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14 Examples for the design of packed columns The relationships discussed in the previous chapters are important for the design and operation of countercurrent packed columns. Examples taken from the fields of desorption, absorption, rectification, and liquid-liquid extraction shall now be given to demonstrate how they can be applied in plant engineering. It is presumed that the reader is acquainted with the principles underlying thermal separation techniques. Fig. 14.1 shows a flow chart for a rectification column with a concentration x of low boil- ers in the feed F, overhead product D, and bottoms B. These fractions are presented quali- tatively in the ylx diagram. The example concerned is the separation of a binary mixture; the equilibrium curve y e = f(x) and the operating lines y = f (JC), viz. BI in the stripping zone and ID in the enrichment zone, are given. Rectification Fig. 14.1. Qualitative determination of transfer units in rectification Reboiler B = F-D h F = feed enthalpy hp = feed enthalpy at boiling temperature Ah v =vaporization enthalpy at feed section Packed Towers in Processing and Environmental Technology. Reinhard Billet Copyright © 1995 VCH Verlagsgesellschaft mbH, Weinheim ISBN: 3-527-28616-0 SOFTbank E-Book Center Tehran, Phone: 66403879,66493070 For Educational Use.

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Page 1: Examples for the Design of Packed Columns - ssu.ac.irssu.ac.ir/cms/fileadmin/user_upload/Daneshkadaha/dbehdasht/markaz... · 338 14 Examples for the design of packed columns Fig

14 Examples for the design of packed columns

The relationships discussed in the previous chapters are important for the design andoperation of countercurrent packed columns. Examples taken from the fields of desorption,absorption, rectification, and liquid-liquid extraction shall now be given to demonstrate howthey can be applied in plant engineering. It is presumed that the reader is acquainted withthe principles underlying thermal separation techniques.

Fig. 14.1 shows a flow chart for a rectification column with a concentration x of low boil-ers in the feed F, overhead product D, and bottoms B. These fractions are presented quali-tatively in the ylx diagram. The example concerned is the separation of a binary mixture;the equilibrium curve ye = f(x) and the operating lines y = f (JC), viz. BI in the strippingzone and ID in the enrichment zone, are given.

Rectification

Fig. 14.1. Qualitative determination oftransfer units in rectification

Reboiler

B = F-D

hF = feed enthalpyhp = feed enthalpy at boiling temperature

Ahv=vaporization enthalpy at feed section

Packed Towers in Processing and Environmental Technology. Reinhard BilletCopyright © 1995 VCH Verlagsgesellschaft mbH, WeinheimISBN: 3-527-28616-0

SOFTbank E-Book Center Tehran, Phone: 66403879,66493070 For Educational Use.

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338 14 Examples for the design of packed columns

Fig. 14.2 illustrates the principles of absorption and desorption. The factors given are thegas volumetric flow rate V, the concentration of transfer components y in the gas, the liquidvolumetric flow rate L, and the concentration of transfer components x in the liquid. Thesubscript u indicates the bottom of the column; and the subscript o, the head of the column.

The gas load Y of transfer component is related to the mole fraction y by

Likewise, the liquid load X of transfer component is related to the mole fraction x by

X = T^ <14-2>

The number of transfer units NTUOv required for rectification between zones with molarfractions ya and yb is given by

NTUov = /a~y" In 4 ^ (14"3)Aya - Ayb Ayb

The terms Aya and Ayb in this equation represent the difference between the equilibriummole fraction ye>a or ye>b and the vapour mole fraction ya or yb, i.e.

&ya = ye,a - ya (14-4)

An = ye,b-yb (14-5)

The size of the zones should be selected so that the slope myx of the equilibrium curve ispractically the same in each.

In contrast, the slopes of the equilibrium curves in absorption and desorption processescan be regarded as constant over the entire range of concentrations between the head andthe foot of the column, particularly at low phase loads. In this case, if the gas load isadopted as a measure for the concentration, the number of transfer units in absorption pro-cesses will be given by

where Yu and Yo are the gas loads at the foot and head of the column. The terms AYU andAYO are then defined by

AYu = Yu-mYXXu (14-7)

AYo = Yo-mYXXo (14-8)

The corresponding equations for the liquid load are

NTUOL= f-f I n - ^ (14-9)AXU - AXn AXn

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14 Examples for the design of packed columns 339

A X M _ 1 Y x

mYX

AX0 = —Yo-XomYX

(14-10)

(14-11)

Likewise, the number of transfer units required in desorption processes will be given byEqns (14-12) to (14-14) if the gas load is adopted as the measure for the concentration:

Y -Y° u

AY° (14-12)

Absorption Desorption

ye-

x,y Mole fraction in liquid, gas or vapourmyx Slope of the equilibrium lineL/V Molar liquid-to-gas ratio or slope of

the operating lineX,Y Load fraction of transfer component in liquid /gasL,V Carrier stream of liquid /gas phase

r777'L _ Y0-Yu

V A n — A iiY Q = ' U + *W~

Fig. 14.2. Qualitative determination of transfer units in absorption and desorption

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340 14 Examples for the design of packed columns

Yo = mYXXo-Y0 (14-13)

Yu = mYXXu-Yu (14-14)

The corresponding equations for the liquid phase are

= xu

1

mYX

1

mYX

Yo

Yu

(14-16)

(14-17)

In a rectification process, as illustrated in Fig. 14.1, the reflux ratio is given by

r > r-*n = TTTT (14-18)

The molar flow rate at the head of the column would then be

V= F XF~XB (r + 1) (14-19)XD ~ %B

In an absorption process, as illustrated in Fig. 14.2 (left), the total liquid-vapour ratiomust be higher than the ratio of the carrier liquid, i.e. solvent, to the vapour, i.e.

