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Unsteady state shnulation of “SORBEX” system with nonlinear adsorption isotherms
Unsteady state simulation of “SORBEX” system with nonlinear adsorption isotherms A. K. M. Shamsur Rahman, M. M. Hassan, and K. F. Loughlm Department of Chemical Engineering, Dhahran, Saudi Arabia
King Fahd University of Petroleum
& Minerals,
An unsteady-state model of the “SORBEX” system is developed using a nonlinear equilibrium isotherm. This model is solved from the unsteady state to steady state using the dispersed plug flow model with Danckwert boundary conditions. The effect of various process parameters on the performance of the system are investigated. The present study reveals that the system performance and dynamics are strongly dependent on bed length, column diameter, feed and eluent flow rate, switch time, and nonlinearity of the isotherm. There exists a set of optimum values of these process parameters that represents the proper combination for best performance. The results obtainedfrom the present simulation for the limiting case of linear isotherms (glucose-fructose) and nonlinear isotherms (monoethanolamine-methanol) systems are compared with experimental data and were found to agree well.
Keywords: adsorption;
continuous countercurrent;
modeling; nonlinear isotherm; unsteady state
Introduction In previous work’ a general and efficient unsteady state model with nonlinear equilibrium isotherm for continuous countercurrent adsorption system represented by two sections was developed. Though the system proved efficient for separation of fructose from glucose, the concentration of fructose was very low in the extract. A costly evaporation process would be required to recover the product at a desired concentration level. To overcome this disadvantage, a more practical process called “SORBEX” system was introduced by UOP.’ In this process, the countercurrent system is divided into four sections, and desorption is achieved by correctly adjusting the flow rates in each section using water (eluent) instead of a separate purge column.2-4 The first reported application of this process was by Bieser and deRosset.’ Although some process details have been published both for the linear isotherms glucose-fructose separation6*7*1’*12 and nonlinear isotherms MEA-MOH separation,8-‘0 only limited efforts have been directed toward modeling and experimental investigation of the dynamics of such systems. A general
Address reprint requests to Dr. K. F. Loughlin at the Department of Chemical Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia. Received 9 November 1992; accepted 13 July 1993
0 1994 Butterworth-Heinemann
review of countercurrent systems has been reported by Ruthven and Ching.i3 The simplest theoretical model of the SORBEX system based on steady-state conditions and linear isotherm was presented by Ching et al.’ and was shown to provide a good representation of their experimental data on the glucose-fructose system. The numerical simulation of the unsteady-state case with linear isotherm was published by Hidajat et a1.9 The system was considered as a cascade of ideal theoretical stages with the number of stages determined from pulse chromatographic experiment, which limits its applicability to linear isotherms. Further, dispersed plug flow was assumed in this study. A steady-state model of the SORBEX system has been presented by Ching et a1.8 for the nonlinear isotherm. In most practical systems the concentrations of adsorbable species are large, and therefore the effect of nonlinearity of the isotherm becomes very significant in optimizing the operating parameters. The more general case of solving the unsteady-state system with plug flow for a nonlinear isotherm needs to be solved to comprehend the effects of various process parameters on the system performance . In this article, a general mathematical model of the continuous countercurrent “SORBEX” system is developed that includes the nonlinear (Langmuir) equilibrium isotherm. The equations developed have been solved from unsteady to cyclic steady state. The effect of various operating parameters (viz. switch time, feed
Sep. Technol.,
1994, vol. 4, January
27
Unsteady state simulation
of “‘SORBEX”system:
A. K. M. S. Rahman et al.
flow rate, eluent flow rate, bed length, etc.) on the
Extract
Feed
performance of the system has been investigated. Comparisons of the experimental data for the MEAMOH**‘Oand glucose-fructose system7v9 with the present simulation results show good agreement.
Theoretical model The model is developed for 12 columns with four hypothetical countercurrent sections whose configuration was reported by Ching et al.’ as shown in Figure 1. The system thus may be considered as approximately equivalent to the hypothetical continuous countercurrent arrangement shown in Figure 20. The equivalent solid velocity (u) is given by the ratio of individual column length to switch time. The theoretical model for the equivalent continuous countercurrent svstem can be obtained from an overall mass balance ardund a differential volume of adsorber shown in Figure 2b. The following assumptions are adopted to formulate the model:
E&nt Figure 1 bed.
Schematic diagram of four-section
Raffinatr
simulated
moving
Notation
cij C;
cz,;*
ki L L* Lf Lsj
Pe,. qf
Langmuir equilibrium constant sorbate concentration in feed stream sorbate concentration in fluid phase of component i sorbate concentration in fluid phase for component i in section j dimensionless sorbate concentration in fluid phase for component i in section j inlet concentration of fluid phase for component i at section j initial (t < 0) steady state values of c desorbent flow rate axial dispersion coefficient (for flow in section j) eluent flow rate feed flow rate dimensionless factor, (VjL,)/( Vs4L~j) adsorption equilibrium constant for i(i = A or B) overall effective mass-transfer coefficient liquid flow rate length of adsorption bed length of adsorption bed following the feed point length of adsorption section axial Peclet number for section j( V’jL,l
&j>
average solid phase concentration, is in eauilibrium with fluid ohase concentration of feed stream average solid phase concentration component i in section j
Sep. Technol.,
1994, vol. 4, January
4s * i S t u
vj Yf V,
xi
zj zsj
dimensionless
distance Gzj
*
packed to void ratio, (1 - &)I&
Q,
nonlinear factor, 1 - 5 hi i=l L. dimensionless mass transfer parameter ki f
OLi cu,B
%j ii 7
of
dimensionless solid phase concentration of component i at section j saturated solid phase concentration equilibrium solid phase concentration raffinate flow rate solids flow rate time linear velocity of solid velocity of fluid at section j velocity of fluid at the section following the feed point velocity of fluid at the section following the eluent point mole fraction of component i axial distance coordinate
Greek letters
which
1
28
Q;
separation factor ratio of downflow to upflow rates = (1 - &)K,.UIEVj bed porosity nonlinearity parameter, qo/q, dimensionless time
4
Unsteady state simulation of ‘SORBEX”system: Boundary
A. K. M. S. Rahman et al.
conditions
at Zj = 0, ROf
acJj
firmtO,R
DL
10 rich)
Food,
= -
J aZj
vj(c~lzj=o- cijl,=o+)
(4)
zj=o+
at zj = Lj,
F
acii =
(5)
0.0
aZj
Material balances Material balances for each section are given by the following equations. At the inlet of section IV -
Yoke-w c&4=0-
=
c~31zJ=L,
(6)
3
*R-F1
(E
At the inlet of section III I
c&o- =
iii T
L”
1
2.0
x.0,
ci21zz=O-
Plug flow of solid Axially dispersed plug flow of fluid Isothermal operating conditions Linear driving force expression for mass-transfer
a2cii Li azj
~~+(!+!!!Q J
-
v2)cf
(7) v3
=
cillz,=L,
(8)
=acii + at
(9)
I
Using the following dimensionless C;
Q;
=;
5
t
f$
=
l_a2ch --
=F.
a7
variables
3
‘j = L,
s
’ [ Pej azj2
az, +
aQ!.
yaks
aQ!.
- WKi~a7
J
aQ;_ a7
aZj
&
cillz,=O= (ci41q=Ls4)~
the preceding equations are written for ith component and jth section as
are of nonlinear Langmuir form
Adsorbent is considered to be flowing with a downward velocity u = L*lt, where L* is the individual column length and t, is the switch time, whereas the liquid is flowing upward with a velocity Vj. The basic differential equation describing the system dynamics for ith component and jth section can be written as D
tv3
At the inlet of section I
lb)
Isotherms
+
At the inlet of section II
Figure 2 (a) Schematic diagram of four-section equivalent countercurrent system. (b) Schematic diagram of the mass balance of jth section for four-section equivalent countercurrent model.
1. 2. 3. 4. rate 5.
v*ci21z2=L,I
C&
4
-
l + ~ hi(C~ - 1.0)
1 (10)
Q;
(11) 1
i=l
( ) ly
!.$i
(1)
For a Langmuir type of equilibrium isotherms, the rate equation can be written as
Initial conditions c; = 0.0 Boundary
(2)
(12) conditions
at Zj = 0.0 (13)
Initial conditions cij = 0.0
(3)
where CZ; is the inlet concentration Sep. Technol.,
of i for section j,
1994, vol. 4, January
29
Unsteady state simulation
of “SORBEX”system:
A. K. M. S. Rahman et al.
which can be obtained from the material balance equations .
