Prediction of Chromatographic Separation of Eugenolby the Fast Fourier Transform Method
Wan Ramli Wan Daud+, San Myint*, Abu Bakar Mohamad+ and Abdul AmirHassan Kadhum+
+Department of Chemical & Process Engineerinl5> Univmiti Kebangsaan Malaysia43600 UKM Bangi, Selangor Darul Ehsan, Malaysia
*Department of Chemical Engineering, Yangon University of TechnologyYangon, Myanmar
Received: 15 April 1998
ABSTRAK
Masa pensuisan atau penukaran antara jerapan dan nyah-erapan dalamkromatografi cecair, iaitu ketika kepekatan aliran keluar mencapai nilai bulus,amatlah penting dalam pengendalian, peningkatan skala dan pengoptimumanpemisahan secara kromatografi. Masa pensuisan boleh dianggar dengan simulasikomputer tums kromatografi jerapan. Dalam karya ini, simulasi teori tumskromatografi oleh Chen dan Hsu berdasarkan kaedah jelmaan Fourier pantas(IFP) yang dicadangkan pertama kali oleh Hsu untuk sistem kromatografi,yang menggunakan anggaran pekali resapan paksian, pekali pemindahan jisim,dan keresapan liang yang diperolehi daripada pemisahan peringkat analisis,dibandingkan dengan data uji kaji pemisahan kromatografi eugenol. TeknikJFP digunakan untuk menyelesaikan model ini. Penggunaan JFP dan bukanteknik yang lebih anggun seperti kaedah beza terhingga atau penempatanbersama ortogonal adalah beralaskan pengiraan yang lebih mudah dankedapatan teknik menyongsang yang lebih baik. Model ini disahkan oleh datauji kaji daripada pemisahan kromatografi eugenol pada tums analisis ~BondapakCI8' fasa bergerak metanol-air (80:20), kadar alir 0.5 ml/min, pada penyuntikanlamtan berlainan kepekatan pada keadaan keseimbangan. Data sifat fizik yangdiperlukan untuk pengesahan ini seperti data penjerapan keseimbangan sesuhuditentukan secara uji kaji, dan data pemindahanjisim dihitung dengan korelasilazim dan daripada pemisahan peringkat analisis. Simulasi ini mengesahkandata uji kaji pada nombor Peelet 6000, parameter panjang lapisan 3.0 danbilangan sampel 90.
ABSTRACf
The switching time to change from adsorption to desorption in liquidchromatography, which is the time at which the concentration of the effluentreaches the breakthrough value, is important in the operation, scale-up, andoptimisation of chromatographic separation. The switching time can be estimatedby computer simulation of the chromatographic adsorption column. In thispaper, the theoretical simulation of the chromatographic column of Chen andHsu (1987) based on the Fast Fourier Transform (FFT) method originallyproposed for chromatographic systems by Hsu using estimated axial diffusivity,film mass transfer coefficient and pore diffusivity obtained from analytical scaleseparation, is compared with experimental data of chromatographic separationof eugenol. The use of FIT over more sophisticated techniques such as finitedifference or orthogonal collocation methods was dictated by the simpler
Wan Rarnli Wan Daud, San Myint, Abu Bakar Moharnad and Abdul Amir Hassan Kadhurn
computation and the availability of better inverting techniques. The model wasvalidated by experimental data on chromatographic separation of eugenol onI!Bondapak CIS analytical column, mobile phase methanol-water (80:20), andflow rate 0.5 ml/min, at different solution concentration injection at equilibriumcondition. Physical property data required for validation such as equilibriumadsorption isotherm data was determined experimentally, and mass transferdata was calculated from normal correlations and from analytical scale separation.The simulation agreed with experimental data at a Peclet number of 6000, abed length parameter of 3.0 and number of samples 90.
