Improvement of para-Xylene SMB Process Performance on an

3316

Ind. Eng. Chem. Res. 2010, 49, 3316–3327

Improvement of para-Xylene SMB Process Performance on an Industrial Scale Young-Il Lim* Department of Chemical Engineering, Hankyong National UniVersity, Anseong 456-749, Korea

Jinsuk Lee Samsung Total, Dokgod-ri 411-1, Daesan-up, Seosan-si, Chungnam 356-711, Korea

Suresh K. Bhatia DiVision of Chemical Engineering, UniVersity of Queensland, Brisbane, Queensland 4072, Australia

Young-Sub Lim and Chonghun Han School of Chemical and Biological Engineering, Seoul National UniVersity, Seoul 151-744, Korea

Dead volume classified as bed head, bed tail, and bed line affects the purity and recovery in industrial-scale simulated-moving-bed (SMB) processes. Considering the three types of dead volume, the operation strategies for four, seven, and eight zones are presented for an industrial-scale para-xylene (PX) SMB process, and their performances are compared in terms of purity, recovery, and dilution. The dead volume is treated by a Courant-Friedrichs-Lewy- (CFL-) number-insensitive method of characteristics (MOC). An extended node model integrating the dead volumes has been developed and solved by using the MOC. Seven-zone operation including line and secondary flushes enhances the purity, while keeping almost the same recovery as achieved with four-zone operation. The secondary flush introducing pure PX reduces the dilution of the extract. Eightzone operation with both a secondary flush introducing pure PX and a tertiary flush-out shows high productivity with low dilution and over 99.7% purity. 1. Introduction Simulated-moving-bed (SMB) chromatography, a continuous multicolumn chromatographic process, has emerged as a promising technology for the separation of petrochemicals, sugars, pharmaceuticals, and biomolecules.1-4 SMB chromatography usually works with the inherent advantage of a high driving force because of countercurrent flow, resulting in low solvent consumption, small apparatus scale, and high yield, compared to batch chromatography.5,6 In SMB operation, the countercurrent movement of fluid and solid is simulated by an appropriate flow switching sequence, resolving problems associated with solid circulation in a true-moving-bed (TMB) unit, where liquid and solid flow in opposite directions. The fixed beds of an SMB are divided into several zones by inlet and outlet streams, and the inlet (i.e., desorbent and feed) and outlet (i.e., extract and raffinate) ports move simultaneously one column ahead at a given switching time interval in the direction of the fluid flow.7 The SMB process was developed by Universal Oil Products (UOP, Des Plaines, IL) in the 1960s.8 SMB technology has been successfully commercialized in the petrochemical4 and sugarprocessing9,10 industries and more recently in the area of chiral separations.1,2 Various approaches have been taken to reduce the production costs and improve the separation efficiency of SMB processes by operating the SMB under more complex dynamic conditions, as is the case in Varicol,11 PowerFeed,12 ModiCon,13 and Partial-Discard14 processes. These new operation modes do not keep constant conditions during one switching period, as in a standard SMB, but allow for variation of the column configuration, feed flow rates, feed concentration, and product withdrawal time, respectively. * To whom correspondence should be addressed. Tel.: +82 31 670 5207. Fax: +82 31 670 5445. E-mail: [email protected].

More sophisticated designs and operations at the production scale have been required for complex mixtures, desired purity, and higher productivity with the increasing demand in the petrochemical, pharmaceutical, and food industries. A largescale SMB process with five zones was reported for six-sugar separation from biomass hydrolyzate.10 The Parex unit for paraxylene separation is composed of a seven-zone SMB to increase the purity by flushing bed lines contaminated by impurities.15 The dead volume (i.e., extracolumn dead volume and bed line) have to be properly taken into account in these practical applications.2,15 Even in small-scale SMB units, the dead volume of connecting tubing parts and valves can be comparable to the column volume, and the time delay caused by the extracolumn dead volume has been considered in the modeling approach.16,17 For para-xylene (PX) separation from its C8 aromatic isomers such as meta-xylene (MX), ortho-xylene (OX), and ethylbenzene (EB) with p-diethylbenzene (PDEB) as a desorbent using an industrial-scale SMB process, competitive Langmuir adsorption isotherms were presented for a five-component system.18 Optimization of the operating conditions has been performed in modeling approaches,19-21 a parallel two-zone and four-zone SMB hybrid process has been developed,22 the effect of the decrease in the adsorbent capacity on the SMB unit performance has been studied,23 and a revamping strategy maximizing productivity with minimum desorbent consumption has been proposed.24 Those approaches did not take into account the dead volume (more specifically, the bed lines). It is recognized that the presence of residual compounds in the bed lines can have detrimental effects on SMB processes.25 The flushing of the bed line used to deliver the feed stream to the adsorbent bed was found to increase the purity of the extract.15,26 The capacity of the PX SMB process has been increased by flushing the contents of the bed line (or transfer

10.1021/ie901097z  2010 American Chemical Society Published on Web 02/19/2010

Ind. Eng. Chem. Res., Vol. 49, No. 7, 2010

line) just used to withdraw the raffinate stream from the adsorbent bed,25,27 where the feed stream to the process was used as the flushing liquid in Noe27 and the stream trapped in the bed line used to withdraw the raffinate stream was flushed out in Frey.25 In the three patents in refs 25-27, the improvement expected from flushing of the bed lines was verified by using a computerized model that was shown to accurately predict and correlate with the actual operation of commercial-scale PX SMB units. However, there was no detailed description of the operating conditions and model used in these patents. The influence of the bed line (or transfer line) connecting the beds to the rotary valve has been investigated in detail for a seven-zone SMB unit.15 Because the concentrations of the dead volume trapped in the bed line have a temporally discontinuous feature, the dynamics caused by the bed line was numerically examined using an explicit time integrator, dividing one switching period into three different states like time events.15 However, it is not trivial to treat the time events caused by the bed line for the implicit time integrators (e.g., Gear method)19 commonly used for solving the SMB model. Grosfils28 divided the dead volume into moving and fixed parts. The extracolumn dead volumes located before and after an adsorptive column (bed head and bed tail, respectively) were considered to be part of the moving dead volume, whereas the bed line connecting the inlet and outlet streams to an adsorptive column was classified as the fixed dead volume. The time delay caused by the dead volume was expressed by a time-delayed exponential function that was a kind of continuously stirred tank reactor (CSTR) model. The CSTR model was used to calculate time-delayed concentrations passing through the bed line for the feed inlet stream.28 However, the model cannot be applied generally to bed lines passing streams with large variations in concentration profiles, for which a series of the CSTR models or the plug-flow model is appropriate. In this study, the dead volume including the bed head, bed tail, and bed line is treated within the framework of an extended node model with a method of characteristics (MOC) modified for convection-dominated diffusion problems that accurately tracks the concentration profile within dead volume. The extended node model makes it possible to use an implicit time integrator without time events, separating the dead volume dynamics from the adsorptive column dynamics. An eight-zone SMB operation at the industrial scale is proposed to improve the purity and productivity of PX, taking into account flushing of the streams trapped in bed lines. The influence of the inlet composition of the secondary flush on the purity and recovery was also investigated. 2. Process Description The Parex para-xylene SMB process is designed to recover more than 97 wt % of the para-xylene (PX) from the feed, while achieving a product purity of 99.7 wt %. The SMB unit has 24 adsorbent beds and 24 bed lines connecting the beds to the rotary valve.29 Because of practical construction considerations, the unit consists of two adsorption chambers in series with 12 beds each, as shown in Figure 1. Each bed is connected to a flow directing device, known as a rotary valve, by a bed line. The pump provides liquid circulation from the bottom of a chamber to the top of another chamber. Usually, desorbent (D) comes out of the SMB unit with both extract (E) and raffinate (R) and is later separated in distillation columns. The port switching is realized by the rotation of the unique rotary valve. Every line connecting the rotary valve to the adsorbent beds is shared by inlet and outlet