Table 1 Parameter MOH system
values for the glucose-fructose
Parameter
5
0.0
=
(14)
dZi
Material
balances
At the inlet of section IV (15)
CZ& = Cl%,= 1.0
and MEA-
Linear case of Ching et aL7
Nonlinear case of Ching et aLB
5,5 30.5 10.0 38.8 13.8 16.8 100 4.3.3.2 5.1 0.0.0.0 0.88 0.50
20.10 22.1
Feed composition (%A,%B) Switch time, min Feed flow rate, mL/min Eluent (desorbent), mL/min Raffinate rate, mL/min Extract rate, mL/min Bed length, cm Configuration Column diameter, cm A(A,B) KA
Kt?
375:: 13.7 44.0 100 4.3.3,2 5.5 0.435,o.o 1.24 0.63
At the inlet of section III Note: A = fructose or MEA; B = glucose or MOH.
W2lz*=,.o + cz,
w3
-
V2)
=
(16) v3
MI
A M2,l C’A,,,,
At the inlet of section II cc2
=
Ci),lz,
+
C i=2
AM2,iCa,,,i
+
(17)
= 1.0
At the inlet of section I CZi, = (C.&= ,.I))$
(18)
I
The system of coupled differential equations described by Equations lo-18 has been solved from transient to steady state conditions by the method of orthogonal collocation. Equations 10 and 11 with boundary conditions represented by Equations 13 and 14 may be expressed in the collocation form for component A and section 1 as
AM~.M~C~,,,M~
=
0
(21)
where CHZ = CZJ,, the inlet dimensionless concentration of component A to section I. The detailed derivation of Equations 19-21 is shown elsewhere.14 Similar equations can be developed for all the four sections. For the system in the present study, two columns in section IV, three columns in sections II and III, and four columns in section I have been considered. This system configuration was used by Ching et al.’ in their experiments. Sixteen collocation points were used for each section, which requires the solution of 256 simultaneous nonlinear ordinary differential equations. The preceding sets of differential equations have been solved using the functional iteration method.
Results and discussion
Lg. pe,
+
-
+
C'A.,,j
‘I’K@a, 1 +
Q
h.l, ,I1
Boundary
Effects
Y@Aj,M2QA,,,M2 - Aj,M2C~,I%M~
J,M~
AA(Ca,,,j
-
I)
+
hB(Ch,,,j
-
‘1
(19)
conditions
are written as
1(
A,,,G,,,i
+ A,,.wCL,,JQ + 2 A,,iC,k,,,i i=2
and 30
Sep. Technol.,
1994, vol. 4, January
(20)
of process parameters
on separation
The proposed theoretical model was solved for different cases to observe the effects of various parameters on the performance of the system. In Table 1, a set of parameters for the MEA-MOH system is tabulated that was reported by Ching et al.’ and Ching et al.,* and is considered our base case. The results of the numerical simulation from transient to the steady state conditions for various system parameters are shown in Figures 3-8. The effect of these changes in parameters on the different dimensionless groups are shown in Table 2. It may be noted here that the mass-transfer resistance for MEA-MOH system has been reported to be very 10w,~ and therefore the dimensionless parameter (Yhas no effect on the system performance. The results of the present simulation are analyzed in terms of degree of separation in extract and raffinate, which is defined as E = (CA - CL)/(Ch + Cj& and R = (CL - C’J/(Ck + CA) where E and R refers to the extract and raffinate phases, and CA and CL are dimen-
Unsteady state simulation
of ‘SORBEX”system:
A. K. M. S. Rahman R, E
--1:-,:----------------_________________________________________ -
.,
et al.
_.
E
__
,.
E
.
‘0 c
0.60-
L 1
0.40-
8
0.20 -
t E
0.00 -’
.z 6 b
- 0.20 -
j;
- 0.40-
5
-
t zb
- 0.60 -
0.60
-
-Configuotion
- 3,2,2,1
‘..“.-Configuration
- 4,3,3,2
----Configuration
* 6,6,6,2
- l.OO-
I 500
I 1000
I 1500
I 2000
I 2soo
I 3000
I 3600
I
I
4000
4300
time (minutrrl
Figure 3
Effect of configuration
on the performance
of the four-section
sionless concentrations of MEA and mOH, respectively. Using this definition the degree of separation can be represented in a - I to + 1 scale. As the degree of separation approaches 1, a better separation is achieved. Alternatively, when the degree of separation approaches - I, this implies that the E phase is component B rich, and in the R phase the concentration of component A that is the strongly adsorbed species is high. At degree of separation 0 there is no separation between the components. As may be observed in Figure 3, a relatively pure product can be obtained in both extract and raffinate streams using a 4,3,3,2 bed configuration. When the sizes of the sections are doubled, the separation improves. But when the bed number is reduced by one in each section, the separation becomes relatively poorer in the extract. The steady-state concentration indicates that both the previous configurations produce relatively pure products. It is also observed that except for the E curve of 3,2,2,1 configuration, all curves reach steady state after about 1,000 min. In case of 3,2,2,1 arrangement the E curve takes about 1,500 min to attain the steady state. The change in column configuration has a tremendous effect on all of the dimensionless groups of Table 2 except for yij. The yti criterion for good separation as described by Ching et a1.,7*8which is section section sectlon section
IV: ylIv > 1, y21v > 1 III: yurl > 1, y2u, < 1 II: yllr > 1, yzrr < 1 I: yu < 1, y2* < 1
is followed in all sections. If yti values are compared for both 8,6,6,4 and 3,2,2,1 configurations, it can be seen that they are identical and match exactly with
equivalent
System.
that of the base case. For the 8,6,6,4 configuration the Peclet numbers for all four sections are increased by about 100%. Conversely, at 3,2,2,1 arrangement flow ratio Fs are decreased by 30%, and the Peclet numbers are reduced by 100%. Therefore, it can be concluded that the degree of separation is more strongly dependent on yij rather than on the other dimensionless numbers. Figure 4 shows the effect of switch time on degree of separation. It is clear that the switch time of 22.1 min gives the best product separation among the three switch times reported here. When the switch time is increased to 30.4 min the degree of separation is reduced both in the extract and raffinate phases. This behavior can be explained by the change in the dimensionless groups. The change in switch time affects the solid phase velocity, which eventually changes the Peclet numbers because the dispersion coefficient used in the definition of Peclet number is taken to be a function of equivalent solid phase velocity also. At a 15min switch time and at a 30.4-min switch time the magnitudes of Peclet numbers are decreased and increased, respectively, by about 20% and 30%. Because yii is a strong function of solid phase velocity, the effect is quite significant. At a switch time of 30.4 min y21v is less than 1 and thus falls into the bad separation category. Conversely, at a 15min switch time, the magnitude of yy for MOH in sections III and II and yu for MEA in section I are greater than 1, which violate conditions of good separation. At lower switch time, though the rtinate produces almost pure MEA instead of MOH, as indicated by degree of separation (- l), lack of separation (-0) of MOH in extract makes this switch time unacceptable. The effect of individual bed length while maintaining
Sep. Technol.,
1994, vol. 4, January
31
Unsteady state simulation of ‘SORBEX” Table 2
Effect of process parameters
system: A. K. M. S. Rahman et al.
on dimensionless
groups for nonlinear
MEA-MOH
system Section
Effect
Fs
Fz
FI
Pe,
PeJ
Pe*
Pe,
014
a3
a2
Ql
IV
Yl
Y2
Section III
Yl
Y2
Section II
Yl
Y2
Section I
Yl
Y?
