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7/25/2019 Rigorous simulation and design Plate Column.pdf
1/11
Comput ers & Chemi cal Engineeri ng,Vol. IO, No. 5, pp. M -515, 1986
Printed in Great
Britain. All rights reserved
0098-1354/86 3.00 + 0.00
Copyright 0 1986Pergamon Journals Ltd
RIGOROUS SIMULATION AND DESIGN OF COLUMNS
FOR GAS ABSORPTION AND CHEMICAL
REACTION-II
PLATE COLUMNS
L. DE LEYE and G. F. FROMENT
Laboratorium voor Petrochemische Techniek, Rijksuniversiteit, Gent, Belgium
(Received 22 January 1985; revisi on r eceiv ed 5 Sept ember 1985;
receiv ed for publ icat io n 20 January 1986)
1. INTRODUCTION
In Part I [l, this issue, pp. 4935041 of this paper the
mathematical modelling of absorption accompanied
by chemical reaction was developed both for simple
and complex cases and attention was focused upon
application to packed columns. Part II applies the
theory to the design or simulation of plate columns.
These are preferred to packed columns when widely
varying loadings may be expected. Also, large values
of the mass-transfer coefficients and large interfacial
areas can be achieved in traycolumns, which makes
them appropriate not only for the fast reactions
encountered in gas treating, but also, given the high
liquid hold-up, for the slow reactions encountered in
chemical-producing processes.
2. MATHEMATICALMODELLING
The various flows and compositions of the gas and
liquid in the column and on a typical plate are shown
in Fig. 1. Gas and liquid feed or withdrawal on a
plate are also included. The components in the liquid
phase are numbered in the following order: com-
ponents undergoing absorption and reaction, phys-
ically absorbed components, liquid-phase reactants,
reaction products involved in further reactions, final
reaction products and inert liquid-phase components.
When the total number of plates, the compositions,
flow rates, temperatures and pressures of the gas and
liquid feed streams and the flow rates of intermediate
gas or liquid withdrawals are given, the flow rates,
compositions, temperatures and pressures on each
plate have to be calculated. This is the simulation
problem. In the design mode the number of plates
required to achieve a specified absorption has to be
determined. This requires a number of iterations in
the column calculation.
In the model to be described, the gas is assumed to
be in plug flow, while the liquid on the plates is
completely mixed. Non-isothermal and non-isobaric
operation are considered. The equations below are
written for a fairly general example involving simulta-
neous absorption and parallel reactions (Type 1A).
The variation of, the mole fractions of the absorbing
components in the gas phase and of the total gas flow
rate on plate k are given by
F
dy i
l- yj p E?
di
I= N j l y=O
(1)
= -Njly=i AtR*
forj=l,...,nA,
and
(2)
while for non-absorbing components,
FYI constant for j = nA + 1, . . . , n,.
(3)
The boundary conditions are
for 2 = O,yj=yjpk
F=@
and
I
forj=l,...,no. (4)
for 2 = h, y,= yj,k
F = Fk
Pf and yFk are the gas flow rate and the mole
fractions in the gas entering the plate. These are
related to the quantities leaving the plate k + 1 in the
following way, accounting for side streams:
and
forj=l,...,no. (6)
The equations for the flow rate and composition of
the liquid are derived, by way of example, for the
parallel reactions (33) and (34) (Type 1A) of Part I
[l]. Since the various reactions probably have
505
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506
L. DE LEVEand G. F. FROMENT
X
;j= 1 ..
.f-JL
6
1
-La
Y
;j=l,...,nG
X
, .;j
, , n
L
k-7; ,@,I,
F T
k+lk+l
Gas
Liquid
Fig. 1. Flows and compositions in the column and on a plate.
different reaction rates, the xj,k depend upon the
for the remaining absorbed components,
appropriate Hatta number.
