Thermal Operation of Four-Zone Simulated Moving Beds - Industrial

Sep 20, 2007 - Simulation results with Aspen Chromatography 2004 show that thermal four-zone simulated moving beds (SMBs) operated in the traveling ...
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Ind. Eng. Chem. Res. 2007, 46, 7208-7220

SEPARATIONS Thermal Operation of Four-Zone Simulated Moving Beds Weihua Jin† and Phillip C. Wankat* School of Chemical Engineering, Forney Hall of Chemical Engineering (FRNY), Purdue UniVersity, 480 Stadium Mall DriVe, West Lafayette, Indiana 47907-2100

Simulation results with Aspen Chromatography 2004 show that thermal four-zone simulated moving beds (SMBs) operated in the traveling wave mode (fluid is heated or cooled) can significantly improve the separation without radial heat transfer limitations. For toluene/p-xylene separation (linear isotherms) in a four-zone SMB, the average purity increased from 84.8% to 99.2% and from 92.0% to 99.99% with four heat exchangers for one and two columns per zone, respectively. The average purities increased from 84.8% to 93.2% and from 92.0% to 99.0% when cold feed and hot desorbent were used with no heat exchangers for one and two columns per zone, respectively. The additional dead volumes introduced by heat exchangers had an insignificant effect. For separation of p-xylene from other C8 isomers (nonlinear isotherms), a p-xylene purity of 99.9% and recovery of 98.6% were obtained with a thermal SMB with significantly fewer columns/sections than an isothermal SMB. Introduction Simulated moving beds (SMBs) are an effective method to perform large-scale continuous chromatographic separations. They were first commercialized by UOP in the 1960s for the separation of hydrocarbons.1-4 SMBs are now extensively used for large-scale fractionation or purification of numerous mixtures of importance ranging from petrochemicals,1-3 to sugars5-10 and pharmaceuticals.11-14 Figure 1 shows a typical four-zone SMB with one column per zone for binary separation. This system simulates a counter current process by switching the inlet and outlet ports to a closed loop of fixed bed columns. A four-zone SMB with multiple columns per zone is usually preferable if very high productivity and recovery are desired.1-4 Although the most widely used scheme among simulated moving bed processes is the four-zone SMB, usually with multiple columns per zone, there are alternative schemes that may be more suited to various particular cases. New SMB configurations have been developed, such as nine-zone SMBs,9,15,16 five-zone SMBs,10,17-22 three-zone SMBs,5,23-25 two-zone SMBs,26-29 and one-zone analogs.30-32 New operating strategies were also developed to improve the SMB efficiency, such as partial or power feed operation,25,33,34 ModiCon,35 VARICOL,36-38 and the M3C process39 or enriched extract SMB (EE-SMB).40 Local equilibrium or triangle theory is commonly used to guide the initial design of SMB systems since it is simple to use and helps to visualize solute movement in columns.4,41-44 Standing wave analysis45,46 and scaling methods27,47 include mass transfer effects. Detailed simulations are usually used for final designs. Simulated moving beds are usually operated under isocratic conditions. However, operating SMBs with gradients including * To whom correspondence should be addressed. Phone: 765-4947422. Fax: 765-494-0805. E-mail: [email protected]. † Current address: GTC Technology, 1001 S. Dairy Ashford Road Ste 500, Houston, TX 77077. E-mail: [email protected].

