Separation of Simple Sugars by Selectivity Inverted Parametric Pumping

A laboratory study of a two-column, selectivity inverted, direct-mode parametric pump is reported. An anionic resin in carbonate form and a cationic r...
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Ind. Eng. Chem. Res. 1998, 37, 4808-4815

Separation of Simple Sugars by Selectivity Inverted Parametric Pumping Peizhu Sheng and Carlos A. V. Costa* LEPAE, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua dos Bragas, 4099 Porto Codex, Portugal

An alternative process to separate the isomeric mixture of frutose and glucose is presented. A laboratory study of a two-column, selectivity inverted, direct-mode parametric pump is reported. An anionic resin in carbonate form and a cationic resin in calcium form are used as adsorbents for the columns. The experimental results show that it is possible to simultaneously obtain separation and concentration with this system. A kinetic model assuming linear equilibrium, intraparticle pore diffusion, and axial dispersion is proposed and solved. The model solutions are compared with experimental results, and the comparisons indicate good prediction capabilities. Introduction Sugar is an extremely important food ingredient. Several industrial processes to convert starch into fructose syrup have been developed, as referenced by Ching.1 The isomerized fructose corn syrup typically contains 42% fructose, 50% glucose, and 8% oligosaccharides on a dry-weight basis. Because of the lower cost of fructose syrup for equivalent sweetness, it is used as a sucrose replacer in some foods and beverages. Because fructose is 1.3-1.8 times sweeter than sucrose and has a higher solubility in water at low temperatures, a syrup with 55-97% fructose content is interesting as a low-calorie sweetener. In addition, because of certain recognized short-term physiological effects, fructose is used as a sweetener for special dietary purposes. Because of the similarity of fructose and glucose physical and chemical properties, they cannot be separated from one another by conventional means.2,3 The separation of fructose from naturally occurring fructosecontaining syrup or isomerized fructose corn syrup has been studied and proposed using the solubility differences between the sugars; by adding solvents such as ethanol or propanol,4 or salts such as CaCl2 or NaCl that can form complexes preferentially with one of these sugars,5 or solvent and salts together;6 or by using reverse osmosis7 or ion-exchange/adsorption chromatography.8-10 These latter processes have been the most successful. Systems for large-scale separation of fructose from glucose have been commercialized using the chromatographic technique in a Xyrofin plant in Thomson, IL, was designed and built by the Finnish Sugar Company Ltd.,11 and using the UOP Sarex process.12 The basic separation mechanism involved is the formation of a loose chemical complex between the calcium ions on the adsorbents and the fructose molecules. This procedure causes a preferential retardation of fructose, while glucose is carried through with the mobile phase. Different configurations for simulated moving bed adsorbers have been studied by Hashimoto et al.,13,14 Barker and co-workers,15-20 Ching and her colleagues,21-29 and Lee and Lee.30 Dore and Wankat31 studied the * Corresponding author. Telephone: 351 2 2041670. Fax: 351 2 2000808. E-mail: [email protected].