For the absorbed components undergoing a very
fast reaction (appropriate Hatta number > 3),
(7)
ik=O forj=l,...,nv;
for those involved in a moderately fast reaction
(appropriate Hatta number between 0.3 and 3),
forj=n,+l,...,n,. (10)
X/k(L+
Ww~)=xj,k-,L;_,
+xw,,k
WV,
+NjIy-.vL
A:Rh, - aj,jrj(l - A,y,)Rh,c,
The mole fractions of reactants, reaction products
=x,~k_,L;_,+xw,,kwk T f Q
I- I
a/,/
and inerts in the liquid on the plate are given by
X,,.k(G + WW,)
forj=n,+l,...,n,+n,; (8)
x
{(@Y - F,Y,,,) -
[x,Ow~ + 4)
for the absorbed components undergoing a very slow
reaction (Ha c 0.3)
-(G-I%-, + W,XW,,,)l~
forj=n,+l,...
,+,+nR+nP (11)
and
+y~kkFl~-Yj,kFk-Uj, jrj(l -A$,)Rh,C,
Xj,k L;+ WWt)=Xj,k-IL;-I+X~,.~Wv~
forj=nv+n,+l,...,n,+nM+n,; (9)
forj=n,+n,+n,+l,...,n,. (12)
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Simulation of absorption and reaction in columns-II
507
The minus sign in equation (11) applies to the
reactants, the plus sign to the reaction products.
The absorption fluxes of the different components
are determined from
~jl,=,=kG,j Pt)k[Yj-H~ Xj.k)il
forj=l,...,nA, (13)
and from the application of Ficks law for diffusion:
du,
NjIy=o=
-
Djckdy=o
forj=l,...,n, (14)
and
N J = = -
Dj Ck
dY
YL
forj=n,+l,...,n,. (15)
For the determination of these fluxes, the concen-
tration profiles of the absorbed components, under-
going fast reactions in the liquid film, have to be
computed from the following set of second-order
differential equations:
Djdzx=%r.
or
j=
I,...
dy2 C, *
,nv+n,; (16)
and for the liquid-phase reactant participating in the
fast reactions,
Da+rFr,
/=I k
with boundary conditions
at
y=o
dx,=
Njly=o
dy
-- forj=l,...,nv+n,
DjCk
dxa
- = 0 for the liquid-phase reactant
dy
ticipating in the fast reactions
andat y=y,,
xj = 0 forj=l,...,nv
xj=xik forj=nv+l,...,nv+n,
xa = x, k for the liquid-phase reactant
ticipating in the fast reactions.
par-
(17)
par-
When the kinetic expressions of the nv very fast
and nM moderately fast reactions have the following
simple forms:
rj = kjC_?lC~R
for j = 1,
. . . , nv
(18)
and
rj =
kjC,CtR
for j = nv + 1, . . . , n, +
nM,
(19)
the interfacial fluxes of the absorbed components that
undergo the fast reactions, obtained through the
approximate solutions of Onda et al. [2],
Njly-0 =
fi
1
Hi
tanh (Ha;)
~ -
ko.j(Pt)k + kL,j(Pt)k
Hay
forj=l,...,nv, (20)
are not necessarily computed from the integrated
equations (16) and (17), but may also be obtained
through
HjXj,k
Njly-o= 1
-
cash (Ha;)
Hj
tanh(Ha;)
ko,jG,)k + kL.j(Jt)k
HaJ
forj=n,+l,...,nv+n,
and
Njly-yL=
Ha ,k ,c xj,k>i-xj,kcosh Ha~)
I
LJ k
sinh (Ha;)
forj=nv+l,...,nv+n,
with
HI = Hi(Pth
I
ck
and provided that Ha; is expressed by
(21)
(22)
Haj =
mj,,y+aj, k,C - I (xi k)?J - (xK ,+)yDj
kLJ
forj=l,...,nv (23)
and
/
kL.j
for j = nv + 1, . . . , n, + nM.
(24)
If one or more of the fast reactions have a more
general kinetic expression, the set of second-order
differential equations (16) has to be solved numer-
ically. The integration is performed by means of a
variable-step finite-difference method for the solution
of boundary-value problems.