Y > T" (14"2°)

The flow rate of solvent in this case is given by

Lm = V lu~*° (14-21)

In desorption, as illustrated in Fig. 14.2 (right), the total vapour/liquid ratio must behigher than the ratio of the stripping gas to the liquid, i.e.

V V

The flow rate of stripping gas in this case is given by

Vm = L ^ ^ - (14-23)x o,m x u

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14 Examples for the design of packed columns 341

In absorption and desorption, the total molar flow rate of vapour, consisting of the carriergas and the transfer components, is given by

V =V(\ + Y) where V = Vu (1 - yu) (14-24)

and the total molar flow rate of liquid, consisting of the carrier liquid and the transfer com-ponents, by

L = L(l+X) where L = Lo(1 -xo) (14-25)

The column diameter ds can be expressed in terms of the free cross-sectional area As, i. e.

ds = \ —As (14-26)y JI

If uv is the superficial gas velocity, As can be defined by

As = ^ ^ (14-27)Uy Qy

Thus the column diameter can be calculated from the operating parameters V [kmol/h],uv [m/s], T [K], and p [bar], i. e.

ds = 5.4 • 1(T3 \l V — — (14-28)17 p Uy

Fig. 14.3 illustrates liquid-liquid extraction in which the specific gravity of the continuousphase (Subscript C) is greater than that of the dispersed phase (Subscript D). In this case,the total number of transfer units NTUOc derived from the HTU-NTU model is given by

NTUoc = Cc'°~Cc'u In ̂ (14-29)Aco - Acu Acu

where Aco is the driving concentration difference at the head of the column, as defined byEqn (14-30), and Acu is the driving concentration difference at the foot of the column, asdefined by Eqn (14-31), i. e.

Aco = cc,o - ~ - cDtO (14-30)

AcM = cc,u - — cD>u (14-31)

Another case to consider is that in which mass transfer is in the C —> D direction and thedesired separation efficiency is given by

^E = 1-££JL (14-32)

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342 14 Examples for the design of packed columns

h CQ.O

CCo

Fig. 14.3. Qualitative determination of transfer units in liquid-liquid extraction

Rearranging this equation gives rise to the following:

CC,u = (1 - (14-33)

from which it can be derived that the concentration of transfer components in the continuousphase decreases from cc>o at the head of the column to cc>u at the foot.

If the phase ratio in the extractor is uc/uD, the concentration of transfer components inthe dispersed phase increases from a value of cD>u at the foot of the column to the followingvalue of cDo at the head of the column:

cD,o — (cC,o ~UD

cD,u (14-34)

Eqn (13-22) allows the effective height H to be determined from NTUOc and HTUOc\and, if the volume flow rate Vc of the continuous phase is given, the column diameter ds canbe obtained from the load uc < 0.7 uc, FI from the following equation:

(14-35)

14.1 Determination of the diameter of an off-gas absorption column withvarious types of packing

Polluted air flowing at a rate of 105 m3/h STP is to be scrubbed with water in a packedcolumn. The liquid-to-gas ratio must be varied between LIV = 1 and L/V = 10, dependingon the degree of contamination. The maximum permissible load is that at the loading point.

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14.1 Determination of the diameter of an off-gas absorption column with various types of packing 343

Under these conditions, what diameter would the column have to be if 50-mm packing ofthe following types had to be installed?Plastics packing: Intalox saddles, Bialecki rings, Pall rings, and Norpac ringsMetal packing: Pall rings, Hiflow rings, Bialecki rings, and VSP rings

Solution

Properties of the system

Density and dynamic viscosity of the gas

QV= 1.19 kg/m3

TJV = 18 • 10~6 kg/msDensity and dynamic viscosity of liquid

QL = 998 kg/m3

TU = 1 • 10"3 kg/ms

The values of Cs required to calculate the resistance coefficients §5 at the loading pointfrom Eqn (4-29) are listed in Table 4.1.

Gas, air 100000 m3/h, Liquid: water, STP, loading capacity

TD

5.4

5.2

5.0

4.8

4.6

4.4

4.2

4.0

3.8

//

/fI1

ijI!1

1

/- Bic

fA

/

j

/

- I N

ilec

/

/

TALOX 5

<i ring

;adc

/

le

y

A-Pall ring

/

/

Packing size 50 mm

-NOR-PAC ring

- Plast IC

•y

1H1

Hifl

/

- v

DW

/

AfSP

rOu 11

my

K

y

<y

>

Bialecki ring

ing

Mr tnl

0 2 6 8 104 6 8 10 0 2 4

Liquid/gas ratio L/V

Fig. 14.4. Column diameter as a function of the liquid-vapour ratio for the data given in Section 14.1

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344 14 Examples for the design of packed columns

The values of §s calculated from Eqn (4-29) for all the packings, together with the asso-ciated values for a and 8, which are also listed in Table 4.1, allow the corrresponding vapourflow rates at the loading point uv = uvs to be determined by iteration as functions of theliquid/vapour ratio LIV from Eqn (11-82).

The evaluated results are plotted in Fig. 14.4. It can be seen that the column diameter ds

required for a ratio LIV = 10 is about 25% greater than that for LIV = 1. The diagramalso shows that the differences in diameter associated with plastics packing are greater thanthose for metal packing.

14.2 Design of a packed column for the rectification of an isobutane/n-butanemixture

An isobutane/n-butane mixture flowing at a rate of 500 kmol/h has to be separated in arectification column. It consists of 60 % of the low-boiling component and 40 % of the high-boiling and enters the column at the boiling point. The overhead product has to consist of99.9% mol of isobutane, and the bottoms may contain only 0 .1% mol of this component.The packing is of the Montz Bl-200 sheet-metal type, and the column operates at an over-head pressure of 3.6 bar and a reflux ratio of 15 under the conditions at the loading point.