Keywords: separation, high performance liquid chromatography, Fast FourierTransform
INTRODUCTION
In practice, liquid chromatography is operated in a cyclic manner alternatingbetween adsorption and desorption. During adsorption, the feed containing asolute at certain concentration is introduced into the bed as a band. Duringdesorption or elution, a carrier fluid free of solute is fed into the system untilthe solute adsorbed on the adsorbent particles is completely recovered.Desorption of the solute is usually initiated when the solute concentration inthe effiuent stream reaches or passes the breakthrough value; in other words,before the bed is completely saturated. Therefore, the switching time to changefrom adsorption to desorption, and vice versa, is important in the operation,scale-up, and optimisation of a chromatographic separation. The switching timecan be estimated by computer simulation of the chromatographic adsorptioncolumn. The simulation model requires equilibrium sorption data which isdetermined experimentally and mass transfer data including inter-particlemass-transfer coefficients and effective diffusivities for transport within theporous adsorbent particles which are determined from available correlations.In this paper, the theoretical simulation of the chromatographic column ofChen and Hsu (1987) based on the Fast Fourier Transform (FFT) methodoriginally proposed for chromatographic systems by Hsu (1979) using estimatedaxial diffusivity, film mass transfer coefficient and pore diffusivity obtained fromanalytical scale separatio~, is compared with experimental data ofchromatographic separation of eugenol.
MATHEMATICAL MODEL
Chen and Hsu (1987) used the fixed bed adsorber model of Rasmuson andNeretnieks (1980) to describe an isothermal adsorption column packed withporous spherical particles of radius a adopted for this simulation work. At timezero, a step change in the concentration of an adsorbable species was introducedinto the flowing stream. The adsorption column was subjected to axial dispersion,pore diffusion resistance, and external film diffusion resistance. After introducingdimensionless variables as suggested by Raghavan and Ruthven (1983), thefixed-bed adsorber may be described by the following set of equations. Mass
218 PertanikaJ. Sci. & Techno!. Va!. 8 No.2, 2000
Prediction of Chromatographic Separation of Eugenol by the Fast Fourier Transform Method
balance in the mobile phase is given by
oU oU 1 02U Ia:; + \jf)8 ox - p. \jf)8 ox2 =-3\jfl~(U - Q 11=)
Particle diffusion is given by
oQ _ 02Q 20Q---+--o't o1l2 II Ol'}
Initial and boundary conditions are as follows:U(x,'t = 0) = 0U(x = O,'t) = 1U(x = oo,'t) = 0Q(ll,x,'t = 0) = 0Q(ll = O,x;.) :f. 00
Multiplying Equation (9) by s gives a transfer function F(s) of the correspondingchromatography system
(10)
Pcr=-!"'-
where 2
F(s) = exp(-crx)
pe2 Pes 3~Pe<l>(s)- +- + --=---"-'--'--'-
4 \jf)8 8
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219
Wan Ramli Wan Daud, San Myint, Abu Bakar Mohamad and Abdul Amir Hassan Kadhurn
ADSORPTION ISOTHERM
Adsorption isotherm was generated by pumping solutions of differentconcentrations of eugenol into a new clean column until it is fully saturated. Astandard analytical CIS J..l Bondapak column 0.39 cm I.D. and 30 cm height, wasused in the experiments. The adsorbent particles size is 10 J..lm. The mobilephase used was a mixture of HPLC grade methanol and doubled distilled waterhaving a ratio of 80:20 by volume. Low pressure column experiments wereconducted with a flow rate of 0.5 ml/min. Concentration of eugenol in thefluid leaving the bed was determined from its absorbance at 280 nm. Thecolumn was stabilised after each experiment by varying the methanol flow ratefor about 5 hours followed by a constant low flow rate of 0.1 ml/min for halfa day. When the inlet and outlet concentrations became identical, the amountof eugenol retained on the adsorbent particles could easily be determined frommass balance, knowing the total amount of eugenol which had been fed to thebed. The linearity of the adsorption system was examined by replicateexperiments in which the concentration of pumping solution was varied from0.1 ml to 0.5 ml eugenol/l00 ml solvent. The capacity (q) is plotted against theequilibrium solution concentrations (C*) as shown in Figure 1. The isotherm islinear in the working range and the expression for the isotherm at roomtemperature is
qa = 1.8703C* (12)
12.-----------------.
