Chemical Enginerruag Science, Vol. 45. No. 1, pp. 183~ 197, 1990. 0009 2509190 $3.00+0.00
Printed in Great Britain. cc‘8 19x9 Per&vnon Press plr
MASS TRANSFER WITH COMPLEX REVERSIBLE CHEMICAL
REACTIONS-II. PARALLEL REVERSIBLE CHEMICAL ,
REACTIONS
G. F. VERSTEEG,’ J. A. M. KUIPERS, F. P. H. VAN BECKUM and W. P. M. VAN SWAAIJ
Department of Chemical Engineering, Twente University of Technology, P.0: Box 217,750O AE Enschede,
Netherlands
(First received 11 November 1987; owing to external reasons accepted in revised form 3 February 1989)
Abstract-An absorption model has been developed which can be used to calculate rapidly absorption rates
for the phenomenon mass transfer accompanied by multiple complex parallel reversible chemical reactions.
This model can be applied for the calculation of the mass transfer rates, enhancement factors and
concentration profiles for a wide range of processes and conditions, for both film and penetration model.
With the aid of this mass transfer model it is demonstrated that the absorption rates in systems with multiple
reversible reactions can be substantially greater than the summation of the absorption rates derived for the
single systems. This latter fact provides a scientific basis for the application of aqueous mixed amine
solutions for industrial sour gas treating. Also it is shown that for kinetic studies by means of absorption
experiments for reversible reactions the presence of small amounts of fast reacting contaminants can have an
overruling effect on the outcome of the determination of the reaction kinetics. It is shown that the concepts of
shuttle mechanism and homogeneous catalysis refer to asymptotic situations, for practical situations
intermediate behaviour was observed which was previously not accessible for analysis. Experimentally
determined absorption rates of CO, in aqueous solutions of various mixtures of alkanolamines
(MMEA-MDEA, MEA-MDEA, DIPA-MDEA and MEA-DEA-MDEA) can be predicted extremely well
for the several mass transfer regimes which were studied experimentally. The experiments were carried out in
a stirred vessel with a flat surface over a wide range of process conditions.
1. INTRODUCTION amine and the hydroxyl ions which are present in the
Absorption accompanied by chemical reactions has liquid due to the protonation of the amine. The
been studied intensively, but the major part of the latter reaction usually has only a very small effect
studies has dealt with absorption followed by a single because of the low concentration of hydroxyl ions for
irreversible reaction. In case a reversible reaction common values of K,. However, in case of sterically
occurs the description of this phenomenon is very hindered amines, which cannot form stable carba-
complex due to the nonlinearity of the expressions for mates (Satori and Savage, 1983), this reaction may
the reaction kinetics. Moreover, the equations of the turn out to be dominant for the absorption rate.
mass transfer mode1 (e.g. penetration or film theory) Another example is the removal of CO, by means of
cannot be solved analytically and therefore numerical amine promoted carbonate processes (Savage et al.,
techniques must be used (Perry and Pigford, 1953; 1984).
Secor and Beutler, 1967; Cornelisse et al., 1980) to Moreover, it should be realized that even in the case
obtain an exact description of these processes. An of single gas absorption the amine gas-treating pro-
alternative approach is approximate analytical sol- cesses may still be processes where several parallel
ution of the equations as originally proposed by van chemical reactions occur because the purity of the
Krevelen and Hoftijzer (1948), but the outcome of this amine used is usually less than 100% (Versteeg and
procedure must be verified by means of a numerical van Swaaij, 1988a), and frequently the contaminants
solution because these approximations usually are not are other very reactive amines. During the regener-
generally valid, see Part I. ation of the loaded solvent at high temperatures
In the process industry, operations accompanied by (Blauwhoff et al., 1985; Kohl and Riesenfeld, 1979) also
several parallel reversible chemical reactions occur for pure amines degradation occurs and sometimes
very frequently. The theory of absorption followed by also fast reacting amines will be produced. A very
several parallel chemical reactions has been studied recent development of amine gas-treating processes is
only for some special processes (Jhaveri, 1969; Alper, the application of blends of amines (a solution of two
1972, 1973; Li et al., 1974; Chang and Rochelle, 1982). , . compositions)
Onda et al. (1970) presented a few approximate sol- ~~ha~~~~~rty~~~;~gs~;in ihd:zEie combination of
utions for specific cases. the absorption characteristics of the amines is used on
A frequently encountered process in which two purpose, leading to an improvement of the treating
parallel reactions are occurring is the absorption of process, especially if deep CO, removal is required.