Solution

Average properties of the system

\iv = 58.124 kg/kmol \iL = 58.124 kg/kmol

QV = 8.398 kg/m3 QL = 561.3 kg/m3

Tjv = 7.76 • 10~6 kg/ms t\L = 0.13078 • 10"3 kg/msDv = 1.17 • 1(T6 m2/s DL = 8.44 • 10~9 m2/sam = 1.35 oL = 8.88-10-3kg/s2

Characteristic data for the packing derived from Tables 4.2, 4.4, and 5.2

a = 200 m2/m3 Cs = 3.116 Cv = 0.3908 = 0.979 m3/m3 CL = 0.971 CP = 0.355

Product streams designated as in Fig. 14.1

kmol 0.6-0.001D 5°° 3OD 5 ° ° i r 0.999-0.001 3O

L = 300.1 kmol/h • 15 = 4501.5 kmol/h= 4501.5 kmol/h • 58.124 kg/kmol = 261645 kg/h

V = 300.1 kmol/h (15 + 1) - 4801.6 kmol/h= 4801.6 kmol/h • 58.124 kg/kmol = 279088 kg/h

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14.2 Design of a packed column for the rectification of an isobutaneln-butane mixture

Resistance coefficient at the loading point according to Eqn (4-29)

9.806

345

261645 / 8.398 \1/2 /0.131-10'U [ 279088 \ 561.3 / \ 7.76 • 10"6

Relationship at the loading point according to Eqn (4-28)

= 0.514

uv,s =/ 9.806^0.514

0.9792001 2001 12 0.131-10-3wL

12 0.131-10-3wL

9.806

561.3 \1/2

8.398

561.3

9.806 561.3

Relationship at the loading point according to Eqn (11-82) for uL and uv = uVtS

uL =261645 8.398279088 ' 561.3uv,s

Vapour load at the loading point determined by solving Eqns (4-28) and (11-82) byiteration

uv>s = 0.489 m/s

Cross-sectional area of column according to Eqn (14-27)

279088/3600As 0.489 • 8.398

Column diameter according to Eqn (14-26)

= 18.88 m2

ds = \—' 18.88 = 4.9 m

Column diameter selected for planning: ds = 5 m.

Cross-sectional area of the planned column

A s = — • 52 = 19.6354

Vapour and liqud loads in the planned column

279088/3600uv =

uL =

8.398 • 19.635

261645/3600561.3 • 19.635

= 0.47 m/s

= 6.59 • 10-3 m3/m2s

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346 14 Examples for the design of packed columns

Theoretical liquid holdup according to Eqn (4-27)

0.131 • 1(T3 • 6.59 • 1(T3 • 200 2 U / 3

HL " I 1 2 ' 9.806 • 561.3

= 0.0422 m3/m2

Particle diameter according to Eqn (4-66)

Factor to allow for end effects {Eqn (4-57)}

4fs = 1 +

- i

= 0.996200 -5

Reynolds number for the stream of vapour {Eqn (4-65)}

0.47 • 0.63 • 10"3 • 8.398(1 - 0.979) 7.76 • 1C

Reynolds number for the stream of liquid {Eqn (4-69)}

6.59 • 10-3 • 561.3

0-996 = 15 200

L 200 • 0.131 • 10-3

Wetting factor for the packing {Eqn (4-68)}

- 141.42

W= exp141.42

= 2.028200

Resistance coefficient for the stream of vapour {Eqn (4-67)}

Pressure drop in the vapour stream {Eqn (4-58)}

200 8.398 - 0.472 1H ' (0.979-0.0422)3 ' 2 ' 0.996

= 0-564 • , n ^ x 3 • ~ T— TTT^T = 128.3 Pa/m

Hydraulic diameter {Eqn (5-15)}

A 0.979= 0.01958 m

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14.2 Design of a packed column for the rectification of an isobutaneln-butane mixture 347

Area of phase contact {Eqn (5-16)}

^ 3 0 979- ( 6-59-10^-561.3a \ 200- 0.13078 • 10~3

' (6.59- 1Q-3)2 561.3 \075 / (6.59 • 10'3)2 200 ̂ 0 4 5

0.00888 -200 / \ 9.806 ~ "

Height of a transfer unit in the liquid phase {Eqn (5-5)}

HTUL =1

0.9710.13078 • 10-3 \1/6 / 0.01958

561.3 • 9.806 8.44 • 10

6.59 • 10"

200 1.045

- 0.083 m

Height of a transfer unit in the vapour phase {Eqn (5-14)}

200 • 7.76 • 10"6 \3M /1.17 • 10~6 • 8.398 \1/3 1

0.47 • 8.398 / \ 7.76 • 10~b / 1.045

= 0.143 m

Determination of the concentration zones (Table 14.1)Calculation for the height of the uppermost zone

Xa = XD = 0.999 kmol/kmol to xb = 0.8 kmol/kmol

Characteristic concentration in the uppermost zonePhase equilibrium concentration corresponding to ya = xa = 0.999 kmol/kmol {Eqn (1-38)}

1 35 • 0 999 = °"93* • = 1 + (1.35-1)0.999

Vapour concentration corresponding to xb = 0.8 kmol/kmol on the operating line for theenrichment zone {Eqn (1-13)}

15 0 999yb = — • 0.8 + -z = 0.8124 kmol/kmol

Phase equilibrium concentration

1 / ( O S - I 0.8= ° - 8 4 3 8

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348 14 Examples for the design of packed columns

Differences in concentration {Eqns (14-4) and (14-5)}

Aya = 0.9993-0.999 = 0.0003 kmol/kmolAj b = 0.8438-0.8124 - 0.0314 kmol/kmol

Number of vapour-side transfer units {Eqn (14-3)}

0.999-0.8124 0.0003

NTUov = o.ooo3-o.o3i4 ' l n "b^TT = 2 8 '

Mean slope of equilibrium curve {Eqn (1-66)}

1.3yx [1 + (1.3 - 1) 0.867]2

Stripping factor {Eqn 1-30)}

X = 0.8184

= 0.8184

4501.5 kmol/h

Number of theoretical stages {Eqn (1-27)}

Height of an overall transfer unit {Eqn (1-62)}

HTUov = 0.143 + 0.8335 • 0.083 = 0.212 m

Height of uppermost concentration zone {Eqn (1-64)} if no allowance is made for endeffects

H = 0.212 • 28.8 = 6.106 m

The results thus obtained for all the concentration zones are listed in Table 14.2.