Figure 1. Standard isothermal four-zone SMB with one column per zone.4 Switching of ports is not shown: (F) feed, (D) desorbent.

temperature, pressure, mobile phase composition, and pH may improve the separation performance. The performance improvement is achieved by tuning the adsorption behavior of the solute along the unit, that is, weakening the adsorption condition in zones III and IV and strengthening the adsorption condition in zones I and II (Figure 1). Pressure gradients are used in supercritical SMBs (SF-SMB).48-52 Solvent gradient operation has been applied for binary separations53-57 and has been extended to ternary separations in a five-zone SMB.58 A pH gradient is used for monoclonal antibody separation in a fourzone SMB.59 There are advantages in operating SMBs under nonisothermal conditions. Thermal SMBs are useful if the mixtures are thermally stable and have significant shifts in isotherms when the temperature changes. Thermal SMB systems (although not called SMBs) were studied in the late 1940s and early 1950s for separation of concentrated hydrocarbons.60 There are two operating modes for thermal SMB systems: direct and indirect modes. In the direct mode,61-63 jackets are used to change the

10.1021/ie070047u CCC: $37.00 © 2007 American Chemical Society Published on Web 09/20/2007

Ind. Eng. Chem. Res., Vol. 46, No. 22, 2007 7209

∂T ∂T + FsCP,s(1 - p)(1 - e) + ∂t ∂t 2 ∂(VT) ∂T - (EDT + DT)FfCP,fe 2 ) FfCP,fe ∂z ∂z ∂T (2) hwAw(Tamb - T) - CP,w ∂t

FfCP,f[e + (1 - e)p]

Local equilibrium theory can be used to determine the initial conditions for thermal SMBs for dilute systems.64,66 The equation used to calculate solute velocity for isothermal systems can still be used for nonisothermal systems.

us,i )

Vj (1 - e) ∂qi (1 - e) 1 + Kdi p + (1 - p) e e ∂ci

(3)

where the term ∂q/∂c is a function of temperature.64,66 Externally changing the temperature will produce a thermal wave going through the column. With the assumption of local equilibrium and negligible heats of adsorption and mixing and thermal axial dispersion, the average velocity of the thermal wave is66 Figure 2. Complete cycle for a thermally assisted four-zone SMB with one column per zone and four external heat exchangers.

column temperatures. Although this approach is convenient in the laboratory, it does not easily scale up. Migliorini et al.63 found that even in a 0.46 cm i.d. column operating with a 10 °C temperature swing, radial heat transfer limits the allowable fluid velocities in a direct mode thermal SMB. The traveling wave mode uses heat exchangers to produce a traveling wave by heating or cooling the fluid before it enters a column.4,60,64,65 The process was analyzed by local equilibrium theory4 and detailed simulations.64 Recently, results were reported for pilot plant studies of a thermal SMB to remove sucrose from raw juice.65 The basic design of the thermal four-zone SMB studied in this research is presented in Figure 2. Heat exchangers are used to change column temperatures. Zone I is cooled resulting in less of the faster component getting into zone IV which in turn will improve the extract purity, while zone IV is heated which leads to removal of more of the slow component thereby cleaning out the column. Zones II and III are cooled to intermediate temperatures at which selectivity is high to separate the two components. Desorbent and feed can enter the columns at any desired temperatures and are part of the heating and cooling process.

uth )

V 1 + (1 - e)p/e + [(1 - e)(1 - p)CP,sFs + (W/Ac)CP,w]/eFfCP,f (4)

In dilute liquid systems, the thermal wave is generally faster than the solute waves at both hot and cold temperatures.

uth > us(Th) > us(Tc), Th > Tc

(5)

The separation constraints of the thermal four-zone SMB are the same as for an isothermal SMB, except solute velocities now depend on temperature. The port velocity is defined as the hypothetical movement of the solid adsorbent, uport ) L/tsw. Separation occurs if solute A moves faster than the port movement in zones II and III and slower than the port movement in zone I, while solute B moves slower than the port movement in zones II and III and faster in zone IV.

us,A,II, us,A,III > uport > us,A,I

(6a)

us,B,IV > uport > us,B,II, us,B,III

(6b)

where us,i,j is the velocity of solute i in zone j. A characteristic or solute movement diagram for the thermal SMB (Figure 2) is shown in Figure 3.