CO,(or H,S) in an aqueous alkanolamine solution. In In Part I the problem of mass transfer accompanied
this solution the CO,(or HZS) reacts with the alkanol- by a single complex reversible reaction was discussed.
183
184 G. F. VERSTEEG et cd.
An improved numerical technique was developed to and
solve the equations which describe this phenomenon
for both the film and penetration theory. Rb.i =&, ~i.4, [Bilml [Oj]“~ [BjlpJ[Di14’
n 2) for the single In the simulations this effect was not taken into
reactions, the enhancement factor for the multiple account because it will be extensively treated in the
reaction process can be derived (Westerterp et al., model of parallel reactions with interaction. More-
1984): over, the calculations were carried out in order to
study the effect of small amounts of contaminants on
E multiple =
Jt i= 1
CEsingle,
j)' (9) the absorption rate for parallel reactions without
interaction. In Table 1 the data are presented which
Mass transfer with complex reversible chemical reactions-II 187
60. [CO2 1, = 0.054 mol.m-3
[COz], = 0.538 mol.m-3
, [C021g = 5.38 mol.m-3
XMEA ,
(mol/mol)
Fig. 1. Effects of the MEA-fraction on the calculated enhancement factor for an aqueous MEA-MDEA
mixture and qoa = 0.05.
Table 1. Conditions for the simulation for the system enhancement factor for the parallel process is ob-
MEA-MDEA without interaction served. In case of low CO, gas-phase concentrations
the enhancement factor for the MEA reaction ulti-
CAminel,,,. 2000 mol mm3
1 x 10m5 ms-’ mately becomes equal to the Ha-number which is
k,
1 x lo* ms-l characteristic for the pseudo first-order regime. For
:; , (MDEA) 4.69 x 10e3 m’mol- s-’ the latter situation the overall enhancement factor for
k:,,_,(MDEA) 3.18 x 1O-5 m3mol-’ s-l the parallel process can be estimated with eq. (9)
k,.,WEA) 5.87 m3mol-‘s-’
1.54X 10-4s-1 because both reactions of CO, with the amines may be
k-,.-,@=A)
regarded as irreversible for the conditions studied.
This system consists of a mixture of a fast reacting
component of a low concentration in combination
were used for the simulations. For the determination with a slow reacting component of a high concentra-
of the physical constants the reader is referred to tion, and the influence of MEA on the enhancement
Versteeg and van Swaaij (1988~). factor (absorption rate) is considerable even for high
In Fig. 1 the enhancement factor calculated accord- CO,-loadings (see Fig. 1) this effect can be explained
ing to the model is presented as function of the molar according to the so-called shuttle-mechanism. The
fraction of MEA for three CO, gas-phase concentra- shuttle-mechanism (Astarita et al., 198 1) describes the
tions and a CO, liquid-loading, acol, of 0.05. Similar process as two parallel reactions, and the fast reacting
calculations were performed for a liquid loading, aco2 component is regenerated by means of the interaction
= 0.01. From both simulations it can be concluded of the equilibrium reactions in the liquid bulk. For the
that small amounts of MEA have a pronounced effect shuttle-mechanism the enhancement factor can be
on the enhancement factor even for CO,-loadings that calculated analytically only for pseudo-irreversible
could imply that no MEA is present in the liquid reactions and the two asymptotic situations of in-
anymore if CO, would react irreversibly and pref- stantaneous reaction regime [eq. (7)] and the pseudo
erentially with MEA. The influence of the small first-order reaction regime [eq. (9)] respectively. In the
amount of MEA is more substantial for low CO, gas- intermediate regimes and for reversible reactions nu-
phase concentrations. This can be explained easily if merical solution of the equations which describe this
the individual enhancement factors are calculated for phenomenon is required. From the fact that for one
the single reactions. For MDEA the absorption pro- asymptotic situation of the simulations the en-
cess takes place in the pseudo first-order regime for all hancement factor for the multiple process can be
conditions, and for MEA the absorption regime de- calculated according to eq. (9), which was derived for
pends on the gas-phase concentration and changes irreversible reactions, it can be concluded that MEA is
gradually from the instantaneous regime (high Pco,) basically regenerated in the liquid bulk and therefore
to the pseudo first-order regime (low P,,,). Due to the the shuttle-mechanism applies to this situation.