0.93
0.83
1.26
17.90
31.77
30.1
53.62
12.05
12.96
14.45
9.57
2.31
1.17
1.85
0.84
1.84
0.94
0.92
0.465
(6)
0.93
0.83
1.28
19.4
34.01
32.4
56.22
10.36
11.14
12.43
8.2
1.98
1.01
1.42
0.722
1.58
0.81
0.79
0.40
cm
(5.1)
0.93
0.83
1.28
18.2
29.16
27.5
50.45
14.34
15.42
17.20
11.39
2.74
1.39
1.97
0.999
2.19
1.11
1.09
0.553
Eluent
(1001
0.86
0.79
1.06
21.0
35.19
33.9
55.94
8.84
10.28
11.2
8.36
1.69
0.86
1.31
0.66
1.43
0.73
0.80
0.41
mLlmin
(75)
1.08
0.93
1.68
13.7
27.34
25.1
50.84
18.75
17.43
20.24
3.59
1.82
2.22
1.13
2.58
1.31
1.07
0.542
Feed
(10)
0.90
0.73
1.10
19.20
33.23
30.1
53.62
10.53
11.75
14.45
2.01
1.02
1.50
0.76
1.84
0.94
0.92
0.465
mLlmin
(3)
0.95
0.88
1.34
17.3
31.14
30.1
53.62
12.79
13.52
14.45
9.57
2.45
1.24
1.72
0.876
1.84
0.94
0.94
0.465
Bed length
(2001
0.93
0.83
1.26
23.0
43.21
40.2
80.64
24.10
25.92
28.91
19.14
4.61
2.34
3.31
1.68
3.69
1.87
1.83
0.93
(50)
0.93
0.83
1.26
12.3
20.77
20.1
32.1
8.03
8.46
7.23
4.78
1.15
0.59
0.83
0.42
0.92
0.47
0.46
0.233
Configuration (8664) (3221)
0.93
0.83
1.26
35.7
63.54
80.3
107.2
25.92
28.91
19.14
2.31
1.17
1.65
0.84
1.84
0.94
0.92
0.465
0.70
0.63
0.84
8.9
21.18
20.1
40.21
6.03
8.64
9.64
7.18
2.31
1.17
1.65
0.84
1.84
0.94
0.92
0.485
(30.4)
0.93
0.83
1.28
21.0
36.45
35.0
59.0
12.05
12.96
14.45
9.57
1.68
0.85
1.20
0.81
1.34
0.88
0.67
0.338
(15)
0.93
0.83
1.28
14.2
26.0
14.4
46.38
12.05
12.96
14.45
9.57
3.40
1.73
2.44
1.24
2.72
1.38
1.35
0.685
Base Diameter
cm
Switch time min
Note: 1 = MEA;
2 = MOH
24.1
11.1 9.57
in y.
the bed configuration of the base case is shown in Figure 5. For bed length of 50 cm, separation in both raffinate and extract has become poorer. In case of bed length of 200-cm raffinate gives pure MEA; however, the separation between MEA and MOH is very low (- - 0.1) in the extract. Among these bed lengths, only the lOO-cm-long columns produce concentrated MEA and MOH. Though change in bed length has changed the dimensionless parameters of Table 2 moderately, it affects the yij values in all the four sections. It is clear from Table 2 that at higher bed length yy values for MOH in sections II and III and y,, of MEA in section I are much higher than 1 and thus fall into the poor separation category. At a bed length of 50 cm -yzj for MOH in section IV and yu for MEA in sections II and III are less than 1, resulting in a poor separation.
The magnitudes of Peclet numbers in all four sections are increased or decreased by 30% when the individual bed length is increased or decreased by a factor of two. At 50 cm bed length curves E and R reach steady state at about 500 and 1500 min. The E curve shows a peculiar behavior at lower time, the degree of separation drops sharply to - 1 level, and then slowly increases to its steady state value. The effect of column diameter is shown in Figure 6. At a diameter of 5.5 cm, separation in both extract and rafhnate is very good but with the increase or decrease of diameter slightly, the degree of separation decreases both in extract and raffinate streams. The change in column diameter changes the flow rates in each section, thereby changing all the dimensionless parameters except the Fs of Table 2. At a diameter of
z
z 1 t‘i e
-------.---.--____.__. __ .. ..-___.___---.-....... --.--.-._ E ~.____.-____._____________.-..---.---_.-----------.--------.- R
W -c s t
-0.20
-
-0.40
-
B 8
-
6 ::
-0.60
-
b 0’
-0.80
-
- 1.00
-
Switch Time
---- Switch Tlme
= 30.4 min.
I 1000
I 1500
I
moo
I
I
2500
3000
I 3500
Time (minutes)
32
Effect of switch time on the performance
Sep. Technol.,
I min.
= 22.
R
I 500
Figure 4
= 15.0 min.
....“’ Switch Time
1994, vol. 4, January
of the four-section
equivalent
system.
I 4000
I 4500
Unsteady state simulation
of ‘SORBEX”
system: A. K. M. S. Rahman et al.
-Bed
L*lgth
....--6.d
Lsngth
=IDO.oan
---Bed
Length
=2OO.ocm
= 5O.Ocm
Time (minutor) Figure 5
Effect of individual
bed length on the performance
of the four-section
equivalent
system.
-------------_.__... _______...-- .---__.- -
6 z
-0.60
-
-1.00
I
I
500
I
I
I
1000
1500
2000
--- Diameter
=5.1 cm
......’Diameter
- 5.5cm
-
=6.0cm
I
I
2500
R
3000
Diameter
I
I
3500
4000
I
4500
Time tminutrs)
Figure 6 Effectof column diameter on the performance of the four-section equivalent system.
6 cm, which is about 10% more than that of the base
case, Peclet numbers are increased by lo%, whereas at a 5.1-cm column diameter, these parameters are decreased by the same percentile. At a diameter higher than that of the base case, rii values follow the specified criterion for good separation except for Q, which barely satisfies the criterion. In case of lower column diameter, yZII and yu do not satisfy the conditions that are required for better separation.
Figure 7 depicts the effect of eluent flow rate on the performance of the system. The degree of separation is largest when the eluent flow rate is 87.4 mL/min. As the eluent rate is increased to 100 mL/min, the degree of separation decreases to 0.5. At an eluent rate of 75.0 mL/min separation becomes zero. This behavior can be explained from the rii values reported in Table 2. At the higher eluent rate yZIv of MOH in section IV is less than 1 and thus violates the criterion Sep. Technol.,
1994, vol. 4, January
33
Unsteady state simulation
co
g E E P i
L z w .E L ‘; e :: J; 6 : b B
of ‘SORBEX”
system: A. K. M. S. Rahman et al.
0.80 0.60 0.400.20
-
0.00
-‘.
-0.20
-
-0.40
-
---- Eluent
= 100.0ml/mi
-
=
Elurnt
...“.. Eluant -0.60
-
-0.80
-
75.0 ml/min
= 87.4 ml/mir
- 1.00 I
I
I
I
I
I
I
I
1000
1500
2000
2500
3000
3500
4000
4500
I
500
Time (minutes) Figure 7
Effect of eluent flow rate on the performance
1.00 - -_
equivalent
system.
....*
--.
--. --._
---_..--_
--I___
0.80 -
of the four-section
0.60
R E
%\ -----------‘~-._.___-_._.__-..-_..._._..___. .._.-_._._._ ___ E ‘\\ L\ ‘--.---- ---._..._.. _______________._ ___.- R
0.40 0.20
----Food
- 10.0 ml/min
-F..d Fee,, ..
= 5. Oml/
= 3.0 ml/min min
0.00
-0.60 -I
500
1000
1500
2000
2500
3000
3500
4000
4500
Tim0 (minutes) Figure 8
Effect of feed flow rate on the performance
of the four-section
of good product purity. Conversely, at a low flow rate, -ya for MOH in sections II and III and y,* for MEA in section I are much higher than 1, leading to a poorer separation. Besides yii, other parameters are not significantly affected by change in eluent rates though this change is affecting the fluid phase velocity in all four sections. The concentration profiles in unsteady region for both higher and lower eluent rates are quite interesting. At an eluent rate of 100 mL/min curve R reaches 34
Sep. Technol.,
1994, vol. 4, January
equivalent
system.
to its steady state value at about 2,000 min. It may be further observed that at lower time up to 1,200 min it produces almost pure MOH in the raffinate stream after which the degree of separation drops to 0.4. At the lower eluent rate the unsteady profiles for both E and R show that both the curves drop to zero separation, which is their steady state value after about 1,800 min of operation. Figure 8 shows the effect of feed flow rate. It can
Unsteady state simulation of *SORBEX”system:
A. K. M. S. Rahman et al.
1.00 Section I ‘0
Section I I
0.60-
5 ._ 5
0.60-
,:’
.’