separation of fructose and glucose by the cycling zone adsorption technique using DBAE-cellulose as adsorbent. Also, the continuous separation of mixtures of fructose, glucose, and sucrose has been investigated by a laboratory-scale continuous annular chromatograph (CAC) with the calcium form of Dowex 50W-X8 ionexchange resin by Howard et al.32 The objective of this paper is to present a laboratoryscale study where a selectivity inverted parametric pumping system33,34 is used to perform the separation of the isomeric mixture. A kinetic model for the system is also proposed, solved, and compared with experimental results, demonstrating good predictive properties. Kinetic Model for the Selectivity Inverted Parametric Pumping As shown in Figure 1, the selectivity inverted parametric pumping system for separation of glucose and fructose uses two adsorption columns. Column A is packed with an adsorbent that prefers glucose and column C with an adsorbent with higher affinity for fructose. They are coupled by the intermediate reservoirs (R1 and R2) that make better use of the selectivity reversal. The pump is operated in thermal direct mode. During the cold half cycle, adsorption takes place. This cold half cycle is followed by the hot half cycle to carry out regeneration by refluxing part of the product and reversing the flow direction inside the column. During the cold half cycle, the fresh feed and the material received from the last hot half cycle of column C (held at the intermediate reservoir R1) are fed to column A. Column C is fed with the fresh feed and the effluent from column A during the last hot half cycle (saved in reservoir R2). Because columns A and C preferentially adsorb glucose and fructose, respectively, a fructose-rich product will be produced from column A and a glucoserich product will be obtained from column C. Part of these products are kept in product reservoirs RT and RB, respectively. When the system shifts to the hot half cycle, the change in equilibrium isotherms causes the transfer of solutes excess to the liquid phase. Part of the products in RT are refluxed to column A to purge the solutes adsorbed (mainly glucose). The exiting stream will be more concentrated in glucose than the

10.1021/ie980066r CCC: $15.00 © 1998 American Chemical Society Published on Web 10/22/1998

Ind. Eng. Chem. Res., Vol. 37, No. 12, 1998 4809

each component within each column

R f(τ)

∂C ∂C ∂Csa R ∂2C )0 + + ∂x ∂τ ∂τ Pe ∂x2

(

(1)

)

∂Csa Ω h Det0 1 -  Csa ) C2 ∂τ  K R p

(2)

In eqs 1 and 2, the initial and boundary conditions are

C ) Ci0

τ ) τ0 f(τ) ) 1:

f(τ) ) -1:

Csa ) Csa0

x)0

C ) Cf0

x)1

∂C )0 ∂x

x)0

∂C )0 ∂x

x)1

C ) Cf1

The parameters Cf0 and Cf1 are obtained as follows by the mass balance around the reservoirs: Reservoir R1

FT ) RCA - (RCC - ΦB)ECA

(3)

RCACf0,n ) FT × C0 + DVR1 × Cf0,n-1 + RHCCC2, n-1ECA (4) Figure 1. Schematic diagram of the 2-column, thermal parametric pumping: DT-1-DT-4, liquid level monitors; F, fresh feed tank; V1-V16, solenoid valves; P1-P4, 2-channel peristaltic pumps; FC, fraction collector; TP and BP, top and bottom products, respectively; R1, R2, RT, and RB, intermediate reservoirs.

feed, so it is sent to reservoir R2 and will feed column C during the next cold half cycle to produce the glucoserich product. Column C is purged with a reflux stream from RB, and the effluent is concentrated in fructose and sent to reservoir R1 to feed column A in the next cycle to obtain the fructose-rich product. Equilibrium models34 are very helpful for visualizing the separation and as a conceptual tool in developing new cycles. Equilibrium theory yields the maximum separation that can be achieved in a given system if the separation is not kinetic. In fact, this limit of separation can never be achieved in a practical process. Real separation is always less effective because of at least two counteractions: diffusion due to non-instantaneous interphase mass transfer and axial fluid-phase dispersion. The use of more detailed kinetic models is desirable for system design and optimization. The kinetic models, which include mass transfer resistances and axial dispersion, are not, in general, analytically solvable. Computer numerical integration is used to solve these models and predict the real separation. For simplicity, the modified linear driving force approximation35 was used to represent the intraparticle mass transfer, and we assume that the external film resistance is negligible and that the intraparticle diffusion process is controlled by pore diffusion.36 Also, we use direct-mode operation for demonstrating the process, thus avoiding the complexity introduced by the moving temperature wave. Instantaneous heat transfer is assumed for the laboratory-scale, direct-mode pump. The kinetic model is composed of two equations for

Reservoir RT

DVRT × Cf1,n-1 + RHACT,n ) (DVRT + RHA) × Cf1,n (5) Reservoir R2

FB ) RCC - (RCA - ΦT)/ECA

(6)

