Liquid entrainment in tray columns with downcomers

145

Liquid Entrainment with Downcomers Mitreil3en von Fliissigkeit

in Tray Columns

in Bodenkolonnen

mit uberlaufwehren

A. KOZIOE: Institute of Chemical Engineering and Heating Norwida 416, 50-373 Wroclaw (Poland)

Equipment

I-13,

TeChnical University

of Wrociaw,

J. MAcKOWIAK* ENVICON

ENGINEERING,

Baj3feidshof 4-6,

4220 Din&ken

(F.R.G.)

Dedicated to Professor Dr. habil.-Ing. R. Koch on the occasion of his 7&h birth&y

(Received

October

4, 1989; in final form November

24, 1989)

Abstract In this paper a new dimensionless correlation for calculating the liquid entrainment of trays operated in the spray regime is presented. This correlation is generally valid for all types of trays, such as sieve, bubble cup, valve, tunnel, and cross-flow trays, with downcomers. It describes the data from the literature and new data obtained in columns with large diameter by Kozid more exactly than any correlations known so far. Its validity was confirmed on systems with widely differing physical properties. According to the presented analysis of the influence of errors in the determination of liquid entrainment on the calculation errors of tray efficiency, the mean weighted absolute deviation between the calculated and the experimental data is the most important factor. A further aim of this work was the formulation of a new criterion to compare the accuracy of the correlations used in describing the liquid entrainment on a tray. Finally, a numerical example determining the entrainment according to the new correlation is presented.

Kurzfassung Im Beitrag wird eine neue dimensionslose Korrelation zur Bestimmung des MitreiBens in Bodenkolonnen im Spriihbereich vorgestellt, welche fiir Siebbiiden, Glockenboden, Ventilboden, Tunnelboden und Kreuzstrombiiden mit ffberlaufwehren giiltig ist. Mit dem neuen Ansatz werden die MeBergebnisse aus der Literatur sowie die neuen Daten von Koziol genauer wiedergegeben als es bis jetzt mit den bekannten Korrelationen der Fall war. Die neue Korrelation ist in den weiten Bereichen der variierten Stoffwerte anwendbar. Desweiteren wird ein neues Kriterium fur den Vergleich verschiedener Ansiitze zur Bestimmung des MitreiDens in Bodenkolonnen angegeben. Aufgrund der durchgefiihrten Analyse zum EinfluB des Fehlers bei der Bestimmung der von Gas mitgerissenen Fhissigkeitsmenge auf den Fehler bei der Ermittlung des Punktverstarkungsverhaltnisses wurde festgestellt, da8 die gewichtete, mittlere, absolute Abweichung zwischen den berechneten Daten und den experimentellen Daten einen wichtigen Faktor fur die Bewertung von den einzelnen Korrelationen zum MitreiBen darstellt. AnschlieDend wird an einem Zahlenbeispiel der Rechengang bei der Bestimmung des MitreiDfaktors eL mit dem neuen Ansatz vorgestellt.

Wnopse Im vorliegenden Beitrag wird aufgrund experimenteller Untersuchungen von Koziol [8] sowie von *Author to whom correspondence should be addressed. 0255.2701/90/$3.50

Chem.

Eng. Process.,

27(1990)

Literaturdaten [5, 9- 121 eine neue dimensionslose Korrelation zur Bestimmung des Mitre@ens in Bodenkolonnen unterschiedlicher Bauart vorgestellt. Der Schwerpunkt der Ausftihrungen betr@ a’en Betriebsbereich ‘Spriih-Regime’, welcher ftir den Kolonnenbetrieb unter Vakuum und im Normaldruckbereich von Bedeutung ist. 145-153

