Modeling and Simulation of a Simulated Moving Bed for the

The industrial-scale adsorptive separation of p-xylene from a mixture of C8 aromatics ... Zinnen12 examined the influence of the water content of the ...
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Modeling and Simulation of a Simulated Moving Bed for the Separation of p-Xylene Mirjana Minceva and Alirio E. Rodrigues* Laboratory of Separation and Reaction Engineering (LSRE), Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal

The industrial-scale adsorptive separation of p-xylene from a mixture of C8 aromatics in a foursection simulated moving bed (SMB) unit is analyzed through simulation. In the order to describe the behavior of the SMB unit by means of a mathematical model, two approaches were used: the true moving bed (TMB) approach and the SMB approach. Both approaches assume a constant selectivity nonstoichiometric Langmuir isotherm, an axial dispersion for the fluid flow, and a linear driving force for the intraparticle mass transfer. The TMB and SMB model predictions of steady-state performance of the SMB unit are very close. Therefore, the TMB model was selected to study the effect of the switching time period, adsorbent deactivation, and mass-transfer resistances on the process performance. The adsorbent deactivation which occurs during its lifetime will influence the SMB performance; to keep the p-xylene purity and acceptable recovery, the switching time should be decreased. The TMB package is a useful tool for fast visualization of the SMB process behavior under particular operating conditions. The novel “separation volume” methodology is used to find the operating conditions of the SMB unit in the presence of masstransfer resistances. Introduction Xylenes are used on a large scale as industrial solvents or intermediates for many derivatives.1 The most important isomer, p-xylene, can be oxidized to terephthalic acid, which is used in the production of polyesters. The use of polyester films and fibers is increasing rapidly, mainly in the Pacific Rim countries. Several industrial processes have been developed in the past, usually coupled with an isomerization process aimed to transform some or all of the other isomers into p-xylene. The first separation processes were based on crystallization.2 At present, there are three main industrial processes: UOP’s Parex,3 Toray’s Aromax,4 and IFP’s Eluxyl.5 All of these processes operate on the principle of simulated moving bed (SMB) technology, which makes it possible to achieve the separation performance of a true moving bed unit (TMB) while avoiding the difficulties in the movement of the solid phase. Separation is accomplished by exploiting the differences in affinity of the adsorbent for p-xylene relative to the other C8 isomers. In 1971, UOP first commercialized the Parex process for p-xylene recovery from a mixture of C8 aromatics, one of several adsorption processes that constitute UOP’s Sorbex SMB adsorption technology. The heart of the Parex is a rotary valve which periodically changes the position of the feed, desorbent, extract, and raffinate lines along the bed. As of 1995, 59 units had been licensed.6 The Aromax process was developed in the early 1970s by Toray Industries, Inc., in Japan. The adsorption column consists of a horizontal series of independent chambers containing fixed beds of adsorbent. Instead of a rotary valve, a sequence of specially designed on-off valves under computer control is used to move inlet and withdrawal ports around the bed.6 In * To whom correspondence should be addressed. Phone: 351 22 5081671. Fax: 351 22 5081674. E-mail [email protected].

1994, IFP commercialized the Eluxyl adsorption process. Individual on-off valves controlled by a microprocessor are used to simulate the movement of the adsorbent.6 On the basis of the patent literature, the zeolites used in the SMB p-xylene separation processes appear to be mono or dual metal ion-exchanged Y or X zeolite.7-13 It is also possible to use ZMS11 and ZMS5 zeolites for selectively adsorbing p-xylene. Unfortunately, because of commercial importance, there is not much information in the open and patent literature about preparation parameters leading to high selectivity of adsorbents. Zinnen12 examined the influence of the water content of the adsorbent on its p-xylene selectivity and masstransfer rate. Recently, Hotier and co-workers14 have found out that injection of water into the feed and/or into the desorbent reduces the desorbent demand at constant purity and recovery. Benzene, toluene, or p-diethylbenzene are mentioned as desorbents in the above patents. The adsorption of xylenes on ion-exchanged faujasitetype zeolites has been extensively studied in the liquid15-19 as well as in the vapor phase.20-26 The potential of using medium-pore-size zeolites, instead of large-pore-size zeolites, has been investigated by Yan.27 A detailed analysis of the design and optimization of a four-section SMB unit for separation of a mixture of o-, m-, and p-xylene and ethylbenzene, operating at liquid and vapor phases, has been presented by Storti et al.28 Appropriate flow-rate ratios for each section were established from equilibrium theory. The aim of this paper is to study through simulation an industrial-scale SMB unit for separation of p-xylene from the C8 aromatics fraction. Therefore, the influence of the adsorbent deactivation, operating conditions, and model parameters on the SMB unit performance was examined. The “separation volume” methodology was used in the determination of the separation regions.