RCCCf0,n ) FB × C0 + DVR2 × Cf0,n-1 + RHACA2,n-1/ECA (7) Reservoir RB

DVRB × Cf1,n-1 + RHCCB,n ) (DVRB + RHC) × Cf1,n (8) In eqs 3-8, where R is the fluid displacement coefficient during a half cycle (R ) uto/L), u is the fluid phase interstitial velocity, t0 is the half cycle time, L is the length of the fixed bed, f(τ) is the square wave function (equal to +1 for up flow), C is the dimensionless solute concentration in the interparticle space, Csa is the normalized solid-phase concentration, x is the dimensionless axial coordinate, τ is the dimensionless time, Pe is the axial mass Peclet number (Pe ) uL/DL), T is temperature, De is the effective intraparticle diffusivity, and Rp is the particle radius. The dimensionless variables are defined as

C)

c c0

Csa )

Fcsa(1 - ) c0

x)

z L

τ)

t t0

where c is the solute concentration in the interparticle space, c0 is a reference concentration, csa is the average

4810 Ind. Eng. Chem. Res., Vol. 37, No. 12, 1998

solute concentration over the adsorbent particle, t is time, z is the axial coordinate of the adsorbent bed,  is the bed voidage, F is apparent particle density, K is the adsorption equilibrium constant, and τ0 is the dimensionless initial time of a half cycle (twice the number of cycles). The parameter Cf0 is the dimensionless solute concentration of the entering stream during the cold half cycle; Cf1 is the equivalent for the hot half cycle; CA2 and CC2 are the hot half cycle column A and column C effluent average dimensionless concentrations, respectively; CT and CB are column A and column C product stream average dimensionless concentrations, respectively; FT and ΦT are dimensionless fresh feed and product volumes for column A, respectively, and FB and ΦB are those for column C, DVR1, DVR2, DVRT, and DVRB are dimensionless dead volumes in reservoirs R1, R2, RT, and RB, respectively. ECA is a coefficient defined as ECA ) LCSCC/LASAA ()1 throughout this work), where S is the column cross-sectional area; and Ω h is the global linear driving force (LDF) rate coefficient. The arithmetic average rate coefficients for the unequal, half-period, square-wave perturbation discussed in our previous paper35 were used. The individual coefficients for the corresponding equal, half-period perturbation can be calculated according to eqs 9 and 10

ln Ω ) 1.5834 - 0.5051 ln s

2 × 10-4 e s < 0.1 (9)

ln Ω ) ln π2 + 0.7020 exp(-4.3953s)

s > 0.1 (10)

where s is the dimensionless half cycle time, s ) Det0/ (R2pK). With the experimental conditions of this paper, only eq 10 is used, with Ω h = 15. For the binary separation in the dual-column pump, the complete model includes four sets of equations already described. The software package PDECOL37 was used to numerically solve the kinetic model equations. In this study, the integration was repeated for each half cycle to follow the flow reversal, and the column state at the end of a half cycle (solute concentration at each collocation point and the concentration gradient at the ends of the columns) was used as the initial condition for the next half cycle. The block diagram for the simulation in shown in Figure 2. The spatial domain was equally divided into 20 intervals (NINT). A polynomial of order 4 (KORD) was used for each subinterval, and the continuity (NCC) of the approximate solution and of its first spatial derivative at the breakpoints and hence on the entire domain [0, 1] was imposed. The method flag (MF) and the relative time error bound (EPS) were set to 22 and 10-5, respectively. The aforementioned parameters gave good precision for the simulation. PDECOL requires that the system boundary conditions must be consistent with the initial conditions. This consistency could be satisfied in three ways, as discussed by other authors:38 (1) Simply set the initial conditions equal to the boundary conditions at initial time, for example,

C|x)0, τ)τ0 ) Cf0|τ)τ0

(11a)

for the cold half cycles, and

C|x)1, τ)τ0 ) Cf1|τ)τ0 for the hot half cycles.

