed acc. to the Frössling equation acc. to Eq. (13) presented by Hughmark (1967). 1/3
The correlations for predicting the hold-up of liquid for ReL < 2 and ReL > 200 and in the range above the loading point ´ are presented in the literature (Mackowiak, 2010). The contact paths l in Eq. (8) for the random packing was determined on ´ the basis of the following empirical correlation (Mackowiak, 2011): 1/2
5/6
uL
D g 1/2 a 1/6 L
15.1
ShV,T = 2 + CV RenT ScV
l = 0.115(1 − P )2/3 dh
g
For the operating range above the loading line up to flooding line 0.65 FV,Fl < FV < FV,Fl the following Eq. (12) is valid:
3. ´ Acc. to Mackowiak (2010), the liquid hold-up hL in random packings for turbulent liquid flow ReL ≥ 2 in the range below the loading point FV ≤ 0.65 FV,Fl can be described by Eq. (9) ´ (Mackowiak, 2010):
hL = 0.57FrL
L
(7)
[m/s]
for
D g 1/2 a 1/6 L
15.1
×
The contact time in Eq. (7) is described by the time that a droplet needs to cover the distance 1 between two contact points within the packing. Hence:
=
where, dh is the hydraulic diameter of packed beds ´ 2010) and the form factor ϕP is a geometrical (Mackowiak, parameter of the individual packing. The numerical value of the form factor represents the proportion of the perforated ´ surface area of a packing element (Mackowiak, 2010) and amounts e.g., ϕP = 0 for ceramic Raschig rings (no perforated surface), ϕP = 0.28 for metallic Pall rings and ϕP = 0.5–0.8 for ´ 2010). metallic modern lattice type packings (Mackowiak, Substitution of the relations of Eq. (8) into Eq. (7) and of Eq. (9) into Eq. (6) leads to the Eq. (11) for the prediction of the volumetric mass transfer coefficient ˇL ·ae in columns with random packing in the operating range below the loading line ´ FV ≤ 0.65 FV,Fl and for turbulent liquid flow ReL ≥ 2 (Mackowiak, 2011):
[m] ,
(10)
(13)
hL →0
where, ShV,T =
ˇV,ThL →0 dT
hL →0
ReT =
uR dT V
DV
(14)
(15)
31
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 2 – Comparison between evaluated volumetric mass transfer coefficient ˇL ·ae in the liquid phase acc. to eqn. 11, 12 and experimental data of EDB for investigated random packings of 1st–4th generation for dS = 0.15–1.2 m (Ma´ckowiak, 2011) for system no. 25, according to Table 1. ScL =
L DL
(16)
For a falling swarm of droplet in random packings, the mass transfer intensity decreases in comparison to single droplet flow and mass transfer can be described with the following relation Eq. (17):
ˇVhL >0 = ˇV,ThL →0 1 −
hL ε
m (17)
[m/s]
the volumetric mass transfer coefficient in the vapour phase ˇV ·ae will be estimated acc. to Eq. (18) (ˇV ae ) = ˇV,hL >0 ae =
DV hL 1/3 2 + CV RenT ScV 1− dT ε
m h L 6
dT
[1/s] (18)
as the product of Eqs.(6) and (17), in which the constants CV and exponents “n” and “m” must be evaluated from the experimental data.
4.
