Rigorous simulation and dessign Packing Column.pdf

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Compurers Chemical Engineering,

Vol. 10, No. 5, pp. 493-504,

1986

0098-l 354/86 3.00 + 0.00

Printed in Great Britain. All rights reserved

Copyright 0 1986 Pergamon Journals Ltd

RIGOROUS SIMULATION AND DESIGN OF

COLUMNS FOR GAS ABSORPTION AND

CHEMICAL REACTION-I

PACKED COLUMNS

L. DE LEYE and G. F. FROMENT

Laboratorium voor Petrochemische Techniek, Rijksuniversiteit, Gent, Belgium

Receiv ed 22 Januar y 1985; revi sion recei ved 5 Sept ember 1985;

recei ved for publ i cati on 20 January 1986)

Abstract-A rigorous computer model is developed for the simulation of absorption and single or complex

reactions in packed or plate columns.

Part I deals with the packed-column version. It allows the computation of the concentration and

pressure profiles along the column and of the concentration profiles in both the gas and liquid film at

any height in the column. The use of mass-transfer coefficients leads to the real-not the theoretical-

height of the column. The rigorous solution is compared with approximate solutions.

Part II deals with the plate-column version. Here too, mass-transfer coefficients are used. Non-

isothermal conditions are taken care of through enthalpy balances.

The computer program is presented in some detail and applications to industrial situations are

illustrated.

ScoPe--The absorption of gaseous components by means of a reacting liquid is encountered in both

purification and production processes. There are numerous examples of both situations, e.g. the

absorption of CO, C02, H,S, SO, and NH, out of process streams or the chlorination or oxidation of

hydrocarbons to produce solvents or chemical intermediates. Until now the design or simulation of these

operations has been based upon rather strongly simplified models. The present paper develops rigorous

models for absorption and reaction and applies them to complex industrial situations.

Conclmions and Signilicnnce-The

paper presents and applies a general methodology, reflected in a general

computer program, for the design and simulation of packed and plate columns used in the absorption

of gases in inert or reacting liquids. Various types of complex parallel and consecutive reactions can be

handled. Since mass-transfer coefficients are used, real column heights or number of plates are calculated.

Non-isothermal and non-isobaric conditions are rigorously accounted for. The possibility of side-stream

addition or removal is also incorporated. The rigorous approach yields profiles of concentration,

temperature and pressure along the column, but also concentration profiles in the gas and liquid films

at any height, so that the results based upon various approximations used until now can be tested. Such

approximations pertain, for example, to the kinetics or to the neglection of either gas or liquid film

resistance.

The program has been applied to real, complex cases encountered in industrial practice, like the

absorption of CO, in a monoethanolamine solution, the simultaneous absorption of H,S and CO, in an

aqueous diethanolamine solution or in an aqueous NaOH solution.

1. INTRODUCTION

In many industrial processes gases are contacted with

liquids, either to remove certain components or to

produce desired chemicals. Examples of the first

situation are the removal of CO2 from steam re-

forming effluent gas, or the removal of CO2 and H,S

from refinery streams. Usually chemicals are added to

the liquid which enhance the rate of absorption of the

gaseous components by chemical reaction. Examples

of the second situation are to be found in oxidations,

chlorinations or the production of nitric acid.

The modelling of the phenomenon has generally

been based upon the two-film theory. Analytical

solutions for the flux of absorbed components at the

gas-liquid interface were developed for simple, if not

unrealistic reaction-rate equations: first-order irre-

versible reaction and instantaneous irreversible

second-order reaction [l-4]. Later, Van Krevelen and

Hoftijzer [5] presented an approximate solution for

second-order irreversible reactions with finite rate,

but nevertheless completed in the film. Their ap-

proach was followed and extended to nth and mth-

order reactions by Hikita and Asai [6]. There are

practically no examples in the literature of design

calculations or simulations of commercial processes

carried out in packed or plate columns which show

the variation of partial pressure and concentration

profiles with column height. Comprehensive books

[l-3] almost exclusively deal with expressions for

interfacial fluxes at a point in a column only, and do

not go beyond the methodology of design. The

problem resides, of course, in the extensive calcu-

lations involved in the design or simulation of exist-

493


2/12

494

L. DE LEYEand G. F. FROMEN?

F

In

PA

1;

f I

, OYt

I --

(CA )y

(CR, )y ; / =1

...nR

(C,

1: ' =

.,n

I

P

Fig. 1. Definitions of flows and compositions in a packed counter-currently operated column for

absorption accompanied by a single reaction in the liquid phase.