10.1021/ie010095t CCC: $22.00 © 2002 American Chemical Society Published on Web 06/06/2002

Ind. Eng. Chem. Res., Vol. 41, No. 14, 2002 3455 Table 1. SMB Operation Conditions and Model Parameters operating conditions SMB unit geometry

case 1

case 2

model parameter

Lc )113.5 cm dc ) 411.7 cm Vc )15.1 × 106 cm3 no. of columns ) 24 configuration ) 6-9-6-3

T ) 180 °C, liquid phase t* ) 1.16 min Q/F ) 1.45 × 106 cm3/min Q/E ) 1.65 × 106 cm3/min Q/R ) 2.69 × 106 cm3/min Q/D ) 2.89 × 106 cm3/min Q/IV ) 5.39 × 106 cm3/min

T ) 180 °C, liquid phase t* ) 1.1 min Q/F ) 1.45 × 106 cm3/min Q/E ) 1.65 × 106 cm3/min Q/R ) 2.69 × 106 cm3/min Q/D ) 2.89 × 106 cm3/min Q/IV ) 5.65 × 106 cm3/min

Pe ) vkLk/DLk ) 2000 k ) 2 min-1 dp ) 0.092 cm  ) 0.39 F ) 1.39 g/cm3 qmPX(MX;OX;EB) ) 130.3 mg/g KPX ) 1.0658 cm3/mg KMX ) 0.2299 cm3/mg KOX ) 0.1884 cm3/mg KEB ) 0.3067 cm3/mg qmPDEB ) 107.7 mg/g KPDEB ) 1.2935 cm3/mg

Mathematical Models To describe the behavior of the SMB unit by means of a mathematical model, two modeling approaches were used: the TMB approach and the SMB approach. The first one treats the SMB process as the equivalent true moving system. The second approach represents the actual SMB configuration. Both approaches assume constant selectivity axial dispersion for the fluid flow and linear driving force for the intraparticle mass transfer. The differential mass balance equations can be found elsewhere.29 In the formulation of these models, the following assumptions have been considered: (i) thermal effects are negligible; (ii) mass-transfer coefficients and physicochemical parameters are independent of the mixture composition; (iii) the bed void fraction, radius, and porosity of the particles are constant along the column; (iv) flow rates are constant in each section; (v) the pressure drop is negligible. The system is approximated as a constant separation factor system, although, in fact, some variation of the separation factor with composition is observed.25 The nonstoichiometric Langmuir isotherm was used to describe multicomponent adsorption equilibria.

q/ij )

qmiKicij NC

1+

(1)

Kjclj ∑ l)1

TMB and SMB model equations were solved using the gPROMS, general process modeling system,30 a software package for modeling and simulation of processes with both discrete and continuous as well as lumped and distributed characteristics. The mathematical models involve a system of partial differential and algebraic equations (PDAEs). An orthogonal collocation method on finite elements was used for the discretization of the axial domain. Each column was divided into six equal elements with two collocation points in each element. For a typical simulation, CPU times of about 1.5 h for the TMB model and about 8.5 h for the SMB model were required on a Pentium III 1000 MHz processor with 725 Mb RAM memory. Simulation Results and Discussion In the patent literature,11 the following data for the SMB units can be found: the total length of the adsorption columns is between 10 and 30 m, preferably between 15 and 25 m. This length is subdivided into a number of beds, usually from 6 to 24, placed in 2-4