low MEA-concentrations the enhancement factor in From the simulations it can be concluded that for
the instantaneous regime, IZinc,, nearly equal to unity
is kinetic studies by means of absorption experiments
for high CO, gas-phase concentrations and therefore the presence of small amounts of fast reacting con-
hardly any influence of the presence of MEA on the taminants can have an overruling effect on the absorp-
188 C. F. VERSTEEG et al.
tion rate depending on the experimental conditions. enhancement factor for reversible multiple reactions
Therefore it is necessary to cleck the influence of can be substantially higher, as can be seen in Table 3.
contaminants with a mass transfer model in order to This striking effect can be explained if the concen-
be able to choose suitable experimental conditions tration profile in the elements as conceived in the
and to determine the reaction kinetics correctly. penetration theory at the end of the contact time of the
The second system that was simulated consisted of multiple system is compared with those of the single
two parallel reactions with a moderate and a low value systems, see Fig. 2, case 1. It should be noted that both
of the equilibrium constant respectively. Both reac- concentration and spatial coordinates are dimen-
tions had identical reaction equations: sionless. The slopes of the profiles of the non-volatile
components are equal to zero at the interface, how-
A(g) + 2B(I) * C(I) + D(Z) (I 5)
ever, this cannot be concluded always directly from
A(g) + 2E(I) +i F(I) + G(Z) (16) the figures. The liquid-phase components are normal-
ized on the bulk concentrations of each reactant
and identical reaction rate equations:
respectively, and the gas-phase component on the
R A.1 ~~,.,C~lC~12-~-~.-~C~lC~l
- (17) bulk gas-phase concentration corrected for the sol-
ubility. From Fig. 2 it can be concluded that due to the
R A.Z_-~,.,C~lC~12-~-~.--IC~IC~I- (18) presence of E the concentration of B near the
Examples of this system are mixtures of primary gas-liquid interface was increased by the reactions (15)
and/or secondary amines, e.g. MEA-MMEA or AMP and (16) according to:
(amino-methyl-propanol)-DEA. In this system also C+DeA+2B (19)
one of the reactants (B) can be regarded as a contami-
nation which is present in the liquid in a very low A+2EeF+G (20)
concentration. In Table 2 the values of the physico- and although no direct interaction exists, an equilib-
chemical constants which were used for the calcu- rium shift reaction has the following effect:
lations of the enhancement factors and concentration
C+D+ZEtiF+G+28. (21)
profiles are presented.
In Table 3 the outcome of the calculations for the Near the reaction zone component f? is regenerated by
enhancement factor is presented together with the component E from the reaction products C and D with
enhancement factor which would be attained if the the simultaneous production of the other reaction
simulations were performed for the individual sys- products F and G. This regeneration of B reduces its
tems. The first reaction (eq. 15) is instantaneous with diffusion limitation from the liquid bulk to the inter-
respect to mass transfer and the second reaction (eq. face and therefore an essentially higher concentration
16) can be regarded as a pseudo first-order reaction as of B is present near the interface and therefore the
can be calculated from the data presented in Table 2. overall enhancement factor will be increased.
Contrary to the situation for irreversible reactions the In Fig. 3 the concentration profiles for case 2 are
presented for the system with the parallel reactions. In
this figure it can be seen that the concentration of B is
Table 2. Conditions for the simulation for the locally even greater than the liquid bulk concen-
system A + 2B and A + 2E without interaction
tration. This implies that the production of B accord-
0.1 mol m-3 ing to (21) exceeds the transport to the bulk by means
&$ 100molm~3 of molecular difusion.