Model evaluation
The ENVIMAC data bank (EDB) was used to check the model presented here for 25 different test systems, 115 random packing types of 1st–4th generation with size of d = 8–100 mm made of metal, ceramic and plastic. The total number of experimental data evaluated within this work was about 1050 for distillation systems and 3100 data points for absorption and 1000 data points for desorption systems. The list of the systems and the physical properties of used systems is presented in Table 1. Physical properties were calculated local for each vapour and liquid from the top to the bottom according to recommendations of Poling et al. (Poling et al., 2007). ´ 1980, 1984, 1985, Literature data (Billet and Mackowiak, ´ 1988; Mackowiak, 1990, 2011; Bornhütter and Mersmann, 1993; Billet, 1979; Billet et al., 1987, 1983, 1986) including experiments with packing height of H = 1.3–4 m and column diameter of dS = 0.15/0.5/0.8 m were taken into account for model evaluation. The test plants with diameter of 150–1400 mm used in investigations are described in the literature (Billet and ´ ´ Mackowiak, 1980, 1984, 1988, 1985; Mackowiak, 1990, 2011; Billet et al., 1987, 1983, 1986). For each distillation run, all operating parameters as temperature of the vapour on the bottom and top, top pressure, cooling water flows for heat balance of the plant, packed
bed pressure drop and liquid reflux flow, were measured and recorded. The steady state was indicated through measurement of temperature and concentration profile of the lighter component on the top in liquid xD and at the bottom in the vapour yB . The vapour flow capacity factor FV in the column was evaluated even from the heat balance of the condenser on the top of column, where the vapour from the column was condensed using cooling water and additional verified with the measurement of flow meter. The samples of vapour after condensation and cooling down to 20 ◦ C were analysed with the density techniques acc. to recommendation of EFCE for test systems (Zuiderweg, 1969). The study of the kinetics of the mass transfer in the gas phase for absorption systems was carried out using the test systems: NH3 –air/water, NH3 –air/1 M H2 SO4 , SO2 –air/water and SO2 –air/1 M NaOH under atmospheric conditions and for mass transfer resistance in the liquid phase into the gas phase was investigated by using the system CO2 –water/air also under atmospheric conditions in columns with diameters of 150–1000 mm for packing height of H ≤ 2.5 m. A two types of liquid distributor with approximately B = 250/450/600 drip points/m2 was installed directly above the packing layer to distribute uniformly the liquid at the column top. The experimental distillation data were evaluated using the differential method based on the evaluation of mean local separation efficiency (nt /H)i or (HTUOV )i -values in each differential packing height unit hi .
n nt
n t
H
m
i=1
=
n
(HTUOV )m =
n t
H
m
=
H
i
n
[1/m]
(19)
(HTUOV )i
i=1
n
+1 1 (HTUOV )m 2
[m]
(20)
[1/m]
(21)
From the measured concentration of lighter component in the liquid on the top xD and vapour in the bottom yB the overall number of height units HTUOV and number of theoretical stages nt was calculated using the rigorous model ´ (Mackowiak, 1990). The schema of the evaluation procedure of experimental data is as follows: the packed bed height was divided into “n” differential packed bed heights of hi = 0.020 to 0.10 m. For each column height hi , all physical properties,
32
Table 1 – The physical properties of investigated systems for distillation and absorption, low and normal pressure range. System
pT mbar
TS K
V kg/m3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Chlorobenzene/ethylbenzene (n) Chlorobenzene/ethylbenzene (n) Chlorobenzene/ethylbenzene (n) Chlorobenzene/ethylbenzene (n) Chlorobenzene/ethylbenzene (n) Chlorobenzene/ethylbenzene Toluene/n-octane (n) Toluene/n-octane (n) Toluene/n-octane (n) Ethanol/water (p) Ethylbenzene/styrene Ethylbenzene/styrene Trans-decaline/cis-decaline (p) Methanol/ethanol (n) 1,2-dichlorethane/toluene (n) 1,2-propylene/ethylene glycol Methanol/water Methanol/water P-xylene/m-xylene NH3 –air/water NH3 –air/1 M H2 SO4 SO2 –air/water SO2 –air/1 n NaOH Cyclohexane/n-heptane CO2 –water/air
33 67 133 267 533 1000 80 133 267 1000 66.7 133 13 1000 1000 13.3 466.7 1000 66.7 1000 1000 1000 1000 1620 1000
314 329 345 364 385 407 321 327 345 352 335 350 336 343 365 381 338 338 411 293 293 303 293 378 293
0.140 0.268 0.510 0.967 1.827 3.241 0.373 0.473/0.525 0.90 0.8–1.294 0.30 0.483 0.066–0.095 1.2–1.4 3.20 0.076 0.54 1.10 0.25 1.183 1.18 1.150 1.19 4.97 1.183
n = negative system; p = positive system.