0

Elsevier Sequoia/Printed in The Netherlands

146 (1) In der Einleitung werden zuniichst die wichtigsten Arbeiten zur genannten Problematik kurz vorgestellt. In Tabelle I sind niihere Angaben zu den Gtiltigkeitsgrenzen der vorgestellten Korrelationen aus der Literatur gemacht. Fur die weiteren Ausfiihrungen sind die Arbeiten von Stichlmair [4] sowie Kister und Haas [5] von Bedeutung, deshalb wird ihnen mehr Platz eingertiumt. (2) Unter Punkt 2 wird der EinfluJ des Fehlers bei der Bestimmung des Mitretyfaktors eL auf den Fehler bei der Bestimmung des Punktverstiirkungsverhaltnisses E, analysiert. Die Basis fir eine derartige Analyse liefert die Gl. (3)-(5) in Verbindung mit der Beziehung (6) [6], die die Bestimmung des Punktverstarkungsverhiiltnisses E, eines Bodens in Anwesenheit von Mitretpen ermiiglicht. Durch die Dtflerentiation der Gl. (6) erhiilt man dann die Beziehung (9) wonach der relative Fehler bei der Bestimmung der Bodentrennwirkung E, proportional dem absoluten Fehler des Mitreipkoefizienten Ae, und dem Wert der Gewichtungsfunktion W(eL, E) ist. Aus dem in Bild I gezeigten Diagramm geht hervor, daJ der Wert der Funktion W(eL, E) fur eL = 0,. . . , I immer kleiner als I ist. Daraus folgt die Ungleichheit (14). Mit Hilfe der Gl. (IS) kann anschliepend der absolute, gewichtete Fehler der Bestimmung des Mitretpfaktors de, ermittelt werden, der die Genauigkeit der Bestimmung der Bodentrennwirkung wesentlich beeinflu$It (s. GI. (9)) und somit als Kriterium der Giite verschiedener Korrelationen bei der Bestimmung des Mitretpens verwendet werden SON. (3) Unter Punkt 3Jindet man nahere Angaben zu dem Versuchsprogramm und zum Umfang der neuen Versuche von Koziol [8]. Die Versuchsanlage mit einem Durchmesser von 0,38m bis 1 m ist schematisch in Bild 2 gezeigt. Anschlieflend werden die Arbeiten genannt, aus welchen die 767 Me@kzten zur Erstellung der neuen Korrelation entnommen wurden. (4) Die Gegentibersteilung der Ergebnisse der Auswertung von MeJIdaten mit Hilfe von Ansdtzen aus der Literatur ist zahlenmd$ig in der Tabelle 2gezeigt. (5) Die Herleitung des neuen Ansatzes zur Bestimmung des Mitretpens wird unter Punkt 5 vorgestellt. Aufgrund der theoretischen Betrachtungen von Stichlmair [4]iiber das Mitretpen am Boden im Spriihbereich und aufgrund der Aussagen von Kister und Haas [5] sowie Fair [14] und Kozioi [8] erwies es sich als zweckm@ig, das MitretJIen mit Hilfe von fiinf dimensionslosen Kennzahlen: We, Co, Fro, Fr,, FI, nach GI. (26) zu beschreiben. Die Auswertung von 767 MeJdaten verschiedener Autoren [5, 8-121 mittels eines PC-Rechners fuhrte zur Ermittlung der Konstante C und der Exponenten n,, n2, n,, n4, fiir GI. (27). Ein Vergleich der Abweichungen der MeJwerte von der Rechnung nach Gl. (28) ergab, da8 mit den neuen Korrelationen nach Gl. (28) die MeJdaten genauer wiedergegeben wet&n konnen als es mit a’en anderen bekannten Ansiitzen miiglich ist, s. hierzu Tabelle 2. Die Gegeniiberstellung der gerechneten eL- Werte mit den experimentellen eL, exp- Werten zeigt Bild 4. In der Tabelle 3 sind fiir die verschiedenen unter-

suchten Bodentypen die konstruktiven Gr@?en eingetragen, die zur zahlenm$%gen Bestimmung der einzelnen Kennzahlen in Gl. (28) erforderlich sind. Aus der Tabelle 4 sind ferner die stoflichen und die konstruktiven Parameter der einzelnen Bodentypen ersichtlich, fur welche die MeJdaten zur Erstellung von Gl. (28) vorlagen. (6) Zahlenbeispiel: AnschlieJend wird an einem Zahlenbeispiel die Bestimmung des Mitretpens an einer Siebbodenkolonne bei der Rekttjikation des Gemisches EthylbenzollStyrol bei 133 mbar gezeigt.