The fluxes of the remaining absorbed components,
undergoing a very slow reaction or which are only
physically absorbed, are given by
Yj- HjXj*k
Njly-o= 1
Hj
ko,j(Pt)k + kL,j(Pt)k
forj=nv+n,+l,...,n,. (25)
The temperature on a plate is determined from an
enthalpy balance around the plate:
7/25/2019 Rigorous simulation and design Plate Column.pdf
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508
L. DE LEYEand G. F. FROMENT
G-IL;-, ? Xj,k-ICpL.,-Tk
Fk f yj,kCpc;.j
with
j=l
j=l
Q = (-AH,b)(Ft_YFk FkJj,k)
+ (WW, + Li) 5 Xj.kCpL,
forj=l,...,n,+ (27)
,=I
t Tk+,
[
(Fk+\- VW,+)) 2 Yj,k+lCpG.,
and
j-l
+Tvk+,l/ ,k+, j Yv,,, + I CPO., + Twt WV,
Q~k= -AH~ )~,{ ~~Y~k-F,Yj.k)
O L
-[xj,k L;+ W~,)-(~;-,~,k-,
x c xw,.kcPL.,
j=l
= Q: -, , Q;? - 5 Q; , (26)
,= I
+ WVkXW,,,I)
forj=l,...,n,. (28)
start
NO
Gas withdr.
YES
Estimate
I
ITER = 1
k=l
DETERM. PHYS. PROP.
kG kL
PLATE CHARACT.
I
Determine
Haj j = 1 . . . I-IR
YES
NO
Fig. 2(a)
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Simulation of absorption and reaction in columns-11
Equation (26) is written in the following form: 3. A COMPUTER PROGRAM, A-Tray
509
Tk_,A;+TkB;+Tk+,C;=D; k=l,..., N,
The second subprogram of A-Tower, specifically
(29)
with A; = 0 and CN = 0, so that the coefficient matrix
of the set of non-linear algebraic equations (29) is
reduced to a tridiagonal matrix.
The pressure drop on a plate depends upon the
type of tray (sieve, bubble caps, valve, . . . , etc.).
Correlations are available in the literature and these
were incorporated into the program A-Tray.
Ha .
3'
j = l,n
V + M
I
dealing with plate columns is called A-Tray. It com-
prises three modules: one for physical absorption,
one for single absorption accompanied by a single
reaction, reversible or irreversible, and one for mul-
tiple absorption accompanied by a set of parallel or
consecutive reactions, with kinetic regimes ranging
from very slow to instantaneous and non-isothermal,
non-isobaric operation. It is clear from the previous
section that the calculations lead to the number of
xI
; j = l,n
j,k
V + M
I
'k
I
Determine PHYS. PROP.
Determine PHYS. PROP. 1
kG' kL
kG kL
I
Plate
charact.
RUKUGILL Num. Int.
Eqs (l),(2)
y;:k
; j = 1,nA
F;
Eq (3)
';:k
; j=n
A
+ 1,n
G
Eqs (5),(6)
Fk+l
'i,k+l'
j = l,nG
Combin.
Eqs (11),(12)
_ *
L'k
Eqs (11),(12)
'j,k'
j = nA t l,nL
Eqs (8),(9),(10)
'j,k'
j = *v t l,nA
Eqs (23),(24)
Ha :
3'
j = l.nV t nM
Calculate Ck
I
Plate chat-act.
I
RUKUGILL Num. Int.
Eqe (l),(2)
y;:k
; J = l,n
A
F;
Eq (3)
y;;k
; j = nA + l,nG
Eqs (5),(e)
Fk+l
yj,ktl'
j = 1,n
G
Num.
Integr.
2ndorder
Diff.
eqs (16)
xI.
j = 1,
J*k
V + M
dc.
5-l YYL
; j = nv t l,nV t M
Eqs (8),(9),(10)
'j,k'
j = nv t l,nA
Calculate Ck
d
Fig. 2(b)
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510
L.
DE LEYE nd G. F.