‘i
g
0
.’
__‘.
0.40-
1.00
‘0
z
x’-
,
0.80 -
...x...
.. ..”
.,
,_,
.. 1:
i’
0 L
E t 5
0
0.60-
.‘. E
.- .. .,
0.40-
0.20 0 0.00
-
I
0.00
I
0.20
I
0.40
1
I
0.60
I
I
0.80
g * z .c z p”
I
Experimental
and theoretical
concentration
. ..
0.00
.. . .
‘... .... ‘....
3 I
Length (Dimenrknlers Figure 9
‘.,.,,
I
I
0.20
I
I
0.40
I
0.60
Comparison with experimental data Linear system. In Figure 9, results of the steady-state solution of the present model is presented for the limiting case of linear system (glucose-fructose) for which the parameters are taken from the reported values of
.“_‘... I
0.60
.
,),._, I
1.00
1
profiles of glucose and fructose (experimental:
be seen that at feed rates of 5.0 and 3.0 mL/min the degree is almost equal, and the degree of separation magnitudes are approximately 1 in both extract and raffinate, which indicates a very efficient separation. At higher feed rates the degree of separation in both the streams declined. As can be seen from Table 2, at both high and low feed flow rates yij values obey the good separation criterion. However, in section IV at high feed flow rate y21v for MOH is very close to 1, which leads to a relatively poorer product composition. The unsteady profiles of both E and R curves for both base case and a feed flow rate of 3 mL/min are quite similar. In both cases curve R reaches steady state instantly, but curve E attains its steady-state value after about 1,300 min. At a feed rate of 10 ml/mitt, curve E reaches to its steady-state value at about 1,500 min and curve R at 2,300 min. But up to about 1,500 min the degree of separation in R stream was + 1, and after that it drops down to its steady-state degree of separation of 0.6. It should be noted that the change in feed flow rates changed only the parameter values of postfeed sections.
I
x, glucose; 0, fructose).
Ching et al.’ and are presented in Table I. In this figure results obtained from experimental studies of Ching et al.’ are also shown. From this figure it can be concluded that the present model, which is a more general one, provides a good representation of the performance of an equivalent continuous countercurrent adsorption system. Nonlinear system. To check the validity of the present model for nonlinear system, computations were performed for the MEA-MOH system. Figure 10 shows a comparison between the steady-state solution of the present model for the MEA-MOH system and the experimental results reported by Ching et al.* and Hidajat et a1.9 This figure shows the profile when only MEA follows a Langmuir type of equilibrium isotherm but MOH follows linear relationship, and there is no isotherm dependency between MEA and MOH. All the curves agree very well with the experimental results. Also shown in this figure are the profiles if both isotherms are chosen linear. It is evident that the prediction is not good with linear isotherm assumption. In Figure II, the performance of the system is shown for the case in which a nonlinear binary Langmuir isotherm for MEA and linear isotherm for MOH are considered. This would make the isotherms coupled as can be observed from Equation 2. It can be seen from this figure that concentration and purity of product in both
Sep. Technol.,
1994, vol. 4, January
35
Unsteady
state simulation
of “‘SORBEX”system:
A. K. M. S. Rahman
et al.
0.70 -% Section
f
Section
0.600.50-
E a”
c .P
0.40-
5 ,0 ‘;
E
0.30-
‘0
‘(! ,’ ,/“
W
E :: 5 0
II
.I’
/’
MEA 1 ”,...;:_.._______-~~.~,~..i~_-;~.~.~~~‘~----~~~~~~-~~~--------- ____-_
0.20-
0.10 0.00 4 0.10 -
I
Section III MOH 0.60 +C-______________X~~=.~-.---.-,T-_____
b s ‘G 2 Z :5
‘..’ ‘. .i&y;,. “I,
o.so-
0.30
1
I
I
I
,
,
I
Section IV
E ._ lf u 5
\.q’i. ‘<..
0.40 -
1
‘\‘.. ‘i.. f5 \” J a” :;r. \;.
-
0
0.00
0.20
0.40
0.60
0.60
Length Figure 10
Experimental
and theoretical concentration
0.00
0.20
0.40
0.60
0.60
I.
(Dimensionless)
profiles of monoethanolamine
and methanol (experimental:
0, MEA; X, MOHI.
0.70 Section
I
Section
II
0.60 -
0.70 Sect ion III
Section
MEA 0.50 ‘0 5 z L E
0.40
-
0.30
-
0.20
-
0.10
....‘.
“-_..
MOH
“....
1
0.00
”
I 0.00
I
0.20
I
I 0.40
I
I 0.60
I
I 0.80
I
I
11
0.00
1
0.20
II
0.40
I
0.60
LengthIDimensionlesrI Figure 11
36
Effect of coupling between isotherms on the concentration
Sep. Technol.,
IV
E I? L z C e :
0.60
1994, vol. 4, January
profile of MEA-MOH
system.
I
I
0.60
.. . . . . .
I
1.00
Unsteady state simulation
extract and raffinate streams become poorer compared with the uncoupled case.
Conclusion A theoretical model of SORBEX system for unsteady state is developed for the nonlinear MEA-MOH system. The model equations are solved to investigate the effect of various process parameters on the performance of this widely used countercurrent adsorption system. The present study reveals that the system performance as well as dynamics are very much dependent on some physical parameters of the system (viz. bed length and diameter of the adsorption columns). Other operating parameters like feed flow rate, eluent flow rate, and switch time affect the performance of the process considerably. The system is very sensitive to these parameters and should be chosen carefully. The results obtained for the case of MEA-MOH, when MEA follows nonlinear (Langmuir) and MOH follows linear equilibrium isotherms, were compared with the experimental results of Ching et al.* and Hidajat et a1.9 at steady state. Also the glucose-fructose systems was investigated and compared with result of Ching et al.’ Good agreements are observed with the predictions from the present model for both systems. The effects of various parameters were obtained for uncoupled isotherm relation between MEA and MOH. The effect of coupling between the isotherms on the system performance was also computed, which indicated that the overall performance becomes poorer. The present model can be employed to predict the performance of countercurrent adsorption systems for various combinations of isotherm relationship (viz. linear-linear, linear-nonlinear, nonlinear-nonlinear, etc.).
of ‘SORBEX”system:
A. K. M. S. Rahman
et al.
The preceding features make the present model more general and versatile for simulation of continuous countercurrent systems from unsteady to steady state conditions for various types of equilibrium isotherms.
Acknowledgments The authors wish to acknowledge the support provided by King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia.
References 1.
2. 3. 4. 5. 6. 7. 8. 9. IO. 11. 12. 13. 14.
Hassan, M.M., Rahman, A.K.M.S. and Laughlin, K.F. Sep. Z’echnol. 1994,4, 15-26 Broughton, D.B., U.S. Patent 3,291,726, 13 December 1966 Broughton, D.B., Chem. Eng. Prog. 1968,64,60 Broughton, D.B., Euzil, R.W.N., Pharis, J.M. and Brearley, C.S. Chem. Ena. Prop. 1970, 66. 70 Bieser, H.J. anddeRo&et, A:J. 28th Starch Convention, Detmold, West Germany, 27-29 April 1977 Ching, C.B., Hidajat, K., Ho, C. and Ruthven, D.M. Chem. Eng. Sci. 1987,42, 2547-2555 Ching, C.B., Ruthven, D.M. and Hidajat, R. Chem. Eng. Sci. 1985.40, 1411-1417 Ching, C.B., Ho, C. and Ruthven, D.M. Chem. Eng. Sci. 1988,43, 703-711 Hidajat, K., Ching, C.B. and Ruthven, D.M. Chem. Eng. J. 1986,33, B55-B61 Hidajat, K. and Ching, C.B. Truns Z Chem. Eng. 1990, 68, 104-108 Neuzil, R.W. and Jensen, R.A. 85th National Meeting AICHE, Philadelphia, June 1978 de Rosset, A.J., Neuzil, R.W. and Korous, D. Znd. Eng. Chem., Process Des. Dev. 1976, 15,261-266 Ruthven, D.M. and Ching, C.B. Chem. Eng. Sci. 1989, 44, 101I-1038 Rahman, A.K.M.S. MS. diss., 1992. King Fahd University of Petroleum & Minerals, Dhahran
Sep. Technol.,
1994, vol. 4, January
37
King Fahd University of Petroleum
& Minerals,
An unsteady-state model of the “SORBEX” system is developed using a nonlinear equilibrium isotherm. This model is solved from the unsteady state to steady state using the dispersed plug flow model with Danckwert boundary conditions. The effect of various process parameters on the performance of the system are investigated. The present study reveals that the system performance and dynamics are strongly dependent on bed length, column diameter, feed and eluent flow rate, switch time, and nonlinearity of the isotherm. There exists a set of optimum values of these process parameters that represents the proper combination for best performance. The results obtainedfrom the present simulation for the limiting case of linear isotherms (glucose-fructose) and nonlinear isotherms (monoethanolamine-methanol) systems are compared with experimental data and were found to agree well.