1. Introduction A new method to calculate the efficiency of tray columns with downcomers taking into account the influence of liquid entrainment and weeping has been presented recently by Koziol [ 1, 21. The formulae obtained may be applied if the entrainment coefficient eL defined by eL = LJL

(1)

is known. According to the literature, to calculate the amount of entrained liquid L, a large number of different equations and correlations may be used. An exhaustive review of this topic was published by Lockett [ 31, in which the most important correlations are given. The largest analysis of liquid entrainment behaviour was carried out by Stichlmair [4]. Stichlmair assumed that liquid entrainment depends on the hydrodynamic regime on the plate. Based on the analysis and on the experimental results from the literature, he worked out a graph for liquid entrainment valid for small holes of diameter d,, c 0.010 m. The graph gives a dependence

1 where Fa, max L “=f G

F,

[ F,,max’

(H--h,)

Apg

(Fa,max)’

(2)

denotes the maximum value of the F-factor at which the liquid layer disintegrates on the tray. Stichlmair’s graph for the dependence of LJG on F, IF,, max for three operating regimes shows that liquid entrainment is highest in the spray regime for F, IF,, max> 0.65, and for values of the ratio LJG higher than 2 x 10w4. On the other hand, the effect of liquid entrainment on the tray efficiency is noticeable for high values of the ratio L,/G. Thus, an exact description of liquid entrainment in the spray range is very important. However, Stichlmair shows that at values of d,, > 0.010 m the deviation of his correlation from experimental results in the spray regime is large. Kister and Haas [S] give an analytical correlation for liquid entrainment valid only for the spray regime. These authors based their correlation on their own experimental investigations carried out with the system air/water and on FRI data given by Sakata and Yanagi [6]. The correlation is useful because the physical properties of the gas and liquid

147 are taken into account. Although the final form of the correlation is dimensionless the main exponent in this correlation is dimensional. Moreover, a few parameters in the correlation are determined with the aid of empirical dimensional formulae valid in limited ranges only. Zuiderweg [7] published his own correlation, also valid in the spray regime, which was also based on the FRI data [6]. The Zuiderweg formula does not take into account the physical properties of the gas and liquid. The main aim of this work is to develop a new method to predict the liquid entrainment in the spray regime for trays of various types. An accurate prediction of the entrainment coefficient e,_ is an important factor in calculating the tray efficiency. Thus, a criterion which can be used to evaluate the influence of the entrainment on the tray efficiency may be formulated. Such a criterion can also be used to compare different methods of liquid entrainment determination.

The mass transfer efficiency on a plate can be calculated if the extent of liquid entrainment is known. An error is connected with each determination method, which in turn is a source of a given error in efficiency calculations. A determination of the mutual relation between these errors would enable a criterion to be formulated by which a suitable method of entrainment determination may be chosen. Such a criterion could be a quantity proportional to the relative error of the corrected efficiency of the tray, 6E,. Let us assume that by applying a given method of liquid entrainment determination the value of the entrainment coefficient 5, is obtained. This value is determined with an absolute error Ae, according to Ae, = &_ - er

(3)

cowhere er is the true value of the entrainment efficient. As a result of application of the & value in formulae determining the tray efficiency, a value Ea(&) is obtained which is determined by the absolute error AE, according to

6E, = AEJE,

1)(2+e,)]

F=l+eL

F[ ““P(&)-‘1

(7)

(8) where E: is the derivative of function E,(e,). Determining this derivative from formulae (6) and (7) and taking into account estimation (8) we obtain PE, I = f+‘(eL 3E) Ibe, I