3317

Figure 1. Schematic diagram of eight-zone PX SMB process: D, desorbent; LFo, line-flush outlet; E, extract; SFi, second-flush inlet; LFi, line-flush inlet; F, feed; TFo, third-flush outlet; R, raffinate.

streams (i.e., desorbent, feed, extract, and raffinate). For example, the same bed line is used for introducing the feed (F) into the unit and later for withdrawing the extract from the unit in the four-zone operation.15 Therefore, the bed lines will be contaminated by other inlet or outlet streams, resulting in product purity reduction, unless appropriate actions are taken. To prevent the extract stream from being contaminated by xylene isomers and to increase the recovery, the SMB unit has internal outlet (LFo) and inlet (LFi) line-flushing sequences. The line-flush inlet stream (LFi) trapped inside the bed line, which contains mainly PX and desorbent, is flushed into the eighth bed by the secondary-flush inlet flow (SFi).26 The raffinate flushing flow (tertiary flush-out; TFo) is preferably drained out, because the raffinate flow is a mixture of MX (meta-xylene), OX (ortho-xylene), and EB (ethylbenzene). Therefore, the eightzone SMB is designed and operated to increase the purity and recovery in the industrial-scale SMB unit with the bed lines. In Table 1, the geometry and operating conditions of the industrial-scale PX SMB unit are shown, where the column configuration and four-zone flow rates were take from Minceva and Rodrigues15 without modification. Three bed configurations of four, seven, and eight zones were considered. The dead volumes (bed head, bed tail, and bed line) are reported in Table 1. The bed tail (BT) exists only in the 12th and 24th beds, and the length of BT (LBT) is set to 0.12 m, when the dead volume space is converted to have the same diameter as the bed. The length of the bed head (LBH) for every bed is given as 0.02 m (about 2% a bed). The bed-line volume (VBL) is fixed equally for all beds at 0.145 m3 (1% of the volume of a bed). The inlet and outlet flow rates are given for four-, seven-, and eight-zone operations in Table 1. The flow rates of desorbent

3318


Table 1. Simulation Parameters for Four-, Seven-, and Eight-Zone p-Xylene SMB Processes Design Parameters bed configuration 6-9-6-3 εb 0.39 1-5-1-6-2-6-3 1-5-1-6-2-4-1-4 Lc (m) 1.1 LBH (m) 0.02 for each bed head dc (m) 4.1 LBT (m) 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.12 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.12 Fp (kg/m3) 1390 VBL (m3) 0.145 for each bed line

column model5,7,15,19,30,31 with competitive Langmuir adsorption isotherms is expressed by partial differential equations (PDEs) in time (t) and axial distance (z) as

(

(1) dni ) ki(n*i - ni) dt n*i )

Operating Parameters 3

QD (m /min)

2.89

QLFo (m3/min) QE (m3/min) QSFi (m3/min)

0 or 0.15 1.65 or 1.8 0 or 0.15

QLFi (m3/min) QF (m3/min) QTFo (m3/min) QR (m3/min) Qrecycle (m3/min)

0 or 0.15 1.45 0 or 0.115 2.69 or 2.575 5.39

components (5) PX (product), MX, OX, EB, PDEB (desorbent) CF (kg/m3) 171, 360, 92, 101, 0 CD (kg/m3) 0, 0, 0, 0, 724 CSFi (kg/m3) 712, 0, 0, 0, 0 or 0, 0, 0, 0, 724 τ (min) 1.15 Nswitch 240 (10 cycles)

1.0 × 10-3VL Pe 1100 5.0 × 10-3VL Pedead 220 2.0 for each component 3 316, 68, 56, 91, 317 bi (m /kg) 1.07, 0.23, 0.19, 0.31, 1.29 Computational Parameters

Nmesh ∆z (m) NCFL,max

16 0.073 0.630

Ntime ∆t (min)

(2)

aiCi 1+

(3)

∑bC

j j

j

Model Parameters Dax (m2/min) Dax,dead (m2/min) ki (min-1) ai

)

∂Ci 1 - εb ∂(Ci) ∂Ci ∂ ) + VL Dax k (n* - ni) ∂t ∂z ∂z ∂z εb i i

where VL is the interstitial velocity, assumed to be constant within the bed; Dax is the axial dispersion coefficient; and εb is the bed voidage. The liquid and solid concentrations are Ci and ni, respectively, for each component i. n*i is the equilibrium concentration defined by the Langmuir adsorption isotherm, eq 3, which has two parameters (ai and bi) for each component. The LDF model with a lumped mass-transfer coefficient (ki) is employed in eq 2. Because the Peclet number (Pe ) VLLc/Dax, where Lc is the column length) is usually large in this column model, the system is called a convection-dominated PDE. In eqs 1 and 2, two initial conditions (ICs, t ) 0) for two time derivatives and two boundary conditions (BCs, z ) 0 and Lc) for the convection and diffusion terms are required IC )

40 0.029

(QD), feed (QF), and recycle (Qrecycle) are set to be same for the three operations. The flow rate of the line-flush outlet (QLFo) is the same as that of the line-flush inlet (QLFi). The flushing flow rates of QLFi, QLFo, and QSFi are the same as that being able to flush 120% of BL volume (VBL) during the switching time (QLFi ) QLFo ) QSFi ) 0.15 m3/min). For the tertiary flush, only 90% of the bed line volume (QTFo ) 0.115 m3/min) is flushed out at the exit of 16th bed to prevent additional PX loss from the tertiary flush. The inlet concentrations of feed (CF), desorbent (CD), and secondary flush (CSFi) are given for the five components, where PX is the product; PDEB (p-diethylbenzene) is the desorbent; and MX, OX, and EB are the xylene isomers as impurities. Pure PX or pure PDEB is introduced into SFi to investigate the effect of its composition on the SMB process performance (i.e., recovery and purity). The density of PX (712 kg/m3) is a little lower than that of PDEB (724 kg/m3). The switching time (τ) is 1.15 min, and the simulation results are analyzed after 240 switchings (or 10 cycles). The seven- or eight-zone operations with flushing make the analysis of the PX SMB process much more difficult and lead operators to rely on operating experience. In this study, four-, seven-, and eight-zone PX SMB operations are analyzed by means of a modeling approach with an efficient dead volume treatment method. 3. SMB Model Description The SMB model representing realistic port switching by the node model5,7,30-32 is used in this study to consider periodic dynamics of SMB operation. The linear driving force (LDF)