Keywords: adsorption;
continuous countercurrent;
modeling; nonlinear isotherm; unsteady state
Introduction In previous work’ a general and efficient unsteady state model with nonlinear equilibrium isotherm for continuous countercurrent adsorption system represented by two sections was developed. Though the system proved efficient for separation of fructose from glucose, the concentration of fructose was very low in the extract. A costly evaporation process would be required to recover the product at a desired concentration level. To overcome this disadvantage, a more practical process called “SORBEX” system was introduced by UOP.’ In this process, the countercurrent system is divided into four sections, and desorption is achieved by correctly adjusting the flow rates in each section using water (eluent) instead of a separate purge column.2-4 The first reported application of this process was by Bieser and deRosset.’ Although some process details have been published both for the linear isotherms glucose-fructose separation6*7*1’*12 and nonlinear isotherms MEA-MOH separation,8-‘0 only limited efforts have been directed toward modeling and experimental investigation of the dynamics of such systems. A general
Address reprint requests to Dr. K. F. Loughlin at the Department of Chemical Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia. Received 9 November 1992; accepted 13 July 1993
0 1994 Butterworth-Heinemann
review of countercurrent systems has been reported by Ruthven and Ching.i3 The simplest theoretical model of the SORBEX system based on steady-state conditions and linear isotherm was presented by Ching et al.’ and was shown to provide a good representation of their experimental data on the glucose-fructose system. The numerical simulation of the unsteady-state case with linear isotherm was published by Hidajat et a1.9 The system was considered as a cascade of ideal theoretical stages with the number of stages determined from pulse chromatographic experiment, which limits its applicability to linear isotherms. Further, dispersed plug flow was assumed in this study. A steady-state model of the SORBEX system has been presented by Ching et a1.8 for the nonlinear isotherm. In most practical systems the concentrations of adsorbable species are large, and therefore the effect of nonlinearity of the isotherm becomes very significant in optimizing the operating parameters. The more general case of solving the unsteady-state system with plug flow for a nonlinear isotherm needs to be solved to comprehend the effects of various process parameters on the system performance . In this article, a general mathematical model of the continuous countercurrent “SORBEX” system is developed that includes the nonlinear (Langmuir) equilibrium isotherm. The equations developed have been solved from unsteady to cyclic steady state. The effect of various operating parameters (viz. switch time, feed
Sep. Technol.,
1994, vol. 4, January
27
Unsteady state simulation
of “‘SORBEX”system:
A. K. M. S. Rahman et al.
flow rate, eluent flow rate, bed length, etc.) on the
Extract
Feed
performance of the system has been investigated. Comparisons of the experimental data for the MEAMOH**‘Oand glucose-fructose system7v9 with the present simulation results show good agreement.
Theoretical model The model is developed for 12 columns with four hypothetical countercurrent sections whose configuration was reported by Ching et al.’ as shown in Figure 1. The system thus may be considered as approximately equivalent to the hypothetical continuous countercurrent arrangement shown in Figure 20. The equivalent solid velocity (u) is given by the ratio of individual column length to switch time. The theoretical model for the equivalent continuous countercurrent svstem can be obtained from an overall mass balance ardund a differential volume of adsorber shown in Figure 2b. The following assumptions are adopted to formulate the model:
E&nt Figure 1 bed.
Schematic diagram of four-section
Raffinatr
simulated
moving
Notation
cij C;
cz,;*
ki L L* Lf Lsj
Pe,. qf
Langmuir equilibrium constant sorbate concentration in feed stream sorbate concentration in fluid phase of component i sorbate concentration in fluid phase for component i in section j dimensionless sorbate concentration in fluid phase for component i in section j inlet concentration of fluid phase for component i at section j initial (t < 0) steady state values of c desorbent flow rate axial dispersion coefficient (for flow in section j) eluent flow rate feed flow rate dimensionless factor, (VjL,)/( Vs4L~j) adsorption equilibrium constant for i(i = A or B) overall effective mass-transfer coefficient liquid flow rate length of adsorption bed length of adsorption bed following the feed point length of adsorption section axial Peclet number for section j( V’jL,l
&j>
average solid phase concentration, is in eauilibrium with fluid ohase concentration of feed stream average solid phase concentration component i in section j
Sep. Technol.,
1994, vol. 4, January
4s * i S t u
vj Yf V,
xi
zj zsj
dimensionless
distance Gzj
*
packed to void ratio, (1 - &)I&
Q,
nonlinear factor, 1 - 5 hi i=l L. dimensionless mass transfer parameter ki f
OLi cu,B
%j ii 7
of
dimensionless solid phase concentration of component i at section j saturated solid phase concentration equilibrium solid phase concentration raffinate flow rate solids flow rate time linear velocity of solid velocity of fluid at section j velocity of fluid at the section following the feed point velocity of fluid at the section following the eluent point mole fraction of component i axial distance coordinate
Greek letters
which
1
28
Q;
separation factor ratio of downflow to upflow rates = (1 - &)K,.UIEVj bed porosity nonlinearity parameter, qo/q, dimensionless time
4
Unsteady state simulation of ‘SORBEX”system: Boundary
A. K. M. S. Rahman et al.
conditions
at Zj = 0, ROf
acJj
firmtO,R
DL
10 rich)
Food,
= -
J aZj
vj(c~lzj=o- cijl,=o+)
(4)
zj=o+
at zj = Lj,
F
acii =
(5)
0.0
aZj
Material balances Material balances for each section are given by the following equations. At the inlet of section IV -
Yoke-w c&4=0-
=
c~31zJ=L,
(6)
3
*R-F1
(E
At the inlet of section III I
c&o- =
iii T
L”
1
2.0
x.0,
ci21zz=O-
Plug flow of solid Axially dispersed plug flow of fluid Isothermal operating conditions Linear driving force expression for mass-transfer
a2cii Li azj
~~+(!+!!!Q J
-
v2)cf
(7) v3
=
cillz,=L,
(8)
=acii + at
(9)
I
Using the following dimensionless C;
Q;
=;
5
t
f$
=
l_a2ch --
=F.
a7
variables
3
‘j = L,
s
’ [ Pej azj2
az, +
aQ!.
yaks
aQ!.
- WKi~a7
J
aQ;_ a7
aZj
&
cillz,=O= (ci41q=Ls4)~
the preceding equations are written for ith component and jth section as
are of nonlinear Langmuir form
Adsorbent is considered to be flowing with a downward velocity u = L*lt, where L* is the individual column length and t, is the switch time, whereas the liquid is flowing upward with a velocity Vj. The basic differential equation describing the system dynamics for ith component and jth section can be written as D
tv3
At the inlet of section I
lb)
Isotherms
+
At the inlet of section II
Figure 2 (a) Schematic diagram of four-section equivalent countercurrent system. (b) Schematic diagram of the mass balance of jth section for four-section equivalent countercurrent model.
1. 2. 3. 4. rate 5.
v*ci21z2=L,I
C&
4
-
l + ~ hi(C~ - 1.0)
1 (10)
Q;
(11) 1
i=l
( ) ly
!.$i
(1)
For a Langmuir type of equilibrium isotherms, the rate equation can be written as
Initial conditions c; = 0.0 Boundary
(2)
(12) conditions
at Zj = 0.0 (13)
Initial conditions cij = 0.0
(3)
where CZ; is the inlet concentration Sep. Technol.,
of i for section j,
1994, vol. 4, January
29
Unsteady state simulation
of “SORBEX”system:
A. K. M. S. Rahman et al.
which can be obtained from the material balance equations .