columns. The number of the zones is at least 4.11 There is a distribution plate placed between each two consecutive beds, connected to the rotary valve by a single transfer line. Each transfer line is used for introducing and withdrawing the process streams (feed, extract, raffinate, and desorbent). This means that the same transfer line is used for introducing the feed into the unit and later for withdrawing the extract from the unit. This could result in a reduced product purity due to contamination of the withdrawn extract. This problem can be overcome by employing separate transfer lines for each stream or by removing the residue from the transfer lines by flushing them with a medium which would not affect the extract purity. Each of the transfer lines is flushed during the time after the introduction of the feed and before withdrawal of the extract and during the time after withdrawal of the extract and before introduction of the desorbent, to get p-xylene with a high purity. For this purpose two additional streams are employed, flush-in and flush-out streams.31 The p-xylene SMB separation unit operating temperature is between 140 and 185 °C, preferably between 150 and 175 °C.11 The average interstitial velocity is in the range of 0.4-1.2 cm/s. The ratio of the desorbent and the feed flow is between 1.20 and 2.5, and the ratio of the recycling and the feed flow is between 5 and 12.11 The zeolite is used in the form of spherical particles with diameters from 0.25 to 1 mm. The water content of the zeolite is below 6 wt %, preferably 3 wt %.11 Taking into account the above information and zone constraints, an industrial-scale SMB unit and operating conditions were chosen. Completely potassium-exchanged Y zeolite and p-diethylbenzene were selected as the adsorbent and desorbent. The feed was considered to be a typical C8 aromatics mixture containing 23.6% p-xylene, 49.7% m-xylene, 12.7% o-xylene, and 14% ethylbenzene. The equilibrium data for p-, m-, and o-xylene, ethylbenzene, and p-diethylbenzene at 180 °C were provided by Azevedo et al.18 The equilibrium data, operating conditions, and model parameters used in the simulation study are summarized in Table 1. At this stage of the work, the flush-in and flush-out streams were not considered. The industrial-scale SMB unit used in the simulation corresponds to an ideal SMB unit employing a separate transfer line for each process stream (feed, raffinate, extract, and desorbent) for each distribution plate in the SMB unit. SMB and TMB simulation packages were used for the prediction of the steady-state internal concentration profiles of the SMB unit. To determine when the cyclic steady state in the SMB operation is reached, the global error should be lower than 1%. The global error was

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desorbent consumption QD/cPX E QE

(3c)

adsorbent productivity cPX E QE/Vs

Figure 1. Comparison of the prediction of internal concentration profiles at cyclic steady state (the full line is for the TMB approach; the dotted line is for the SMB approach).

defined as the sum of the relative errors between the average concentrations of each component i in the extract (E) and raffinate (R) streams for two consecutive iterations k - 1 and k

(E + R) relative error % ) 100 ×

∑i

(

[(

|cjEi k - cjEi k-1| jcEi k

|cjRi k - cjRi k-1| jcRi k

)]

)

+

(2a)

and the mass balance relative error

MB relative error % ) 100 × |QFciF - (QEcjiE + QRcjiR)|

∑i

QFciF

(2b)

The system reached cyclic steady state after 16 cycles. Figure 1 compares the steady-state internal concentration profiles obtained with both modeling approaches, for the reference case 1 in Table 1. The concentration profiles refer to the half of the 12th switching time period. The concentration profiles for the SMB model are calculated as the average concentration over the 12th switching period. Because the objective of the SMB unit for the separation of p-xylene from the C8 aromatics mixture is to produce high-purity p-xylene (above 99% purity), with desirable p-xylene recovery, productivity, and desorbent consumption at the same time, the SMB performance is characterized by

purity of p-xylene in the extract cPX E MX OX EB cPX E + cE + cE + cE

× 100

(3a)

recovery of p-xylene cPX E QE cPX F QF

× 100

(3b)

(3d)