{

C(z, 0) ) Cinitial(t ) 0, ∀z) n(z, 0) ) ninitial(t ) 0, ∀z)

{|

VL(Cz)0 - Cin) ) Dax

BC )

∂C ∂z

) 0, z)Lc

∂C ∂z

|

z)0

(4)

, ∀t

(5) ∀t

where Cin is the inlet concentration entering the column, which is determined by the operating conditions (or calculated by the node model). The node model represents the periodic operation through the port switching and delivers the inlet concentration (Cin) needed in the boundary conditions. In this study, an extended node model that contains concentration dynamics within the dead volume is proposed. The interand intrabed dead volume is conceptualized by the bed head (BH) and the bed tail (BT), which are called the extracolumn dead volume in the literature.16,33 The external connecting line to the bed (i.e., rotary valve to the bed) is called the bed line (BL). As shown in Figure 2, the Nth dead volume consists of the Nth BH, the Nth BT, and the Nth BL, which are all nonadsorptive regions. BH corresponds to all of the volumes of valves and tubing parts connecting the port to the bed, a distribution plate space, and other physically occupied volumes at the top of the adsorptive bed. BT contains mainly the volume of tubing parts connecting the adsorptive bed end to the port. BL includes the volume of the pipe introducing the inlet (i.e., desorbent and feed) or outlet (i.e., extract and raffinate) stream. When the inlet and outlet streams are shifted one bed ahead, streams in BH and BT flow without interruption, but the role of BL (inlet, outlet or resting) is changed according to the port switching. The conventional node model representing the port (or physically the valve) between two beds has been described for inlet and outlet streams according to the port switching without considering the


3319

the Appendix, the temporal and spatial discretization of MOC is developed, satisfying the CFL (Courant-Friedrichs-Lewy) condition. Concentration dynamics within the dead volume are calculated in a manner that is insensitive to the CFL number [NCFL ≡ VL(∆t/∆z)]. Equation 7 is represented by a set of linear equations, resulting in a symmetric band matrix. The node model is now extended to a port switching model involving the streams of BH, BT, and BL. The extended node model calculates both the time delays of dead volume concentrations by MOC and the flow rates by mass conservation. The novel approach makes it possible to separate the adsorption bed model from the dead volume model and to solve the dead volume model exactly (eq 6) in a computationally efficient manner. It is stressed that the adsorptive bed model can be solved by using any type of time integrators and that the MOC results provide boundary values of the adsorptive model. In the lower part of Table 1, both the model parameters and computational parameters are shown. The axial diffusivity (Dax) is assumed to be proportional to the fluid interstitial velocity (Dax ) VLLc/Pe). The lumped mass-transfer coefficient (k ) 2 min-1)15 is taken to be equal for all components. It is noted that the first Langmuir coefficient (ai) is obtained as follows ai )

Figure 2. Schematic diagram of extended node model considering bed head, bed tail, and bed line.

dead volume.5,7,30-32 BH and BT (or extracolumn dead volume) were treated as a part of the bed, and a convection-diffusion model without adsorption was solved16,28,33,34 ∂Ci ∂Ci ∂2Ci ) Dax,dead,i 2 + Vdead ∂t ∂z ∂z

(6)

where Vdead is the superficial velocity of the fluid and Dax,dead is the axial dispersion coefficient of each component i in BH, BT and BL. Therefore, two different PDEs (adsorption and nonadsorption bed models) are solved simultaneously. It is more complicated to solve the dynamics of BL showing a discontinuous feature with time. Even though the BL model is the same as eq 6, this equation should be solved with BL only being used at the actual time. However, it might not be necessary to solve eq 6 together with the adsorption PDE model, eq 1. Equation 6 has been solved very accurately by the method of characteristics (MOC),35,36 which is a well-known analytical method for the convection PDE. The analytical solution of the convection PDE shows that the initial condition, Ci,0(z), moves along a characteristic line: z ) z0 - Vdeadt. The numerical solution of eq 6 on the characteristic line was given by Bruneau et al.35 Cni,l -

Dax,dead,i∆t 2

∆z

n n (Ci,l-1 - 2Cni,l + Ci,l+1 ) ) C˜ni,l

(7)

where the subscript l and superscript n denote the spatial and temporal mesh indexes, respectively; ∆z and ∆t are the uniform spatial and temporal step sizes, respectively; and n n-1 is the value interpolated from the known values (Ci,l ) C˜i,l n-1 at the previous time level [t ) (n - 1)∆t] using MOC. In

Fp n b 1 - εb m,i i

(8)

where Fp is the particle density and nm,i is the saturation concentration of component i in the absorbed phase. nm,i and bi were taken from Minceva and Rodrigues.15 The maximum CFL number (NCFL,max ) VL,1∆t/∆z) is obtained from the zone 1 between desorbent and line-flush outlet (or extract). The calculation was performed on a personal computer (2.5 GHz dual-core CPU and 3 GB RAM). An explicit time-space conservation element and solution element (CESE) scheme37,38 was used to solve the adsorptive bed model, eqs 1-3. The inlet BC of the adsorptive bed is given by a BH exit value obtained from the CFL-insensitive MOC proposed in this study. The concentration propagation inside BT is also calculated by the MOC. The node for port switching is situated in front of the bed head and transfers an inlet value of BH for MOC calculation. This extended node model also contains MOC for BL transporting the inlet or outlet streams. The extended node model thus plays a central role in connecting the three types of dead volume treated by MOC, as shown in Figure 2. Attention is paid to the calculation sequence of bed-line MOC, because the velocity of BL has a positive, negative, or zero value according to the port switching. For convenience, the first mesh of all BL is fixed at the starting point from the bed outside to the bed. 4. Case Studies In total, eight runs were performed in four-, seven-, and eight-zone operations with and without dead volume, as shown in Tables 1 and 2. The dispersion coefficient of the dead volume was set to be the 5 times that of the adsorptive bed. It has been experienced that the extended node model based on the CFL-number-insensitive MOC is computationally efficient, because the CPU time increases by 0.5%, even though the axial direction is enlarged by about 4% by the dead volume in the four-, seven-, and eight-zone operations with BH, BT, and BL. Four process parameters, namely, purity, recovery, productivity, and dilution were evaluated for each run. The purity at the extract is defined excluding the desorbent concentration (CE,PDEB)

3320


purity (%) ) 100 ×

j E,PX C

j E,PX is also obtained the first and third stages (tlag,E e t e τ). C in the presence of BL from the first and second stages

j E,PX C j E,OX + C j E,EB j E,MX + C +C

(9) j E,i is the time-average fluid concentration in the extract where C for component i. The recovery of PX is determined by the ratio of the PX amount in extract to that in the inlet recovery (%) ) 100 ×

j E,PXQE C QFCF,PX + CSFi,PXQSFi

(10)

j E,PX ) C

productivity [kg/(h m3)] ) 60 ×

24(1 - εb)Vc

(11)