CEI 2000 molm-J For this process the shuttle-mechanism is not able
He 0.60 mol mol - 1 to explain the observed results as the fast reacting
k, 1 x 10m3 ms-’
1 x lo* ms-’
component is completely regenerated near the gas-
k 2(B) 1 x IO6 mdmol-*s-’ liquid interface. According to Astarita et al. (1981) this
k:,,-,(B) 1 x 10’m3mol-‘s~’ situation seems to be similar to the homogeneous
k,.z(A) 1 x 10e3 mb molm2 s-l catalysis mechanism which assumes an instantaneous
k-,,-,(A) 1 x 10-5 m3mol-’ S-I
regeneration of the fast reacting component. However,
Case 1 Di = 1 x 10m9m’s_’ this mechanism is basically identical to an increase of
Case 2 D,= I x 10eLo m’s_’ the reaction rate constant and in Fact the system with
Case 3 D,= 1 x lO-‘O m’s_’ parallel reactions reduces to a system with only one
Case 4 D,= D,= I x 10-‘0m2s-’ reaction. It should be noted that the mechanisms
proposed to describe the observed phenomena,
shuttle-mechanism and homogeneous catalysis, are
Table 3. Results simulation for the system A + 2B and A only valid for asymptotic situations and processes
+ 2E without interaction with irreversible reactions. For reversible processes
approximate solutions of these mechanisms are not
Case 1 Case 2 Case 3 Case 4
generally valid and their applicability is therefore very
507 221 507 276 restricted. With the model presented in this work no
198 198 194 198 restrictions are imposed and it is valid for all asymp-
2530 792 2257 1499
totic situations and the intermediate regions.
Mass transfer with complex reversible chemical reactions-II 189
3.2. Parallel reactions with interaction the following overall reaction equation for the reac-
For this group of multiple parallel reactions absorp- tion with CO,:
tion experiments of CO, in aqueous solutions of
CO, + (1 + p) Amine, + (I- 8) Aminei
mixtures of amines have been carried out and are
compared with the outcome of the numerical simu- & Amine, COO + ,!JAmine, H +
lations. In these aqueous solutions, simultaneous with
+ (1 -/?) AminejH+. (23)
the reaction between CO, and the amines, additional
reactions occur between the protonated amines and Due tothe implementation of eq. (22) in the mass
the unprotonated amines according to: transfer model this change in the stoichiometry of the
reaction between CO, and the several amines has been
Amine,H+ + Aminei F? Amine, + AminejH+
taken into account.
(22)
and for the situation that one of the amines is a Mixture of MMEA and MDEA. In Table 4 the
primary or secondary amine this eventially leads to experimental conditions are summarized. This com-
(a) A+26 - C+D
case 1
1.0
(b)
co
t 1 A+ZE - F+G E
t--j
A
0.5- case 1
o \ F,G
I I I 1
0 1 2 3 L
Z
o-
Fig. 2. (a) and (b).
G. F. VERSTEEG et al.
A+ZB- C+Cl
A+2E- F+G
0.5 - case 1
A
I I 1
Fig. 2. Dimensionless concentration profiles for (a) the system A + 2B-- C + D, (b) the system A +2E++
F+G, (c) the system A+2B++C+D and A+2E++F+G.
B
A+20 -c+o
A+2E -F+G
case 1
Fig. 3. Dimensionless concentration profiles for the system A + 28 ++ C + D and A + 2E CI F + G.
position can be regarded as an MDEA solution therefore the reaction between CO, and MMEA can
contaminated with a small amount of MMEA. In Fig. be regarded as instantaneous with respect to mass
4 the experimental results are compared with the transfer. Nearly all of the protons of MMEAH* are
outcome of the numerical simulations and from this transferred to MDEA which can be concluded from
figure it can be concluded that the model presented in the profiles of MMEACOO- and MMEAH+ leading
this work is able to calculate the molar flux for this =
to /3 0 in eq. (23) because in the absence of reaction
system extremely well. (22) both profiles must be similar. Moreover, the
In Fig. 5 a typical example of the liquid concen- difference between these concentrations must remain
tration profiles at the end of the contact time is constant and equal to that in the liquid bulk in case
presented for a high CO, gas-phase concentration. In that p= 1; however, this only occurs in case of equal
this figure can be seen that the MMEA concentration diffusivities for both components.
decreases substantially towards the interface and It should be noted that the slopes near the interface
Mass transfer with complex reversible chemical reactions-II 191
Table 4. Conditions for the exper- of all components except that for CO, are equal to
iments for the system zero, this may not be directly clear from the presented
CO,-MMEA-MDEA
concentration profiles.