:::. 10ECJ
'0 8Q)
"0:e[ 6Q)
:;Q) 4"0'inc~2
O~--------------J
o 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6C· (in mobile phase) gmtl
Fig 1. Adsorption isotherm oj eugenol at room temperature Jrom packed bedequililJrium adsorption experiments on C18 )J. Bondapak column (30 em x 3.9 mm i.d.);
mobile phase, methanol/water (80:20); Jlowrate, 0.5 ml/min.
220 PertanikaJ. Sci. & Techno\. Vo\. 8 No.2, 2000
(13)
(14)
(16)
(15)
Prediction of Chromatographic Separation of Eugenol by the Fast Fourier Transform Method
PARAMETER ESTIMATION
The molecular diffusivity, D.., of eugenol in methanol-water mixture was estimatedby Wilke and Chang (1955) correlation:
1 173 X1O-16("f M )O.5 TD = . 'Y2 2
m I..l.vt6
where M2
is the molecular weight of the solvent, T is the temperature in • K,I..l. is the solvent viscosity (Pa s), '112 is the association factor and VI is the molalvolume (km3/kg mole). The dependence of external film mass-transfercoefficient klan flow rate may be obtained from the following Wilson andGeankoplis correlation (Geankoplis, 1983) for Reynolds number between 0.0015and 55.
1.09u [ ]-2/3kf =-- ReScE
The axial dispersion coefficient of liquid flowing through fixed beds can beobtained from the correlation equation of Wen and Fan (1975):
1 = DLP = ReSc I..l. 0.2 +0.011 Re°.48
For systems in which the main mechanism of intraparticle diffusion is moleculardiffusion within the macropores, intrapore diffusivity Raghavan and Ruthven,1983) is given as
D=::EpDj{,
SIMULATION OF THE PACKED BED SYSTEM
Parameters used in the simulation estimated from the defined data fromexperimental analytical scale separation are assigned as shown in Table 1.
TABLE 1
Parameter Value
298 K3.385
0.33850.5117
4.4076 X lO·2cm2/sec4.89 X 10""cm2/sec
5.168 X 1Q-7cm2/sec0.0456000
Following the methods of Hsu (1979), Hsu and Dranoff (1987) and Chen andHsu (1987), the Fast Fourier Transform was applied to solve the fixed-bed
PertanikaJ. Sci. & Techno!. Vol. 8 No.2, 2000 221
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Wan Rarnli Wan Daud, San Myint, Abu Bakar Moharnad and Abdul Amir Hassan Radhurn
adsorption problem equation (1) to (10). If inversion ofF(s) in equation (11),named f('t) can be found, then U at bed length x and time 't can be obtainedby integrating f('t) from zero to 't with respect to 'to The inversion ofF(s) by FITis given by
f(t) = f('t) = f(j6.T)
1N-11 ) {2 Ok)=-L ik-; ex ..!!L2T k=O T N,
where j = 0,1,2, ..... , Ns - 1
RESULTS AND DISCUSSION
Figure 2 shows effluent concentration profile for injection of different solutionconcentration to an initially new clean bed versus different length of elutiontime. It also shows that the effluent concentration first approached the feedconcentration and then is reduced to zero at the end of the period. Thebreakthrough curves at different injection concentration were presented inFigure 3.
Figure 4 to Figure 7 show the theoretical simulation results of the adsorptionof a single component eugenol onto a fixed bed of ( Bondapak C18 analyticalcolumn. The parameters used in the calculation are all estimated from theoptimum analytical scale separation. Figure 4 displays the chromatographicelution curves at different bed length parameters calculated from the proposedmodel. It shows that the elution curves peak height is dependent on the bedlength parameter.