1 τ

∫

j E,PX CF,PX - C CF,PX

(12)

Because the extract diluted with desorbent is sent to the distillation column for separation of PX from the desorbent,29 it is preferrable to minimize the dilution unless the productivity decreases.5 When pure PX is introduced at SFi in the sevenand eight-zone operations, the mean concentration of extract j E,PXQE - CSF ,PXQSF )/(QE - QSF ), j sE,PX ) (C PX is equivalent to C i i i which is used for dilution calculations. 4.1. Four-Zone SMB with and without Dead Volume. Four simulations were carried out for four-zone operation at the same flow rates, namely, without dead volume; with BH and BT; with BL; and with BH, BT, and BL. The four-zone design and operating conditions are shown in Table 1. The time-average j E,PX) is determined from the mass extract concentration of PX (C conservation of PX, when periodic steady state is attained in the four-zone SMB unit j E,PX ) C

j R,PXQR CF,PXQF - C QE

(13)

j R,PX is the time-average raffinate concentration of PX where C during one switching time. When there is BL, it is necessary to distinguish three different stages during one switching period.15 In the first stage, the feed stream trapped in BL is withdrawn for the time required to pass through the extract BL, 0 e t e tlag,E. In the third stage, the extract stream trapped in BL is injected into the desorbent column at the next sixth switching time for τ e t e τ + tlag,E. The second stage is defined between

τ

tlag,E

τ

CE,PX dt )

(

)

j R,PXQR tlag,E CF,PXQF - C C QE τ F,PX

(15)

1 int j E,PX C ) τ

∫

τ

tlag,E

CE,PX dt +

1 τ

∫

τ+tlag,E

τ

4

7 8

no BHb + BTc BLd BH + BT + BH + BT + BH + BT + BH + BT + BH + BT +

BL BL BL BL BL

pure PX pure PDEB pure PX pure PDEB

135.85 146.83 144.82 144.93 192.80 133.96 192.85 134.00

(16)

CE,PX dt

where CE,PX of the second term on the right side of eq 16 has the same value as the concentration initially filled in the desorbent BL. Therefore, the internal mean concentration of PX is obtained as int j E,PX C )

(

)

j R,PXQR CF,PXQF - C QE tlag,E 1 C τ F,PX τ

(

∫

τ+tlag,E

τ

)

CE,PX dt

(17)

Equation 17 means that BL has an influence on lowering the internal fluid concentration in the four-zone operation, because j E,PX within the time range τ e t e τ + tlag,E is always CF,PX > C satisfied. jE It should be noted that the mean concentrations (e.g., C j and CR) no longer reach a steady state but rather reach a cyclic steadystate, because of the inhomogeneous length of the bed tail. Figure 3 compares the mean concentration dynamics for the four-zone operations with and without dead j E,PX (squares in Figure 3a) do volume. For the latter case, C not reach a steady state until about 200 switchings. When only BL exists, steady-state concentrations are observed due to the homogeneous BL volume (VBL ) 0.145 m3 for every BL; see Table 1). However, BT located only at the 12th and 24th columns causes a half-cyclic behavior (or a period of 12 switchings) of the PX and MX mean concentrations, as observed in Figure 3. Therefore, the mean concentration of the time-average concentration at each switching over the last cycle from 117 to 240 switchings is used in this study for the SMB performance evaluation.

Table 2. Performance Comparison of PX SMB Process According to Dead Volume and Secondary-Flush Inlet Composition j E,PXe (kg/m3) zone dead volume composition of SFi C purity (%) recovery (%) productivity [kg/(h m3)] a

(14)

CE,PX dt

tlag,E

j int The intracolumn mean concentration of PX in the extract (C E,PX) is defined within the second and third stages as

where the column volume is Vc ) (πdc2/4)Lc. The dilution is defined as dilution (%) ) 100 ×

∫

where tlag,E is the time lag necessary to pass through the extract BL (tlag,E ) VBL/QE). The first term on the right side of eq 14 is the PX portion coming from the BL stream trapped during feeding. Combining eq 14 with eq 13, the mean concentration in the second stage is given by

where CSFi,PX is the PX concentration of SFi, and its value is null in the four-zone operation. The productivity of PX for the adsorbent used is obtained as j E,PXQE - CSF ,PXQSF C i i

tlag,E 1 C + τ F,PX τ

97.67 99.95 79.56 81.30 99.88 99.82 99.88 99.82

90.48 97.79 96.45 96.52 97.88 97.33 97.91 97.36

63.29 68.41 67.47 67.52 67.83 68.08 67.86 68.10

dilution (%) 20.49 14.06 15.24 15.18 14.78 21.60 14.75 21.57

j E,PX ) time-average PX concentration in the extract during the last No ) no dead volume. b BH ) bed head. c BT ) bed tail. d BL ) bed line. e C cycle (10th cycle). a


3321

j i) at the exit of the extract or raffinate with respect to number of switchings (Nswitch) in the four-zone operation. Figure 3. Dynamics of mean concentrations (C

Figure 4. Comparison of liquid concentration distributions with and without dead volume over 24 beds at three different times within the last switching time in four-zone operation.

Table 2 compares the process performances (purity, recovery, productivity, and dilution) for each run. Because the operating conditions in the four-zone SMB (see Table 1) are adjusted in the presence of the three types of dead volume, the flow rates of four-zone operation without dead volume, which is illustrated in comparison with three other configurations at the same flow rates, are set to be higher than those at the optimum conditions. Thus, low recovery and low productivity are observed in the

four-zone operation without dead volume. However, the purity is relatively high, because of the absence of a bed line. BH and BT cause the time delay of the fluid concentration,16 whereas BL lowers the extract concentration inside the column,15 as mentioned above. The delayed fluid concentration of PX in the four-zone operation with BH and BT yields the highest productivity of the eight runs. For the four-zone operation with only BL, the average PX concentration is lowered, and the purity

3322


Figure 5. Comparison of liquid concentration distributions with pure PX and PDEB injection at SFi over 24 beds at three different times within the last switching time in seven-zone operation.