FROMENT
real-not theoretical-trays. By way of example, the
algorithm used for the case whereby the absorption
A tray-to-tray method is used, starting at the top
plate of the column. The calculation of the successive
is accompanied by Type 1A parallel reactions,
defined in Part I [1] of this paper, is shown in Fig. 2.
estimates of the unknown variables at the top and the
various plates is reduced to the problem of solving a
NO
I
(APt)k-+.(Pt)k; k = 1 . . . N
M0
c
I
Estimate
Estimate
yj,l'
j = 1 . . . nC-1
'j,l'
j = 1 . . . nA
F1
L
I
TV
ITER = ITER t 1
I
b
(x. k)E
SSQ,
=
Z( J9
- (x. k)C 2
('j,k)E
) tZ(
(Ha" .jE - (Ha .)
-q2 t
(
(Ha j)E
('k)E - ('k)C)2
(=k)E
(Xi k)E -
(Xi,k)C 2
(x*, )E - (Xi,
SSQ, = Z(
('j,k)E
) + Z( .lgk
J,k)'
('I. )E
)2
+ (
(CkjE - (CkjC 2
)
J,k
(=k)E
(x. k)E
SSQ, = Z(
- (x. k)C 2
) +(
Cc,), -
(=k)C 2
('j,k)E
('k)E
)
Fig. 2(c)
Fig. 2(a-c). Flow chart of the algorithm for the simulation of a plate column in which absorption is
accompanied by a Type IA system of parallel reactions.
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Simulation of absorption and reaction in columns---II
511
Table 1. Constructive details of the valve trays in
the H,S-DEA column
Property
Active area, n (m) 0.4225
Relative free area on plate
0.153
Weir length (m)
0.872
Weir height (m)
0.066
Valve thickness (m) 0.00188
Table 3. Commuted results for the H,S-DEA absorption column
Top
column
Bottom
column
set of non-linear algebraic equations. For this pur-
pose the program contains Wegsteins method [3] and
the generalized secant method [4]. The application of
A-Tray to a couple of important industrial processes
is illustrated in the next section.
L (kmol/h)
F (kmol/h)
YHB
xti,s
+wx-I
XHS-
;;;y
T (R)
A: (m2/m)
ko, HZ (kmollm h b)
F. ::)(mih)
F
LI
2208.8
2247.9
161.69
200.8
0.13 x lo-
0.195
0.0
0.134 x 10-J
0.41 x lo-
0.230 x IO-
0.0
0.173 x 10-l
0.0
0.173 x 10-l
7.47
7.590
318.15
321.5
535.68
292.45
0.442
0.443
0.367
0.387
0.153 0.169
0.371
0.328
No. of iterations: 4
CPU time used (Data General MV 6000): 25 s
4. EXAMPLES OF THE APPLICATION OF A-Tray
4.1. The absorption of H2S in an aqueous di-
ethanolami ne (DEA) solut ion
I n this example a DEA solution is used for the
removal of H,S from a refinery stream. The gas feed
has an average molecular weight of 24.9 kg/kmol and
contains 19.5 mol of Hz S. The flow rate, temperature
and pressure of the gas feed are 200.85 kmol/h,
318.15 K and 7.6 b, respectively. A 20 wt% DEA
solution at a temperature of 318.15 K is used as
solvent. Its flow rate is 2208.8 kmol/h. The column
has a diameter of 0.98 m and is equipped with 18
Glitsch Vl-ballast trays. The constructive details of
the plates are summarized in Table 1.
The solubility of H,S in the solution was taken
from Kent and Eisenberg [8].
The standard correlations incorporated in the pro-
gram, which are listed in Table 2, were used for the
determination of the mass-transfer coefficients and
the different plate characteristics.
The initial estimates of temperature and pressure
on each tray were 3 18.15 K and 7.6 b. The mole
fraction of HIS at the top of the column was esti-
mated to be 1 x lo-, the convergence tolerance was
set equal to 10-j. The results of the computations are
summarized in Table 3.
The absorption of H2S in this solution is accom-
panied by the following overall reaction [5,6]:
H, S + R,NH & HS- +
RNH;
.
(30)
The variations of the mole fractions of H,S in the
gas phase, of DEA and the reaction products in the
liquid phase and of the gas and liquid flow rates along
the column are shown in Fig. 3.
Figure 4 shows the computed temperature and
pressure profiles in the column.
This reaction is instantaneous and reversible.
