Optimization of continuous countercurrent adsorption systems

ELSEVIER

Separations

Technology

6 (1996) 19-27

Optimization of continuous countercurrent

adsorption systems

M.M. Hassan* , K.F. Lmghlin, M.E. Biswas Drpatttnent of Chemical

Engineeting, King Fahd University of Petroleum & Minerals, Dhahran-31261. Received

26 July 1995; accepted

20 November

Saudi Arabia

1995

Abstract The operation of a continuous countercurrent adsorption system is modelled and optimized. The objective is to maximize the recovery of the less strongly adsorbed species in the raffinate for a specified purity of the product. The optimization is carried out for a system with linear and non-linear isotherms. The optimization results indicate that the optimum values of parameters are significantly different for linear and non-linear isotherms. An optimal choice of operating variables corresponding to a compromise between recovery and purity is also suggested. Keywords:

Adsorption;

Continuous

countercurrent;

Optimization:

1. Introduction Continuous countercurrent systems reduce the adsorbent requirement by maximizing the mass transfer driving force. The major problems of earlier versions of continuous countercurrent adsorption processes were associated with the recirculation of the solid adsorbent, which proved to be uneconomic. Such problems have been eliminated by the use of simulating moving bed systems. The continuous countercurrent contact is achieved by keeping the solid beds fixed while moving the fluid inlet and outlet points simultaneously at set time intervals in the direction of flow of the fluid phase as shown in Fig. 1. Continuous countercurrent processes are now in extensive industrial use for several hydrocarbon separations [l], in the separation of glucose and fructose in the production of high fructose syrup [2], and in the separation of monoethanol amine and methanol [3]. The mathematical modelling of continuous countercurrent systems has also been reported by several investigators. Two basic approaches have been used in modelling these systems: (1) the system is considered as an equivalent countercurrent process involving both

xCorresponding

author.

0956.9618/96/$15.00 ‘C 1996 Elsevier SSDl 0956.9h18(95)001?7-M

Science

Ireland

Non-linear

isotherm

fluid and solid velocities with fixed (time independent) boundary conditions, and (2) the system is modelled as a simulated countercurrent system consisting of various sections with each section comprised of a number of columns and where the boundary conditions change with switch time. Models for the first approach, the countercurrent operation [4-191 and for the second approach, the simulated countercurrent operation [4,15,16,20] have been presented in the literature. A reasonable representation of the actual process is depicted by both of the approaches. Indeed, the agreement between the theoretically predicted results and the experimentally observed data is excellent using either of the approaches thereby establishing the validity of the models. All previous studies show that the effect of various parameters are strongly coupled and, it is therefore, very difficult to predict the optimal choice of parameters in these systems. The situation is further complicated by the presence of non-linearity of isotherm. For the case of linear isotherm Ching and Ruthven 112,131 show that an efficient separation of glucose and fructose occurs for a wide range of operating conditions provided that the ratio of downflow to upflow rates of fructose is greater than one and for glucose this ratio is less than one in both prefeed and post feed sections. However, this criteria was found to be insufficient for non-linear

Ltd. All rights reserved.

20

MM. Hassan et al. /Separations

Experimental determinations of this optimum set requires a trial and error procedure which may become very time consuming and uneconomic. In the present study, therefore, a systematic theoretical evaluation of this optimum set of operating parameters is performed with the objective of obtaining maximum recovery of the less strongly adsorbed species in the raffinate for a specified concentration of the more strongly adsorbed species. Further, the best choice of optimum operating sets which yields high recovery at an acceptable purity is determined. This numerical scheme is applied for the glucose-fructose system on Duolite C-204 resin to investigate the effects of both linear and non-linear isotherms.

Feed

of fluid

flow

and port

Technology 6 (1996) 19-27

rotation

2. Theory The numerical scheme for optimization of operating parameters consists of two parts: (1) the theoretical model and (2) the optimization of process variables.