The extract performances predicted using the TMB strategy were purity ) 99.92%, recovery ) 98.33%, desorbent consumption ) 0.0119 m3/kg, and productivity ) 111.43 kg/m3‚h. The same performances calculated by the SMB strategy are 99.78%, 98.20%, 111.29 kg/m3, and 0.0119 m3/kg, consecutively. Considering the small differences between performances calculated with both models, from the one side, and the big difference in the computing time required by them (see previously), on the other side, the TMB model was selected to study the effects of the switching time, mass-transfer resistances, and adsorbent capacity on the SMB performance. Effect of the Switching Time. The effect of switching time on the performance parameters is shown in Figure 2. The operating conditions and model parameters are those for case 1 in Table 1. It can be seen that only the values of the switching time between 1.16 and 1.37 min lead to p-xylene with purity and recovery above 99%, maximum productivity, and minimum desorbent consumption. The values of the switching time between 0.93 and 1.16 min and between 1.37 and 1.70 min also yield p-xylene with purity above 99% but p-xylene recovery under 99%. This means that a part of p-xylene is lost in the raffinate. Therefore, if we want to obtain p-xylene with both purity and recovery above 99%, we should choose the operating conditions that yield high extract and raffinate purity at the same time. Effect of the Adsorbent Deactivation. The adsorbents used in the industrial SMB units are designed to be continuously used for a long time (10-20 years). However, there is a slow deactivation of the adsorbent, and it is interesting to see how the adsorbent capacity affects the process performance. The influence of the adsorbent deactivation was examined by repeating the simulation study for the effect of the switching time period in the case of the adsorbent with a capacity of 20 and 30% lower than its original value. Figure 3 shows the influence of the adsorbent capacity on the p-xylene purity (Figure 3a) and recovery (Figure 3b). It can be seen that with decreasing adsorbent capacity the region of the p-xylene purity above 99% is getting narrower and is displaced to the region of lower switching time values. Also, with decreasing adsorbent capacity for 20 and 30%, we cannot obtain p-xylene recovery above 99%. Therefore, the switching time should be decreased in order to keep the p-xylene purity and acceptable recovery. Effect of Intraparticle Mass Transfer. The influence of the mass-transfer resistance on the p-xylene performances at steady state was studied for the reference case 2 in Table 1. The intraparticle mass-transfer coefficient k ) 15Dp/rp2 was varied in the range between 0.6 and 6 min-1. This range of k values for the homogeneous LDF model was based on a particle diameter dp ) 9.2 × 10-2 cm and a tortuosity factor between 1.6 and 8. Neves32 reported 5Dp/rp at 180 °C in the range of 9.2 × 10-2-1.1 × 10-1 cm/min, for the particle diameter 5.5 × 10-2 cm and the tortuosity factor 2.64. Storti et al.28 assumed k ) 0.25 min-1 for the

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Figure 2. Effect of the switching time on p-xylene: (a) purity and recovery; (b) productivity and desorbent consumption.

liquid-phase operation (at 57 °C) and k ) 2.9 × 102 min-1 for the vapor-phase operation (at 170 °C), for the particle diameter 0.13 cm and the tortuosity factor 2.15. The estimated values of p-xylene purity, recovery, productivity, and desorbent consumption for k ) 0.6 min-1 are 93.92%, 57.92%, 65.63 kg/m3‚h, and 0.0201 m3/kg; for k equal to 1 min-1, the values are 98.23%, 77.34%, 87.65 kg/m3‚h, and 0.0151 m3/kg; for k ) 2 min-1, the values are 99.91%, 97.54%, 110.541 kg/m3‚ h, and 0.0120 m3/kg; and for k ) 6 min-1, the values are 99.99%, 99.99%, 113.50 kg/m3‚h, and 0.0116 m3/kg, consecutively. It can be observed that the p-xylene performance parameters are more sensitive to the values of k between 0.6 and 1 min-1. Prediction of the Separation Regions and Process Performance. The successful design and operation of SMB units depends on the correct selection of operating conditions and, in particular, of the flow rates in each zone and the switching time, i.e., solid-phase velocity (us ) Lc/t*). Some constraints have to be met if we want to recover p-xylene in the extract and the rest of the C8 aromatics in the raffinate. These constraints are expressed in terms of net fluxes of components in each zone and can be found in many papers dealing with the design of SMB, for example, in work by Pais et al. (1998).33 Because of the complex dynamics of the process, the choice of the operating conditions is not easy and straightforward. Most of the known design approaches