(12a)

Figure 2. Block diagram for the kinetic simulation.

(2) Express the boundary conditions by exponential approximations, for example,

C ) Cf0 + (Ci0 - Cf0)e-m(τ-τ0)

(11b)

for the cold half cycles, and

C ) Cf1 + (Ci0 - Cf1)e-m(τ-τ0)

(12b)

for the hot half cycles, where m is a constant. Under this modification, the boundary conditions are identical to the initial conditions at initial time (τ ) τ0) and reach the true values quickly when a suitable m is used. A m of 1000 proved to be enough in our case. These two approaches give quite close computing results for the system performance simulation, the first approach was used in the simulations presented in this work. (3) Use the so-called Danckwerts boundary conditions, which gives results similar to algorithm (2) in the range of Pe number we used. Experimental Section The general arrangement of the experimental system is shown schematically in Figure 1. The system consists of two identical jacketed glass columns (Amicon Moduline Medium-Pressure Laboratory Column) of internal diameter 0.022 m and length 0.50 m. Column A is packed with strong base-anion exchanger carbonate form Amberlite IRA-900 and column C with a strong acid-cation exchanger Amberlite 200 in calcium form and they are coupled by two intermediate reservoirs (R1 and R2). A liquid level monitor (E2K-X8MF1 capacitive proximity switch) was mounted in each reservoir. Four 2-channel peristaltic pumps (Gilson Miniplus 3) are included in the system. Pump P2 delivers fresh feed, pumps P1 and P3 feed the columns during the hot and cold half cycles, respectively, and pump P4 is used for product withdrawal. During operation, the end of each half cycle is determined by the level switch that

Ind. Eng. Chem. Res., Vol. 37, No. 12, 1998 4811 Table 1. System Equilibrium and Transport Parametersa sugar

fructose glucose

fructose glucose a

T, K

K

Table 2. Summary of Experimental Conditions

De × 1010, m2/s

Ca2+ Amberlite 200 (p ) 0.37)  ) 0.37 Rp ) 4.25 × 10-4 m 2uRp/DL ) 0.377 283.15 0.60 313.15 0.50 283.15 0.42 313.15 0.41

0.603 1.339 0.619 1.373

CO32- Amberlite IRA-900 (p ) 0.37)  ) 0.37 Rp ) 4.15 × 10-4 m 2uRp/DL ) 0.201 283.15 0.95 313.15 0.92 283.15 1.24 313.15 1.04

0.887 1.968 0.930 2.060

operating parameter RCC RCA ΦT ΦB TC, K TH, K t1, s t2, s tpc, s tph, s u, m/s

runs 1 & 3 10-5

runs 2 & 4

1.0 (6.54 × 1.0 (6.54 × 10-5 m3) 0.1 (6.54 × 10-6 m3) 0.1 (6.54 × 10-6 m3) 283.2 313.2 981 883 150 150 4.7 × 10-3 m3)

2.0 (1.308 × 10-4 m3) 2.0 (1.308 × 10-4 m3) 0.1 (6.54 × 10-6 m3) 0.1 (6.54 × 10-6 m3) 283.2 313.2 1308 1243 150 150 7.1 × 10-4

Reference 36.