Purge Fig. 1. Schematic

diagram of a two section simulated

moving bed.

systems [19]. Although the theoretical and experimental studies reveal the existence of an optimum set of operating variables, very little attention has been given towards the systematic evaluation of this optimum set of parametric values.

2.1. The theoretical model The system described in Fig. 1 may be considered as approximately equivalent to the hypothetical continuous countercurrent arrangement shown in Fig. 2a.

Plug flow of solid

z

z=o, I

,-

c=co Feed

’ Z=‘s,, , C’C( Bulk fluid

Axial dispersed plug flow or fluid (b)

-ij a Eluent

h-l Fig. 2. (a) Schematic

Purge

diagram of a two section equivalent

for a two section equivalent

countercurrent

system.

countercurrent

system. (b) Schematic diagram of the mass balance of the jth section

21

MM. Hassan CI al. / Srparalions 7‘eclrr~~loyvh (19%) 19-27

Assuming plug flow of solid and axially dispersed plug flow of fluid, the basic differential equation describing the system dynamics for ith component and jth section can be represented by the following set of equations:

(1) For Langmuir type of equilibrium isotherm, b/q, c,,

4; =

(2)

b,c,,

1+ i i= I

Boundary conditions dc

D ri I.1dz, : =,)+

at z, = 0

= -r(c,,l;

,=o -c+*) dc ‘/ =o.o dz,

at z, = L,

+

i

4i J

(C,,L=L.,,

--C!,l;_,,)

F(x)

(4)

where recovery is defined as

(5)

=

1 Recovery of A

(3)

where 47, is the solid concentration which is in equilibrium with the fluid phase concentration for component i in section i. A mass balance over any section may be written as:

q~,l-_.=r_,, =q,,L

volves five independent variables: feed flow rate, F; eluent flow rate, E; switch time, T; column diameter, D; and column length, L. These can be termed as the manipulating variables for this system. However, the model equations contain three dependent variables: fluid velocity in each section, “;; Peclet number in each section, Pe, and solid velocity, u. These three dependent variables CV;, Pe, and u) are functions of (F, E, T, D and L) the five manipulating variables. The primary objective is to find the optimum set of parameter values in this system, which yields maximum recovery of the less strongly adsorbable composubject to the nent (A) in the raffinate product constraints of a tightly specified concentration of strongly adsorbable component (I?). The goal of the optimization function is to maximize recovery of A at the outlet of postfeed section using the following minimizing function Minimize

Recovery =

ConcAl(M2) X Raffinate flowrate ConcCoA x Feed flowrate

(8)

(9)

Here ConcAl(M2) is the concentration of A at the exit of section 1 (post feed section) and ConcCoA is concentration of A in the feed. The above optimization function is subject to the following two constraints:

Using the following dimensionless variables G(1) = 1.1 x ConcBs - ConcBl(M2)

c,, = >

Qi,= )

0

z,=$,

F, 0

‘I

&E 4,

Eqs (1) and (2) can be written as d’C,, dZ;

- (Pe, +Sl)s

+Pe.j.St[(C,,l;,-,

- aQ;;I:,=,)

1 -(C,,I,

QC = K,CJ, [

,=,, L-

aQ:,l:,=t,+)]

1.0 - CA; 1 + C/\,(C,, - 1.0)

of process

- 0.9 x ConcBs

where ConcBl(M2) is the calculated concentration of B at the outlet of the section 1 (postfeed section) and ConcBs is the desired concentration of I3 at the outlet and its value has to be specified. Physically, the above constraints are equivalent to

=O

1

The model equations are essentially similar to equations at steady state presented earlier by Hassan et al. [19] and are repeated here only for convenience. 3. Optimization

G(2) = ConcBl(M2)

(10)

variables

The continuous countercurrent system with two section configuration described in Figs. 1 and 2a in-

o.90

~

ConcBl(M2) Cone Bs

5 1.10

(11)