Data for the determination of the equilibrium
constant of the reaction, K,, were taken from the
literature [7,8].
4.2. The simul t aneous absorpti on of H,S and CO2 i n
an aqueous NaOH solut ion
Densities and viscosities of the solution and
The absorption of H2S and CO2 in an aqueous
diffusivities of the reactants in the solution were
NaOH solution is applied in the purification of the
calculated out of the experimental values [9] and
effluent resulting from the thermal cracking of naph-
literature data [lo, 111. For the determination of the
tha for the production of ethylene. The absorption is
diffusivity of the H,S in water, Wilke-Changs cor-
carried out in a plate column with two NaOH
relation was used. This diffusivity was corrected for
circuits, one with a concentrated and one with a lean
the composition of the aqueous solution according to
caustic solution. The configuration of the tower is
the Stokes-Einstein relationship.
schematically represented in Fig. 5.
Table 2. Standard correlations in
the A-Tray program for the deter-
mination of the mass-transfer
coefficients and the plate character-
istics
Property
ko
k,
A:
h,
f,
&,
h
Correlation
Stichlmair [I 21
Stichlmair [12]
Stichlmair [12]
Stichlmair (121
Stichlmair [I21
Glitsch Inc. [13]
The gas feed to the column, F,, equals
5800 kmol/h. The feed temperature and pressure are
3 13.15 K and 12.8 b. The composition of the gas feed
is given in Table 4. 2510 kmol/h of an aqueous
solution containing 4 wt% of NaOH are fed at the
top of the column. 1500 kmol/h of the liquid solution
is withdrawn from tray 15 and 2300 kmol/h of a
1 wt% NaOH solution is added on the underlying
tray.
The column, with a diameter of 2.764m, is
equipped with 30 V,-Glitsch Ballast trays. The con-
structive details of these trays are given in Table 5.
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512
L. DE LEYE nd G. F.
FROMENT
Gas or liquid flaw rate kmol/h)
0
1000
2000
I
t
TOP
0
0.1 x10-
02x10-
I
0.3 x10- 0.4 x10-
l-
I
I I
I
x, mole fraction
5-
y, mole fraction
Fig. 3. Variation of the mole fractions of H,S in the gas phase, of DEA and the reaction products in
the liquid phase and of the gas and liquid flow rates along the column.
Total pressure b)
TOD
7.5 8.0
x
I _
320
330
Temperature K
1
Fig. 4. Temperature and pressure on each tray in the H,S-DEA absorption column.
The absorption of H,S in an NaOH solution is
accompanied by the following overall reaction [14]:
H,S + NaOH 2 NaHS + H20.
(31)
This reaction is instantaneous and reversible.
In strong OH solutions CO2 is undergoing the
following overall reaction [15, 161:
COz + 2NaOH - Na2 CO3 + H,O.
(32)
Since NaOH and the salt products are completely
dissociated, reactions (31) and (32) can be presented
in ionic form:
H2S + OH- & HS- + Hz0
(33)
and
CO2 + 20H- - CO:- + H,O.
Fig. 5. Schematic representation of the H,S-CO,-NaOH
(34)
column.