50---I' 0.532 gm ougoool/'''''"'
/t 2.128 gm eugenolJ1ClOm1
Ci40 )l 4.256 gm eugenoll100m1
3I .. 532"gm ougenoll'OOml
Z0 30
~a:f-z 20wu
~Iz0U 10
0) ~~~\.
0 2 4 6 8 10 12 14 16 18 20
TIME(min)
Fig 2. Chromatogtaphic elution curves of eugenol on Jl. Bondapak CISanalytical column, mobile phase methanol-water (80:20), flow rate 0.5 ml/min,
at different solution concentration injection at equilibrium condition
222 PertanikaJ. Sci. & Techno\. Vo\. 8 No.2, 2000
Prediction of Chromatographic Separation of Eugenol by the Fast Fourier Transform Method
analytical column, mobile phase methanol-water (80:20), flow rate 0.7 ml/min,at different bed length parameters, (1) 8=3.0, (2) 8=0.3
Figure 5 shows the effect of number of sampling points on the elution CUIVesat Peclet number 6000 for analytical column. Increasing the sample numbers to64 gives a higher peak height and vary smoothly than that computed at samplenumber 32. Figure 6 shows the theoretical chromatographic CUIVes of eugenolat different Peclet number. Increasing the Peclet number to 10,000 shows a
PertanikaJ. Sci. & Techno!. Vo!. 8 No.2, 2000 223
Wan Ramli Wan Daud, San Myint, Abu Bakar Mohamad and Abdul Amir Hassan Kadhum
little difference in curve profile height than at Peclet number 6000 of theoptimum analytical scale separation condition. At very low Peclet number 60,the elution curve is skewed and shallow indicating very slow saturation.
25r--------------.
Pe =6000
0.2 0.4 0.6 0.8't
1.2 1.4 1.6
Fig 5. Theoretical chromatographic elution curve of eugenol on )J. Bondapak CIa
analytical column, mobik phase 11U!thanol-water (80:20), flow rate 0.7 ml/min,0=0.3, at different sampk points(N)
10..----------------r-----..."
8
Ns=32
~Pe=6000
'- Pe=10000
-0- Pe=60
0.2 0.4 0.6 0.81
1.2 1.4 1.6
224
Fig 6. Theoretical chromatographic elution curve of eugenol on )J. Bondapak CIa
analytical column, mobik phase 11U!thanol-water (80:20), flow rate 0.7 ml/min,0=0.3, at different Peckt number
PertanikaJ. Sci. & Techno\. Vo\. 8 No.2, 2000
Prediction of Chromatographic Separation of Eugenol by the Fast Fourier Transform Method
Figure 7 demonstrates the breakthrough curves at different Peclet numbersof 6000 and 10,000 showing initial sharp rise of the curves due to the smallparticle size of the packing material, followed by a much more gradual increasetowards the feed concentration during the later part of the curves. In Figure 8the experimental elution curve of eugenol at real elution time 0.42 minutes(Figure 5.3.3) was compared with the theoretical simulation data at variousPeclet numbers. The results show that the experimental data agree with thetheoretical model of Chen and Hsu (1987) well at Peclet number (P) near6000 and sample number (N) 90.