detects when all the solution contained in the related reservoir has been transferred; the products are withdrawn in such a way that the volume of solution to be transferred in a hot half cycle is the same as the setting. This procedure minimizes the potential effects of flow fluctuations on the system stability. In total, 16 solenoid valves are used to control the flow routes in the system; V11 to V16 are operated at the end of each half cycle to shift the supply of heating and cooling water from the hot and cold baths (Edmund Bu¨hler UKT80) to the columns jacket. Bubble catchers (not included in the diagram) are positioned on both top and bottom ends of each column to avoid separation being deteriorated by gas bubbles entering columns. Experiments were started with the clean resins to simplify the analysis of the results. The preload technique is not practical for the configurations adopted in the study, as demonstrated by Sheng and Costa.35 Top and bottom products (TP and BP) were analyzed with a Gilson HPLC unit (305 pump, 805 Manometric module, and 132 RI detector) with a 0.2 m × 0.0046 m S5 NH2 Spherisorb HPLC column. The mobile phase was 80% acetonitrile (Merck, Germany) and 20% distilled water, and the flow rate employed was 1.67 × 10-8 m3/s. An HITACHI EB-64CRP programmable controller (PC), which consists of a CPU, program memory, image memory of each input/output, input circuit, output circuit, and power supply, was used to perform the process control. The PC sequentially executes the written program (instructions) from its first step to the last step, then return to the first step again and repeats the operation. Results and Discussion In the preliminary runs it was found that the sugar (glucose, fructose)-loaded carbonate form Amberlite IRA-900 was experiencing some irreversible changes in its characteristics at the higher temperature (e.g., 333.15 K). The higher operating temperature was then limited to 313.15 K (TH). It has been shown that the isotherms of fructose and glucose on both the carbonate form Amberlite IRA-900 and the calcium form Amberlite 200 are linear and uncoupled,36 and the system equilibrium and kinetic parameters36 are given in Table 1. In the kinetic simulations, it is assumed that there is no extra mass transfer during the delay periods of

Figure 3. Experimental and calculated concentration transients for Run 1: Rp,A ) 4.15 × 10-4 m; Rp,C ) 4.25 × 10-4 m; LA ) LC ) 0.465 m; RCA ) RCC ) 1.0 () 6.54 × 10-5 m3); ΦT ) ΦB ) 0.1 () 6.54 × 10-6 m3); t1 ) 981s; t2 ) 883 s; DVRT ) DVRB ) DVR1 ) DVR2 ) 0.2 () 1.31 × 10-5 m3); TC ) 283.2 K; TH ) 313.2 K; Ω h FA ) 10.24; Ω h FC ) 10.22; Ω h GA ) 10.47; Ω h GC ) 9.98. Key: (s- - - -) equilibrium model, fructose; (- - - - -) equilibrium model, glucose; (s - -) kinetic model, fructose; (s) kinetic model, glucose; (O) experimental, fructose; (4) experimental, glucose.

the cycle (precooling and preheating periods that are used to allow the columns to reach the operating temperature). This assumption will not introduce a large derivation because the waiting periods (250 s) are short in comparison with the diffusion time constant (836-2995 s). In addition, all reservoirs were treated as completely mixed and an average dead volume of 1.31 × 10-5 m3 (∼20% of the void volume of the resin bed) in each reservoir is taken into account in the calculations (eqs 4, 5, 7, and 8), although these volumes are really located at the bubble catchers and flow tubes. With the peristaltic pump, flow rates suffer from undesirable changes due to the aging of the tubing, especially for long-term operation. In general, such variations are small and thus do not affect the separa-

4812 Ind. Eng. Chem. Res., Vol. 37, No. 12, 1998

Figure 4. Experimental and calculated concentration transients for Run 2: Rp,A ) 4.15 × 10-4 m; Rp,C ) 4.25 × 10-4 m; LA ) LC ) 0.465 m, RCA ) RCC ) 2.0 () 1.308 × 10-4 m3); ΦT ) ΦB ) 0.1 () 6.54 × 10-6 m3); t1 ) 1308 s; t2 ) 1243 s; DVRT ) DVRB ) DVR1 ) DVR2 ) 0.2 () 1.31 × 10-5 m3); TC ) 283.2 K; TH ) 313.2 K; Ω h FA ) 10.03; Ω h FC ) 10.02; Ω h GA ) 10.17; Ω h GC ) 9.90. Key: (s - - - -) equilibrium model, fructose; (- - - - -) equilibrium model, glucose; (s - -) kinetic model, fructose; (s) kinetic model, glucose; (O) experimental, fructose; (4) experimental, glucose.