V × 106 m2 /s 52.4 28.7 15.8 8.8 4.9 2.9 19.1 15.3 8.5 8.2 25.6 15.9 105.8 8.4 3.2 281.3 21.9 10.5 29.1 15.1 15.2 15.9 15.1 1.65 15.1
DV × 106 m2 /s 64.8 35.8 19.9 11.1 6.3 3.7 21.0 17.0 9.5 14.5 34.0 19.9 120.0 9.1 4.0 336.5 34.4 18.0 3.62 23.9 24.0 13.1 12.3 2.18
ScV 0.809 0.803 0.793 0.791 0.785 0.780 0.908 0.96 0.894 0.4–1.25 0.752 0.798 0.881 0.929 0.806 0.836 0.724 0.728 0.685 0.633 0.632 1.220 1.224 0.756
L kg/m3
L × 106 m2 /s
956 941 926 908 887 866 779 774/780 758 787 837 835 846 739 968 1020 778 760 830 998 1033 989 1039 641 998
0.59 0.52 0.45 0.39 0.34 0.30 0.53 0.50 0.43 0.53 0.53 0.45 1.24 0.54 0.35 3.92 0.53 0.43 0.46 1.03 1.05 0.99 1.15 0.35 1.03
L × 103 kg/s2 28.5 26.9 25.1 23.2 21.1 19.0 23.1 22.5/24 20.7 25.7/40 25.0 21.0 26.0 17.2/16.5 22.3 35 21.7 19.8 24.2 72.7 59.4 70.0 54.6 13 72.7
DL ×109 m2 /s 2.33 2.85 3.50 4.33 5.41 6.67 2.33 2.53 3.18 3.42 3.06 3.64 1.04 4.75 4.86 0.98 2.5 3.39 3.25 2.13
ScL 255/270 125/255/270 128 89 62 45 195 171/190 118 82/105 173 123 850–1020 113/150 64 4000–10000 200 119 148 483
1.87
530
6.19 1.80
57.2 572
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
No.
33
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 3 – Local concentration (above) and separation efficiency (below) profile along the column height from the top to the bottom, for non-ideal system ethanol/water for 50 mm ceramic Pall rings.
Fig. 4 – Local concentration (above) and separation efficiency (below) profile along the column height from the top to the bottom, for ideal system ethylbenzene/styrene for 50 mm metal Pall rings; experimental data acc. to Billet (Billet, 1979). correlation, Eq. (22): (ˇV ae ) = 6
concentrations and vapour and liquid flows were evaluated acc. to correlation presented by Poling et al. (2007). These parameters change very much with column height for non ideal systems and were calculated as described above. The physical and diffusion properties of non ideal system methanol/water and ethanol/water change extremely from the top to the bottom of column, what influences strongly values of gas load factor (FV )i , specific liquid load (uL )i and also Reynolds numbers (ReV )i and (ReL )i , Schmidt numbers (ScV )i and (ScL )i and the slope of the equilibrium line myx,i and thereby have important influence on the calculation of the mass transfer efficiency and also on the concentration profile along packed bed. This procedure is essential for the evaluation of the experimental data for non-ideal systems, such as ethanol/water, Fig. 3, where the local separation efficiency (HTUOV )i or (nt /H)i declines with increasing packing bed height, because of change of the individual mass-transfer resistances due to the change of the mixture composition and change of the mxy value. Whereas for ideal system ethylbenzene/styrene, Fig. 4, the local separation efficiency (HTUOV )i or (nt /H)i is approximately constant and does not change along the height of packed bed H. Evaluation of all experimental distillation and absorption data of the data bank (EDB) allows the determination of model parameter CV , n and m in Eq. (18) what leads to the following
hL
DV d2T
2 + 0.0285
uR dT V
1/3 V
DV
1−
hL ε
6 [1/s] (22)
The model parameters in Eq. (22) were found according to optimisation of middle value of relative error ı¯ (ˇV ae ). The relative mean error for evaluated volumetric mass transfer coefficients ˇV ·ae in the gas phase for absorption systems was found to be 17.3% for the operating range below the loading line and also 17.3% for the entire range up to about 90% of the flooding point, Fig. 5.