j int deteriorates. The internal average concentration in eq 17 is C E,PX ) 140 kg/m3, and the average concentration passing through j E,PX ) 144.82 kg/m3. extract BL is C Figure 4 shows the concentration profiles along the bed number for the four-zone operations at three different times (i.e., beginning, middle, and last moments) during the last switching period. The fluid concentration distributions with no dead volume are depicted in the lines in comparison with the results with BH, BT, and BL (symbols in Figure 4). In zone 3 between the feed and raffinate, the fluid concentrations of MX, OX, and EB are more developed in the presence of dead volume than without dead volume. 4.2. Seven-Zone SMB with Dead Volume. The seven-zone operation with flushing aims to resolve the two problems caused by BL: purity deterioration in the extract and recovery reduction. As shown in Table 2, the seven-zone operation improves the purity to the desired value (over 99.7%) and increases the recovery. When the fresh pure PX is introduced into the secondary-flush inlet (QSFi), the purity and recovery are slightly higher than with pure PDEB (desorbent) injection. However, the productivity is not improved for the seven-zone operation with pure PX injection into SFi. This is because a small portion of pure PX injected into SFi is lost from the raffinate, whereas that loss does not occur when pure PDEB is injected into SFi (see the definitions of recovery and productivity in eqs 10 and 11, respectively). The dilution (21.6%) increases significantly with the desorbent injection at SFi, because the desorbent trapped within BL during the SFi injection comes out at the beginning of extract withdrawal (see also Figure 7b, below). The seven-zone operation with pure PX injection takes advantage of higher

purity and lower dilution than that with pure PDEB injection at the cost of a reduction of productivity. For the two seven-zone operations, fluid concentrations are compared along the column at the three different time levels in Figure 5. Owing to the additional PX injection at SFi (120% of BL volume), the PX concentration in the extract section is higher than that with the desorbent injection, resulting in slight increases in purity and recovery (see Table 2). Because it is preferable to adjust the flushing flow rates (LFi, LFo, and SFi) to be as low as possible for higher purity and productivity,15 there will be room for improvement of the seven-zone operating conditions. The internal mean PX concentration is obtained in the case of the PX injection at SFi as int j E,PX C )

(

j R,PXQR CF,PXQF + CSFi,PXQSFi - C

(

QE tlag,E 1 C τ SFi,PX τ

∫

)

-

τ+tlag,E

τ

)

CE,PX dt

(18)

The extract PX concentration within the time range τ e t e lag,EC τ + tlag,E is obtained from the numerical results, (1/τ)∫τ+t τ E,PX j int dt ) 10.0 kg/m3, and the internal mean PX concentration is C E,PX ) 153.0 kg/m3. 4.3. Eight-Zone SMB with Dead Volume. The impure stream trapped during raffinate withdrawal is removed in the eight-zone operation. Pure PX or PDEB is injected at SFi. As reported in Table 2, the two eight-zone operations increase slightly in productivity (or recovery) in comparison with the


3323

Figure 6. Comparison of liquid concentration distributions with seven- and eight-zone operations in pure PX injection at SFi over 24 beds at three different times within the last switching time.

seven-zone operations. For the two cases, the productivity of the eight-zone operation increases by 0.02-0.03 kg/(h m3) over that of the seven-zone, which corresponds to about 40 tons of PX/year in this SMB unit. To achieve high productivity with low dilution, the eight-zone operation with PX injection at SFi is considered as the most promising operating setup satisfying over 99.7% purity in the presence of BL.

Figure 6 compares the fluid concentrations of seven-zone operation with those of eight-zone operation for pure PX injection at SFi. The left tails of the MX, EB, and OX concentrations of the eight-zone operation are slightly higher than those of the seven-zone operation, and the right tail of PX is a little lower. The tertiary flush-out (TFo) removes raffinate residue from the BL, and slightly higher concentra-

j i) at the exit of the extract or raffinate with respect to number of switchings (Nswitch) in the four- and eightFigure 7. Dynamics of mean concentrations (C zone operations.

3324


tions of PX, MX, EB, and OX than those of the raffinate are introduced in the beginning of feeding. This results in a higher productivity of PX than for seven-zone operation. The internal concentration of PX is defined for the eight-zone operation as int j E,PX ) C

(

j R,PXQR - C j TF ,PXQTF CF,PXQF + CSFi,PXQSFi - C o o

(

QE tlag,E 1 C τ SFi,PX τ

∫

τ+tlag,E

τ

)

)

CE,PX dt

-

(19)

j TF ,PX ) 2.0 kg/m3, and (1/τ)∫τ+t j R,PX ) 2.8 kg/m3, C lag,EC with C τ E,PX o int j E,PX dt ) 10.1 kg/m3 from the simulation results, C ) 153.1 kg/ m3 is obtained for the pure PX injection at SFi. The internal average concentration is slightly higher than that of the seven-zone operation, because of the tertiary flush-out. In Figure 7, PX concentration dynamics for the four- and eightzone operations at the exit of extract BL are compared during the last switching (Nswitch ) 240). In the four-zone operation, the extract PX concentration is the same as the feed concentration within the time (tlag,E ) 0.08 min) taken to pass through the bed line, which results in purity deterioration (i.e., CF,PX ) 171 kg/m3 and CF,MX ) 360 kg/m3; see Table 1). The extract is diluted in the eightzone operation with desorbent (PDEB) injection at SFi, because of the desorbent flows during the time lag (tlag,E), as shown in Figure 7b. The eight-zone operation with the PX injection at SFi enables the extract to keep a high purity and not be dilute (see Figure 7a). Therefore, the eight-zone operation with PX injection is suggested at the given values of QD, QF, and Qrecycle (see operating parameters of Table 1) to improve the productivity over the purity of 99.7% and to reduce the dilution. The effect of the dispersion inside the dead volume on the extract concentration as a function of time is clearly shown in Figure 7. When MOC for dead volume is solved without dispersion (Dax,dead ) 0), a quasidiscontinuous concentration front appears in both parts a and b of Figure 7. With dispersion (Dax,dead ) 5 × 10-3Vdead; see Table 1), a smoothed concentration profile is obtained in the beginning of the extract. 5. Conclusions Dead volumes are always present because of tubes, valves, and pumps and can account for up to 3% of the unit volume in industrial- or pilot-scale plants. The dead volume affects the purity, recovery, and dilution in industrial-scale simulated-moving-bed (SMB) processes. For a classical four-zone SMB unit with inlet and outlet stream bed lines (desorbent, extract, feed, and raffinate), flushing is required intrinsically to increase the purity. The flushing flow of the extract bed line (the so-called line flush) is internally connected to another bed prior to the feed bed, if the extract flow is a product to be recovered. The feed stream trapped inside the bed line is reused by flushing into the bed. It is preferable to drain out the raffinate flushing flow if the raffinate flow is not a product. Therefore, an eight-zone SMB is designed and operated to increase the purity and recovery for the four-zone SMB unit in the presence of a bed line. The extended node model representing realistic port switching of an SMB was developed to treat the three types of dead volume (bed head, bed tail, and bed line) in a unified way on the basis of the CFL-number-insensitive method of characteristics (MOC). The MOC approach was constructed to produce maximum accuracy of the fluid concentration passing through the dead volume at a given CFL number. Dispersion inside the dead volumes was fully taken into account by the MOC modified for convection-diffusion