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Simulation of absorption and reaction in columns-11 513
Table 4. Composition of gas feed
for the H,S-CO,-NaOH absorp-
tion column
Component
Mole fraction
KS
0.00079
CO,
0.00055
CH,
0.28612
GH,
0.31337
C,H,
0.07493
C,H,
0.10218
C,H,
0.0442
C,H,s
0.0171
H,
0.16076
Table 5. Constructive details of the ballast trays in
the H,S-CO,-NaOH absorntion column
Prooertv
Active area, C2(m*) 5.072
Relative free area on plate 0.1869
Weir length (m) 2.259
Weir height (m) 0.05
Valve thickness (m)
0.00188
Density material (kg/m) 8169
The equilibrium constant K, of the first reaction is
W-1
K1 = (HrS)(OH-)
The kinetic expression of the reaction with CO2 has
the following form:
r =
kCco,
CoH
For the determination of the equilibrium constant
K, , data of Edwards et al. [17] were used. The
reaction rate coefficient
k
in equation (36), as a
function of temperature and ionic strength of the
Table 6. Compositions, flow rate and temperature
of the intermediate liquid withdrawal (W,,,) and
liquid feed (WV,,) in the H,S-CO,-NaOH absorp
tion column
W (kmol/h)
XHlS
xcol
hOH
%w-IS
%&go,
T
(K)
Stream Wwll Stream IV,,,
1500
2300
0.123 x lo-
0.0
0.0
0.0
0.183 x lo-
0.4529 x IO-
0.602 x 10-J
0.0
0.710 x lo-*
0.0
314.63
313.15
Table 7. Computed results for the H -CD-NaOH absorption
column
L (kmol/h)
F (kmol/h)
YH2.s
Y,Z
+s
xcol
+&OH
+WiS
XN.EO,
P, b)
T (K)
A ; (m2/m)
IC0.u2skmollm2 h b)
ko.,,, (kmol/m h b)
k,n,, (m/h)
k,, co1 (m/h)
hF (m)
el.
Haco2
Top
Bottom
column
column
2510 3314.6
5792.2 5800
0.103 x 10-r
0.792 x 10-s
0.132 x 10-s
0.551 x lo-
0.0 0.903 x 10-s
0.0 0.0
0.1842 x 10-l
0.551 x 10-Z
0.0
0.138 x 1O-2
0.0 0.930 x 10-a
12.569 12.79
314.11 313.78
525.7 523.1
0.401 0.381
0.392 0.378
0.390 0.313
0.429 0.410
0.159 0.170
0.225 0.226
76.1 39.3
No. of iterations: 8
CPU time used: 242 s
Flow rote (kmol/h)
0
2500
5000
b
0. 1 x10 1
I
I
x, mole fraction
5
-
NoOH
10
25
Bottom
0
0.1 x10-3
0.5 x10-3
01 x10-z
02x10-4
I
*
F
y, mole fraction
Fig. 6. Variations of the mole fractions of the different components in the gas and liquid phases and of
the gas and liquid flow rates along the H,S-CO,-NaOH absorption column.
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514
L. E LEYEand G. F. FROMENT
TOP 12 0
,
1
Total pressure (b)
12 5 130
30
ottom >\:
3,0
315 320
5
0): 15
T
10
Temp mtermed
is
laquld feed
i
4
f;
a
20
T
25
Temperature
1
K)
Fig. 7. H -CO, absorption in NaOH. Temperatures and
pressures along the column.
solution, is given by Hikita et al. [16] and Pinsent et
al. [18].
The simultaneous absorption of H,S and CO2 in
the NaOH solution is accompanied by a Type 1B
system of parallel reactions.
The diffusion coefficients of H,S and CO, in Hz0
were determined from experimental data [9, 191.
These coefficients were corrected for the composition
of the liquid using the Stokes-Einstein relationship.
For the determination of the diffusion coefficients of
the ionic species the correlation of Nernst-Haskell
[20] was used.
The solubilities of H,S and CO, in H,O were
computed from data by Edwards et al. [17]. They
were corrected for the ionic strength of the solution.
Again, the standard correlations (see Table 2) in
the program were used for the determination of the
mass-transfer coefficients and plate characteristics.
The initial estimates of temperature and pressure
on each tray were 313.15 K and 12.8 b. The mole
fractions of H,S and CO2 at the top of the column
were estimated to be 1 x lOen and 1 x 10m6. The
convergence tolerance was set equal to lo-. The
computed results are summarized in Tables 6 and 7.
The reaction with CO2 is in the very fast regime.
The variations of the mole fractions of the different
components in the gas and liquid phases and of the
gas and liquid flow rates along the column are shown
in Fig. 6. Fig. 7 shows the computed temperatures
and pressures along the column.