(9)

where We,,

E) =

B’b + 2B - ( 1 + 2e,)/b Bb -eL

1

(11)

expb-1

B2 E E

B’=-[l-(1-b)expb]

(12)

b=-

(13)

1 +e,

According to eqn. (9) the relative error of the calculated value of Ea is proportional to the absolute error of the entrainment coefficient Ae, and to the value of the function W(eL, E) which can be called the ‘weighted function’. The graph of the function for eL in the range O-l is shown in Fig. 1. The dependence of the function W on the point of efficiency E is very slight and therefore it has been assumed in the following calculations that E = 1. Moreover, the graph in Fig. 1 shows that values of W(e,, E) are always less than unity. Therefore, we can write laE,I < I&l

(14)

This inequality proves that the use of the relative error of eL as a criterion in the determination of a suitable correlation for eL is incorrect. For small values of eL, values of IAe,] are also small and in turn values of 16E,I are equally small. On the contrary, the relative error 6eL in such a case can even

to

(3

Now let us try to estimate the 6E, value assuming that Ae, is known for the case of no liquid weeping and no liquid mixing for a value of the stripping factor 1 = 1. Under these assumptions, based on the model described by Koziol [ 11, the following equation can be obtained:

(6)

For small AE, and Ae, values these quantities can be approximated using the corresponding differentials dE, and de,. Therefore ,

(4)

A& = Ea(2~)- 4(eL) and by the relative error 6E, according

1 +e,[EF-(F-

where

B=

2. Influence of errors in liquid entrainment determination on errors connected with tray efficiency calculations

EF

E, =

Fig. 1. Graph of function W(e,,

E)

148 be very high. The correct criterion is the so-called ‘mean weighted error’ G defined by _ Ae,

t

We,, i, 1) I(ei_,&I= - (et+ i)exp)

=i=’

(15)

Definition ( 15) can be used to compare different literature correlations for liquid entrainment. For such comparisons a large set of experimental data was created. 3. Experiments

8

considered

t

In the experiments presented by Koziol [8] an air/water system under normal conditions was used. A schema of the experimental apparatus is shown in Fig. 2. The characteristics of the trays investigated are given in Table 1. During the investigations, the value of the F-factor based on the active area of the tray, Fa, was varied in the range l-3.5 Pa’/*. The liquid flow rate in relation to the length of the weir was varied between 1 and 14 m3 m-i h-‘. In the experiments the classical method was used, depending on the measurement of the filling time of a sealed vessel with entrained liquid. The entrainment liquid was recirculated to the column. More details of the experiments may be found in ref. 8. As a result, 441 experimental data points were obtained, constituting the first main part of the data set. The second part was formed from literature data. The first 68 points are results from the investigations published by Friend et al. [9] and Lemieux and Scotti [IO]. In these experiments the liquid entrainment on sieve plates comprising a wide range of design variables and tray spacing between 0.15 and 0.45 m was investigated. The next part of the created set consists of the

TABLE

I

10

9 I

I

Fig 2. Schema of the experimental apparatus [8]: 1, column; 2, bottom plate investigated; 3, top plate investigated; 4, plate scparating entrained liquid; 5, cyclone separating rest of entrained liquid; 6, measurement point of liquid entrainment; 7, inlet of liquid into column; 8, liquid outlet from column; 9, liquid tank; 10, gas inlet into column; 11, gas outlet from column.

experimental data published by Puppich and Goedecke [ 1 I, 121. The data (82 points) refer to different types of trays: sieve, bubble cap, tunnel and cross-flow. Finally, the last set of 176 points was calculated from the Kister and Haas correlation [5] which describes the FRI data obtained by Sakata and Yanagi [ 61 on a pilot-plant scale. In these experiments a column of diameter 1.2 m and various distillation systems were used. The physical properties of the gas and the liquid were also changed over a wide range.