The constraints, therefore, force the calculated concentration values within the range 90-110% of the specified value. The constraints provide a narrow bandwidth of acceptable concentrations in which the optimization is performed. The algorithm of the optimization procedure is described in the flow-sheet given in the attached Fig. 3. The method of orthogonal collocation has been used to obtain a solution of the model equations

22

M.M. Hassan et al. /Separations

using the NEQNF subroutine in the IMSL library. The optimization function is solved by using NCONF subroutine in the IMSL library. The method is based on the iterative formulation and solution of quadratic programming subproblems by using a quadratic approximation of the Lagrangian and by linearizing the constraints. A quadratic programming subproblem is obtained by using a quadratic approximation of the Lagrangian and by linearizing the constraints. This involves construction of a (n x n) Hessian matrix, where IZis the number of optimization variables. This method, therefore, optimizes values of all variables simultaneously. However, the method can be used to solve either a global qr local optimization problem. Details of the solution procedure of the quadratic subproblem are given by Gill et al. [21]. Many optimization functions possess more than one extremum. Hence we must recognize that the maximum or minimum which we may have found at some particular point is not necessarily the largest maximum or the smallest minimum in the entire region of interest. An extremum that exists at a point within some subregion R' of the region R is called a relative or local extremum; the greatest maximum (or the smallest minimum) in R is called an absolute or global maximum (or an absolute or global minimum.). Only local optimization (no global) has been carried out in the present study. A narrow bandwidth of all process variables were given. If too wide a bandwidth which is required for global optimization is used, the optimization will not converge. 4. Results and discussions The above optimization scheme was applied to evaluate the optimized set of parameters for glucosefructose system on Duolite C-204 resin with both linear and non-linear isotherms. Two different cases of optimization were carried out. In one case the length and diameter of the column were kept fixed at the experimental values reported by Ching and Ruthven [12] and Hidajat and Ching [3]. This case would then yield the optimized set of parameters for the experimental set up used by these authors. In the other case, optimization is carried out by including the length and diameter as variables and, therefore, this would then represent a more general case. The optimized parameters for glucose-fructose system for linear case (AA = A, = 0) with fixed column diameter and column length are presented in Table 1. The optimization was run for various fructose concentrations in the raffinate or (purity). The values of each variable (F, E and r) represent the optimized values at the specified fructose concentration. It may be mentioned here that run 2 corresponds to the experi-

Technology 6 (1996) 19-27

FLOW DIAGRAM

Call Optimization Program 1 Run Model

I

I

Fig. 3. Flowsheet showing the algorithm of optimization procedure.

mental conditions (run 4) reported by Ching and Ruthven [12]. Fig. 4 shows at the optimal conditions, the recovery and purity of glucose in the raffinate at various fructose concentrations. It is observed that the recovery increases with the increase of fructose concentration in the raffinate but at the expense of lower purity. Based on a compromise between the purity and recovery, one may consider run 6 in Table 1 as the optimal choice for operation which yields 99% recovery of glucose at a purity of 97.3%. The steady state concentration profile for this case is shown in Fig. 5. A comparison with run 2, the experimentally reported case by Ching and Ruthven [12], shows that a small reduction in the feed rate and switch time would give a higher purity product with recovery as high as 99% [Run 61. The optimized set of parameters for the glucosefructose system with non-linear isotherm are presented in Tables 2 and 3. The corresponding recovery and purity plots are also shown in Fig. 4 for (A, = 0.10 and ha = 0.17) and (h, = 0.20 and A, = 0.345) cases. It is observed that for the non-linear case (hA = 0.10 and ha = 0.17) the purity values are still very close

M.M. Hassan et al. /Separations

Technolog-v 6 (1996) 19-27

i! :I ! :

80

.c ‘000

I .00100

1

I

Dimensionless

I

I

.00200

I

I

fructose concentration

while the recovery is lower compared to those for the linear case (Table 1). However, as the non-linearity increases (AA = 0.20 and A, = 0.345) the purities are lower at the expense of higher recovery compared to both the linear case and non-linear (AA = 0.10 and A, = 0.17) case. This may be attributed to the interactions of the optimized parameters which are quite different for each case. Specifically, the feed rate is very different for linear and non-linear (A, = 0.20 and A, = 0.345 > cases as shown in Table 3. Further, the

Recovery

-

Purity

I

.00300

Fig. 4. Plot of Recovery and Purity at various dimensionless Fructose concentrations h, = A, = 0; 0~) A, = 0.1 and A, = 0.17; and (c) A,., = 0.2 and A, = 0.345.