Total theoretical height if no allowance is made for end and distribution effects

2 H = 15 m.

14.3 Scaling up measurements performed in pilot plants

In mass transfer studies in a column with a new type of packing, a total of NP>a = 5.6transfer units was measured for a height of HPa = 1.5 m. Hence the number of transfer unitsper unit height of bed was (NIH)P>a = 3.733 m"1. In a control experiment with a bed heightof HPb = 2 m, the number of transfer units measured was NPft> = 6.8. What would the error

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14.3 Scaling up measurements performed in pilot plants 349

be if the efficiency determined for a height HPa = 1.5 m were to be taken as a basis in cal-culating the height HT of an industrial-scale column required to realize NT = 20 transferunits on the assumption that the inlet distribution remains unchanged? For the purpose ofthe calculation, assume that the height of the inlet zone Ht is less than HPa = 1.5 m.

Solution

If no allowance is made for end effects, the height of the column would be

H w _ _ g t _ = - | L = 5.36 m

If it is assumed that the separation efficiency remains constant in the H > Ht zone, thefollowing applies for Hi < HP

dN \ NPb-NPa 6 .8-5 .6 „ A -,:.4 mdHJH>Hi HP>b-HP>a 2 - 1 . 5

According to the model presented in Fig. 8.4, the end effects (Nd + ANt) can be deter-mined by rearranging Eqn (6-8) for the case of H = HPa, i. e.

)n lH>Hi

= 5 .6-1 .5 • 2.4 = 2

The relative difference in height required to compensate end effects can then be obtainedfrom Eqn (8-15), i.e.

7 ^1-2Q 1+JJ'2A

According to Eqn (6-35), this corresponds to an efficiency ratio of

rjr = 1 - 4 r " = X " °-285 = °-715HT

The actual column height required can then be calculated from Eqns (6-35) and (6-39),i. e.

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350 14 Examples for the design of packed columns

The same result can be obtained from Eqn (6-28). Thus

P_a Nd + AN(\H jP,a

1= 7.49 m

3.7331.5 2

Hence, the absolute value for the additional height required is

AH = 4 ^ " HT = 0.285 • 7.49 = 2.13 m.HT

This figure agrees with that for the difference between the values calculated for HT and

HT(P), i- e.

AH = HT-HT(P) = 7.49-5.36 = 2.13 m.

Hence, if the column design were to be based on the measured value for (N/H)P>a =3.733 m"1, the height of the bed would be too short by an amount

AH 100 = 28.5%.HT

14.4 Design of an absorber for removing acetone from process air

The spent air from a production plant contains 1 % mol of acetone and flows at a rate of2000 m3/h at 27 °C. The acetone has to be removed to a final concentration of 100 mg/m3 byabsorption in water in a column packed with 50-mm metal Pall rings. The main dimensionsof the column, which is operated at the loading point, have to be determined for the case inwhich the water consumption is 1.4 times higher than the minimum.

Solution

Average propert ies of the gas phase

\iv = 28.96 kg/kmol

QV = 1 . 1 6 2 kg /m 3

T]v = 18.13 • 10~6 kg /ms

Dv = 10.8 • K T 6 m 2 / s

Molar mass of acetone

1^ = 58.08 kg/kmol

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14.4 Design of an absorber for removing acetone from process air 351

Average properties of the liquid phase

\iL = 18.02 kg/kmolQL = 997 kg/m3

T)L = 0.857 • 10"3 kg/msDL = 1.18 • 10~9m2/soL =12- 10-3 kg/s2

Slope of equilibrium curve for the acetone-air/water absorption system

YYlYx = 2.314

Packing characteristics (Tables 4.1, 4.3, 4.6 and 5.1)

a = 110 m2/m3 C5 = 2.725 CP = 0.763

E = 0.952 m3/m3 CL = 1.192 Ch = 0.784Cy = 0.410

Product streams (Fig. 14.2, left)

Vu = 2 0 0 0 ^ • , 1 ^ 2v ^ m 3

| = 80.25 kmol/hft 28.96 kg/kmol

yM = 0.01 kmol/kmol

yM = ° ^ ^ = 0.01 kmol/kmol

V = 80.25 (1-0.01) = 79.45 kmol/h

= i n o28.96 kg/kmol

m3 58.08 kg/kmol -1.162 kg/m3

= 4.291 • 10"5 kmol/kmol

4 291 • 10~5

4 2 9 11 -4,291k m o l / k m o 1

= 4 3 2 2 " 1 0 3 k m o l / k m o 1

L = 1.4 • 183.04 = 256.26 kmol/h = Lo

xu = 0 + T 9 ; 4 ^ (0.01 - 4.291 • 10'5) = 3.087 • 10~3 kmol/kmol256.26

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352 14 Examples for the design of packed columns