1. Characteristics of the sieve trays investigated by Koziol [8]

Parameter

Column diameter, d, (m) Fraction of hole area per unit active area, q (%) Hole diameter, d,, x IO3 (m) Tray spacing, H (m) Weir height, h, x lo3 (m) Weir length, I, x 10’ (In) Number of experimental points, n

Tray number 1

2

3

4

5

6

I

8

9

0.38

0.38

0.38

0.38

0.38

0.38

1.0

1.0

1.0

2.70

1.55

31.56

3.03

12.50

34.3

9.8

14.1

19.3

6

6

6

6

6

6

6

15

15

0.4

0.4

0.4

0.4

0.4

0.4

0.6

0.6

0.6

60

20-80

60

60

20-80

60

40

40-80

40

275

275

275

283

284

283

730

730

730

8

68

11

7

114

14

87

94

38

149

4. Comparative calculations The set of n = 767 points was used as a basis for comparative calculations applying different known correlations. For these calculations the five most often applied major correlations were due to Hunt et al. [ 131, Fair [ 141, Stichlmair [4], Zuiderweg [7], and Kister and Haas [S]. For all calculations, an Amstrad CPC 6128 microcomputer was used. In the case of graphical correlations the corresponding diagrams were approximated using analytical formulae. For each point the er,_, value was calculated and thereafter the de, value of the whole set using eqn. (15). The number of points for which the absolute error Ae, exceeded 0.05, 0.1 and 0.15 was also determined. The results obtained are given in Table 2. From an analysis of the results it is evident that relatively good agreement with the experimental data is obtained by the simple correlation of Hunt et al. [ 131 and the recently published correlation of Kister and Haas [ 51. The agreement for the other correlations is rather poor. In the case of the Stichlmair correlation this is due to the fact that in the droplet region where entrainment is high the graphic correlation leads to

TABLE

approximate values because an exact approximation of Stichlmair’s diagram is difficult to achieve in this region. 5. Development of our own correlation The mechanism of liquid entrainment was analysed exactly by Stichlmair [4]. According to his considerations the liquid entrainment mainly depends on the ratio I;,/F,,,,, (see eqn. (2)). A theoretical formula for F,, lllpx derived by Stichlmair refers to the case when the tray spacing H is large (H > 0.9 m). In practical cases, values of H are lower. Taking into account this fact, Koziol [ 151 suggested that the value of F,,,,, should be dependent on the construction parameters of the tray and introduced a dimensionless construction number Co for the tray such that cpH d, ‘I2 (16) dS 0 d, The dimensionless number Co groups the construction parameters of the tray having an influence on

PH

=-

Co = (d, d,,)“2

2. Comparison of correlations for liquid entrainment Mean weighted error G x 100%

References and formulae

Hunt et al. [Ill

3.2

Fair [ 121 Graphic correlation Stichlmair [ 131 Graphic correlation

Number of points such that ]Aee,Jis: >o.os

>O.l

>0.15

Tray type and operating regime

2.95

138

66

43

Sieve Indefinite

7.05

139

78

47

Sieve Indefinite

187

127

100

14.9

Sieve, valve, bubble cap Bubble froth, spray

Zuiderweg [ 141 15.7

308

216

158

Sieve Spray

103

55

36

Sieve

Kister and Haas [9] ? = 4.742n’.m,

x0

where a=(lOfr)“Z x = f(u,, uL>rp, H, 4, h,, I,,

4.44 PL, PG.

Koziol and MaEkowiak; this work Equation (28) in text

Srw

4

1.84

72

28

13

Sieve, valve, bubble cap, tunnel Spray, froth

VALVE

TRAY

the effect of tray spacing H on the liquid entrainment. However, exact determination of this parameter in the spray regime is very difficult, because of inaccuracies in the determination of the height of the gas-liquid layer, hb. It is appropriate to introduce another dimensionless number which depends on the tray spacing H but is easier to determine. Such a number is the so-called e‘ xtended Froude number’ Fr,, defined by