Fig. 5 – Comparison between evaluated volumetric mass transfer coefficient ˇV ·ae in the gas phase acc. to eq. 22 for absorption systems and experimental data of EDB for investigated random packings of 1st–4th generation.
34
The presented model based on the droplet flow model in packed columns filled with random packing allows the prediction of the separation efficiency for all investigated types of packings of 1st–4th generation in the entire operation range up to 90–95% of the flooding point with a satisfactory accuracy for practical applications. For the determination of the
14.33 400 19.24 226 31.06 400 49.45 78.8 214
400
14.73 14.80 2084 1684 15.26 14.34 1203 977 23.44 21.63 2084 1684
ı (HTUOV )m [%] ı (HTUOV )m [%] No. of exp. data ı (HTUOV )m [%] No. of exp. data ı (HTUOV )m [%]
30.84 26.42 2084 1684 69.9 67.11 973 759
Total Loading range FV < 0.65 FV,Fl Below flooding 0.65 ≤ FV /FV,Fl < 1
Final remarks
No. of exp. data
The results of the evaluation of the absorption and desorption data from the EDB-data bank for gas–liquid systems with different correlations from literature is shown in Table 2. The model presented in this work allows prediction of the separation efficiency HTUOV below the loading line with similar accuracy to the model of Billet and Schultes (1993, 1999), but with a higher accuracy above the loading line and for twice more different packing types and systems. A generally better prediction of the separation efficiency is achieved compared to classical correlations like that of Onda et al. (1968), Zuiderweg (1978) and Zech and Mersmann (1978), which were developed for classical packings of 1st and 2nd generation only. This can be confirmed by the data listed in Table 3 which shows a comparison of calculated separation efficiencies to experimental distillation data of Billet (Billet, 1979). It becomes apparent that previous correlations of Onda et al. (Onda et al., 1968), Zuiderweg (Zuiderweg, 1978), Zech and Mersmann (Zech and ´ ´ (Mackowiak, 1990) are useful Mersmann, 1978) and Mackowiak for calculation of separation efficiency for classical packings of 1st/2nd generation in the range below loading line, but correlation presented in this work leads to best accuracy.
ı (HTUOV )m [%]
6. Comparison of the presented model with correlations from literature for gas-liquid systems
No. of exp. data
Figs. 12–14 present the comparison of the experimentally determined separation efficiency HTUOV with calculated values acc. to model presented here. Figures are valid for the absorption system ammonia–air/water for different packings type in the operating range up to the flooding line, see Table 4.
7.
Billet and Schultes (1993, 1999)
Absorption data
Table 2 – Results of exp. data evaluation for gas/liquid systems – comparison with correlation from literature.
5.2.
No. of exp. data
Figs. 6 and 7 present the comparison between the experimentally determined separation efficiency nt /H for 25 and 50 mm metallic Pall rings, calculated nt /H values acc. to model presented here valid for different distillation systems and experimental data of Billet (Billet, 1979) in the operating range up to 90–95% of flooding point. The Fig. 8 shows the comparison of the model with experimental data for lattice type Nor-Pac packing of the 3rd generation. The Figs. 9–11 show the parity plots for different packing types of 1st, 2nd, 3rd and 4th generation for experimental distillation data in the operating range up to 90–95% of the flooding point. The estimated mean relative error of all data evaluated for packings of 2–4th generation in the Figs. 10 and 11 is in the range between 3.15% and 15.5% and for different packing of 1st generation in the Fig. 9 between 11.2% and 27.5%.
Zech and Mersmann (1978)
Distillation data
Zuiderweg (1978)
5.1.
Onda et al. (1968)
Model validation
Author
5.