Table 1 Parameter MOH system
values for the glucose-fructose
Parameter
5
0.0
=
(14)
dZi
Material
balances
At the inlet of section IV (15)
CZ& = Cl%,= 1.0
and MEA-
Linear case of Ching et aL7
Nonlinear case of Ching et aLB
5,5 30.5 10.0 38.8 13.8 16.8 100 4.3.3.2 5.1 0.0.0.0 0.88 0.50
20.10 22.1
Feed composition (%A,%B) Switch time, min Feed flow rate, mL/min Eluent (desorbent), mL/min Raffinate rate, mL/min Extract rate, mL/min Bed length, cm Configuration Column diameter, cm A(A,B) KA
Kt?
375:: 13.7 44.0 100 4.3.3,2 5.5 0.435,o.o 1.24 0.63
At the inlet of section III Note: A = fructose or MEA; B = glucose or MOH.
W2lz*=,.o + cz,
w3
-
V2)
=
(16) v3
MI
A M2,l C’A,,,,
At the inlet of section II cc2
=
Ci),lz,
+
C i=2
AM2,iCa,,,i
+
(17)
= 1.0
At the inlet of section I CZi, = (C.&= ,.I))$
(18)
I
The system of coupled differential equations described by Equations lo-18 has been solved from transient to steady state conditions by the method of orthogonal collocation. Equations 10 and 11 with boundary conditions represented by Equations 13 and 14 may be expressed in the collocation form for component A and section 1 as
AM~.M~C~,,,M~
=
0
(21)
where CHZ = CZJ,, the inlet dimensionless concentration of component A to section I. The detailed derivation of Equations 19-21 is shown elsewhere.14 Similar equations can be developed for all the four sections. For the system in the present study, two columns in section IV, three columns in sections II and III, and four columns in section I have been considered. This system configuration was used by Ching et al.’ in their experiments. Sixteen collocation points were used for each section, which requires the solution of 256 simultaneous nonlinear ordinary differential equations. The preceding sets of differential equations have been solved using the functional iteration method.
Results and discussion
Lg. pe,
+
-
+
C'A.,,j
‘I’K@a, 1 +
Q
h.l, ,I1
Boundary
Effects
Y@Aj,M2QA,,,M2 - Aj,M2C~,I%M~
J,M~
AA(Ca,,,j
-
I)
+
hB(Ch,,,j
-
‘1
(19)
conditions
are written as
1(
A,,,G,,,i
+ A,,.wCL,,JQ + 2 A,,iC,k,,,i i=2
and 30
Sep. Technol.,
1994, vol. 4, January
(20)
of process parameters
on separation
The proposed theoretical model was solved for different cases to observe the effects of various parameters on the performance of the system. In Table 1, a set of parameters for the MEA-MOH system is tabulated that was reported by Ching et al.’ and Ching et al.,* and is considered our base case. The results of the numerical simulation from transient to the steady state conditions for various system parameters are shown in Figures 3-8. The effect of these changes in parameters on the different dimensionless groups are shown in Table 2. It may be noted here that the mass-transfer resistance for MEA-MOH system has been reported to be very 10w,~ and therefore the dimensionless parameter (Yhas no effect on the system performance. The results of the present simulation are analyzed in terms of degree of separation in extract and raffinate, which is defined as E = (CA - CL)/(Ch + Cj& and R = (CL - C’J/(Ck + CA) where E and R refers to the extract and raffinate phases, and CA and CL are dimen-
Unsteady state simulation
of ‘SORBEX”system:
A. K. M. S. Rahman R, E
--1:-,:----------------_________________________________________ -
.,
et al.
_.
E
__
,.
E
.
‘0 c
0.60-
L 1
0.40-
8
0.20 -
t E
0.00 -’
.z 6 b
- 0.20 -
j;
- 0.40-
5
-
t zb
- 0.60 -
0.60
-
-Configuotion
- 3,2,2,1
‘..“.-Configuration
- 4,3,3,2
----Configuration
* 6,6,6,2
- l.OO-
I 500
I 1000
I 1500
I 2000
I 2soo
I 3000
I 3600
I
I
4000
4300
time (minutrrl
Figure 3
Effect of configuration
on the performance
of the four-section
sionless concentrations of MEA and mOH, respectively. Using this definition the degree of separation can be represented in a - I to + 1 scale. As the degree of separation approaches 1, a better separation is achieved. Alternatively, when the degree of separation approaches - I, this implies that the E phase is component B rich, and in the R phase the concentration of component A that is the strongly adsorbed species is high. At degree of separation 0 there is no separation between the components. As may be observed in Figure 3, a relatively pure product can be obtained in both extract and raffinate streams using a 4,3,3,2 bed configuration. When the sizes of the sections are doubled, the separation improves. But when the bed number is reduced by one in each section, the separation becomes relatively poorer in the extract. The steady-state concentration indicates that both the previous configurations produce relatively pure products. It is also observed that except for the E curve of 3,2,2,1 configuration, all curves reach steady state after about 1,000 min. In case of 3,2,2,1 arrangement the E curve takes about 1,500 min to attain the steady state. The change in column configuration has a tremendous effect on all of the dimensionless groups of Table 2 except for yij. The yti criterion for good separation as described by Ching et a1.,7*8which is section section sectlon section
IV: ylIv > 1, y21v > 1 III: yurl > 1, y2u, < 1 II: yllr > 1, yzrr < 1 I: yu < 1, y2* < 1
is followed in all sections. If yti values are compared for both 8,6,6,4 and 3,2,2,1 configurations, it can be seen that they are identical and match exactly with
equivalent
System.
that of the base case. For the 8,6,6,4 configuration the Peclet numbers for all four sections are increased by about 100%. Conversely, at 3,2,2,1 arrangement flow ratio Fs are decreased by 30%, and the Peclet numbers are reduced by 100%. Therefore, it can be concluded that the degree of separation is more strongly dependent on yij rather than on the other dimensionless numbers. Figure 4 shows the effect of switch time on degree of separation. It is clear that the switch time of 22.1 min gives the best product separation among the three switch times reported here. When the switch time is increased to 30.4 min the degree of separation is reduced both in the extract and raffinate phases. This behavior can be explained by the change in the dimensionless groups. The change in switch time affects the solid phase velocity, which eventually changes the Peclet numbers because the dispersion coefficient used in the definition of Peclet number is taken to be a function of equivalent solid phase velocity also. At a 15min switch time and at a 30.4-min switch time the magnitudes of Peclet numbers are decreased and increased, respectively, by about 20% and 30%. Because yii is a strong function of solid phase velocity, the effect is quite significant. At a switch time of 30.4 min y21v is less than 1 and thus falls into the bad separation category. Conversely, at a 15min switch time, the magnitude of yy for MOH in sections III and II and yu for MEA in section I are greater than 1, which violate conditions of good separation. At lower switch time, though the rtinate produces almost pure MEA instead of MOH, as indicated by degree of separation (- l), lack of separation (-0) of MOH in extract makes this switch time unacceptable. The effect of individual bed length while maintaining
Sep. Technol.,
1994, vol. 4, January
31
Unsteady state simulation of ‘SORBEX” Table 2
Effect of process parameters
system: A. K. M. S. Rahman et al.
on dimensionless
groups for nonlinear
MEA-MOH
system Section
Effect
Fs
Fz
FI
Pe,
PeJ
Pe*
Pe,
014
a3
a2
Ql
IV
Yl
Y2
Section III
Yl
Y2
Section II
Yl
Y2
Section I
Yl
Y?