V-l

(22)

BUBBLE

CAP

Fig. 3. Meaning

The Froude number defined by eqn. (22) is based on the gas velocity in the holes. This parameter influences the initial velocity of the liquid droplets and thereafter the liquid entrainment. The liquid entrainment also depends on other parameters. According to Porter and Jenkins [ 171 liquid entrainment increases with decreasing liquid load in the spray regime. The same effect was also noticed by Koziol [8] and Fair [ 181. The liquid load may be taken into account with the aid of the dimensionless Froude number for the liquid phase,

TRAY

of parameter

d,, for different

types of tray.

the liquid entrainment. The hole diameter d,, in the definition is the most important parameter which characterizes the type of tray. The correct value of the parameter d,, for the trays investigated should be used according to Fig. 3. By introducing the Co number into the formula for F,. maxa simple formula which is a generalization of Stichlmair’s dependence has been obtained [ 151:

E,

Inax

=

Co"'(a

Ap g) “4

(17)

According to Stichlmair’s analysis, liquid entrainment depends strongly on the diameter of the liquid droplet distribution. Both gas velocity and droplet diameter can be taken into account by introducing the dimensionless Weber number, defined by

(18) If, following Mackowiak [ 161, we assume that the diameter of a liquid droplet, dp, can be expressed by 112 (19) we obtain the formula for the Weber number: Fa2 (20) (0 Ap 9)“’ Taking into account definition (16) and formulae ( 17) and (20), we can express the ratio F,/F,, max as follows:

We=

(21) The second parameter Stichlmair’s analysis is (H - hs) AP g/V,,

taken

into

account

in

Fr,=d

4g

where, following ref. 8, w _Ul+e,)

(24)

LHd,

The parameter wL determined by formula (24) is a liquid velocity based on the longitudinal cross-sectional area of the tray space. This parameter is proportional to the horizontal component of the droplet velocity on the tray. The expression (1 + eL) in formula (29) takes into account the fact that the real amount of liquid on the tray increases because of the return of the entrainment liquid into the column [ 81. The next important parameter influencing liquid entrainment is the droplet terminal velocity [4]. Droplets having higher terminal velocity are less entrained than droplets having lower terminal velocity. According to the analysis of Mersmann [ 191 and Mersmann et al. [20] the terminal velocity of liquid droplets depends on the physical properties of the gas and liquid grouped in the dimensionless fluid number Fl defined by C’PG2 Fl z ___ vlo4

AP

g

(25)

The effect of the surface tension, gas density, and gas viscosity on the liquid entrainment was confirmed empirically by Kister et al. [21]. Taking into account the above-mentioned considerations it can be assumed that the entrainment ratio LJG in the spray regime depends on five dimensionless numbers:

mJ2

According to Stichlmair this term takes into account

In the next step it was assumed that function (26)

151 has the form

TABLE 3. Ranges correlation (28)

of validity

for the parameters

changed

in

(27) Values of the coefficients C, n,, n,, n3, and n4 were obtained with the aid of a computer program which minimized the mean value of the weighted error, &, for the 767 experimental points of the data set described in $3. The final form of the evaluated correlation is given by L

-Z = 0.37 Fr,2~3Fr,-‘/~Fl-‘/3 G where n4 = 133.7 Fl-‘lb

(29)

The comparison between the experimental data of various authors [5,8- 121 and the calculations according to eqns. (28) and (29) is presented in Fig. 4. The results of the calculation according to the new formula (28) for the data set are listed in Table 2. The value of 1.84% obtained for the mean weighted error G calculated according to formula (28) compared with the corresponding values for different correlations is the lowest. Taking into account the inequality (14) we can write the following inequality valid for correlation (28) : aE, x 100% < 1.84% This inequality states that the relative error in the calculation of the corrected efficiency E, using formula (6) and correlation (28) must not be higher than 1.84%. It has to be added that this concerns only the error caused by inaccuracies in the determination of the magnitude of the liquid entrainment.