0.103 = 0.679
model. Similar to the system MMEA-MDEA it could T= 293 K
be concluded from the calculated concentration pro-
files that the reaction between MEA and CO, is
instantaneous with respect to mass transfer. Therefore Table 6. Conditions for the exper-
reaction (22) has a large effect on the absorption rates. iments for the system
CO,-DIPA-MDEA
From the data in Table 5 it is possible to approximate
the absorption region with eqs (8) and (IO). 0.274 < [CO,], < 2.69 mol m 3
The results of the comparison for the system 3 are 6.00 < [CO,], < 223 mol m 3
presented in Fig. 8. For the major part of the exper- k, = 1.01 x 10-5ms-’
imental conditions the reactions between CO, and [DIPA] = 826 molmm3
[MDEA] = 1034mol m-3
both MEA and MDEA turned out to be pseudo first- He,,, = 0.722
order reactions and for this regime reaction (22) has no T=298K
noticeable effect on the absorption rate.
From these figures it can be concluded that also for
this mixture of amines the present model is able to experimental conditions are summarized. The exper-
predict the absorption rates within 20%. imental results are compared with the outcome of the
numerical simulations in Fig. 9. From this figure it can
Mixture of DIPA and MDEA. In Table 6 the be concluded that the model is able to predict the
Mass transfer with complex reversible chemical reactions--II 193
[MEA] = 37 mol.m3
[MDEA] 3 2990 mol.rn3
[CO,l,=8.19 mol.m-3
[CO,lg 2.73 mdm-3
10
[CO,],= 0.55 mol.m-3
[CO2 I g= 0.27 mol.m-3
0
0 10 20 30 40 50 60
IO’. J_
W
mol.m-2.s -l
Fig. 7. Comparison between the measured and the calculated absorption rates of CO, in an aqueous
mixture of MEA and MDEA.
40
1
105-J”Um 30
mol.m-2s -1
10 qr 0 [CO,l,= 2.19mol.m-3
/m
I ICO,l,= 1.10 mol.m-3
I [CO,],= 0.55 mol.me3
UU [C021g= 0.27 mol.m-3
In
0 I I I I r
0 10 20 30 40
105.Jexp
+
mol.m-2.s-1
Fig. 8. Comparison between the measured and the calculated absorption rates of CO, in an aqueous
mixture of MEA and MDEA.
absorption rates fairly well with deviations up to 40%. mined mainly by the reaction rate constant for the
For all experiments the conditions for pseudo first- reaction between CO2 and DIPA. It should be noted
order reaction kinetics were practically always fulfilIed that the reaction rate constant for the deprotonation
and therefore the outcome of the calculations is deter- of the zwitterion by MDEA was calculated from the
194
t 75
90 1 [DIPA]
[MDEA]
= 826
G. F. VERSTEEGet al.
= 1034
mol.m-3
mol.m-3
mol.m-3
mol.m-3
mol.m-3
0 I I I ’ I I I
I
0 15 30 4s 60 7.5 90
lo? JeXP
*
mol.m-2.s
Fig. 9. Comparison between the measured and the calculated absorption rates of CO, in an aqueous
mixture of DIPA and MDEA.
Table 7. Conditions for the experiments amines can be regarded as an instantaneous reaction and
for the system CO,-MEA-DEA-MDEA in this figure it can be seen that nearly all the
protons produced by the various reactions are trans-
0.274 S [CO,], < 16.2 molm-3
15.7 Q [CO,], < 670 mol mm3 ferred to MDEA and that b + 0 for both the reactions
3.60 x 10-6ms-1 < k, < 5.60 [eq. (14)] between CO, and MEA and DEA respect-
x 10m6 ms-’ ively. For absorption in the pseudo first-order regime
[MEA] =500 molm-’ the calculated enhancement factor is equal to the
[DEA] = 1010 molm-3
[MDEA] = 2546 mol mm3 summation of the enhancement of the individual
He,,, = 0.662 reactions between CO, and the amine.