.

(C,, lb

cc,,,;

j =1

Cp,)r ;

j=l,

?nR

7 P

ing commercial processes. The present paper devel-

ops an entirely general approach for single and

complex reactions which led to a general computer

package for column design and simulation. The

examples given pertain to gas purification processes.

This part deals with packed columns, Part II [7, this

issue, pp. 505-5151 with plate columns.

2. ABSORPTION ACCOMPANIED BY

A SINGLE REACTION

The symbols used in the description of the counter-

current operation of a packed column for absorption

and reaction are shown in Fig. 1.

The model to be developed in what follows can be

used for the design of a new column or the simulation

of an existing one. The design problem can be stated

as follows: for a given packing, inlet flow rates and

composition of the gas and liquid feed streams,

determine the height and diameter required to satisfy

the exit specifications for the gas and liquid streams.

In the simulation problem the column height and

diameter and the packing characteristics are given,

together with the inlet flow rates of the gas and liquid,

so that the outlet flow rates of both phases have to

be checked.

Let a general single, irreversible reaction be written

ast

QG +

j$ R,

Ri ,

jtl P,

Pi

(1)

and let the kinetic equation of the chemical reaction

occurring in the liquid phase be

(2)

j-l

1

tSymbols are defined in the Nomenclature at the end of

Part II [7].

A is the component of the gas phase which absorbs

and reacts with the liquid phase components Rj to

yield the products Pi.

The continuity equation for A in the gas phase

flowing as a plug through the column may be written

181as

F

dhh

=

-N,l,,,a;R.

Pt

-(PAI dz

(3)

When the mole fraction of A in the gas phase is

relatively high the variation of the total molar flow

has to be accounted for:

dF

z-

- -N. _oalR.

The interfacial flux NAl, _,, is a function of (P*)~,

(CA)b, (C,),. The continuity equation for A in the

bulk liquid phase, also assumed in plug flow, is

L d(C,&

- = N,lY,,,.a:Q -

u,r,U - AVyLkLR.

5)

dz

The rate of reaction also contains the (CR, J. These

concentrations are obtained in the simulation case,

e.g. from a mass balance over the top of the column:

x

{

i

[F(PA~ - F PAXI

- [L(C,), -

Lyc*)I:]

11

for j = 1, . . . , nR, (6)

in which the second term inside the braces represents

the amount of A transferred from the gas phase that


3/12

Simulation of absorption and reaction in columns-l

495

has not reacted yet. Analogous equations can be

written for the product concentrations (C,),. The

liquid flow rate may have to be updated in each

increment used in the integration of the set of equa-

tions (3)-(S), according to

L(z + AZ) = L(z)

x l+

I

~Kc,),(z

Z) - (CA>&>I

+jzl

1

WR,MZ + AZ) - CC~,h(zll

-

+ , , 2 KG, )& + AZ) - (CP, )&)I

. (7)

i

Equations (3) and (4) contain NA 1,_ 0 and equation

1% N&=yL.

These fluxes are obtained from

N&Cl

= %i[(pA), -

(PAhI

=

_I),3

dv y-o

and

(8)

(9)

so that the con~ntration profile of A in the liquid

ti is required. For this purpose the following

continuity equations for A and Rj (and also Pj when

the reaction is reversible) have to be integrated:

UW

I)

d2C,,.

R1 dy

= aR,rl

for j=I,...,na

(lob)

and

&%= -up,rl for j=l,..., np, (10~)

/ dy*

with boundary conditions

CA = tcA ) i

CR,

= CcR

Ii

for j=l,..,,aR

at y=O (lla)

5,

=

CcPj

X

for j=l,...,n,

r

and

cA =

(cA)b

CR, = (CR, )b

for j=l,...,n,

CP, = (cl, )b

for j=I,...,n,

rat y =yt. (llb)

The concentrations of the liquid phase reactants,

CR, and of the products C?, can be related to that of

the absorbed component m the liquid film. Indeed,

subtraction of equations (lob) and (10~) from equa-

tion (10a) leads to

D

d2&

aA

Aw

--Da%=0 for j=l,...,na

aR,

J dy2

and

(12)

DA

d2cA aAL) s=O for j=l,...,n,.

dy2+< pI dy2

(13)

Integrating twice and accounting for the boundary

conditions

d& NA/ =o

dy=-D

dC

dy

=0 for j=l,...,aa

1

at y =0 (14a)

s=O for j=l,...,np

dy

J

and

cA = cCA)b, cR, = ccR, )b,

CP, = (CP, )b

yields

at Y =yL, 14b)

~R,=(~R,~b+~~fcA-(cA)bl

A

R~

and

~Pj=(~P,~b-~~[cA-(cA)bl

A PI

W)

Equations (4)-(15b) form the set of model equations.