Figure 5. Experimental and calculated concentration transients for Run 3: Rp,A ) 2.5 × 10-4 m; Rp,C ) 2.5 × 10-4 m; LA ) LC ) 0.465 m; RCA ) RCC ) 1.0 () 6.54 × 10-5 m3); ΩT ) ΦB ) 0.1 () 6.54 × 10-6 m3), t1 ) 981 s, t2 ) 883 s, DVRT ) DVRB ) DVR1 ) DVR2 ) 0.2 () 1.31 × 10-5 m3); TC )283.2 K; TH ) 313.2 K; Ω h FA ) 9.88; Ω h FC ) 9.87; Ω h GA ) 9.89; Ω h GC ) 9.87. Key: (s - - - -) equilibrium model, fructose; (- - - - -) equilibrium model, glucose; (s - -) kinetic model, fructose; (s) kinetic model, glucose; (O) experimental, fructose; (4) experimental, glucose.

tion very much, and the designed product withdrawal mode ensures the mass balance in the system for every cycle and the separations proceed in the right way. If using the time mode operation where the shift between the cold and hot half cycles is controlled by the timers, once a material accumulation happens in any reservoir because of the unstable flow, the separation will be very difficult to predict. Four experiments were performed to separate the glucose-fructose-water system, all with the same feed of equal amounts of glucose and fructose (5% each). The experiment were conducted under two sets of operating conditions. The details are shown in Table 2, where TC and TH are the cold and hot operating temperatures, t1 and t2 are the duration of cold and hot half periods, tpc and tph are precooling and preheating times, respectively. Fixed displacement was employed in the operation, and thus any flow variation along the operation will cause the corresponding change in cycle time. A constant average flow velocity was assumed in the models for simulation. Run 1 and Run 2 were carried out with larger particles (Rp,A ) 0.0415 cm, Rp,C ) 0.0425 cm). The experimental transient glucose and fructose concentrations in the product streams are shown in Figures 3 and 4. To improve the separation, the smallest available fractions of resins were used in Run 3 and Run 4. As can be see from eq 2, the interphase mass transfer rate

is inversely proportional to the square of the particle radius. Using smaller particles leads to a shorter diffusion time and reduced mass transfer resistance, so a better separation can be achieved. This relationship is confirmed by the experimental results, as shown in Figures 5 and 6. The fructose purity in TP (product of column A) went up to 74.46% in Run 3 from 64.86% obtained in Run 1, and glucose in BP (product of column C) increased from 52.61% in Run 1 to 71.16% in Run 3. The same tendency is observed in Runs 2 and 4. The experimental product purities at cyclic steady state are summarized in Table 3. In the kinetic model simulation, we assume that the bed voidage and particle Pe number do not vary with the particle size. In Figures 3-6, the equilibrium model predictions are also presented. The results show that a complete separation in column A and an incomplete separation in column C could be obtained in Runs 1 and 3, and that both columns A and C are able to give complete separation in Runs 2 and Run 4. The characteristic parameters of the system are summarized in Table 4. In this table, Ai(T)j; is the equilibrium constant of solute i on adsorbent j at temperature T, related to K by

A(T) )

1- K(T) 

(13)

and A(TC) > A(TH). The parameters DFA, DGA, DFC, and DGC are the net movements of fructose and glucose

Ind. Eng. Chem. Res., Vol. 37, No. 12, 1998 4813 Table 4. Equilibrium Model Characteristic Parameters characteristic parameter

runs 1 & 3

runs 2 & 4

RCA/[1 + AF(TC)A] RHA/[1 + AF(TH)A] RCA/[1 + AG(TC)A] RHA/[1 + AG(TH)A] RCC/[1 + AF(TC)C] RHC/[1 + AF(TH)C] RCC/[1 + AG(TC)C] RHC/[1 + AG(TH)C] DFA DGA DFC DGC

0.3817 0.3502 0.3215 0.3249 0.4950 0.4865 0.5814 0.5294 0.0315 -0.0034 0.0085 0.0520