Figure 3. Effect of the adsorbent capacity on p-xylene: (a) purity; (b) recovery.

are based on a steady-state model of the corresponding TMB process, e.g., works by Ma and Wang,34 Chiang,35,36 Storti et al.,28,37 and Mazzotti et al.38-40 In all of these approaches, the flow rates and the switching time have to be derived from the equilibrium theory. The design based on the equilibrium theory can serve as an initial guess for the optimal operating conditions, when mass transport resistance is important. Mass-transfer effects in the SMB design were addressed by Pais et al.,33-41 who described intraparticle mass-transfer effects with LDF approximation. It was shown that the set of values of fluid/solid flow rate ratios in zones 2 and 3 that yield separation is considerably reduced when mass-transfer effects are present. Azevedo and Rodrigues42 proposed two different strategies for the determination of the regions of separation in a three-dimensional space (“separation volumes” methodology) in the presence of mass-transfer resistance. They have shown that the constraints on zones 1-3 are more restrictive than those derived from the equilibrium model, whereas the constraint on zone 4 was less affected. To analyze the influence of mass-transfer effects on the separation region (region where both the extract and

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raffinate purities are above 99%), the TMB steady-state model was used. The equivalent TMB model was modified by setting the time derivatives to zero, which reduces the PDE system to an ordinary differential equation system of equations. The gPROMS package was again used as a solver. The steady-state model requires a lower computing time (only 3 min) and provides results similar to those of the transient TMB model at steady state. The numerical procedure was used to find the separation region for several values of mass-transfer coefficients. This strategy consists of fixing at the same time the value of the switching time (t* ) 1.1 min) and the values of the flow rates in zones 1 (Q1* ) 8.56 × 106 cm3/min) and 4 (Q4* ) 5.67 × 106 cm3/min). The flow rates in zones 1 and 4 were chosen to be sufficiently high and low, respectively, in such a manner to satisfy the constraints for these zones:

cmx(ox,eb)4 v4  1 us 1 - Fpqpx1

and

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Figure 6. Effect of the extract (0.47 × 10-6 cm3/min [A] - 2.1 × 10-6 cm3/min [B]) and feed (0.14 × 10-6 cm3/min [C] - 4.84 × 10-6 cm3/min [D]) flow rate changes on the region of the operation of TMB shown in the γ2-γ3 plot.

Figure 5. (a) Influence of γ1 on the separation region shown in the γ1 × γ2 × γ3 plot, for γ4 ) 0.066. (b) Influence of γ4 on the separation region shown in the γ4 × γ2 × γ3 plot, for γ1 ) 0.61.

for the values of γ1 above 0.066. It is interesting to notice that the separation regions for γ4 from 0.105 to 0.066 are expanding starting from the higher values of γ2 and γ3 in the direction to the γ2 ) γ3 diagonal. Also the separation regions for γ4 of 0.086 and 0.105 do not touch the γ2 ) γ3 diagonal. A similar behavior of the separation regions was reported by Azevedo et al.43 The possible explanation can be the contribution of the masstransfer effects and γ4 in the determination of the constraints on zones 2 and 3. It must be pointed out that for the values of γ4 higher than 0.11 there is no separation region. The explanation for this behavior is that γ4 is not small enough to satisfy the constraint on zone 4. The effect of the extract and feed flow rate on the extract and raffinate purity was studied. Figure 6 presents the lines in the γ2-γ3 plot describing the effect of changes in the extract and feed flow rate. In the study of the effect of the extract flow rate, feed and desorbent flow rates were kept constant and equal to QF* ) QF ) 1.45 × 106 cm3/min and QD* ) QD ) 2.89 × 106 cm3/ min, respectively. In the study of the effect of the feed flow rate, extract and desorbent flow rates were kept constant and equal to QE* ) QE ) 1.65 × 106 cm3/min and QD* ) QD ) 2.89 × 106 cm3/min, respectively. Notice that in both studies the flow rates in zones 1 and 4 are