The integration of the set of second-order

differential equations (1Oa-c) for the concentration

profiles in the liquid film has to be carried out for

each increment used in the integration of equation (3)

and this is a very time~onsuming task.

Equations (3)-(15b) are in fact general for single

irreversible

reactions.

In some cases some

simplifications are justified for specific situations.

These are based on the classification into so-called

regimes, which depend upon a number of factors

conveniently grouped into the Hatta number, as

extended by Hikita and Asai [6]:

Ha,=;

LA

/&aAL cF- [p, (cRj)?)A~

(16)

Hatta numbers ~0.3 are encountered with very slow

reactions. For moderately fast reactions Ha, is com-


4/12

496

L. DE LEYE nd G. F. FROMENT

prised between 0.3 and 3, for very fast reactions

Ha, > 3. Bimolecular irreversible reactions are con-

sidered as instantaneous when

Ha > 10 1 ; A DRYdb

%c,

A

oi

The most general situation is that whereby the reac-

tion takes place in both the film and the bulk, i.e.

when 0.3 < Ha < 3 and the reaction is moderately

fast only. Some of the simplifications concern the

boundary conditions only, so that the solution still

requires numerical integration of equation (3), be it

in a simplified form. Others are more drastic and lead

to an analytical, but generally approximate solution

for the interfacial flux. The program in its most

general form permits a check of these solutions.

For a reaction which is intrinsically very slow when

compared to the mass transfer, the amount converted

in the film is negligible, so that the reaction essentially

takes place in the bulk and the fluxes at the bound-

aries become

k+k

GA L,A

Equation (17) has the form encountered in purely

physical absorption. For moderately fast reactions,

with the particular kinetic equation

r, = k C CrnRi

I

A R, 9 18)

Hikita and Asai [6] derived the following approxi-

mate solutions for the fluxes in the liquid film,

essentially by reducing the kinetic equation to pseudo

first order by keeping Ca, constant over a certain

Very fast reactions are completed in the film, so

that (CA), = 0 Or (CA), = (CA)?. In such a

Caw, On l y

has to be calculated. For the rate equation

skL;e flux N

A y _ o is still obtained from equations

(19) and (21), but with (CA), = 0.

In Example 5.1 a column is simulated for the

absorption of CO, by means of monoethanolamine.

The result obtained with equation (19) to express the

flux at the interface [in which Ha, is given by

equation (21), but with mR, = l] is in complete agree-

ment with those calculated for this flux through

equations (IOa-c), but requires only 33 s CPU time

instead of 233 s.

For a rate equation of the type

r, = k,C,CmRj

RI

Hikita and Asai [6] derived an approximate solution

corresponding to equation (19) but with (CA), = 0

and

Ha;=;

J

UAk,(CA~-l(C~~)~R,DA.

(22)

L.A

A

For a very fast but reversible reaction,

aAAG + a,RL P apIPk + +,Pk

with the kinetic equation

(23)

r,=k, C;l*C

(

p-;cRcp )

>

(24)

I

Onda et al. [9] derived the following approximate

equation for the interfacial flux of A:

NA\J=o

= kL, A CA )iFA 7

25)

with

F

A

=[I $$](l+~)+BI{~~- $$ tl

s~ch(Wl}

1 +

B,taWBd -

Bz

B,

(26)

distance Ay close to the interface: where

NA~ J-o =

(pA)b -

Hl(CA)b

cosh(Ha;)

