rigorous simulation and dessign packing column.pdf
TRANSCRIPT
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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
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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
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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-
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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
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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
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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.
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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)
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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.
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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.
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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
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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.
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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).
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(1980).
13. L. De Leye and G. F. Froment, (Ed.),
Proceedings of
Chemcomp 1982. KVIV, Antwerp (1982).
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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).