0.7634 0.7393 0.6431 0.6859 0.9901 1.0270 1.1628 1.1176 0.0241 -0.0428 -0.0369 0.0452

Figure 6. Experimental and calculated concentration transients for Run 4: Rp,A ) 2.5 × 10-4 m; Rp,C ) 2.5 × 10-4 m; LA ) LC ) 0.465 m; RCA ) RCC ) 2.0 () 1.308 × 10-4 m3); ΦT ) ΦB ) 0.1 () 6.54 × 10-6 m3); t1 ) 1308 s; t2 ) 1243 s; DVRT ) DVRB ) DVR1 ) DVR2 ) 0.2 () 1.31 × 10-5 m3); TC ) 283.2 K; TH ) 313.2 K, Ω h FA ) Ω h FC ) Ω h GA ) Ω h GC ) 9.87. Key: (s - - - -) equilibrium model, fructose; (- - - - -) equilibrium model, glucose; (s - -) kinetic model, fructose; (s) kinetic model, glucose; (O) experimental, fructose; (4) experimental, glucose. Table 3. Experimental Product Purities at Cyclic Steady State run no. 1 2 3 4

TP (product from column A)

BP (product from column C)

fructose

glucose

fructose

glucose

64.86 59.12 74.46 65.48

35.14 40.88 25.54 34.52

47.39 42.99 28.84 38.29

52.61 57.01 71.16 61.71

concentration waves on column A and column C during a complete cycle, calculated by the equilibrium theory

DFA ) DGA ) DFC ) DGC )

RCA 1 + AF(TC)A RCA 1 + AG(TC)A RCC 1 + AF(TC)C RCC 1 + AG(TC)C

-

-

-

-

RHA 1 + AF(TH)A RHA 1 + AG(TH)A RHC 1 + AF(TH)C RHC 1 + AG(TH)C

(14)

(15)

(16)

(17)

The equilibrium model is apparently inadequate to make a reasonable prediction of this system because of the existence of a nonnegligible intraparticle mass

Figure 7. Product concentration transients predicted by the kinetic model: Rp,A ) Rp,C ) 5 × 10-5 m; LA ) LC ) 0.93 m; RCALASAA ) RCCLCSCC ) 6.54 × 10-5 m3; ΦTLASAA ) ΦBLCSCC ) 6.54 × 10-6 m3; t1 ) 981 s; t2 ) 883 s; DVRT ) DVRB ) DVR1 ) DVR2 ) 0; TC ) 283.2 K and TH ) 313.2 K for column A; TC ) 283.2 K and TH ) 333.2 K for column C; Ω h FA ) Φ h FC ) Φ h GA ) Φ h GC ) 9.87. Key: (1) fructose; (2) glucose.

transfer resistance. The kinetic model provided a good representation of the experimental data as expected. Generally, the parapump separation will increase when the temperature difference increases and when the cycle period is longer (slow flow), which allows for a closer approach to equilibrium. With open systems, the larger the shift in equilibrium with temperature, the lower the reflux ratio (defined as the ratio of the fluid returned to the column to that exiting column) can be and purer products will be produced. It proved difficult to apply large temperature differences to the present system. The higher temperature is limited by the anion exchanger used. This limited temperature difference coupled with the moderate temperature dependence of adsorption isotherms limited the separation (product purity and productivity). Increased sys-