T=293 K
3.3. Parallel reactions with a common product
results of Blauwhoff et al. (1984), who suggested a For this group of parallel reactions only numerical
relation between the deprotonation rate constant and simulations have been carried out. Actually, this
the PG._,_. Therefore this value must be regarded as a group of parallel reactions can be considered as a
rough estimation only. mixture of the previous two groups, i.e. independent
parallel reactions with an interaction by means of the
Mixture o/MEA, DEA and MDEA. In Table 7 the common product. Therefore it can be expected that
experimental conditions are summarized. The exper- the phenomena observed for the other groups will
imental results are compared with the outcome of the occur also for this group.
numerical simulations in Fig. 10. From this figure it
can be concluded that the model is able to predict the
absorption rates satisfactory within 35%. The
average deviation between the experimental results
and the numerical calculations for this mixture is 4. DISCUSSION
greater compared to those observed for the other The direct implementation of complex absorption
systems, this probably can be ascertained to the large models in for instance column calculations is until
number of parameters which have to be estimated as now very restricted due to the required amount of
for instance the diffusivities of the ionic species. computational time. However, these kind of models
Especially for the instantaneous reaction regime the can be very helpful to study absorption regimes which
values of the diffusivlty have a pronounced effect on may occur during an absorption process. From the
the outcome of the calculations. obtained numerical results and concentration profiles
In Fig. 11 a typical example of the concentration an approximation of the actual process can be derived
profiles is presented. From these concentration pro- which can be applied in the computational procedures
files it can be concluded that the reaction of CO2 and the for the column calculations.
Mass transfer with complex reversible chemical reactions--II 195
IMEAl = 500 mol.m-3
IDEA] = 1010 molm-3
lh4DEAl= 2546 mol.m-3
104.J,“,
mol.m-2.s -I
0 [C021g= 10.9 mol.m-3 n = 0.66 s-l
104.J,xp
&
mol.m-2.s
Fig. 10. Comparison between the measured and the calculated absorption rates of CO, in an aqueous
mixture of MEA, DEA and MDEA.
The above-mentioned procedure, the derivation of tions can be calculated over a wide range of liquid
an approximated, simple description of the absorption compositions, number of reactions and process condi-
process with the aid of numerically solved model in tions with the numerical solution method presented in
which all possible interactions have been taken into this study.
account, has not been proposed in literature so far. From the outcome of the calculations for systems
Actually, the reverse action, afterwards numerical consisting of several different reversible reactions it
verification of approximated solutions, has been can be concluded that the enhancement factor for the
presented (Onda et ul., 1970), although often this multiple reactions system can be substantially higher
verification has been excluded for a variety of reasons than the summation of the enhancement factors for
(Astarita et al., 1981; DeCoursey, 1982). the single reactions. This effect was not observed for
It is clear that due to large number of parameters it irreversible reactions where the enhancement for the
is impossible to incorporate the numerical results into multiple system is always smaller than the summation
a simple, general applicable correlation of one sort or of the single reactions.
another. It is shown that for kinetic studies by means of
Another possible way to incorporate the present absorption experiments for reversible reactions the
model into an overall absorption module is variation presence of small amounts of fast reacting contami-
of the number of grid points. In Part I it is shown that nants can have an overruling effect on the outcome of
due to the additional transformations even for a small the determination of the reaction kinetics.
number of grid points (e.g. 10 x lo), which requires The numerical mass transfer model is able to predict
only a negligible amount of computational time, a cxtrcmely well the experimentally observed absorp-
satisfactory accuracy can be obtained already. If tion rates of CO, in aqueous solutions of mixtures of
constant concentration profiles over the absorber are various amines. As already mentioned in Part I, the
reached after several column interactions, the number discrepancy between the simulations and the exper-
of grid points can be increased to increase the overall iments may be attributed to the occurrance of inter-
accuracy. facial turbulence (Marangoni effects).