u0.4
0.2
O'o 0.2 0.4 0.6 0.8,
~Pe=100001~.<- Pe=6000
1.2 1.4 1.6
Fig 7. Theoretical breakthrough curve oj eugenol on }J. Bondapak Cl8 analytical column, mobikphase methanol-water (80:20), flow rate 0.7 ml/min, 8=0.3, at different Peckt number
0.6r----------;=======i1
5~ 0.5o~a:~ 0.4w()Zo~ 0.3rJ)w..JZQ 0.2rJ)zw~
o 0.1
- Experimental
-+- Pe= 500
x- Pe= 1000
-<>- Pe= 6000
*Pe= 10.000
O~--------------l
o 1 2 3 4 5 6 7 8 9 1011 121314't
Fig 8. Experimental elution curve oj eugenol superimposed on theoretical predictions elution curveat different Peckt numbers. (Experimental conditions }J. Bondapak C
Wan Ramli Wan Daud, San Myint, Abu Bakar Mohamad and Abdul Amir Hassan Kadhum
CONCLUSION
The elution profile and the breakthrough curves depend on Peclet number(P), bed length parameters (8) and number of sample points (N). Theproposed model of Cheng and Hsu (1987) and the accuracy and high computingspeed of the FIT technique of Hsu (1979) gives satisfactory agreement betweentheoretical model and experimental data of chromatographic separation ofeugenol.
NOMENClATURE
C concentration of solute at time 8, (gm / ml)Co inlet concentration in fluid(mol / cmfl)C equilibrium solution concentration (gm / 1)C
pinlet concentration in particle (mol / crdl)
D intrapore diffusivity (em2 / sec)D
Laxial diffusivity (crrt / sec)
DM
molecular diffusivity (crrt / sec)K
Jequilibrium constant
L length of the column (em)M
2molecular weight of solvent
N number of sample pointss
P Peclet numbert
Q volumetric mobile phase flow rate (ml / sec)Re Reynolds numberSc Schmidt numberT half-period of function being consideredU dimensionless fluid phase concentrationV average linear pore velocity,(em / sec)V
Jmolal volume(ml / gm mol)
a radius of the particle, (em)kI
mass transfer coefficient (em / sec)m = e / (1-e)q. adsorbent capacity (gm / ml)r radial distance from centre of spherical particles, (em)x dimensionless axial distancez axial distance (m)
e bed porosity, (m3/ m3)
ep macropore porosity8 time(sec)<l> frequency function11 dimensionless radial distance in particle~ solvent viscosity (cp)~ film resistance parameter'Ill distribution ratio'11
2association factor
226 PertanikaJ. Sci. & Techno!' Vo!. 8 No.2, 2000
Prediction of Chromatographic Separation of Eugenol by the Fast Fourier Transform Method
't contact time parametero bed length parametercr constantX tortuosity factor
ACKNOWLEDGEMENTS
The authors would like to thank Universiti Kebangsaan Malaysia for supportingthis research, the Government of Malaysia for granting a scholarship under theMalaysian Technical Aid Program to Dr. San Myint to pursue this research andthe Yangon Institute of Technology and the Government of Myanmar forgranting study leave to Dr. San Myint.
REFERENCES
CHENG, T. L., and]. T. Hsu 1987. Prediction of breakthrough curves by the applicationof Fast Fourier Transform. AlChE] 33(8):1387 - 1390.
GEANKOPLIS, C.]. 1983. Transport Process and Unit operations. Massachusetts: Allyn andBacon, Massachusetts.
Hsu,j. T. 1979. Computer simulation of cascade chromatography and the application ofFast Fourier Transform to distributed-parameter model. PhD. Thesis, NorthwesternUniversity.
Hsu, j. T. and j. S. DRANOFF 1987. Numerical inversion of certain Laplace transform bythe direct application of fast Fourier transform (FFT) algorithm. Comput. Chem.Engng. 11(2):101 - 110.
RAGHAVAN, N. S. and D. M. RUTHVEN 1983. Numerical simulation of a fixed-bed adsorptioncolumn by the method of orthogonal collocation. AlChE] 29:922.
RAsMUSON, A. and 1. NERETNIEKS 1980. Exact solution of a model for diffusion in particlesand longitudinal dispersion in packed beds. AlChE] 26:686.
WEN, C. Y. and L. T. FAN 1975. Models for Flow Systems and Chemical Reactors. ew York:Marcel Dekker
WILKE, C. R. and P. CHANG 1955. Correlation for diffusion coefficients in dilute solutions.AlChE] 1:264.