This work
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Table 3 – Comparison of the model prediction of the separation efficiency acc. to Eqn. (12,22,21) with literature correlations and experimental data of Billet (Billet, 1979); below ˙ V˙ = 1. loading line FV /FV,Fl ≤ 0.65 for various low and normal pressure distillation systems for random 15–50 mm metallic Pall rings, dS = 0.5 m, L/ Packing type and system
pT [mbar] dS [m]
Ethylbenzene/styrene
Methanol/ethanol 35 mm Pall ring, metal Ethylbenzene/styrene
Methanol/ethanol 25 mm Pall ring, metal Ethylbenzene/styrene
Methanol/ethanol 15 mm Pall ring, metal Ethylbenzene/styrene
Methanol/ethanol Mean absolute deviation [%] a
FV [Pa0.5 ]
nt /H [1/m]
Onda et al. (1968)
nt /H [1/m]
ı(nt /H) [%]
Zuiderweg (1978)
nt /H [1/m]
ı(nt /H) [%]
Zech and Mersmann (1978)a nt /H [1/m]
ı(nt /H) [%]
´ Mackowiak (1990)
nt /H [1/m]
13 0.5
2.2
1.25
1.17
−6.4
1.22
−2.2
1.25
0.4
1.4
133 0.5
1.93
1.95
1.68
−13.7
1.64
−16.1
2.66
36.6
1000 0.5
1.95
2.01
1.73
−13.9
1.97
−1.8
3.3
133 0.5
1.77
2.15
2.53
17.8
1.83
−14.7
1000 0.5
1.50
2.60
2.73
5.0
2.10
133 0.5
1.7
2.40
3.54
47.4
1000 0.5
1.67
3.15
3.52
133 0.5
1.7
3.36
3.75
1.2 1000 0.5 9 measuring points
ı(nt /H) [%]
Billet and Schultes (1993) nt /H [1/m]
´ Mackowiak (this work)
ı(nt /H) [%]
nt /H [1/m]
ı(nt /H) [%]
12.4
2.03
62.7
1.24
−0.5
1.66
−14.8
2.73
40.1
1.82
−6.8
64.4
1.74
−13.3
3.26
62.0
2.26
12.2
2.73
27.0
1.97
−8.3
2.44
13.5
2.05
−4.7
−19.2
3.38
30.0
2.02
−22.3
2.87
10.3
2.46
−5.5
2.07
−13.6
2.73
13.9
2.32
−3.4
2.79
16.2
2.32
−3.5
11.7
2.56
−18.9
3.21
1.8
2.13
−32.5
3.11
−1.3
2.62
−16.8
2.65
−21.2
2.63
−21.6
2.86
−14.8
3.22
−4.2
3.32
−1.1
3.02
−10.2
2.58
−31.1
2.66
−29.1
3.10
−17.2
2.47
−34.2
3.41
−9.0
3.10
−17.4
18.7
15.2
22.9
16.2
24.0
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
50 mm Pall ring, metal Trans-/cis-decaline
Exp. data Billet (1979)
8.6
Method not generated for those packing types, for calculation mean constants have been used.
35
36
Table 4 – Comparison of the model prediction of the separation efficiency acc. to Eqn. (3,11,22) with literature correlations and experimental data of this work below loading line FV /FV,Fl ≤ 0.65 for absorption system NH3 -air/water for random 15–50 mm metallic Pall rings, 1 bar, 293 K, dS = 0.3–0.45 m. pT [mbar]
uL [m/h]
dS [m]
FV [Pa0.5 ]
Exp. data Billet (1979)
HTUOV,exp. [m]
Onda et al. (1968)
Zuiderweg (1978)
HTUOV [m]
ı(HTUOV ) [%]
HTUOV [m]
ı(HTUOV ) [%]
Zech and Mersmann (1978)a
´ Mackowiak (1990)
Billet and Schultes (1993, 1999)
´ Mackowiak (this work)
HTUOV [m]
HTUOV [m]
HTUOV [m]
ı(HTUOV ) [%]
HTUOV [m]
ı(HTUOV ) [%]
ı(HTUOV ) [%]
ı(HTUOV ) [%]
50 mm Pall ring, metal
1000 0.45
10.01 2.1
0.467
0.706
51.3
0.359
−23.1
0.448*
−4.2
0.472
1.0
0.442
−5.3
0.547
17.1
35 mm Pall ring. metal
1000 0.3
9.98 2.21
0.419
0.558
33.2
0.312
−25.6
0.442*
5.4
0.390
−6.9
0.484
15.4
0.476
13.6
25 mm Pall ring. metal
1000 0.3
9.98 1.99
0.369
0.361
-2.1
0.244
−33.9
0.422*
14.3
0.303
−18.0
0.388
5.3
0.387
4.9
15 mm Pall ring. metal Mean absolute deviation [%] Total mean deviation [%] for (a) and (b)
9.98 1000 0.3 1.71 4 measuring points
0.275
0.477
73.4
0.186
−32.4
0.319*
38.5
0.223
−19.0
0.311
13.0
0.297
7.9
∗
13 measuring points
40.0
28.8
15.6
11.2
9.8
10.9
25.3
19.4
20.7
14.7
19.7
9.3
Method not generated for those packing types, for calculation mean constants have been used.