(1%

and

~~~~~~~ (Ha;&,

x ccA h - CA), coWW >

sinh(Ha;)

(20)

with

Ha; = -- ,/aAk,(CR, )FVDA.

L,A

(21)

When m,, = 0, equation (21) reduces to the well-

known equation for first-order irreversible reactions,

a case for which an analytical solution is available.

B (CA,: mAcP, i - (cP,)?9

2=3--

(GP

and

B,=Ha;

In the case of an instantaneous irreversible reac-

tion, the reaction zone is reduced to a sharp front,

located somewhere in the liquid film. The interfacial

flux of A is given by

aA

Dk

PA)b + ----H, Ck)b

NA~,=II =

ak DA

1

H

(27)

r+F-

.A L,A


5/12

Simulation of absorption and reaction in columns--I

497

where the index

k

refers to the liquid-phase reactant

Rj which gives the lowest absorption flux.

The reaction front coincides with the interface

when the bulk concentrations of all the liquid-phase

reactants exceed the values

(C ,),=~~pA(p,), for j=l,...,ns. (28)

A R, L.A

The interfacial flux is then given by

NA&O = h,A@A)b*

With an instantaneous reversible reaction, the

equilibrium is reached everywhere in the liquid film,

i.e. at the gas-liquid interface and at the liquid

film-liquid bulk interface as well [IO]. The equi-

librium conditions are expressed by

,fi CC,,)?

(cA)? fi ccR, ):/

= K, at y = 0 (29)

and

j-l

jfi (C,,)F

tcA)? f (CR, ti

= K, at y = y,. (30)

j-1

Equations (29) and (30), together with equation (6)

allow the variation of A, Rj and Pj along the column

to be calculated; the continuity equation for A in the

liquid [equation (5)] does not have to be solved in this

case. The flux at the gas-liquid interface is obtained

from

(31)

and

(32)

3. SIMULTANEOUS ABSORPTION OF

GAS-PHASE COMPONENTS ACCOMPANIED

BY CHEMICAL REACTION

Let Type 1A of parallel reactions correspond to

a&JAY + f &,,I R+ 2

aP,,l /

L

(33)

j-1 j-1

and

%,,rA: + 2 OR,,2 -

-* j , aP zPiL.

j - l

(34)

Type 1B only differs from Type IA in that one

reaction, labelled the first, is reversible and instanta-

neous.

In Type IA reactions the gas-phase continuity

equation for the

nA

absorbed components is written

as

F

dh,

)b =

dz

flA

x ,T,NA,Iy=Il

1

dn

for j = 1, . . . , nA (35)

and the continuity equation for these components in

the liquid phase is

L d(cA,b

dz

= NA, Iy=y,dfi

-

aA,.jrj(l -

4YLhQ

for j=l,...,n,. (36)

The variation of

F

with z is given by an equation

analogous to equation (4) but with

2 NAjlY=o replacing NAIy=o.

j = l

The variation of liquid flow rate is given by an

equation similar to equation (7). The further equa-

tions of the model are straightforward developments

of those derived in Section 2, but a distinction has to

be made between the reactions, which may be each in

a different regime. Type 1B is representative of the

simultaneous absorption in alkanolamine solutions

of H,S, which is accompanied by a reaction which is

instantaneous and reversible and of C02, which is

accompanied by a reaction which is irreversible and

of finite rate. In this case rigorous calculations would

be extremely time-consuming, not only because the

system of equation analogous to equations (1Oa-c)

has to be solved numerically, but also because the

concentrations have to satisfy the equilibrium condi-

tions of the first reaction in each point of the liquid

film.

Ouwerkerk [l l] proposed an approximate model

for this case which was further developed by Cor-

nelissen [12]. It assumes that all the reactions take

place in a front inside the liquid film or at its

boundaries. Consequently, all the concentration

profiles are linear. The gas-phase continuity equation

for A,, the component undergoing an instantaneous

reversible reaction is given by equation (35). In the

bulk liquid its concentration is

(CA, )b = (CA, )?.

(37)

The concentrations of the components involved in

the instantaneous reversible reaction have to satisfy