Figure 7. Effect of the extract flow rate on p-xylene: (a) purity and recovery; (b) productivity and desorbent consumption.

constant (Q1* ) 8.54 × 106 cm3/min and Q4* ) 5.65 × 106 cm3/min). The other operating conditions and model parameters used were those for case 2 presented in Table 1. The influence of the extract flow rate on the SMB performance is shown in Figure 7. Increasing the extract flow rate, i.e., moving from point A to point B in Figure 6, we can observe a central region were p-xylene has both high purity and recovery. The deviation of the value of the extract flow rate left and right from its

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affect the separation region. It was also found that the choice of the flow rates in zones 1 and 4 is of great importance, because they affect the size of the separation region. Finally, the TMB package is a useful tool for fast visualization of the SMB process behavior under particular operation conditions. The simulation package can be easily modified and adapted for any industrial SMB separation and used for selecting the best operating conditions, once the details of flushing-in and flushingout streams are considered. Acknowledgment M.M. gratefully acknowledges the financial support of “Fundac¸ a˜o para a Ciencia e a Tecnologia” (Grant PRAXIS XXI/BD/19503/99) and thanks D. C. S. Azevedo for helpful discussions. Notation

central region affects the p-xylene recovery and purity, respectively. Increasing the extract flow rate improves the desorbent consumption but reduces productivity. The influence of the feed flow rate on the SMB performance is shown in Figure 8. Increasing the feed flow rate, i.e., moving from point C to point D in Figure 6, improves productivity and desorbent consumption but reduces both purity and recovery.

Ci ) fluid-phase concentration of component i, kg/m3 DL ) axial dispersion coefficient, m2/s dc ) column diameter, m dp ) particle diameter, m Ki ) adsorption equilibrium constant of component i, m3/ kg ki ) intraparticle mass-transfer coefficient of component i, min-1 Lc ) column length, m Qj ) fluid flow rate in zone j, m3/s QS ) solid flow rate, m3/s q/i ) adsorbed phase concentration in equilibrium with ci, mg/g qmi ) adsorbed phase saturation concentration of component i, mg/g t* ) switching time, s us ) interstitial solid velocity, m/s Vc ) column volume, m3 Vs ) volume of the solid phase, m3 vj ) interstitial fluid velocity in zone j, m/s  ) bed porosity γi ) fluid/solid velocity ratios in zone j Fp ) apparent particle density, kg/m3

Conclusions

Subscripts and Superscripts

Figure 8. Effect of the feed flow rate on p-xylene: (a) purity and recovery; (b) productivity and desorbent consumption.

TMB and SMB modeling approaches were used to describe the behavior of the SMB unit for separation of p-xylene from a mixture of C8 aromatics. The comparison of the steady-state performance of the SMB unit calculated by both approaches showed that the TMB approach can be used for the prediction of the performance of the SMB operation. The TMB model was used for examining the effect of the switching time period, adsorbent capacity, and mass-transfer coefficient on the SMB performance. The adsorbent deactivation which occurs during its lifetime will influence the SMB performance; to keep the pxylene purity and acceptable recovery, the switching time should be decreased. The novel “separation volume” methodology is used to find the operating conditions of the SMB unit. This work suggested a numerical procedure for defining the separation volume (product purities above 99%) in the presence of mass-transfer resistances. The study of the effect of the mass-transfer resistance on the shape and location of the separation region was performed. It was observed that the mass-transfer resistances significantly

* ) operating conditions in the SMB approach i ) adsorbable components (i ) PX, MX, OX, EB, D ) PDEB) j ) number of zones (j ) 1-4) k ) number of columns (j ) 1-24)

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Received for review January 31, 2001 Accepted February 21, 2002 IE010095T