Lo = 256.26 kmol/h • 18.02 kg/kmol = 4617.7 kg/h

Vo = 79.45 (1 + 4.291 • 1(T5) = 79.45 kmol/h

= 79.45 kmol/h • 28.96 kg/kmol = 2301 kg/h

Resistance coefficient {Eqn (4-29)}

9.806

2.7252 L 1 6 2

2301 \ 997 / \ 18.13 • 10~6

Vapour velocity at the loading point {Eqn (4-28)}

= 0.629

uv,s =9.8060.629

0.9521101 -no1 12 0.857 uL

12 0.857 • 10~3 uL

9.806 997

9.806 997

1 /6 / 9 9 7 \ i / 2

1.162

Liquid velocity at the loading point {Eqn (11-82)} for uL and uv = uv,s

4617.7 1.162

Gas velocity at the loading point determined by solving Eqns (4-28) and (11-82) byiteration

uv>s = 1.988 m/s

Cross-sectional area of column {Eqn (14-26)}

2300.9/3600 2A ° 2 7 71.162 • 1.988

Column diameter {Eqn (14-27)}

ds=\—' 0.277 = 0.594 m

Column diameter selected for planning: ^ = 0.6 m

Cross-sectional area of planned column

As = — • 0.62 = 0.2827 m2

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14.4 Design of an absorber for removing acetone from process air 353

Vapour and liquid loads in the planned column

2300.9/3600Uv= 1.162-0.2827 = 1 - 9 4 5 m / s

4617.7/3600 3 3 2

^ = = 4 5 5 ' 1 0 m / m S^ 997 - 0.2827 4 ' 5 5 1 0 m

Theoretical liquid holdup {Eqn (4-27)}

/ 0.857 • 10-3 • 4.55 • HT3 • HO2 \1/3

)

Particle diameter {Eqn (4-66)}

dp = 6 • 1 - ^ p 9 5 2 = 2.618 • 10-3 m

Wall factor {Eqn (4-57)}

/ A \"1

= 0.9429

Reynolds number for gas flow {Eqn (4-65)}

1.945 • 2.618 • 10~3 • 1.162v (1-0.952) 18.13 • 10-6

Reynolds number for liquid flow {Eqn (4-69)}

° 9 4 2 9 -

4.55 • I P 3 • 997

-3 " 4 8 1 2u 110.0 • 876 • 10

Wetting factor for the packing {Eqn (4-68)}

Resistance factor in gas flow {Eqn (4-67)}

= 277.2 Pa/m

Pressure drop per unit height in gas flow {Eqn (4-58)}

Ap 110 1.162 • 1.9452 1()R2

H (0.952 - 0.0387)3 2 0.9429

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354 14 Examples for the design of packed columns

Hydraulic diameter {Eqn (5-15)}

rf, = 4 . ^ f = 0.0346m

Phase contact area {Eqn (5-16)}

Eh. — a . n QS?0-5 -a " 3 ° - 9 5 2 1 110 • 0.857 • 10-3

(4^55 • 1 0 - y 997 \015 ( (4.55 • 10'3)2 110 ,— U.u/^0.072 -110 / \ 9.806

Height of transfer unit in the liquid phase {Eqn (5-5)}

L0.857 • 10-3

1.192 \ 997 • 9.806

= 0.539 m

0.0346 \1/2 /4.55 • 101.18 - KT9 / \ 110 / \ 0.672 /

Height of a transfer unit in the gas phase {Eqn (5-14)}

HTTJ l rnos? n ^ ^ i / 2 0-03461/2 1.945HTUv = ^^ (0'952 " ° ° 3 8 7 )^ T ^ 10.8 • 10-6

/IIP - 18.13 • IP"6 \3/4/l0.8 • IP'6 • 1.162 \1/3 / 1 \\ 1.945 • 1.162 ) \ 18.13 • 10~6 / \ 0.672/

= 0.456 m

Differences in gas loads {Eqns (14-7) and (14-8)}

AYU = 0.01-2.314 • 3.807 • 10~3 = 2.864 • 10~3 kmol/kmol

AYO = 4.291 • 10~5 -2.314 • 0 = 4.291 • 10"5 kmol/kmol

Overall number of gas-side transfer units {Eqn (14-6)}

MTTI 0.01-4.291 -HP5 2.864 - IP'3

NTUov = 2 .864-10- 3 -4 .291-10- 5 ' l n 4.291 • 10"5 = U ^

Stripping factor {Eqn (1-68)}

- 2.314 • I9*™1* ^ 0.7174256.26 kmol/h

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14.5 Design of a desorber for removing carbon dioxide from process effluents 355

Overall height of a transfer unit {Eqn (1-62)}

HTUov = 0-456 + 0.7174 • 0.539 = 0.843 m

Height of bed of packing without allowance for end and distribution effects

H = 0.843 • 14.826 = 12.49 m

14.5 Design of a desorber for removing carbon dioxide from process effluents

The carbon dioxide content of a process effluent flowing at a rate of 4 m3/h is to bereduced from 1.5 kg/m3 to 0.02 mol/m3 by desorption with air in a packed stripper columnoperating at 20°C and 1 bar. The carbon dioxide content of the inlet air is 0.03% vol., andthat of the air leaving the desorber outlet must not exceed 1 % vol. The desorption columnis to be packed with 35-mm plastics Pall rings. Determine its main dimensions.