NOMENCLATURE
A, = Absorbed component j
a = Stoichiometric coefficient
A, = Gas-liquid interfacial area per unit liquid
A: = Gas-liquid interfacial area per m3 froth on the
volume (m2/m3)
plate (m2/m3)
a; = Interfacial area per unit of packed column
(mlm)
C, = Molar concentration of component A
(kmol/m)
C, = Total molar concentration in the liquid on
plate k (kmol/m)
cP= Specific heat (kJ/kmol K)
D = Molecular diffusivity (m2/h)
dk = Column diameter (m)
F =
Total molar gas flow (kmol/h)
F, = Enhancement factor
Fk = Molar gas flow rate leaving plate k (kmol/h)
Hj =
Henrys coefficient for absorbed component j
(b m3/kmol)
Ha, Ha = Hatta number, modified Hatta number
-AH, = Heat of absorption of component j (kJ/kmol)
-AH? =
Heat of reaction of reaction i (kJ/kmol)
& = Froth height on plate (m) .
Ki =
Equilibrium constant of reaction j
k
kj = Reaction-rate coefficient of reaction j
o, A, = Gas-side
mass-transfer
coefficient for
k
absorbed component A, (kmol/m2 h b)
, *. =
Liquid-side mass-transfer coefficient of
-_I absorbed component A, (m/h)
L = Volumetric liquid flow rate (m3/h)
L = Molar liquid kow rate (kmoljhj
L& = Molar flow rate of liquid feed to column
(kmol/h)
L; = Molar flow rate of liquid stream leaving plate
k (kmol/h)
mj,, = Reaction order with respect to component j
in reaction I
h4 = Molecular weight (kg/kmol)
m = Reaction order
Njl,-0
= Interfacial flux of component j per unit
gas-liquid interfacial area (kmol/m2 h)
n, = Number of absorbing components
n, = Number of reactions in the liquid phase
no = Total number of components in gas phase
nL = Total number of components in liquid phase
nM = Number of gas-phase components involved in
moderately fast reactions
np = Number of reaction products in the liquid
phase
na = Number of reactants in liquid phase
n, = Number of gas-phase components involved in
very slow reactions
nv = Number of gas-phase components involved in
very fast reactions
p = Partial pressure (b)
pt =
Total pressure (b)
P, = Product j
r = Reaction rate (kmol/m h)
Rj = Liquid-phase reactant j
Q = Total heat of absorption of component j on
plate k (kJ/h)
QF = ;f;;;,heat of cooling taken away from plate
QTk = T )heat of reaction of reaction j on plate k
Tk =
Temperature on plate
k
(K)
T,, = Temperature of intermediate gas feed to plate
k (K)
T,, =
Temperature of intermediate liquid feed to
plate k (K)
V,, = Flow rate of intermediate gas withdrawal
from plate k (kmol/h)
X, = Mole fraction of component j in the liquid
bulk
V,, = Flow rate of intermediate gas feed to plate k
(kmol/h)
.x~,~ Mole fraction of component j in the bulk of
the liquid stream leaving plate k
x~,,~ = Mole fraction of component j in the inter-
mediate liquid feed to plate k
y = Coordinate perpendicular to the gas-liquid
interface (m)
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yr, = Location of reaction front of reaction j (m)
yo = Gas-film thickness (m)
y, = Mole fraction of component j in the bulk of
the gas phase
yik = Mole fraction of component j in the bulk of
the gas stream leaving plate k
y, = Liquid-film thickness (m)
J+,,~ = Molar fraction of component j in the inter-
mediate gas feed to plate k
z = Axial coordinate in the froth on the plate (m)
Greek symbols
eL = Liquid hold-up of packing or fraction of
liquid in the froth
pL = Liquid density (kg/m3)
R = Cross-section of tower (m2)
R, =
Active area of plate (m)
Subscripts
A, = With respect to absorbed component j
b = In the bulk of the gas or liquid phase
Cj = With respect to the consecutive component j
G=Gas
i = At gas-liquid interface
j = Co&one& index
k = Plate number
14.
5.
6.
7.
8.
9.
10.
11.
12.
13.
L = Liquid
Pj= With respect to product j
RI= With respect to reactant j
15.
16,
Superscripts
G = In gas phase
L = In liquid phase
in = At inlet
out = At outlet
eq = Equilibrium value
abs = Absorption
R = Reaction
C = Cooling
17.
18.
19.
20.
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