the equilibrium relationship

jc (CP,pJ

c,)p fi CR,)yb

= K,

j=1


6/12

498

L. DE LEYE nd G. F. FROMENT

with the index =i for y =0 and =b for y =y,.

The flux of A, at the interface can be written as

N*~y=O=kG.A~~ PA~)b- PA,)il

=

D

CcAI)i -

CcA,

Al

YF,

(38)

The irreversible reaction(s) may be very fast, mod-

erately fast or slow. With very fast reactions

(Ha > 3):

(cAj))b=O j=2,...,h,+l

and the interfacial flux is given by

(39)

NA,Iy-O= 1

(PA, b

Hi tanh(HaJ)

r+-

G,A, h,A, Ha;

=DQ

YF,

j=2,...,n +1

3 (40)

where yF, is the location of the reaction front for

reaction j and for first order with respect to Aj:

Ha; = $-

J

A,dkjipI (C,,)zlJ DA,.

(41)

L,Al

I

The concentrations to be substituted into Ha; are

those at the reaction front of reaction j.

For those components undergoing a moderately

fast reaction the fluxes are those given by equations

(18) and (19), but also, since the profiles are consid-

ered to be linear, by

NA,I~=o=DA,

CA,

)i - (CA, ye,

YFi

and

for

j = n, + 2,.

. . , n, + nM +

1

(42)

NAjIy-y~ = DA,

cAj )yF,

ccA,

)b

YL-YF

The combination of equations (18) and (19) and

equation (42) leads to the location of the reaction

front yF,.

The fluxes of the other components undergoing

very slow reactions (j = nv + nM + 2,

. . . , fzA)

are

given by equation (21) and the reaction front is

considered to coincide with the plane y = y,.

4.

A COMPUTER PROGRAM: A Tower

Based upon the general model described above, a

computer program, A-Tower was developed for the

simulation of existing or the design of new towers.

The program consists of two subprograms A-Pack,

for packed columns and A-Tray for plate columns.

VERY SLOW

REGIME

MOD. FAST

REGIME

A-PACK

ABSORPTION

or

- AND SINGLE

A-TRAY

REACTION

Type 1

A,+ RI-C, -

A?+ C,--P,

ABSORPTION

CONSECUTIVE

TVP~ 2

AND COMPLEX

REACTION

REACTION

A,+ RI-C, _ -VERY SLOW

A,+ C,eP,

REGIME

REACTIONS

Type IA

A,+ R,-P, ___

MOD. FAST

AZ+ R, + P2

REGIME

Type IS

VERY FAST

A,+ R\=P, _ -

REGIME

AZ+ R,- Pp

TYPO 2

A,+ RI-P, -

A,+ R2-P2

Fig. 2. Overview of the A-Tower program.


7/12

Simulation of absorption and reaction in columns-I

499

Each of them contains the modules shown in Fig. 2

Chemeng, contains the routines for the calculation

[13]. The number of parallel or consecutive reactions

of the characteristic properties of the tower and its

that can be handled amounts to five. In addition, operation, i.e. the mass transfer coefficients, the liq-

A-Tower contains four libraries. The first, Phypro, uid hold-up, the pressure drop etc. The third library,

contains a number of routines for the calculation of Maths, contains the mathematical routines, i.e.

thermodynamic and physical properties. The second, one- and multidimensional equation solvers, numer-

NO

YES

Estimate

Determine

out

('A)b

d

P

I I

f

IITER =

z=o

CHOOSE AZ

CALCUL. PHYS. PROP.

CALCUL. kG, kL

CHARACT. PROP.

PACKING

0

(5)-F (z + AZ)

Mum. Integr.

gE ORDER DIFF. EQ

-Profile C,

.

dC

Num.

Diff. 2

dyl Y=Y~

Eq (lO)-NAlyzy

L

RUKUGILL

Num

Integr.

Eq (6)-(CA)b (2 + AZ)

Estimate Ha l

I

RUKUGILL Num. Integr.

Eq (4)-(PA)b (2 + AZ)

(5)-F (z + AZ)

(6)-(CAlb (2 + AZ)

I

Eq

(7)-(CR,)b(~ + AZ)

3

(16)+(cRj)i

(20)+Ha l

NO

Eq (7)-

(Cpjjb (2 + Az);j=l,np

Fig. 3 continued overleaf)


8/12

500

L. DE LEYEand G. F. FROMENT

I

Eq (8)-

L(z + AZ)

z = z + AZ

T

NO

YES

NO

CALCUL. PHYS. PROP.

CALCUL. KG, KL

CHARACT. PROP.

PACKING

(Ha

SSQ, =

l)E - (Hal)C

(HaljE

SSQ,

=

c,), z t

AZ)), - ((C,),(z + A&

((C,),(z +

i-11,

SSQ, =

((PA)JE - ((PA)JC

[(A)iE

VA)yl -

(PAjh(h)

SSQ, =

(PA);

Fig. 3.

Flow diagram of the solution algorithm for absorption accompanied by a moderately fast reaction.


9/12

Simulation of absorption and reaction in columns-I ,

501