L

/

,./

/I

Parameter

Range

Column diameter, 4 (m) Fraction of hole area in active area, rp (%) Hole diameter, dh x lo3 (m) Tray spacing, H (m) Weir height, h,., x 10’ (m) Gas load coefficient based on active plate area, F, (PalIz) Liquid flow over weir length (m’ m- ’ h-‘) Gas density, pG (kg rnp3) Liquid density, pL (kg m-‘) Surface tension, cr (N m-‘) Liquid viscosity, qL x 10’ (Pa s) Gas viscosity, qG x IO6 (Pa s)

0.38- 1.2 2.7-34.3 6-15 0.15-0.6 O-80

Correlation (28) is valid for the range of parameters given in Table 3.

6. Conclusions (1) In the case of liquid entrainment, application of the relative error as a measure of the deviation of calculated data from experimental data is incorrect. The mean weighted error defined by formula ( 14) is a correct measure of the deviation. (2) The investigations performed revealed no significant influence of weir height on the magnitude of liquid entrainment in tray columns with downcomers. (3) A correlation, eqn. (28), was obtained, enabling the amount of entrained liquid to be calculated for a wide range of design and process parameters as well as physical properties of the gas and liquid phases. This correlation describes the experimental and literature data much better than other literature correlations (see Table 2). Formula (28) can be applied for sieve, valve, bubble cap, and tunnel trays with downcomers. (4) Correlation (28), generally valid for the spray regime, may be used in practice in the froth regime where absolute values of the entrainment coefficient eL are lower. (5) Correlation (28) considers the real liquid velocity on the plate, therefore, to apply it, an iterative method has to be used, as shown in the example.

7. Numerical

0

4

8

7.2

16

20

Fig. 4. Graphical comparison of evaluated entrainment data eL, _, from eqns. (28) and (29) with the experimental data eL, exp for eL in the range O-20%: +, Koziol (4 = 1 m) [S]; x, Koziol (d, = 0.38 m) [8]; A, Friend er al. [9] and Lemieux and Scotti [IO]; m, Kister and Haas [ 51; 0, Puppich and Goedecke [ 1 I, 121.

I-3.5 l-14 0.4-4.8 640-1000 0.0135-0.0724 0.24- 1 6.9- 18.2

example

The value of the liquid entrainment coefficient e,_ in the top part of a distillation column with sieve trays for the system ethylbenzene/styrene at a pressure of 13.3 kPa is to be calculated. Gas-phase Liquid

flow rate = 2180 kg h- ’

phase flow rate = 2000 kg h

1

152 Construction

parameters:

for

cp = 0.1375,

H = 0.5 m,

d, = 0.8 m,

dh = 0.0125 m

A, = 0.4347 m*

Fr,,,

= 4.15 x IO-‘,

eL, 2 = 0.078

The final value of the entrainment e,_ = 0.078.

coefficient

is

Gas and liquid properties: pL = 829.6 kg rnm3,

pG = 0.485 kg m-3

qc = 7.6 x 1O-6 Pas,

0 = 0.0217 N m-’

Solution = 0.6697 x 10e3 m3 s-l 3600 x 829.6 2180 G=mG= = 1.2486 m3 s- ’ 3600 x 0.485 PG G 1.2486 I; = 0.6697 x IO-3 = 1864.4 1.2846

G

-

Ma= A, = 0.4347

=

= 2 Pa”*

2

= 14.545 Pa’/’ cp 0.1375 Ap =p,-pp,=829.6-0.485=829.1

kgmm3

(14.545)2 = 0.052 0.5 x 829.1 x 9.81 22 We = (0.0217 x 829.1 x 9.81)“* = o’301 0.1375 x 0.5 Co = (0.8 X O-0125) ‘/2= o’6875 Fr, =

Fl =

eqn. (22) eqn. (20) eqn. (16)