0.93
0.83
1.26
17.90
31.77
30.1
53.62
12.05
12.96
14.45
9.57
2.31
1.17
1.85
0.84
1.84
0.94
0.92
0.465
(6)
0.93
0.83
1.28
19.4
34.01
32.4
56.22
10.36
11.14
12.43
8.2
1.98
1.01
1.42
0.722
1.58
0.81
0.79
0.40
cm
(5.1)
0.93
0.83
1.28
18.2
29.16
27.5
50.45
14.34
15.42
17.20
11.39
2.74
1.39
1.97
0.999
2.19
1.11
1.09
0.553
Eluent
(1001
0.86
0.79
1.06
21.0
35.19
33.9
55.94
8.84
10.28
11.2
8.36
1.69
0.86
1.31
0.66
1.43
0.73
0.80
0.41
mLlmin
(75)
1.08
0.93
1.68
13.7
27.34
25.1
50.84
18.75
17.43
20.24
3.59
1.82
2.22
1.13
2.58
1.31
1.07
0.542
Feed
(10)
0.90
0.73
1.10
19.20
33.23
30.1
53.62
10.53
11.75
14.45
2.01
1.02
1.50
0.76
1.84
0.94
0.92
0.465
mLlmin
(3)
0.95
0.88
1.34
17.3
31.14
30.1
53.62
12.79
13.52
14.45
9.57
2.45
1.24
1.72
0.876
1.84
0.94
0.94
0.465
Bed length
(2001
0.93
0.83
1.26
23.0
43.21
40.2
80.64
24.10
25.92
28.91
19.14
4.61
2.34
3.31
1.68
3.69
1.87
1.83
0.93
(50)
0.93
0.83
1.26
12.3
20.77
20.1
32.1
8.03
8.46
7.23
4.78
1.15
0.59
0.83
0.42
0.92
0.47
0.46
0.233
Configuration (8664) (3221)
0.93
0.83
1.26
35.7
63.54
80.3
107.2
25.92
28.91
19.14
2.31
1.17
1.65
0.84
1.84
0.94
0.92
0.465
0.70
0.63
0.84
8.9
21.18
20.1
40.21
6.03
8.64
9.64
7.18
2.31
1.17
1.65
0.84
1.84
0.94
0.92
0.485
(30.4)
0.93
0.83
1.28
21.0
36.45
35.0
59.0
12.05
12.96
14.45
9.57
1.68
0.85
1.20
0.81
1.34
0.88
0.67
0.338
(15)
0.93
0.83
1.28
14.2
26.0
14.4
46.38
12.05
12.96
14.45
9.57
3.40
1.73
2.44
1.24
2.72
1.38
1.35
0.685
Base Diameter
cm
Switch time min
Note: 1 = MEA;
2 = MOH
24.1
11.1 9.57
in y.
the bed configuration of the base case is shown in Figure 5. For bed length of 50 cm, separation in both raffinate and extract has become poorer. In case of bed length of 200-cm raffinate gives pure MEA; however, the separation between MEA and MOH is very low (- - 0.1) in the extract. Among these bed lengths, only the lOO-cm-long columns produce concentrated MEA and MOH. Though change in bed length has changed the dimensionless parameters of Table 2 moderately, it affects the yij values in all the four sections. It is clear from Table 2 that at higher bed length yy values for MOH in sections II and III and y,, of MEA in section I are much higher than 1 and thus fall into the poor separation category. At a bed length of 50 cm -yzj for MOH in section IV and yu for MEA in sections II and III are less than 1, resulting in a poor separation.
The magnitudes of Peclet numbers in all four sections are increased or decreased by 30% when the individual bed length is increased or decreased by a factor of two. At 50 cm bed length curves E and R reach steady state at about 500 and 1500 min. The E curve shows a peculiar behavior at lower time, the degree of separation drops sharply to - 1 level, and then slowly increases to its steady state value. The effect of column diameter is shown in Figure 6. At a diameter of 5.5 cm, separation in both extract and rafhnate is very good but with the increase or decrease of diameter slightly, the degree of separation decreases both in extract and raffinate streams. The change in column diameter changes the flow rates in each section, thereby changing all the dimensionless parameters except the Fs of Table 2. At a diameter of
z
z 1 t‘i e
-------.---.--____.__. __ .. ..-___.___---.-....... --.--.-._ E ~.____.-____._____________.-..---.---_.-----------.--------.- R
W -c s t
-0.20
-
-0.40
-
B 8
-
6 ::
-0.60
-
b 0’
-0.80
-
- 1.00
-
Switch Time
---- Switch Tlme
= 30.4 min.
I 1000
I 1500
I
moo
I
I
2500
3000
I 3500
Time (minutes)
32
Effect of switch time on the performance
Sep. Technol.,
I min.
= 22.
R
I 500
Figure 4
= 15.0 min.
....“’ Switch Time
1994, vol. 4, January
of the four-section
equivalent
system.
I 4000
I 4500
Unsteady state simulation
of ‘SORBEX”
system: A. K. M. S. Rahman et al.
-Bed
L*lgth
....--6.d
Lsngth
=IDO.oan
---Bed
Length
=2OO.ocm
= 5O.Ocm
Time (minutor) Figure 5
Effect of individual
bed length on the performance
of the four-section
equivalent
system.
-------------_.__... _______...-- .---__.- -
6 z
-0.60
-
-1.00
I
I
500
I
I
I
1000
1500
2000
--- Diameter
=5.1 cm
......’Diameter
- 5.5cm
-
=6.0cm
I
I
2500
R
3000
Diameter
I
I
3500
4000
I
4500
Time tminutrs)
Figure 6 Effectof column diameter on the performance of the four-section equivalent system.
6 cm, which is about 10% more than that of the base
case, Peclet numbers are increased by lo%, whereas at a 5.1-cm column diameter, these parameters are decreased by the same percentile. At a diameter higher than that of the base case, rii values follow the specified criterion for good separation except for Q, which barely satisfies the criterion. In case of lower column diameter, yZII and yu do not satisfy the conditions that are required for better separation.
Figure 7 depicts the effect of eluent flow rate on the performance of the system. The degree of separation is largest when the eluent flow rate is 87.4 mL/min. As the eluent rate is increased to 100 mL/min, the degree of separation decreases to 0.5. At an eluent rate of 75.0 mL/min separation becomes zero. This behavior can be explained from the rii values reported in Table 2. At the higher eluent rate yZIv of MOH in section IV is less than 1 and thus violates the criterion Sep. Technol.,
1994, vol. 4, January
33
Unsteady state simulation
co
g E E P i
L z w .E L ‘; e :: J; 6 : b B
of ‘SORBEX”
system: A. K. M. S. Rahman et al.
0.80 0.60 0.400.20
-
0.00
-‘.
-0.20
-
-0.40
-
---- Eluent
= 100.0ml/mi
-
=
Elurnt
...“.. Eluant -0.60
-
-0.80
-
75.0 ml/min
= 87.4 ml/mir
- 1.00 I
I
I
I
I
I
I
I
1000
1500
2000
2500
3000
3500
4000
4500
I
500
Time (minutes) Figure 7
Effect of eluent flow rate on the performance
1.00 - -_
equivalent
system.
....*
--.
--. --._
---_..--_
--I___
0.80 -
of the four-section
0.60
R E
%\ -----------‘~-._.___-_._.__-..-_..._._..___. .._.-_._._._ ___ E ‘\\ L\ ‘--.---- ---._..._.. _______________._ ___.- R
0.40 0.20
----Food
- 10.0 ml/min
-F..d Fee,, ..
= 5. Oml/
= 3.0 ml/min min
0.00
-0.60 -I
500
1000
1500
2000
2500
3000
3500
4000
4500
Tim0 (minutes) Figure 8
Effect of feed flow rate on the performance
of the four-section
of good product purity. Conversely, at a low flow rate, -ya for MOH in sections II and III and y,* for MEA in section I are much higher than 1, leading to a poorer separation. Besides yii, other parameters are not significantly affected by change in eluent rates though this change is affecting the fluid phase velocity in all four sections. The concentration profiles in unsteady region for both higher and lower eluent rates are quite interesting. At an eluent rate of 100 mL/min curve R reaches 34
Sep. Technol.,
1994, vol. 4, January
equivalent
system.
to its steady state value at about 2,000 min. It may be further observed that at lower time up to 1,200 min it produces almost pure MOH in the raffinate stream after which the degree of separation drops to 0.4. At the lower eluent rate the unsteady profiles for both E and R show that both the curves drop to zero separation, which is their steady state value after about 1,800 min of operation. Figure 8 shows the effect of feed flow rate. It can
Unsteady state simulation of *SORBEX”system:
A. K. M. S. Rahman et al.
1.00 Section I ‘0
Section I I
0.60-
5 ._ 5
0.60-
,:’
.’
‘i
g
0
.’