ical integration and differentiation routines etc. A

fourth library, Userad, allows the user to imple-

ment his own preferred correlations.

Figure 3 shows the flow diagram of the solution

algorithm for the simulation and design for the case

of absorption accompanied by a moderately fast

reaction. A-Pack calculates the real height of the

packing column, since it contains the mass-transfer

coefficients.

5. EXAMPLES OF THE APPLICATION OF A-Pack

5.1. The absorption of CO2 in a monoethanolamine

(MEA) solution

The absorption in alkanolamine solutions (MEA,

DEA, ADIP, DGA etc.) is, commercially, the most

important process for the removal of CO, from the

synthesis gas for NH3 and CH,OH production, for

the production of H,, in natural gas purification, coal

liquefaction etc. In the present example a gas contain-

ing 13.55 mol % of CO2 is to be purified by absorp-

tion into an aqueous solution of 13.6 wt% MEA. The

column, filled with 0.05 m steel Pall rings, has a

diameter of 1.05 m and is operating at a temperature

of 315 K and a pressure of 14.3 b. The inlet flow rates

of gas and liquid are 497 kmol/h and 76.9m3/h.

Determine the packed column height necessary to

reduce the mole fraction of CO, to 5 x lO-5 at the

top of the column.

The absorption of CO, in an MEA solution is

accompanied by the following overall reaction:

CO, + RNH, + RNHCOO- + RNH:

(43)

with the kinetic equation

r = &o&n,.

W)

Table 1. List of standard correlations for the determination

of ko, k,, o;, the wetting rate, pressure drop and flooding

point incorporated in the A-Pack program

Property Correlation used

ko

Laurent and Charpcnticr [IS]

4

Onda er al. [16]

c

Onda ef AI. [17]

Wetting rate Morns and Jackson [18]

Pressure drop Bckert [I91

Flooding point Bckert 1191

Table 2. Results of the design calculations for the CO,-absorption

column

Top

Flow rates

wlumn

L (ma/h)

76.9

F (kmol/h) 429.1

Gas-phase compo sit ion

PW (W

0.71s x 10-r

Liquid-phase compo sit ion

C, (kmol/m) 0.0

Cauu, (kmoJ/m)

2.220

GNucoo- (kmol/m)

0.0

C&u+ (kmol/m)

0.0

Ha&r )

20.08

a: (ml/m))

90.53

k0,co2 (kmol/m* h b) 0.880

&o, (m/h)

1.386

% of flooding 56

Calculated column height: 11 m

Calculated wetting rate: 0.85 m/h m

Calculated pressure drop: 0.21 x IO- b

CPU time (Data General MV 6000): 30 s

Bottom

wlumn

19.8

491.1

1.954

0.0

0.435

0.825

0.82s

8.700

90.95

1.057

1.416

66

At 315 K the reaction rate constant

k =

5.183 x

IO m6/kmo12 h [14].

For the determination of the gas- and liquid-side

mass-transfer coefficients, the effective specific sur-

face or interfacial area and the wetting rate of the

packing, the pressure drop and flood condition, the

Concentration (kmol/m3 1

00 0. 1

1.0

20

w

I

I

I

Bottom

column

*

00 01

1.0

20

Portia1 pressure (b)

Fig. 4. Composition profiles in the

CO,-MEA column.


10/12

502 L. DE

LEYB nd G. F.

FROMENT

standard correlations incorporated in the program,

shown in Table 1, are used.

For the determination of the viscosity of the solu-

tion and the diffusivity of MEA the experimental

data of Thomas and Furzer [20] are used. Densities

of pure MEA and MEA solutions are found in the

literature [21,22]. The diffusion coefficient of COZ in

pure water [23] was corrected for the presence of

MEA by using the Stokes-Einstein relationship.

Henrys law constant for COZ in H,O equals

48.6 m3 b/kmol at 315 K [24]. This coefficient is cor-

rected for the ionic strength of the solution [3,24].

The geometric specific surface of the packing

equals 105 m2/m3. The calculated results are sum-

marized in Table 2. The calculated wetting rate

largely exceeds the required minimum value of

0.08 m3/h m [18].

The concentration and partial pressure profiles of

Table 3. Absorption of CO, in MEA. Results of the approximate

and exact models