Solution

Average properties of the gas phase

\iv = 28.96 kg/kmolQV = 1.188 kg/m3

r\v = 17.98 • 10~6 kg/msDv = 15.4 • 10~6 m2/s

Data for carbon dioxide

\iA = 44.01 kg/kmolQA = 1.818 kg/m3

Average properties of the liquid phase

\iL = 18.02 kg/kmolQL = 998 kg/m3

r|L = 0.998 • 10"3 kg/msDL = 1.82 • 10~9m2/soL = 72 • 10-3 kg/s2

Slope of equilibrium curve for the carbon dioxide-water/air system

rriyx = 1440

Characteristic data for the packing derived from Tables 4.1, 4.3, 4.6 and 5.1

a = 145 m2/m3 Cs = 2.654 CP = 0.927

8 = 0.906 nr7m3 CL = 0.856 Ch = 0.718Cv - 0.380

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356 14 Examples for the design of packed columns

Product streams corresponding to Fig. 14.2, right

to = 4 • 998 = 3992 kg/h

= 4 • ~ ^ - = 221.53 kmollh

X° = 1"5 ' 4408l'02998 = 6 1 5 4 " 10"4 k m o l / k m o 1

X° = 1 + 0541(Vo-4 = 6-1 5° • 10"4 kmol /kmo1

L = 221.53 (1 - 6.150 • 10"4) = 221.39 kmol/h

° 0 3 10~2 I li 3 ° 2y" = ° 0 3 10 4I01 • liiss = 3 -° 2

3 02 • 10~4

Yu = t "3 Q2 1Q_4 = 3.02 • 10"4 kmol/kmol

= 0.01 • ^ ; \-™ = 0.01007 kmol/kmol

k m o l / k m o 1

18 09= 0.02 • 10"3 • —^— = 3.614 • 10~7 kmol/kmol

Total mass balance

K = 13,80 (1 + 0.01017) = 13.94 kmol/h- 13.94 • 28.96 = 403.71 kg/h

K - 13.80 • 28.96 (1 + 3.02 • HT4) = 399.77 kg/h

3 9 9 - 7 7 = 336.50 m3/h1.188

Lu = 221.39 • 18.02 (1 + 3.614 • 10~7) = 3989 kg/h

Resistance coefficient {Eqn (4-29)}

9.806

2.6543989.45399.77

1.188 1;2 0.998 • 10"998 / 17.98 • 10"

0.4 1-0.652

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14.5 Design of a desorber for removing carbon dioxide from process effluents 357

Vapour velocity at the loading point {Eqn 4-28)}

9.806 \1/2 [ 0.906 1/2 / 12 0.998 • 10~3 uL

1.980 / [ 1451/6 \ 9.806 998

12 0.998 • 10~3 uL \1161 998

9.806 998 / \ 1.188

Liquid velocity at the loading point {Eqn (11-82)} for uL and uvs

3989.45 1.188399.77 998 Uy's

Gas velocity at the loading point determined by solving Eqns (4-28) and (11-82) byiteration

uVjS = 1.195 m/s

Cross-sectional area of column {Eqn (14-26)}

399.77/3600As= 1.188-1.195 =

Column diameter {Eqn (14-27)}

ds = \ — • 0.0739 = 0.316 m

Column diameter selected for planning: ds = 0.32 m

Cross-sectional area of planned column

As = — - 0.322 = 0.0804 m2

Vapour and liquid loads in the planned column

399.77/3600 ^ r n ,Uv= 1.188-0.0804 = 1 - 1 6 3 m / s

3989.45/3600 3

UL = 998 • 0.0804 = 1 3 ' 8 ' 1 0

Theoretical liquid holdup {Eqn (4-27)}

0.998 • 10"3 • 13.8 • 10~3 • 1452 \1/3 = 0.0708

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358 14 Examples for the design of packed columns

Particle diameter {Eqn (4-66)}

= 6 = 3.890 • 1(T3 rn

Wall factor {Eqn 4-57}

Reynolds number for gas flow {Eqn (6-65)}

1.163 • 3.890 • 10~3 • 1.188(1 - 0.906) 17.98 • 10~6

Reynolds number for liquid flow {Eqn (4-69)}

13.8 • 10-3 • 998

0.9206 = 2927

*«• =

145 • 0.998

Wetting factor for the packing {Eqn (4-68)}

Resistance factor in gas flow {Eqn (4-67)}

o-™-j^ - " • " ' ^ 2 9 2 7 ' 2927008M 0.906

Pressure drop per unit height in gas flow {Eqn (4-58)}

= 1.284

Ap 145_

H ~ ' ' (0.906 - 0.0708)3

Hydraulic diameter {Eqn (5-15)}

1.188 • 1.1632 1

0.9206= 240Pa/m

dh = 4 • ° ^ — = 0.02499 m

Phase contact area {Eqn (5-16)}

145

- ( 13-8 • 10-3 • 998 p= 3 • 0.906 (a \ 145 • 0.998 • 10"3

(13.8 • IP'3)2 - 998 \075 / (13.8 • 10"3)2 1450.072 • 145

"3)2 145 \'Q-45

9.806= 0.799

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14.5 Design of a desorber for removing carbon dioxide from process effluents 359

Height of transfer unit in the liquid phase {Eqn (5-5)}

_ 1 / 0.998 • 1(T3 \ 1 / 6 / 0.02499 \ 1 / 2 /13.8 • 10~3 \ 2 / 3 / 1 \L ~ 0.856 \ 998 • 9.806 j \1 .82 • 10~9 f \ 145 / \ 0.799 /

= 0.772 m

Height of a transfer unit in the gas phase {Eqn (5-14)}

145 • 17.98 • 10"6 \3M/15.4 • 10"6 • 1.188 \1/3 / 1 \ _1.163-1.188 / 1 17.98-10-6 / \ o . 799 /~ ° ' 1 8 7 m

Differences in gas loads {Eqns (14-16) and (14-17)}

AXO = 6.154 • 10"4 - ° ' 0 i 0 ^ 7 = 6.083 • 10~4 kmol/kmol1440

3 02 • 10~4

AXU = 3.614 • 10"7 - — = 1.516 • 10~7 kmol/kmol1440

Number of liquid-side transfer units {Eqn (14-15)}

NTUoL ~6.154 • 10~4 - 3.614 • 10~7 / 6.083 • 10"4

oL ~ 6 0 8 3 • 10-4 1516 • lO"76.083 • 10-4 - 1.516 • 10"' \ 1.516 • 10"

Stripping factor {Eqn (1-68)}

= 8.39

221.39 kmol/h

Height of an overall transfer unit {Eqn (1-63)}

HTUOL = 0.772 + X • 0.187 = 0.774 m

Height of bed if end and distibution effects are neglected {Eqn 1-65)}

H = 0.774 • 8.39 = 6.494 m

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360 14 Examples for the design of packed columns

14.6 Determination of the difference between the theoretical and the real liquidholdup

The purpose here is to determine the differences between the theoretical and the realliquid holdups applicable to the loading conditions under which the columns discussed inSections 14.4 and 14.5 were operated.