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Packing type
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
37
Fig. 6 – Experimental verification of the model for distillation systems, valid for 25 mm metallic Pall rings for various column diameters; experimental data according to: (a) and (b) this work (A)/c) and (d) Billet (1973) (Billet, 1979).
Fig. 7 – Experimental verification of the model for distillation systems, valid for 50 mm metallic Pall rings for various systems, experimental data according to Billet (Billet, 1979). separation efficiency of random packing for given system only the physical properties of the systems, operating conditions and packing characteristic data related to the geometrical shape of the packing such as the specific packing area “a”, packing void fraction “ε” and packing form factor “ϕP ” are required. These data are also needed to determine the fluid
´ dynamics of random packings (Mackowiak, 2010). The characteristic packing data for about 150 different types and ´ size of random packing are listed in literature (Mackowiak, 2010). The use of individual packing specific constants for mass transfer prediction is not necessary anymore in the model
Fig. 8 – Experimental verification of the model for distillation systems for plastic 17–50 mm packing Nor-Pac.
38
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 9 – Parity plots for the model for distillation for packings of 1st generation.
Fig. 10 – Parity plots for the model for distillation for packings of 2nd generation.
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 11 – Parity plots for the model for distillation for packings of 3rd/4th generation.
Fig. 12 – Experimental verification of the model for gas-liquid systems for 25 and 50 mm metallic Pall rings.
39
40
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Fig. 13 – Experimental verification of the model for gas-liquid systems for plastic 50 mm Nor-Pac packing for various column diameters.
Fig. 14 – Experimental verification of the model for gas–liquid systems for modern lattice-type packings.
41
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
presented here, what distinguishes the presented model from other models in literature. Table 5 shows the validity range for physical properties of the investigated systems, investigated packings data and data of used column operating range. Application of presented model for predicting the separation efficiency nt /H of random 50 mm metallic Pall rings is demonstrated in the attached numerical example.
Solution: (1) Height of overall transfer unit acc. to Eq. (2): HTUOV = HTUV + HTUL =
(2) Calculation of the volumetric liquid phase mass transfer coefficient ˇL ·ae for FV ≤ 0.65 FV,Fl acc. to Eq. (11): dh = 4
ˇL ae = 15.1
=
(1 − 0.28)
1/3
× 0.03461/4
D g 1/2 a 1/6 L
15.1 (1 − P )
ε 0.952 =4 = 3.462 × 10−2 a 110
1/3 1/4 dh
L
g
The separation efficiency of 50 mm metal Pall rings in a column with diameter dS = 0.5 m should be calculated using the method presented in this paper for the system ethylbenzene/styrene operated under low pressure pT = 133 mbar and ˙ V˙ = 1. total reflux L/ ´ 2010): Technical data of metal 50 mm Pall rings (Mackowiak, a = 110 m2 /m3 ε = 0.952 m3 /m3 ϕP = 0.28 N = 6100 1/m3
1/6
1.61 × 10−3
5/6
=
[1/s]
hL = 0.57
au2L g
= 1.75 × 10−2
1/3
= 0.57
m3 /m3
110 1.61 × 10−3
2 1/3
=
9.81
(3.2) Relative vapour velocity uR uV uL = + hL (ε − hL )
uR =
+
1.61 × 10−3 1.75 × 10−2
2.777 0.952 − 1.75 × 10−2
= 3.064
[m/s]
(3.3) Droplet diameter dT
The conditions are as follows:
system: top pressure reflux ratio diameter ratio vapour capacity factor vapour velocity vapour capacity factor at flooding point specific liquid load
110 9.81
(3) Volumetric vapour phase mass transfer coefficient ˇV ·ae using the following equations (3.1) Liquid hold-up hL acc. to Eq. (9):
Example of calculation
specific packing area void fraction form factor packing density
[m]
uL 5/6 =
1/2
4.66 × 10−9 (833 − 0.483) 9.81 0.022 = 1.14 × 10−2
8.