Approximate

Exact

Property

model model

Column height

11 10.95

Bottom column

L (ml/h)

79.80 79.80

F (kmoljh)

497.70

497.10

PCO~ (W

1.954 1.939

Cc% (kmol/m)

0.0 0.0

Ca,,, (kmol/m)

0.435

0.449

C,,,coo- (kmol/m)

0.852

0.845

CRNH: (kmol/m)

0.852

0.845

CPU time (s)

30

233

the various components in the gas and liquid bulk

along the column are shown in Fig. 4.

The absorption of CO, in the MEA solution is

accompanied by a very fast reaction. For the deter-

mination of the absorption flux, the approximate

(a)

p(b)

C(kmol/m3 1

C (kmol/m3)

Fig.

(b)

p(b)

C

(

kmol/m3)

x10-A A I

0.5 -

-2

0.3 -

-1

C(kmol/m3)

I

I 10-3

-CRN

1

- 0.5

I

- 0.3

0.1 -

- 0.1

0.0

0

0.0

UG

0

(c)

YL

p

(b) C(kmol/m)

C(kmol/m3)

x10-

4

Jo.3

- 0.5

0.0

0.0

0.0

yG

0

JI

5. CO,-absorption in MEA. Partial pressure and concentration profiles in the gas and liquid

at various heights in the column. (The gas and liquid films are not drawn to scale.)

films


11/12

Simulation of absorption and reaction

in columns-1

503

Table 4. Detailed com-

position of the feed to the

DEA-column

Component

mol %

H2

1.6

N,

0.2

co 0.1

CO,

0.13

W

1.94

CH.

44.17

W-L

2.1

WI,

15.0

GH,

5.2

VI,

11.8

G+

11.76

expression (19) with (CA), = 0 and with

m4 =

1 in

equation (21) was used. The example was re-

calculated, determining the absorption flux by nu-

merical integration of the set of second-order

differential equations (11). As shown in Table 3, the

differences are negligible, while the amount of CPU

time, using the rigorous model, is significantly in-

creased.

Figure 5 shows the partial pressure and concen-

tration profiles of CO2 and MEA in the gas and liquid

film at a number of heights in the column. Since CO2

is not very soluble, the absorption of CO* in pure

water is controlled by the resistance to mass transfer

in the liquid film. In an MEA solution, on the other

hand, the absorption is strongly enhanced by the very

fast reaction and the gas-film resistance to mass

transfer becomes important. No depletion of the

reactant MEA is observed at the top of the column

and the reaction is of pseudo-first order. At the

bottom of the column the depletion of the MEA is

almost complete in the liquid film.

Table 5. Rcsu11s of the design calculation of the H,S-CO,-DEA

absomtion column

Flow rates

L

(rnh)

F (ml/h)

Top

column

31.8

842.3

Bottom

column

32.8

860

Gas-phase composition

PHS W

P, @)

Liquid-phase composition

C,,, kmol/m?

Cc,, kmol/m)

c

RINn kmol im)

c

RzNH+ kmol im)

C,,- fkmol/m)

CR,,,-

(kmol/m)

Ha(CQ )

0: (m2/m3)

k,,,,, (kmol/mh b)

ko,col (kmol/m* h b)

k,,, Hs (m/h)

k,,,, (m/h)

% of flooding

0.218 Y W6

0.164

0.4225 Y IO-

0.105 x 10-l

0.0

0.163 x 1O-2

0.0

0.0

1.934

1.313

0.0

0.541

0.0

0.510

0.0

0.317 x 10-l

36.4

24.51

68.00 68.30

1.166

1.185

1.129 1.147

0.385

0.389

0.391

0.394

46

47

Concentration kmol/m3)

10 20

Calculated column height: I1 41 m

Calculated wetting rate: 0.183 m/h m

Calculated pressure drop: 0.224 x IO- b

No. of iterations: 5

CPU time: 230 s

5.2. Parallel reactions: the simultaneous absorption of

H and CO2 in a diethanolamine (DEA) solution

In 1979 more than one thousand alkanolamine

columns for the simultaneous removal of H,S and

CO1 were in operation throughout the world [25]. In

the present example CO, and H,S are to be absorbed

at 8.45 b and 311 K. The detailed composition of the

gas feed is shown in Table 4.

The solvent used is a 20 wt % DEA solution. The

column, packed with 0.05 m steel Pall rings, has a

TOP

column

Portiol pressure b)

Fig. 6. Absorption of CO, and H2S by means of DEA. Bulk partial pressures and concentration profiles

along the column.


12/12

504

L. DE LEYEand G. F. FROMENT

diameter of 1.45 m. The inlet flow rates of gas and