equations. The four-, seven-, and eight-zone PX SMBs were successfully analyzed by using the extended node model. The bed head and bed tail cause a time delay of fluid concentrations. The bed line deteriorates the purity and lowers the average concentration of extract. The seven-zone operation with line and secondary flushes satisfies the desired purity of the extract (over 99.7%) with a high-level recovery. When pure PX is introduced into the secondary-flush inlet stream used for flushing the PX/desorbent mixture trapped in the line-flush inlet bed line, the dilution of extract is decreased. The eight-zone operation with a secondary-flush inlet of pure PX shows a high productivity, satisfying the desired extract purity and reducing the dilution. Acknowledgment The first author thanks The University of Queensland for inviting him as a visiting scholar. The authors acknowledge the financial support of Korea Institute of Energy Technology Evaluation and Planning. Nomenclature a ) numerator parameter of Langmuir isotherms a0 ) concentration at point (t0, zi) a1 ) concentration at point (t1, zi) a2 ) concentration at point (t2, zi) b ) denominator parameter of Langmuir isotherms b0 ) concentration at point (t0, zi+1) b1 ) concentration at point (t1, zi+1) b2 ) concentration at point (t2, zi+1) BC ) boundary condition BH ) bed head as a dead volume BL ) bed line as a dead volume BT ) bed tail as a dead volume C ) fluid concentration (kg/m3) C˜ ) interpolated concentration in MOC (kg/m3) j ) time-average concentration (kg/m3) C CD ) desorbent concentration (kg/m3) CF ) feed concentration (kg/m3) CFL ) Courant-Friedrichs-Lewy Cin ) inlet concentration into the adsorptive bed (kg/m3) j int ) intracolumn time-average concentration (kg/m3) C CSFi ) second-flush inlet concentration (kg/m3) Dax ) axial diffusion coefficient inside the adsorptive bed (m2/ min) Dax,dead ) axial diffusion coefficient inside the dead volume (m2/ min) dc ) column diameter (m) EB ) ethylbenzene IC ) initial condition k ) overall mass-transfer coefficient (min-1) LBH ) length of bed head (m) LBL ) length of bed line (m) LBT ) length of bed tail (m) Lc ) bed length (m) Ldead ) length occupied by the dead volume assuming that its diameter is same as the bed diameter (m) LDF ) linear driving force MOC ) method of characteristics MX ) meta-xylene N ) bed number n ) solid concentration (kg/m3) n* ) equilibrium solid concentration (kg/m3) nm ) saturation concentration in the solid phase (kg/kg) NCFL ) CFL number Nmesh ) number of mesh (or grid) points

Ind. Eng. Chem. Res., Vol. 49, No. 7, 2010 NMOC ) number of mesh points used by MOC Ntime ) number of time levels OX ) ortho-xylene PDE ) partial differential equation PDEB ) para-diethylbenzene Pe ) Peclet number () VLLc/Dax) Pedead ) Peclet number inside the dead volume PX ) para-xylene QD ) desorbent flow rate (m3/min) QE ) extract flow rate (m3/min) QF ) feed flow rate (m3/min) QLFi ) line-flush inlet flow rate (m3/min) QLFo ) line-flush outlet flow rate (m3/min) QR ) raffinate flow rate (m3/min) Qrecycle ) recycle flow rate (m3/min) QSFi ) secondary-flush inlet flow rate (m3/min) QTFo ) tertiary-flush outlet flow rate (m3/min) SMB ) simulated moving bed t ) time (min) tlag ) lag time caused by dead volume (min) VBL ) volume of bed line (m3) Vc ) column volume (m3) Vdead ) velocity inside the dead volume (m/min) VL ) interstitial velocity inside the adsorptive bed (m/min) z ) axial distance (m) z0 ) starting position of the axial distance (m) Greek Letters R ) axial distance moved along the characteristics line (m) β ) axial distance defined as ∆z - R (m) ∆t ) time step size (min) ∆z ) spatial step size (m) ∆zMOC ) spatial step size used by MOC (m) εb ) bed voidage Fp ) particle density (kg/m3) τ ) switching time or switching time (min) Ωt ) physical dependence domain Subscripts and Superscripts hi ) head inlet hm ) bed head index crossed by the characteristic line at the previous time level ho ) head outlet i ) component or mesh index j ) dead volume index (bed head, tail, or bed line) k ) bed number index l ) mesh point index used by MOC n ) time level index ti ) tail inlet tm ) bed tail index crossed by the characteristic line at the previous time level to ) tail outlet

Appendix Because the SMB model with the extended node model is solved numerically (or on discrete points), the analytical solution from MOC has to be represented at the discrete mesh points. In Figure A1, a simple mesh structure of the whole bed (head, adsorptive section, and tail) with the discrete time level is shown in terms of z-t discretization. For simplicity, only the first and last points (zhi, zho and zti, zto) are indicated for both the bed head and tail, respectively. Solid triangles (2) are known values at the previous time level (tn-1). Solid circles (b) are to be calculated from the adsorptive PDE model by using the time integrator. One gray n , disregarding the subscript i for a component) is triangle (Chi the known value as an inlet value from the operating condition,

3325

Figure A1. Mesh structure of the whole bed (head, adsorptive section, and tail) with the discrete time level: black triangles, known values at the previous time level; black circles, values calculated by the time integrator; gray triangles, inlet value from the operating condition (calculated by the node model); gray circles, exit boundary value determined by BC; and open circles, values to be calculated by MOC.

which is calculated by the conventional node model. One gray circle (Cnti) is determined by an exit boundary condition (i.e., the second one of eq 5). Therefore, there are two missing values (O) of the concentration (Cnho and Cnto) to be calculated by MOC at the nth time level (tn). The analytical solution of eq 7 with an initial value (Ci,0) is expressed in the continuous domain as Ci(z, t) ) Ci,0(z - Vdeadt)

(A1)

where Ci,0(z) is the initial value at t ) 0 over z. The analytical n n solution for the two missing concentrations (Cho and Cto ) has the same value as the concentration of the previous time level n-1 (Cn-1 hm and Ctm ) coming up along the characteristics line (dashed arrows in Figure A1). The slope of the pathline is called the CFL (Courant-Friedrichs-Lewy) number39 NCFL,dead ≡ Vdead

∆t zho - zhm

(A2)

n-1 n-1 Because the concentrations (Chm and Ctm ) at zhm and ztm at the previous time level are not always available for arbitrary lengths of the bed head and tail in the discrete numerical domain, an approximation is needed from the known values of the n-1 n-1 n-1 previous time level (Cn-1 hi , Cho , Cti , and Cto ). Using the lever rule, which is simple but exact for linear profiles, the two unknown values at the present time level (tn) are determined as

Cnho

≡

Cn-1 hm

n-1 Cn-1 hi (zho - zhm) + Cho (zhm - zhi) ) zho - zhi

(A3) Cnto ≡ Cn-1 tm )

n-1 Cn-1 ti (zto - ztm) + Cto (ztm - zti) zto - zti

(A4)

where zhm ) zho - Vdead∆t and ztm ) zto - Vdead∆t are predefined by the characteristics line. Equations A3 and A4 imply that the present concentration having passed through the dead volume is the time-delayed concentration of the previous time level. In the extended node model including the bed head (BH), bed tail (BT), and bed line (BL), the exit fluid concentrations of an adsorptive bed and an inlet stream (i.e., desorbent and feed) come into the node (or port) through BT and BL, respectively. The exit fluid concentration of BH is used as the inlet BC of the adsorptive bed model. The withdrawal stream (i.e., extract and raffinate) is collected at the exit of BL.