(0.0217)3(0.485)2 (7.6 x 10-6)4 x 829.1 x 9.81

= 8.858 x 10”

eqn. (25)

n, = 133.7 x (8.858 x 10’“)-“6 L eL=L=zz

= 2.00

eqn. (29)

L G x 1010) -l/3

= 0.37 x (0.052)2’3(8.858

x 1864.4 Fr,-O.* = 4.132 x low3 Fr L -‘.*

eqn. (28)

For the next calculations we must use the iterative method. For eL = 0 we obtain: W L, 0 =

0.6697 x 1O-3 0.8 x 0.5

= 1.674 x lop3 m s- I

FrL.o =

(1.674 x 10-3)2= 0.8 x 9.81

eL,o = 4.132 x lo-’

eqn. (24) 3

57

x

1o-7

’

eqn. (23)

x (3.57 x lO-7)-o.2 = 0.08047

The results of the successive calculations according to eqns. (24), (23) and (28) are the following: for

Fr,. , = 4.17 x lo-‘,

active area of tray, m* hole area, m* a parameter in Kister and Haas correlation B, B’, b parameters defined by eqns. (1 l), (12), and (13) C constant in eqn. (27) co construction number hole diameter, m 4 droplet diameter, m column/ diameter, m point efficiency of tray from Kozid [I] corrected Murphree efficiency of tray 4 = L,/L, liquid entrainment coefficient et_ F parameter defined by eqn. (7) “* 2 form factor based on active F, =%PG area, Pa’/* “* 9 form factor based on hole 6, =UhPG area, Pa’/* Fl fluid number Fr Froude number G gas volumetric flow rate, m3 s-’ molar gas mass velocity, kmol s-’ Ghl gravitational acceleration, m s-* g tray spacing, m h” height of gas-liquid bed on tray, m weir height, m h: L liquid volumetric flow rate, m3 s-’ liquid volumetric flow rate of entrained L, liquid, m3 s-l molar liquid mass velocity, kmol s- ’ LM weir length, m kv m slope of equilibrium line ti mass flow rate, kg s- ’ n number of experimental points, eqn. ( 15) . , n4 exponents in eqn. (27) n,,. gas velocity based on active area of tray, Kl ms-’ gas velocity based on hole area, m SS’ uh liquid velocity based on active area of UL tray, m s-’ weighted function Wet,, E) We Weber number liquid velocity defined by eqn. (24) WL

A, Ah

2

E”

2.8723 m s-’

i;, = I(, p,‘/* = 2.8723 x (0.485)“* F,,F”,

Nomenclature

e,+, = 0.078

denotes absolute error denotes relative error viscosity, Pa s = mGM/LM, stripping factor parameter in Kister and Haas correlation density, kg rnp3 difference of densities, =PL --Gr kg m-’

153 surface

tension, N m ~ ’ fraction of hole area in active area of tray

= Ah/A,,

Indices

cal exp e G L max

calculated value experimental value entrained liquid gas phase liquid phase maximum value parameter determined mean value derivative

I

with some error

References I A. Koziol, Generalization of AIChE and Colburn models for tray efficiency, Chem. Eng. Technol.. I2 (1989) 333 339. 2 A. Kozioi, Effect of simultaneous liquid weeping and entrainment on tray column efficiency (in Polish), Ini. Chem. Proces., 9 (1988) 3633383. 3 M. J. Lockett, Distillation Troy Fundamentals, Cambridge Univ. Press, 1986. 4 J. Stichlmair, Grundlagen der Dimensionierung des Gas/Fliissigkeir-Kontaktapparares Bodenkolonne, Verlag Chemie, Weinheim, 1978. 5 H. Z. Kister and J. R. Haas, Sieve tray entrainment prediction in the spray regime, Inst. Chem. Eng. Symp. Ser. No. 104, (1987) A483-494. 6 M. Sakata and T. Yanagi, Performance of a commercial scale sieve tray, Inst. Chem. Eng. Symp. Ser. No. 56, (1979) 3.2/213.2134.

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