--

I .O )SOO

.00400

in the raffinate in the raffinate

for fixed length

and diameter

optimal choice of operation indicated by the intersection of the recovery and purity curve is also different as shown in Fig. 4. The results for the general case, where the column diameter and length are also included as variables are shown in Tables 4-6 for glucose-fructose systems for various non-linearity of isotherms. For linear case A, = A, = 0 run 2 in Table 4 appears to be the optimal case. It is very interesting to note that the optimized values of all the variables

-fructose --glucose

2

3

4

5

6

7

8

9

IO

COLUMN NUMBER Fig. 5. Concentration

profile for optimal

for (a)

choice of operation

(run 6 in Table

I ).

II

24

M.M. Hassan et al. /Separations

Table 1 Optimized parameters (100.00 cm) Run No.

for glucose(A)-fructose(B)

system for linear case (A, = A, = 0) with fixed column diameter

(5.1 cm), length

Feed rate (ml/min)

Eluent rate (ml/min)

Switch time (min)

Recovery

Purity

Concentration ratio

Raffinate fructose concentration (dimensionless)

7.51 7.50 7.48 7.46 7.44 7.41 7.37 7.32 7.15

110.01 110.00 109.99 109.97 109.95 109.93 109.90 109.87 109.75

15.07 15.00 14.89 14.79 14.65 14.50 14.29 14.02 13.15

99.8 99.8 99.7 99.5 99.3 99.0 98.2 96.4 75.4

93.1 93.8 94.8 95.6 96.5 97.3 98.2 98.9 99.8

11.9 11.9 11.9 12.0 12.0 12.0 12.1 12.0 9.90

0.0088 0.0078 0.0066 0.0056 0.0044 0.0032 0.0022 0.0014 0.0002

Purity = ConcAl(M2)/(ConcAl(M2) and Concentration ratio = ConcAl( postfeed [6,5,12].

+ ConcBl(M2)); Recovery = ConcAl(M2) x Raffinate flow rate/(ConcCoA x Feed flow rate) ConcCoA. Feed composition: 5% A, 5% B; KA = 0.51; K, = 0.88; Configuration-prefeed,

E, T, II,, I,) for this case is very close to the one reported by Ching and Ruthven [12] except the minute change in the diameter of the column. It may be further noted that the recovery remains fairly constant while the purity changes as the concentration of fructose in raffinate is changed.

The optimized values of the parameters for the general case are shown in Table 5 for A, = 0.10 and A, = 0.17 and Table 6 for A, = 0.20 and A, = 0.345, respectively. The influence of the non-linearity parameters A appears insignificant for both the recovery and purity values as shown in Fig. 6. On the other

(F,

Table 2 Optimized parameters for glucose(A)-fructose(B) length (100.00 cm) Run No.