Solution

Known values in Section 14.4

Ch = 0.784 QL = 997 kg/m3 uL = 4.55 • 10~3 m3/m2s

a = 110 m2/m3 i\L = 0.857 • 10~3 kg/ms ReL = 48.12

Froude number for the liquid phase {Eqn (4-27)}

= HO (4-55 • I C Y = . 1Q_4L 9.806

Hydraulic area {Eqn (4-75)}

— = 0.85 • 0.784 • 48.1025 (2.322 • 10~4)01 - 0.760a

Real liquid holdup {Eqn (4-73)}

= 0.0322 m3/m3

Calculated difference between the theoretical and real holdups

AhL 0.0387-0.0322

"TiT= ^ ^ = °'m

Known values in Section 14.5

Ch = 0.718 QL = 998 kg/m3 uL = 13.8 • 10"3 m3/m2sa = 145 m2/m3 r\L = 0.998 • 10~3 kg/ms ReL = 95.17

Froude number for the liquid.phase {Eqn (4-27)}

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14.7 Additional column height required to compensate maldistribution 361

Hydraulic area {Eqn (4-75)}

— = 0.85 • 0.718 • 95.17025 (2.816 • 10~3)01 = 1.060a

Real liquid holdup {Eqn (4-73)}

= 0.0736 m3/m3

Calculated difference between the theoretical and real holdups

AhL 0.0708 - 0.0736hL 0.0708

= - 0.039

14.7 Additional column height required to compensate maldistribution

In a column of ds = 2250 mm diameter packed with 50-mm Pall rings, the liquid distribu-tor gives rise to maldistribution of M = 10%. The phase ratio is LIV = 1. If the maldistri-bution were to remain effective over the entire height of the column, what would be theadditional column height required to compensate the attendant loss in efficiency?

Solution

The loss in efficiency can be read off from the diagram in Fig. 8.12 against the value

4 _ 2250 _d ~ 50 ~ 4 5

The numerical value thus obtained is

AE = 15%.

In other words, the efficiency would be reduced by a factor {Eqn (8-24)}

Hence, the relative increase in height required to compensate the maldistribution is givenby

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362 14 Examples for the design of packed columns

14.8 Retrofitting a plate column with packing for steam distillation of crude oil

In order to avoid thermal decomposition, the partial pressure of the hydrocarbon vapourmust not be allowed to exceed 34 mbar at the lower end of the intermediate zone in avacuum column (pT =100 mbar) designed for fractionating crude oil by steam rectification.The plates previously used (subscript 2) gave rise to a pressure drop of 110 mbar betweenthe head of the column and the intermediate zone. After the column had been retrofittedwith low-pressure-drop packing (subscript 1), the pressure drop was only 70 mbar. Howmuch steam has thus been saved?

Solution

According to Eqn (12-50), the pressure drop after retrofitting is given by

p -PT= {i - l) | -^£-] = 70 mbar

The pressure drop before retrofitting is given by

p -PT= (i - 1) ( - ^ - 1 = 110 mbar

According to Eqn (12-63), the factor k for the difference in pressure drop is given by

A n ol57Ap_\ ~ 70

nt /i

The relative savings in steam achieved by the installation of packing follows from Eqn(12-67), i.e.

AS 1.57-1^ T =

1 5 ? 100-34 = °-226

L 5 7 + ~1Q~

The volume flow rate of steam per unit flow rate of the hydrocarbon vapours after retro-fitting is obtained from Eqn (12-64), i. e.

Sj_= 100 + 7 0 - 3 4

V ~ 34

The corresponding flow rate before retrofitting is obtained from Eqn (12-65), i.e.

$2_ _ 100 + 110-34

V " 34 " 7

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14.9 Reduction in height effected by redistributors 363

Therefore, the savings in steam per unit flow rate of product vapour is as follows:

The same figure can be obtained from Eqn (12-66), i. e.

- ^ - = ^ • • 7 0 (1.57-1) = 1.17

The savings in steam achieved by substituting packing for fractionating plates can bedetermined from the values obtained for AS IV and S2/V, i. e.

100 = v ^ ~ 10° = 22-6 %5.17

14.9 Reduction in height effected by redistributors

It is intended to separate a mixture in a packed column with 30 transfer units, 35-mmmetallic Pall rings, and optimum inlet distribution. How much height would be saved byinstalling three redistributors?

Solution

Assume that the inlet effect and the data describing the efficiency are identical to thoselisted in Table 9.1. In this case, the effective height of the column without redistributors isgiven by Eqn (9-20), i.e.

(HT)nr = o = [30 - (0.5 + 1.9)] • y j ^ = 13 m

The relative reduction in the height of the bed can be read off against nr = 3 in the upperdiagram shown in Fig. 9.7. Thus,

AH/HT = 0.26

The absolute reduction in height is therefore

AH = 0.26 • 13 = 3.4 m

Hence, the total effective height of the bed with three redistributors is

(HT)nr = 3 = 13-3 .4 - 9.6 m

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364 14 Examples for the design of packed columns

and the effective height between the redistributors is

r 3 + 1

This value can also be read off on the axis of abscissae against nr = 3 in Fig. 9.7.