Acknowledgements-These investigations were supported by
5. CONCLUSIONS the Technology Foundation, Future Technical Science
Branch of the Netherlands Organization for the Advance-
The absorption rates for mass transfer accompanied ment of Pure Research (ZWO), and the Koninklijke/Shell
by various groups of parallel reversible chemical reac- Laboratorium Amsterdam.
196 G. F. VERSTEEG er al.
Fig. 11. Dimensionless concentration profiles for the system CO,-MEA-DEA-MDEA at a high PcO,.
NOTATION He dimensionless solubility defined as
A component A CAI,ICAl,, 1
B component B J flux, molar mP2 s-’
C component C K equilibrium constant, rnol(-~~-~.+y~+yd)
component D ,-3(-Y,--Yb+k &Yd)
D subscript diffusivity, m* s- ’ k, gas-phase mass transfer coefficient, m s- l
E component E k, liquid-phase mass transfer coefficient,
enhancement factor defined by eq. (14) or rns-’
(15), 1 reaction rate constant, m3(m+n+p+q--l)
E subscript. cc infinite enhancement factor defined by eq. m0~~~~+~+~+4-l~S-I or m3(r+s+t+o-l)
(25), 1 mO~~<'+S+'+"-I~S-l
F component F I liquid phase
G component G m reaction order, 1
9 gas phase n reaction order. 1
Ha Hatta-number defined by (k,,,,,., [A]“-’ P reaction, order, 1
CBI”C’3’CW~J”~’ A, 1 4 reaction order, 1
Mass transfer with complex reversible chemical reactions-II 197
R reaction rate, mol m- ’ s- ’ Westerterp, K. R., 1985, Absorber design in sour natural
r reaction order, 1 gas treatment plants: impact of process variables on oper-
ation and economics. Chem. Engng Proc. 19, l-25.
s reaction order, 1
Chakravarty, T., Phukan, U. K. and Weiland, R. H., 1985,
t time variable, s Reaction of acid gases with mixtures of amines. Chem.
t reaction order, 1 Engng Progr. April, 32-36.
V reaction order, 1 Chang, C. S. and RocheMe, G. T., 1982, Mass transfer
liquid-phase concentration, mol rn- 3 enhanced by equilibrium reactions. Ind. Engng Chem.
C3 Fundam. 21, 379-m385.
Cornelisse, R., Beenackers, A. A. C. M., van Beckum, F. P. H.
Greek letters and van Swaaii, W. P. M., 1980, Numerical calculation of
constant defined by eq. (14) simultaneous mass transfer of two gases accompanied by
solute loading defined by [A],/[B],, 1 complex reversible reactions. Chem. Engng Sci. 35,
1245-l 260.
film thickness according to the film
Danckwerts, P. V., 1979, The reaction of CO, with ethanol-
model, m amines. Chem. Engng Sci. 34, 443445. -
8 contact time according to the penetration DeCoursey, W. J., 1982, Enhancement factors for gas absorp-
model, s tion with reversible reaction. Chem. Engng Sci. 37,
1483-1489.
Jhaveri, A. S., 1969, Absorption of a gas into a solution
Subscripts
containing two reactants. Chem. Engng Sci. 24, 1738-1740.
a component A Kohl, A. L. and Riesenfeld, F. C., 1979, Gas Purfficarion. Gulf,
an analytical solution Houston, Texas.
b component I3 Kirk-Othmer, 1978, Encyclopedia of Chemical Technology
bulk concentration at bulk conditions (3rd edn). Wiley, New York.
van Krevelen, D. W. and Hoftijzer, P. J., 1948, Kinetics of
component C gas-liquid reactions. Part 1: general theory. Rec. Tram.
: component D Chim. 67, 563-586.
equilibrium Laddha, S. S., Diaz, J. M. and Danckwerts, P. V., 1981, The
component F N,O analogy: the solubilities of CO, and N,O in aquetius
;
solutions of organic compounds. Chem. Engng Sci. 36,
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