4814 Ind. Eng. Chem. Res., Vol. 37, No. 12, 1998

tem flexibility may be achieved by equipping each column with its own temperature-control system and liquid transport pumps. With this configuration, one may optimize the operation by using different cycle periods, temperatures, flow rates, column sizes, etc. for each column. For example, if the bed lengths are doubled (L ) 0.93 m) and the operating temperatures of column C are set to 283.2 K (TC) and 313.2 K (TH), the kinetic model predicts a separation giving 95% fructose in TP and 97% glucose in BP with the same flows and cycle period as in Run 1 and adsorbent particles with Rp ) 0.005 cm. The product concentration transients are plotted in Figure 7. Conclusions The experimental separation of fructose and glucose was carried out on dilute sugar solutions using the selectivity inverted, two-column, thermal, direct-mode, parametric pumping system. The results were compared with the model simulations. The kinetic model predictions using modified linear driving force approximations for interphase mass transfer were in good agreement with the experimental separations, but the equilibrium model showed little potential to represent such a kinetic-controlled process. In the present system, separation is constrained by significant mass transfer resistance, limited temperature difference, and moderate isotherms temperature dependency. Improved separation can be obtained by reducing the mass transfer resistance. It is possible to get two pure products under optimized operating conditions for a system with less important mass transfer resistance. Compared with the simulated moving bed (SMB), the most studied process for the separation of fructose and glucose, the selectivity inverted, two-column, thermal, direct-mode, parametric pumping is simpler and easier in operation. Efficient separation is possible by SMB, but the glucose and fructose concentrations in the product streams are always lower than the feed 21,22,24 under isothermal operation for the linear isotherm. Concentrated products were obtained with the parametric pump studied in this work. Nomenclature Ai(T)j ) linear equilibrium constant of solute i on adsorbent j at temperature T c ) concentration of solute in the interparticle space (liquid phase), kmol/m3 c0 ) initial concentration, kmol/m3 csa ) average solute concentration over the adsorbent particle, kmol/kg adsorbent C ) dimensionless solute concentration in the interparticle space Cf0 ) dimensionless solute concentration in the entering stream during the cold half cycle Cf1 ) dimensionless solute concentration in the entering stream during the hot half cycle Cf0 ) dimensionless initial liquid-phase solute concentration of a half cycle Csa ) dimensionless average solid-phase concentration Csa0 ) dimensionless average solid-phase concentration at the initial state of a half cycle De ) effective intraparticle diffusion coefficient, m2/s D ) net movement of solute concentration wave during a complete cycle DL ) effective axial dispersion coefficient, m2/s DVR1 ) dead volume fraction in reservoir R1

DVR2 ) dead volume fraction in reservoir R2 DVRT ) dead volume fraction in reservoir RT DVRB ) dead volume fraction in reservoir RB f(τ) ) square wave function ECA ) coefficient, ECA ) LCSCC/LASAA FT ) top fresh feed fraction FB ) bottom fresh feed fraction K ) dimensionless combined adsorption equilibrium constant L ) adsorbent bed length, m n ) number of parametric pumping cycles Rp ) radius of the spherical adsorbent particle, m t ) time, s t0 ) time, s t1 ) duration of first half period (adsorption), s t2 ) duration of second half period (desorption), s tpc ) precooling time, s tph ) preheating time, s T ) temperature, K TC ) cold half cycle operating temperature (lower temperature), K TH ) hot half cycle operating temperature (higher temperature), K u ) liquid-phase interstitial velocity, m/s z ) axial coordinate of the adsorbent bed, m Pe ) axial mass Peclet number, defined as Pe ) uL/DL Greek Letters R ) dimensionless fluid displacement coefficient  ) bed voidage Φ ) dimensionless product withdrawal volume F ) apparent particle density, kg/m3 τ ) dimensionless time τ0 ) dimensionless initial time of a half cycle Ω h ) global LDF rate coefficient Subscripts A ) column A, adsorbent A (Amberlite IRA-900 in CO32form) B ) bottom product C ) column C, adsorbent C (Amberlite 200 in Ca2+ form) CA ) cold half cycle and column A CC ) cold half cycle and column C F ) fructose FA ) fructose on column A FC ) fructose on column C G ) glucose GA ) glucose on column A GC ) glucose on column C HA ) hot half cycle and column A HC ) hot half cycle and column C T ) top product

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Received for review February 2, 1998 Revised manuscript received July 6, 1998 Accepted July 9, 1998 IE980066R