myx uL uV + ˙ V˙ ˇL ae ˇV ae L/
ethylbenzene/styrene pT = 133 mbar ˙ V˙ = 1 L/ ϕ = dS /d = 10 √ FV = 1.93 Pa uV = 2.777 m/s √ FV,Fl = 2.975 Pa uL = 1.61 × 10−3 m3 /(m2 s)
Physical properties of the system: All properties refer to a mean mole fraction of the volatile component of ym = 0.60 kmol/kmol.
dT =
L = (L − V ) g
= 1.641 × 10−3
0.022 (833 − 0.483) 9.81
[m]
(3.4) Droplet Reynolds number ReT acc. to Eq. (15): ReT =
uR dT 3.064 × 1.641 × 10−3 = = 318.2 V 1.58 × 10−5
(3.5) Sherwood number ShV and vapour phase mass transfer coefficient ˇV acc. to Eq. for CV = 0.0285 and n = 1: 1/3
ShV,T = 2 + 0.0285Re1.0 T ScV = = 2 + 0.0285 × 318.21.0 × 0.7951/3 = 10.4
slope of equilibrium line density of vapour mixture density of liquid Schmidt number of vapour mixture Schmidt number of liquid vapour phase diffusion coefficient liquid phase diffusion coefficient kinematic viscosity of vapour kinematic viscosity of liquid surface tension of liquid
myx = 0.919 V = 0.483 kg/m3 L = 833 kg/m3 ScV = 0.795 ScL = 121 DV = 1.989 × 10−5 m2 /s DL = 4.66 × 10−9 m2 /s V = 1.58 × 10−5 m2 /s L = 5.64 × 10−7 m2 /s L = 22 mN/m
acc. to Eq. (14): ˇV,T =
ShV,T DV 10.4 × 1.989 × 10−5 = = 0.126 dT 1.641 × 10−3
acc. to Eq. (17):
ˇVhL >0
hL = ˇV,T · 1 − ε = 0.113
6
1.75 × 10−2 = 0.126 1 − 0.952
[m/s]
(3.6) Specific mass transfer area ae acc. to Eq. (6): The experimental data of Billet (Billet, 1979) was evaluated to (nt /H)exp. = 1.95 1/m.