solution are taken from Kent and Eisenberg [27]. The

liquid are 860 kmol/h and 31.8 m/h.

remaining properties were determined the same way

The packed column height, required to reduce the

as in Example 5.1. The convergency tolerance was set

molar fractions of H,S and CO* to 3 x 10m5 and equal to 1 x lo-. The computed results are sum-

5 x 10m5, is to be determined. marized in Table 5 and the partial pressure and

The simultaneous absorption of H,S and CO2 in a

concentration profiles are shown in Fig. 6.

DEA solution is accompanied by the following over-

all reactions [l 1 121:

REFERENCES

H2S + R,NH

KI-HS- + R,NH:

(45)

1. G. Astarita, Mass Transfer w it h Chemi cal Reaction.

Elsevier, New York (1967).

and

2. G. Astarita, D. W. Savage and A. Bisio, Gas Treating

w it h Chemi cal Sofuenrs. Wilev Interscience. New York

CO* + 2R,NH + R,NHCOO- + R NH; . (46)

The first reaction is instantaneous and reversible.

The equations describing the H,S-amine equilibrium

are

H&HS- + H+

(47)

1983).

3. P. V. Danckwerts, Gas-Liquid Reactions. McGraw-

Hill, New York (1970).

4. J. C. Charpentier, Trans. Inst. them. Engrs 60, 131

(1982).

5. D. W. Van Krevelen and P. J. Hoftijzer, Ret Trau. chim.

Pay s-Bas Belg. 67, 563 1948).

6. H. Hikita and S. Asai, Znt. Z. hem. Engng, 4,332 1966).

7. L. De Leye and G. F. Froment, Comput. them. Engng

with K2 = 1.2957 x 10 at 311 K (26),

HS+S2- + H+

(48)

with K3 = 3.18 x lo-) at 311 K (26) and

R,NH: _ct, R,NH + H+

(49)

with & = 1.0074 x 10e9 at 311 K (27).

The second dissociation reaction (48) of HIS can be

neglected here. The equilibrium constant of the first

reaction (45) equals

K, = 2 = 128.62 at 311 K.

1

Hikita ez al. [14] derived the following kinetic

expression for the reaction rate for the reaction with

co, :

r = kCco G ~~ (50)

with k = 1.1053 x 107m6/kmo12hZ at 311 K.

This is an example of a Type 1B system of parallel

reactions. For the solution of the problem an approx-

imate model with linearized concentration profiles in

the liquid film [l 1 121 s used. For the determination

of the gas- and liquid-side mass-transfer coefficients,

the effective specific surface area of the packing etc.,

the standard correlations in the program (see Table

1) are used. The solubility data of H,S and CO, in the

10, 505 (i986).

8. G. F. Froment and K. B. Bischoff, Chemical Reactor

Anal ysis and D esign. Wiley, New York (1979).

9. K. Onda, E. Sada, T. Kobayashi and M. Fujine, Chem.

Engng Sci . 25, 759 1970).

10. D. R. Olander, AZChE JI 6, 233 1960).

11. C. Ouwerkerk, Hyd rocar bon Process. 57 4), 89 1978).

12. A. E. Cornelissen, Trans. Inst. them. Engrs 58, 242

(1980).

13. L. De Leye and G. F. Froment, (Ed.),

Proceedings of

Chemcomp 1982. KVIV, Antwerp (1982).

14. H. Hikita, S. Asai, H. Ishikowa and M. Honda, Chem.

Bngng J.

13, 7 (1977).

15. A. Laurent and J. C. Charpentier, Chem. Engng J. 8,85

1974).

16. K. Onda, H. Takeuchi and Y. Okumoto, J. t hem. Engng

Japan 1, 63 (1968).

17. K. Onda, E. Sada and Y. Okumoto, J. them. Engng

Japan 1, 56 1968).

18. G. A. Morris and J. Jackson, Absorpti on Tow ers. But-

terworths, London (1953).

19. J. S. Bckert, Chem. Engng Prog. 66(3), 39 (1970).

20. W. J. Thomas and I. A. Furzer, Chem. Engng Sci. 17,

115 (1962).

21. Y. M. Tseng and A. R. Thompson, J. them. Engng Data

9 2), 265 1964).

22. J. A. Riddick and W. B. Bunger, Organic Solverus, 3rd

edn. Wiley Interscience, New York (1970).

23. T. Shridar and 0. E. Potter, AZChE JI 23 4), 590

1977).

24. P. V. Danckwerts and M. M. Sharma, Chem. Engr 202,

CE 244 (1966).

25. Hy drocarbon Pro cess. 58 4), 99 1979).

26. Handbook of Physical Constants, Revised edn; Geol.

Sot. Am. M em. 97, Sect. 18 (1966).

27, R. L. Kent and B. Eisenberg, Hydrocarbon Process.

55 2), 87 1976).

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