__‘.
0.40-
1.00
‘0
z
x’-
,
0.80 -
...x...
.. ..”
.,
,_,
.. 1:
i’
0 L
E t 5
0
0.60-
.‘. E
.- .. .,
0.40-
0.20 0 0.00
-
I
0.00
I
0.20
I
0.40
1
I
0.60
I
I
0.80
g * z .c z p”
I
Experimental
and theoretical
concentration
. ..
0.00
.. . .
‘... .... ‘....
3 I
Length (Dimenrknlers Figure 9
‘.,.,,
I
I
0.20
I
I
0.40
I
0.60
Comparison with experimental data Linear system. In Figure 9, results of the steady-state solution of the present model is presented for the limiting case of linear system (glucose-fructose) for which the parameters are taken from the reported values of
.“_‘... I
0.60
.
,),._, I
1.00
1
profiles of glucose and fructose (experimental:
be seen that at feed rates of 5.0 and 3.0 mL/min the degree is almost equal, and the degree of separation magnitudes are approximately 1 in both extract and raffinate, which indicates a very efficient separation. At higher feed rates the degree of separation in both the streams declined. As can be seen from Table 2, at both high and low feed flow rates yij values obey the good separation criterion. However, in section IV at high feed flow rate y21v for MOH is very close to 1, which leads to a relatively poorer product composition. The unsteady profiles of both E and R curves for both base case and a feed flow rate of 3 mL/min are quite similar. In both cases curve R reaches steady state instantly, but curve E attains its steady-state value after about 1,300 min. At a feed rate of 10 ml/mitt, curve E reaches to its steady-state value at about 1,500 min and curve R at 2,300 min. But up to about 1,500 min the degree of separation in R stream was + 1, and after that it drops down to its steady-state degree of separation of 0.6. It should be noted that the change in feed flow rates changed only the parameter values of postfeed sections.
I
x, glucose; 0, fructose).
Ching et al.’ and are presented in Table I. In this figure results obtained from experimental studies of Ching et al.’ are also shown. From this figure it can be concluded that the present model, which is a more general one, provides a good representation of the performance of an equivalent continuous countercurrent adsorption system. Nonlinear system. To check the validity of the present model for nonlinear system, computations were performed for the MEA-MOH system. Figure 10 shows a comparison between the steady-state solution of the present model for the MEA-MOH system and the experimental results reported by Ching et al.* and Hidajat et a1.9 This figure shows the profile when only MEA follows a Langmuir type of equilibrium isotherm but MOH follows linear relationship, and there is no isotherm dependency between MEA and MOH. All the curves agree very well with the experimental results. Also shown in this figure are the profiles if both isotherms are chosen linear. It is evident that the prediction is not good with linear isotherm assumption. In Figure II, the performance of the system is shown for the case in which a nonlinear binary Langmuir isotherm for MEA and linear isotherm for MOH are considered. This would make the isotherms coupled as can be observed from Equation 2. It can be seen from this figure that concentration and purity of product in both
Sep. Technol.,
1994, vol. 4, January
35
Unsteady
state simulation
of “‘SORBEX”system:
A. K. M. S. Rahman
et al.
0.70 -% Section
f
Section
0.600.50-
E a”
c .P
0.40-
5 ,0 ‘;
E
0.30-
‘0
‘(! ,’ ,/“
W
E :: 5 0
II
.I’
/’
MEA 1 ”,...;:_.._______-~~.~,~..i~_-;~.~.~~~‘~----~~~~~~-~~~--------- ____-_
0.20-
0.10 0.00 4 0.10 -
I
Section III MOH 0.60 +C-______________X~~=.~-.---.-,T-_____
b s ‘G 2 Z :5
‘..’ ‘. .i&y;,. “I,
o.so-
0.30
1
I
I
I
,
,
I
Section IV
E ._ lf u 5
\.q’i. ‘<..
0.40 -
1
‘\‘.. ‘i.. f5 \” J a” :;r. \;.
-
0
0.00
0.20
0.40
0.60
0.60
Length Figure 10
Experimental
and theoretical concentration
0.00
0.20
0.40
0.60
0.60
I.
(Dimensionless)
profiles of monoethanolamine
and methanol (experimental:
0, MEA; X, MOHI.
0.70 Section
I
Section
II
0.60 -
0.70 Sect ion III
Section
MEA 0.50 ‘0 5 z L E
0.40
-
0.30
-
0.20
-
0.10
....‘.
“-_..
MOH
“....
1
0.00
”
I 0.00
I
0.20
I
I 0.40
I
I 0.60
I
I 0.80
I
I
11
0.00
1
0.20
II
0.40
I
0.60
LengthIDimensionlesrI Figure 11
36
Effect of coupling between isotherms on the concentration
Sep. Technol.,
IV
E I? L z C e :
0.60
1994, vol. 4, January
profile of MEA-MOH
system.
I
I
0.60
.. . . . . .
I
1.00
Unsteady state simulation
extract and raffinate streams become poorer compared with the uncoupled case.
Conclusion A theoretical model of SORBEX system for unsteady state is developed for the nonlinear MEA-MOH system. The model equations are solved to investigate the effect of various process parameters on the performance of this widely used countercurrent adsorption system. The present study reveals that the system performance as well as dynamics are very much dependent on some physical parameters of the system (viz. bed length and diameter of the adsorption columns). Other operating parameters like feed flow rate, eluent flow rate, and switch time affect the performance of the process considerably. The system is very sensitive to these parameters and should be chosen carefully. The results obtained for the case of MEA-MOH, when MEA follows nonlinear (Langmuir) and MOH follows linear equilibrium isotherms, were compared with the experimental results of Ching et al.* and Hidajat et a1.9 at steady state. Also the glucose-fructose systems was investigated and compared with result of Ching et al.’ Good agreements are observed with the predictions from the present model for both systems. The effects of various parameters were obtained for uncoupled isotherm relation between MEA and MOH. The effect of coupling between the isotherms on the system performance was also computed, which indicated that the overall performance becomes poorer. The present model can be employed to predict the performance of countercurrent adsorption systems for various combinations of isotherm relationship (viz. linear-linear, linear-nonlinear, nonlinear-nonlinear, etc.).
of ‘SORBEX”system:
A. K. M. S. Rahman
et al.
The preceding features make the present model more general and versatile for simulation of continuous countercurrent systems from unsteady to steady state conditions for various types of equilibrium isotherms.
Acknowledgments The authors wish to acknowledge the support provided by King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia.
References 1.
2. 3. 4. 5. 6. 7. 8. 9. IO. 11. 12. 13. 14.
Hassan, M.M., Rahman, A.K.M.S. and Laughlin, K.F. Sep. Z’echnol. 1994,4, 15-26 Broughton, D.B., U.S. Patent 3,291,726, 13 December 1966 Broughton, D.B., Chem. Eng. Prog. 1968,64,60 Broughton, D.B., Euzil, R.W.N., Pharis, J.M. and Brearley, C.S. Chem. Ena. Prop. 1970, 66. 70 Bieser, H.J. anddeRo&et, A:J. 28th Starch Convention, Detmold, West Germany, 27-29 April 1977 Ching, C.B., Hidajat, K., Ho, C. and Ruthven, D.M. Chem. Eng. Sci. 1987,42, 2547-2555 Ching, C.B., Ruthven, D.M. and Hidajat, R. Chem. Eng. Sci. 1985.40, 1411-1417 Ching, C.B., Ho, C. and Ruthven, D.M. Chem. Eng. Sci. 1988,43, 703-711 Hidajat, K., Ching, C.B. and Ruthven, D.M. Chem. Eng. J. 1986,33, B55-B61 Hidajat, K. and Ching, C.B. Truns Z Chem. Eng. 1990, 68, 104-108 Neuzil, R.W. and Jensen, R.A. 85th National Meeting AICHE, Philadelphia, June 1978 de Rosset, A.J., Neuzil, R.W. and Korous, D. Znd. Eng. Chem., Process Des. Dev. 1976, 15,261-266 Ruthven, D.M. and Ching, C.B. Chem. Eng. Sci. 1989, 44, 101I-1038 Rahman, A.K.M.S. MS. diss., 1992. King Fahd University of Petroleum & Minerals, Dhahran
Sep. Technol.,
1994, vol. 4, January
37