ae = 6
[m/s]
hL 1.75 × 10−2 =6 = 64.0 dT 1.641 × 10−3
m2 /m3
6
42
chemical engineering research and design 9 9 ( 2 0 1 5 ) 28–42
Table 5 – Validity range of presented model. V = 0.066–5 kg/m3 L = 641–1100 kg/m3 L = 13–72.7 mN/m ScL = 45–10,000 ScV = 0.4–1.25 V = 6.6–21.4 × 10−6 kg/(m s) L = 0.2–4 × 10−6 kg/(m s)
d = 0.008–0.090 m a = 54.2–550 m2 /m3 ε = 0.696–0.987 m3 /m3 dS = 0.10–1.4 m dS /d ≥ 6 H = 0.8–4 m
(3.7) Volumetric mass transfer coefficient ˇV ·ae : ˇV ae = 0.113 × 64.0 = 7.23
[1/s]
(4) By inserting obtained (ˇV ·ae )- and (ˇL ·ae )-values into the Eq. (3) we obtain: HTUOV = =
myx uL uV + = ˙ V˙ ˇL ae ˇV ae L/
2.777 0.919 1.61 × 10−3 = 0.384 + 0.9186 × 0.141 + × 7.23 1 1.14 × 10−2 = 0.514 [m]
(5) Therefore the separation efficiency nt /H comes acc. to Eq. (21) to: nt = H
1 HTUOV
= 1.87
×
( + 1) 2
=
1 (0.919 + 1) 0, 514
×
2
[1/m]
Calculation results for the separation efficiency of 50 mm Pall ring, metal √ System: ethylbenzene/styrene, FV = 1.93 Pa, dS = 0.5 m, ˙ V˙ = 1 pT = 133 mbar, L/ acc. to Billet (Billet, 1979): acc. to Author 100% = −4.1%
nt H
nt H
exp
= 1.95 1/m
= 1.87 1/m
⇒
ı
nt H
=
1.87−1.95 1.95
×
References ´ Mackowiak, J., 2010. Fluid Dynamic of Packed Columns. Springer, Heidelberg/New York.
FV /FV,Fl ≤ 0.90–0.95 pT = 0.013–2 bar ReL ∈ 1 − 220 ReV ∈ 400 − 17500
Billet, R., Schultes, M., 1993. Chem. Eng. Technol. 16, 1. ´ Billet, R., Mackowiak, J., 1980. Chem. Technol. (Heidelberg) 9, 219–226. Onda, K., Takeuchi, H., Okumoto, Y., 1968. J. Chem. Eng. 1, 56–62. Bolles, W.L., Fair, J.R., Proceedings of the 3rd International Symposium on Distillation (1979), London,;1; p.3.3/35-89. and Chemical Engineering, 12 (1982) p. 109–116. Zuiderweg, F.J., 1978. vt Verfahrenstechnik 12, 674–677. Zech, J.B., Mersmann, A., 1978. Chem. Eng. Technol. 50 (7) (MS 604/78). ´ Billet, R., Mackowiak, J., 1984. Fette. Seifen. Anstrichmittel 86, 349–358. ´ Mackowiak, J., Paper presented on AICHE-Meeting, Chicago (1990), ´ ´ 16. Nov., partly published in J. Mackowiak, J.F. Mackowiak, Random Packings in: Górak A, Olujic´ Zˇ (Eds.), Distillation: Equipment and Processes, Academic Press (Elsevier), 2014. Billet, R., Schultes, M., 1999. Trans. IChemE. 77, 498–504. Chilton, T.H., Colburn, A.P., 1935. Ind. Eng. Chem. 27 (3), 255–260. ´ Mackowiak, J., 2011. Chem. Eng. Res. Des. 89, 1308–1320. Bornhütter, K., Mersmann, A., 1993. Chem. Eng. Technol. 16, 46–57. Higbie, R.R., 1935. AIChE J., 365–389. Hughmark, G.A., 1967. I&EC Fundam. 6, 408–413. Billet, R., 1979. Distillation Engineering. Chemical Publishing Company, New York (or R. Billet, Industrielle Destillation, Chemie Verlag, Weinheim (1973)). Poling, B.E., Prausnitz, J.M., O’Connell, J.P., 2007. The Properties of Gases and Liquids. McGraw-Hill, Boston. ´ Billet, R., Chromik, R., Mackowiak, J., 1987. Chem. Tech. 16 (5), 79–87. ´ Billet, R., Mackowiak, J., 1988. Chem. Eng. Technol. 11, 213–227. ´ Billet, R., Filip, S., Lugowski, Z., Mackowiak, J., 1983. Fette, Seifen, Anstrichmittel 85, 383–391. ´ Billet, R., Mackowiak, J., 1985. Fette, Seifen, Anstrichmittel 87, 201–205. ´ Billet, R., Koziol, A., Mackowiak, J., Suder, S., 1986. Chem.-Ing.-Tech. 58, 897–900. Zuiderweg, F.J., 1969. Recommended Test Mixtures for Distillation Columns. Institute of Chemical Engineering, London.