3326


The dead volume might be different from bed to bed. The number of MOC grids should be determined to ensure the accuracy of the MOC solution. Even though the MOC results come from an analytical solution (eq A1), the numerical error occurring whenever the physical domain (continuous space) is transferred into the numerical domain (discrete space) is inevitable. However, there is no truncation error occurring when the derivatives of PDEs are approximated. The MOC approach has one stability condition depending only on the CFL number.39 A1. CFL Condition For the solution of the convection-dominated PDEs, the time step size (∆t) and the spatial step size (∆z) are subject to the following constraint called the CFL (Courant-Friedrichs-Lewy) condition for a positive fluid velocity39 0 < NCFL,max ≡ VL,max

∆t e 1.0 ∆z

(A5)

where a positive interstitial fluid velocity (VL,max) is defined at a maximum value, because the interstitial velocity varies with the zone flow rates in the SMB system. Given a CFL number (NCFL,max) less than unity and a time step size, the minimum spatial step size allowed to the MOC approach is obtained with the maximum velocity of dead volumes (Vdead,max) ∆zMOC,min ) Vdead,max

∆t NCFL,max

NMOC,max

(

)

Ldead,j,kNCFL,max , Vdead,max∆t

j ) BH, BT, and BL ;k ) 1, 2, 3, ... ,Nbed (A8)

Ldead,j,k NMOC,j,k

n-1 n-1 Cj,k,l-1 (∆zMOC,j,k - zMOC,j,k) + Cj,k,l zMOC,j,k , ∆zMOC,j,k l ) 2, ... , NMOC,j,k + 1

(A10)

where Cj,k,inlet is the inlet concentration given by a boundary value such as desorbent or feed concentration (e.g., j ) BL, k ) desorbent or feeding bed number). zMOC,j,k is defined by the characteristics line within the multiple grid points

(A11)

(A7)

where the subscripts j and k are the type of dead volume and the bed number (N) index, respectively. The spatial step size in the dead volume (∆zMOC,j,k) is thus obtained except for NMOC,j,k ) 0 ∆zMOC,j,k )

n n n Cj,k,1 ) Cj,k,inlet C˜j,k,l )

zMOC,j,k ) ∆zMOC,j,k - Vdead,max∆t

Finally, the grid number in the dead volume is obtained as the integer value of the maximum grid number NMOC,j,k ) integer

means that the MOC approach for the dead volume satisfies the CFL stability condition. Its numerical solution is obtained from the maximum number of grids (i.e., in a maximum accuracy) at a given CFL number. The MOC approach is now ready to be extended to the multiple grid structure with the total grid number NMOC,j,k + 1. The ˜ nj,k,l) to be used in eq 7 is approximated from interpolated solution (C n-1 the real solution (Cj,k,l ) of the previous time level as

(A6)

Vdead,max is always less than VL,max, as the superficial velocity (Vdead) is less than the interstitial velocity (VL). Thus, the spatial step size of the adsorptive bed (∆z) is always larger than that of the dead volume (∆zMOC,min), which means that the numerical accuracy of dead volume is always higher than that of the adsorptive bed. The allowed maximum grid number is given as Ldead LdeadNCFL,max ) ) ∆zMOC,min Vdead,max∆t

Figure A2. Characteristic line displacement on meshes according to CFL number (NCFL) in the CFL-number-insensitive MOC scheme.

(A9)

The time step size (∆t) is usually determined at a fixed value (explicit time integration) or at a variable value (implicit time integration) by the time integrators used for solving the adsorptive PDE model. The spatial step size (∆z) is predefined to convert the SMB PDE system into a set of ordinary differential equations (ODEs) for the adsorptive region of the bed. The CFL number (NCFL,max) is known at a given time level. The BH, BT, and BL lengths (Ldead,j,k) are experimentally measured, and the fluid velocity in the dead volume (Vdead,max) is given by the operating conditions of the SMB. NMOC,j,k is the grid number maximizing the accuracy of the MOC approach satisfying the CFL condition. Therefore, it is always guaranteed that ∆zMOC,j,k is larger than Vdead,max∆t, which

When the positions of the inlet and outlet ports is shifted forward in the direction of the fluid flow, information on the dead volume (Ldead,j,k, NMOC,j,k, and ∆zMOC,j,k) is also shifted one bed ahead. The concentrations trapped in BL are held or are transported with a time delay according to the port switching. As a result, the extended node model has a universal form with the unified dead volume treatment based on the MOC approach. A2. CFL-Number-Insensitive MOC The extended node model based on MOC works well for 0 < NCFL e 0.5. If 0.5 < NCFL e 1.0, the MOC can violate such a constraint that the numerical value should be computed within the physical domain of dependence. This problem is resolved by using double characteristic lines, only if the constraint is active. The physical domain of dependence should be enclosed by the numerical domain of dependence. Stated otherwise, the numerical value should be computed within the physical domain of dependence. The physical domain of dependence at the t1 level includes all the entire spatial region, zi e Ωt1 e zi+1, for 0 < NCFL e 0.5 in Figure A2a, whereas that for 0.5 < NCFL e 1.0 is restricted by zi + R e Ωt1 e zi+1 in Figure A2b. The second case can produce a numerical error. To resolve this problem, a CFL-insensitive MOC is proposed as follows b2 )

a1(R - β) + βa0 , R

when 0 < NCFL e 0.5 (or R g β)

(A12)


b2 )

b1(β - R) + Ra0 , β

when 0.5 < NCFL e 1.0 (or R < β)