Assume further that the height occupied by a redistributor in the column is hr = 0.4 m.According to Eqn (9-50), the relative reduction in the total height would then be

F ^ - H = 1 - — [2.4 (3 + 1) + 3 • 0.4] = 0.169

The absolute saving in the height of the column shell is therefore

AHS = 0.169 • 13 = 2.2 m

14.10 Advantages of geometrically arranged packing in fractionating fatty acids

A modern plant for processing palm-kernel oil consists of nine distillation stages intandem. The plans for process optimization included the improvement of product quality byan appropriate choice of column internals. A Hermann Stage method was adopted forthe design.

Solution

Since the feedstock is sensitive to heat, the distillation stages were designed with struc-tured packing and falling-film evaporators. As a consequence, the residence times were veryshort, and the bottom temperatures were comparatively low (Fig. 14.5). The effects on theproduct quality were as follows.

The overhead product in each stage ranging from Column 2 (octanoic acid) to Column 5(myristic acid) is the pure distillate of the unhydrogenated crude acid concerned. Its purity ishigher than 99 % during continuous operation and even higher than 99.5 % for lauric (Ci2)and myristic (Ci4) acids. Owing to the unsaturated Cw fraction, the purity of the palmiticacid in the sidestream distillate of Column 8 is only just higher than 97 %. Since the linoleicacid fraction (Ci8») in the feed is higher than that of the oleic acid (Ci8), the sidestream dis-tillate in the next column downstream (Column 9) contains only 85% of oleic acid (Ci8H);the remainder consists of 8-10% of linoleic acid (Ci8») and 4 - 5 % of stearic acid. If thetrans-fatty acid content is less than 0.5%, the oleic acid content in this fraction is higherthan that attained in the Henkel or Alpha-Laval detergent processes.

The flow chart shown in Fig. 14.5 for a fatty acid fractionating plant includes the contin-uous cracker, the glycerol-water evaporation unit, and the pure glycerol distillation column.The two latter also incorporate a Hermann Stage process and the associated engineering.The entire plant has been on stream in Malaysia since 1992.

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14.11 Recovery of acetone from production effluents by liquid-liquid extraction 365

O

W)

14.11 Recovery of acetone from production effluents by liquid-liquid extraction

A production effluent containing 0.241 kmol/m3 of acetone is to be purified by liquid-liquid extraction with toluene. The packed column is to be designed and operated for 80 %acetone recovery. The intended packing is 25-mm Bialecki rings. The column diameter andthe effective height of bed should permit the effluent to flow at a rate of 1557 m3/h, thecolumn load may not exceed 35 % of that at the flood point, and the extractant is tolueneflowing at a rate of 2829 m3/h.

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366 14 Examples for the design of packed columns

Solution

Characteristic data for systematically stacked Bialecki rings (cf. Table 13.2)

E - 0.928 Cm = 0.67

/ = 0.050 m Ch = 2.151

Cd = 1

Physical properties of the system

QD = 857 kg/m3 QC =998 kg/m3

T|D = 0.55 • 10~3 kg/ms r|c - 0.893 • 10"3 kg/msDD = 2.478 • 10~9 m2/s Dc = 1.3 • 10"9 m2/sa = 0.026 kg/s2 m = 0.64

Phase flow ratio

uD 2.829= 1.82

uc 1.557

Dispersed phase holdup {Eqn (13-20)}

u (1-822 + 8 • 1.82)1/2-3 • 1.82h = 3 3

4 ( 1 - 1 . 8 2 ) ° ' 3 7 5 m / m

Droplet velocity {Eqn (13-3)}

9.81 (998 - 857) 0.026= 0.1096 m/s

9982

Velocity of continuous phase at the flood point {Eqn (13-16)}

uc,m = 0.67 • 0.928 • 0.1096 (1-0.375)2 (1 - 2 • 0.375) = 6.6 • 10~3 m3/m2s

Velocity of continuous phase under operating conditions

uc = 0.35 • 6.6 • 10~3 = 2.31 • 10'3 m3/m2s

Diameter of extraction column {Eqn (14-35)}

4_ 1.557/3600 _

JT ' 2.31 • 10~3 ~ >488 m

Velocity of dispersed phase under operating conditions

uD = 1.82 • 2.31 • 10~3 = 4.21 • 10"3 m3/m2s

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14.11 Recovery of acetone from production effluents by liquid-liquid extraction 367

Dispersed phase holdup under operating conditions {Eqn (13-11)}

" *

Mass transfer constant {Eqn (13-39)}

Cm i v °-o5°Height of overall transfer unit {Eqn (13-47)}

1 0.0265'8 1TJrTJJ

oc ~ 37.32 ' [9.81 (998-857)]3 /8 • 9981/4' 1.82

1 1 1 998 . „ „ A

+ = 1.14(1.3 • 10"9)1/2 0.64 (2.478 • 10~9)1/2 857

Concentration of continuous phase after extraction {Eqn (14-33)}

cCu = (1 - 0.8) 0.241 - 0.0482 kmol/m3

Concentration of solvent after extraction {Eqn (14-34)}

cD,o = ~rzr (0.241 - 0.0482) + 0 = 0.1059 kmol/m3

1.82

Driving concentration difference at the head of the column {Eqn (14-30)}

Aco = 0.241 -—^— • 0.1059 - 0.0755 kmol/m3

0.64

Driving concentration difference at the foot of the column {Eqn (14-31)}

Acu = 0.0482 -—|— • 0 - 0.0482 kmol/m3

0.64

Number of overall transfer units in the continuous phase {Eqn (14-29)}

0.241 - 0.0482 0.0755 ^ 1 ?oc ~ 0.0755 - 0.0482 ' n

Effective height of bed {Eqn (13-22)}

H = 1.14 • 3.17 = 3.61 m

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