Technology 6 (1996) 19-27

system for non-linear case (AA = 0.10 and A, = 0.17) with fixed column diameter (5.1 cm),

Feed (ml/min)

Eluent (ml/min)

Switch time (min)

Recovery

Purity

Concentration ratio

Raffinate fructose concentration (dimensionless)

7.31 7.30 7.04 7.21 7.20 7.11 7.05 7.00

109.90 109.89 102.91 109.85 109.85 109.81 109.78 109.75

14.22 14.14 14.96 13.85 13.77 13.48 13.22 12.98

99.4 99.2 99.1 98.1 97.7 95.0 90.7 83.3

95.4 96.0 97.2 97.8 98.1 98.9 99.3 99.6

12.2 12.2 12.6 12.2 12.2 12.0 11.6 10.9

0.0060 0.0050 0.0036 0.0028 0.0024 0.0014 0.0008 0.0004

K, = 0.51; K, = 0.88; Configuration-prefeed,

Table 3 Optimized parameters for glucose(A)-fructose(B) length 000.00 cm)

postfeed [5,6,12].

system for non-linear case (AA = 0.20 and A, = 0.345) with fixed column diameter (5.1 cm),

Run No.

Feed (ml/mitt)

Eluent (ml/min)

Switch time (min)

Recovery

Purity

Concentration ratio

Raffinate fructose concentration (dimensionless)

1 2 3 4

4.41 4.31 3.13 2.14

110.18 110.14 117.60 116.76

13.93 13.60 12.68 12.87

99.6 98.8 96.1 95.3

94.7 97.6 99.0 99.3

7.9 7.8 5.4 3.7

0.0044 0.0020 0.0006 0.0002

KA = 0.51; K, = 0.88; Configuration-prefeed,

postfeed [5,6,12].

M.M.

Table

Hnssnn rt 01. /Srpcmtions

‘l‘rchnologv

6 (1006) IO-27

4

Optimized Run No.

parameters

for glucose(n)-fructose(B)

system for general

case with linear isotherm (A,,, =

Feed

Eluent

Switch

Diameter

Bed length

(ml/min)

(ml/min)

time (min)

km)

(cm)

Recovery

Purity

A,, = 0) Concentration

ratio

Rafhnatc fructose concentration (dimensionless)

I

7.50

1 IO.00

15.OU

5.10

100.00

99.8

93.8

I I.‘)

0.0078

3

7.50

I 10.00

14.99

5.14

100.00

99.5

46. I

12.0

0.0048

3

5.94

108.74

15.90

5.22

101.33

99.7

97. I

9.8

o.ooio

4

5.71

104.98

18.46

5.42

105.39

99.9

9x.3

0.0

0.00 I6

Feed composition:

5%’ 11, 5%> B; K,, =

0.51; K,

= 0.88; Configuration-prefeed.

hand, the values of the optimized parameters vary appreciably with h as may be observed in Tables 4-6 for similar values of fructose concentrations. Further, it may be noted that while an appreciable increase in recovery is observed at low fructose concentration for the case where three parameters are optimized (Fig. 4), it was not possible to obtain results in this region for the general case.

.

.

5. Conclusions

postfeed [5,6.12].

for any specified concentration of the more strongly adsorbed species. The optimized values of parameters may become significantly different with the change in the nonlinearity of the isotherm. With the increase in the specified concentration of the more strongly adsorbed species in the raffinate, the purity decreases while the recovery increases and the cross over point of recovery and purity line can be regarded as a compromise between the recovery and purity.

The following conclusions can be drawn from the present optimization studies of continuous countercurrent adsorption system with linear and non-linear isotherm:

Acknowledgement

.

The authors wish to acknowledge the support provided by the King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia.

The optimization scheme presented can successfully evaluate the optimum values of parameters

Table

5

Optimized Run No.

parameters

for glucose(A)-fructose(B)

system for general

case with non-linear

Feed

Eluent

Switch

Diameter

Bed length

tml/min)

(ml/min)

time (min)

km)

(cm)

Recovery

isotherm (h,.r = 0.10 and A, = 0.17) Purity

Concentration

ratio

Raffinate fructose concentration (dimensionless)

I

7.50

110.00

14.99

5.14

100.00

100.0

87.X

12.1

0.0168

2

7.50

110.00

14.99

5.16

100.00

99.9

89.2

12.1

0.0148

3

694

108.37

15.99

5.26

101.30

100.0

92.3

II.5

0.0096

4

5.54

106.76

17.41

5.38

102.54

100.0

94.3

K,., = 0.5 I: K,

Table

=

0.88; Configuration-prefeed,

postfeed

9.5

0.0056

[5,6,12].