(A13) where R ) Vdead∆t and β ) ∆z - R. This CFL-number-insensitive MOC scheme considerably enhances accuracy, when a discontinuous or steep concentration profile passes through the dead volume. Literature Cited (1) Juza, M.; Mazzotti, M.; Morbidelli, M. Simulated Moving-Bed Chromatography and Its Application to Chirotechnology. Trends Biotechnol. 2000, 18, 108. (2) Rajendran, A.; Paredes, G.; Mazzotti, M. Simulated Moving Bed Chromatography for the Separation of Enantiomers. J. Chromatogr. A 2009, 1216, 709. (3) Seidel-Morgenstern, A.; Kessler, L. C.; Kaspereit, M. New Developments in Simulated Moving Bed Chromatography. Chem. Eng. Technol. 2008, 31, 826. (4) Sa´ Gomes, P.; Minceva, M.; Rodrigues, A. E. Simulated Moving Bed Technology: Old and New. Adsorption 2006, 12, 375. (5) Lim, Y. I.; Jorgensen, S. B. Optimization of a Six-Zone Simulated Moving Bed Chromatographic Process. Ind. Eng. Chem. Res. 2007, 46, 3684. (6) Zhang, Z.; Mazzotti, M.; Morbidelli, M. Continuous Chromatographic Processes with a Small Number of Columns: Comparison of Simulated Moving Bed with Varicol, PowerFeed, and ModiCon. Korean J. Chem. Eng. 2004, 21, 454. (7) Pais, L. S.; Loureiro, J. M.; Rodrigues, A. E. Modeling Strategies for Enantiomers Separation by SMB Chromatography. AIChE J. 1998, 44, 561. (8) Broughton, D. B.; Gerhold, C. G. Continuous sorption process employing fixed bed of sorbent and moving inlets and outlets. U.S. Patent 2,985,589, 1961. (9) Wooley, R.; Ma, Z.; Wang, N. H. L. A Nine-Zone Simulating Moving Bed for the Recovery of Glucose and Xylose from Biomass Hydrolyzate. Ind. Eng. Chem. Res. 1998, 37, 3699. (10) Xie, Y.; Chin, C. Y.; Phelps, D. S. C.; Lee, C. H.; Lee, K. B.; Mun, S.; Wang, N. H. L. A Five-Zone Simulated Moving Bed for the Isolation of Six Sugars from Biomass Hydrolyzate. Ind. Eng. Chem. Res. 2005, 44, 9904. (11) Ludemann-Hombourger, O.; Nicoud, R. M.; Bailly, M. The “VARICOL” Process: a New Multicolumn Continuous Chromatographic Process. Sep. Sci. Technol. 2000, 35, 1829. (12) Kearney, M. M.; Hieb, K. L. Time variable simulated moving bed process. U.S. Patent 102,553, 1992. (13) Schramm, H.; Kaspereit, M.; Kienle, A.; Seidel-Morgenstern, A. Simulated Moving Bed Process with Cyclic Modulation of the Feed Concentration. J. Chromatogr. A 2003, 1006, 77. (14) Bae, Y.-S.; Lee, C.-H. Partial-Discard Strategy for Obtaining High Purity Products Using Simulated Moving Bed Chromatography. J. Chromatogr. A 2006, 1122, 161. (15) Minceva, M.; Rodrigues, A. E. Influence of the Transfer Line Dead Volume on the Performance of an Industrial Scale Simulated Moving Bed for p-Xylene Separation. Sep. Sci. Technol. 2003, 38, 1463. (16) Katsuo, S.; Langel, C.; Schanen, P.; Mazzotti, M. Extra-Column Dead Volume in Simulated Moving Bed Separations: Theory and Experiments. J. Chromatogr. A 2009, 1216, 1084. (17) Lee, H. J.; Xie, Y.; Koo, Y. M.; Wang, N. H. L. Separation of Lactic Acid from Acetic Acid Using a Four-Zone SMB. Biotechnol. Prog. 2004, 20, 179.

3327

(18) Minceva, M.; Rodrigues, A. E. Modeling and Simulation of a Simulated Moving Bed for the Separation of p-Xylene. Ind. Eng. Chem. Res. 2002, 41, 3454. (19) Kurup, A. S.; Hidajat, K.; Ray, A. K. Optimal Operation of an Industrial-Scale Parex Process for the Recovery of p-Xylene from a Mixture of C8 Aromatics. Ind. Eng. Chem. Res. 2005, 44, 5703. (20) Kurup, A. S.; Hidajat, K.; Ray, A. K. Comparative Study of Modified Simulated Moving Bed Systems at Optimal Conditions for the Separation of Ternary Mixtures of Xylene Isomers. Ind. Eng. Chem. Res. 2006, 45, 6251. (21) Minceva, M.; Rodrigues, A. E. Two-Level Optimization of an Existing SMB for p-Xylene Separation. Comput. Chem. Eng. 2005, 29, 2215. (22) Jin, W.; Wankat, P. C. Hybrid Simulated Moving Bed Processes for the Purification of p-Xylene. Sep. Sci. Technol. 2007, 42, 669. (23) Sa´ Gomes, P.; Minceva, M.; Rodrigues, A. E. Operation of an Industrial SMB Unit for p-Xylene Separation accounting for Adsorbent Ageing Problems. Sep. Sci. Technol. 2008, 43, 1974. (24) Minceva, M.; Rodrigues, A. E. Understanding and Revamping of Industrial Scale SMB Units for p-Xylene Separation. AIChE J. 2007, 53, 138. (25) Frey, S. J. Product Recovery from Simulated Moving Bed Adsorption. U.S. Patent 7,208,651, 2007. (26) Wei, C. N. Multiple Grade Flush Adsorption Separation Process. U.S. Patent 5,750,820, 1998. (27) Noe, R. J. L. Raffinate Line Flush in Simulated Continuous Moving Bed Adsorptive Separation Process. U.S. Patent 5,912,395, 1999. (28) Grosfils, V. Modelling and Parametric Estimation of Simulated Moving Bed Chromatographic Processes. Ph.D. Dissertation, Universite Libre de Bruxelles, Brussels, Belgium, 2009. (29) UOP Parex Home Page. http://www.uop.com (accessed June 2009). (30) Beste, Y. A.; Lisso, M.; Wozny, G.; Arlt, W. Optimization of Simulated Moving Bed Plants with Low Efficient Stationary Phases: Separation of Fructose and Glucose. J. Chromatogr. A 2000, 868, 169. (31) Lim, Y. I.; Jorgensen, S. B. A Fast and Accurate Numerical Method for Solving Simulated Moving Bed (SMB) Chromatographic Separation Problems. Chem. Eng. Sci. 2004, 59, 1931. (32) Ma, Z.; Wang, N. H. L. Standing Wave Analysis of SMB Chromatography: Linear Systems. AIChE J. 1997, 43, 2488. (33) Migliorini, C.; Mazzotti, M.; Morbidelli, M. Simulated MovingBed Units with Extra-Column Dead Volume. AIChE J. 1999, 45, 1411. (34) Jin, W.; Wankat, P. C. Thermal Operation of Four-Zone Simulated Moving Beds. Ind. Eng. Chem. Res. 2007, 46, 7208. (35) Bruneau, C. H.; Fabrie, P.; Rasetarinera, P. An Accurate Finite Difference Scheme for Solving Convection-Dominated Diffusion Equations. Int. J. Numer. Methods Fluids 1997, 24, 169. (36) Douglas, J, Jr.; Russell, T. F. Numerical Methods for ConvectionDominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures. SIAM J. Numer. Anal. 1982, 19, 871. (37) Chang, S. C. The Method of Space-Time Conservation Element and Solution ElementsA New Approach for Solving the Navier-Stokes and Euler Equations. J. Comput. Phys. 1995, 119, 295. (38) Lim, Y. I.; Chang, S. C.; Jorgensen, S. B. A Novel Partial Differential Algebraic Equation (PDAE) Solver: Iterative Space-Time Conservation Element/Solution Element (CE/SE) Method. Comput. Chem. Eng. 2004, 28, 1309. (39) Mattheij, R. M. M.; Rienstra, S. W.; ten Thije Boonkkamp, J. H. M. Partial Differential Equations: Modeling, Analysis, Computation; SIAM: Philadelphia, PA, 2005.

ReceiVed for reView July 7, 2009 ReVised manuscript receiVed February 1, 2010 Accepted February 10, 2010 IE901097Z

Improvement of para-Xylene SMB Process Performance on an

Recommend Documents