6

Optimized Run No.

parameters

for glucose(n)-fructose(B)

system for general

case with non-linear

Feed

Eluent

Switch

Diameter

Bed length

tml/min)

(ml/min)

time (min)

(cm)

(cm)

Recovery

isotherm (A,., = 0.20 and A, = iI.345I Purity

Concentration

I atio

Raflinate fructose concentratton (dimensionless)

I

7.41

I IO.00

14.94

5.39

100.00

99.9

SY.7

13.7

2

7.4 I

1 IO.00

14.94

5.42

lOQ.00

99.7

Y3.2

Ii.3

0.0096

3

7.4 I

110.00

14.94

5.43

lOtI.

99.6

94.8

13.3

0.0072

4

7.40

1 10.00

14.93

5.45

100.00

09.4

45.7

Ii.4

0.0060

5

7.40

1 IO.00

14.93

5.45

100.00

09.3

96.

13.3

0.0054

K,, = 0.5 I: K,

= 0.88; Configuration-prefeed.

postfeed

[5,6.17].

I

0.0 I50

M. M. Hassan et al. /Separations

26

..-.._!a_!

---..-..-_.._..^.. _.._,__.,_.,_.,__, _.__.,_ _,_..(b)

_.._,,_,,_.._.:,__L’~....“_ _ ..-

.oooo

.0040

Dimensionless

Technology 6 (I 996) 19-27

.._..

-.._I-.-..-..-..---

-..-..

ICI

.0080

fructose

.0120

.Ol60

concentration

.0200

in the raffinate

Fig. 6. Plot of Recovery and Purity at various dimensionless fructose concentrations AA-=0.1 and A, = 0.171and (c) A, = 0.2 and A, = 0.345.

in the raffinatefor general case for

Nomenclature

%

A

sj

saturated solid phase concentration fluid flow rate in section j, ETA hypothetical adsorbent recirculation (l-EM Stantan number, (KiLs,/u> linear velocity of solid fluid velocity in section j axial distance coordinate dimensionless axial distance coordinate

bi ‘ij

cij,

co D

4.

I

E F

ki Ki

L Lsj

Pei 40

cross sectional area of column Langmuir constant dimensionless sorbate concentration in fluid phase for component i in section j sorbate concentration in fluid phase for component i in section j concentration in the feed stream diameter of column axial dispersion coefficient (for flow in section j> eluent flowrate feed flowrate overall effective mass transfer coefficient for component i adsorption equilibrium constants for component i length of the adsorption column length of adsorption section j Peclet number in section j Ct$Lsl!DLj) solid phase concentration in eqmhbrium with feed concentration average solid phase concentration (of component i in section j) dimensionless average solid phase concentration (of component i in section j) dimensionless equilibrium solid phase concentration (of component i in section j) solid phase concentration in equilibrium with concentration of i in feed equilibrium solid phase concentration (of component i in section j)

Qj St U

t;.

(a)

AA = A,

= 0; b)

rate

Greek letters a

Ehi

dimensionless parameter, bed porosity non-linearity parameter

(1 - E)U/E~ for

component

i,

(4Oi/4s)

switch time

7

References

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[21 [31

column chromatography as a predictive tool for continuous countercurrent adsorption separation. Ind. Eng. Chem. Proc. Des. Dev. 15,261-266. Neuzil, R.W. and Jensen, R.A. (1978) Development of the SAREX processfor separationof Saccharides,85th National Meeting AICHE, Philadelphia, PA, U.S.A. Hidajat,, K. and Ching, C.B. (1990) Simulation of the performance of a continuous countercurrent adsorption system by the method of orthogonal collocation with non-linear and interacting adsorption isotherms. Trans. Ind. Chem. Eng. 68, 104108

M.M. Hassan et al. /Separations

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