Theory

Simulation Results for Linear Isotherms

The solute mass balance for each component in the chromatographic columns is66

To validate the thermal operation in SMB systems, simulations were done with Aspen Chromatography 2004 for the separation of a binary mixture of toluene and p-xylene. Aspen Chromatography is an equation-oriented dynamic flowsheet simulation system designed for liquid chromatography and simulated moving bed processes. Since version 12.1, nonisothermal operation has been included. Aspen Chromatography solves the partial differential, ordinary differential, and algebraic equations for mass balance (eq 1), energy balance (complete form of eq 2), mass transfer, axial dispersion, adsorption isotherm, etc. Its dynamic features can handle the short switch interval and cycle times typical of SMB units, which allow rigorous simulations for the processes analyzed in this study. To validate the simulation, benchmarking was done against the

∂(Vsci) ∂ci ∂cji,pore + e + Kdi (1 - e)p + ∂z ∂t ∂t ∂qji ∂2ci - eEz 2 ) 0 (1) (1 - e)(1 - p) ∂t ∂z To simplify the energy balance, we assume instantaneous thermal equilibrium at each cross section; therefore, the solid temperature T h s, pore fluid temperature T h *, wall temperature Tw, and bulk temperature T are all equal (T ) Tw ) T h* ) T h s). The energy balance for both phases (with constant density) is66

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Ind. Eng. Chem. Res., Vol. 46, No. 22, 2007 Table 1. System and Operating Parameters for a Four-Zone SMB with One Column per Zone for the Separation of Toluene/p-Xylene at 25 °C with D/F ) 5.064,69 L Dcol e p dp Ff µ Fs kmap (toluene) kmap (p-xylene) CP,s CP,f

Figure 3. Characteristic or solute movement diagram for a thermal fourzone SMB with one column per zone: (TH) hot temperature; (TC) cold temperature; (TI1, TI2) intermediate temperatures.

analytical solution for a pure thermal wave (with no solute adsorption) as calculated by the Lapidus and Amundson model4 modified to apply to the energy balance. The resulting thermal wave from analytical solution and the one from the final version of Aspen Chromatography 12.1 are a close match.67 The adsorbent used in this system is silica gel, the desorbent is n-heptane, and the operation temperature range is 0-80 °C. The system is modeled with a variable dispersion coefficient that is estimated using the Chung and Wen correlation for each component.68

Pe )

Vsdp ) 0.2 + 0.011(Re)0.48 Ez

(7)

The kinetic model is a linear lumped resistance with constant mass-transfer coefficient, and the driving force used is ∆c. The isotherms are linear and follow an Arrhenius form.69

toluene: qTOL ) 0.0061e2175.3/TcTOL

(8a)

p-xylene: qPX ) 0.01051e2115.1/TcPX

(8b)

where units for qi and ci are g(solute)/g(solid) and g(solute)/ g(solution), respectively. The system and operating conditions are listed in Table 1. The system is operated adiabatically, and wall heat storage is neglected. The temperature changes in the heat exchangers are assumed to be instantaneous. The base case was operated isothermally at 25 °C. Thermal Four-Zone SMB with Four Heat Exchangers. The simulation results for a thermal SMB with one column per zone are shown in Table 2. When only the heater temperature increases (runs 1-5), the raffinate and extract purities both increase and then approach limiting values. The local equilibrium model (Figure 3) can be used to analyze the process. A is the less retained solute (toluene), and B is the more retained solute (p-xylene). At the high temperature, more solute B is desorbed in zone IV, the column is cleaner when it is switched, and the raffinate purity is higher. When more solute B is removed from zone IV, the extract purity is also increased. However, once the temperature is high enough to clean zone IV, further increases in the heater temperature have no effect. We intentionally ran the heater at a very high-temperature (run 5 in Table 2) to see the constant purity region. When only the temperature in cooler 1 was decreased, both raffinate and extract purities increase (compare run 1 to runs 6

System Parameters 200 cm column length 2 cm column diameter 0.43 external void fraction 0.5 internal void fraction 100 µm adsorbent particle diameter 0.684 g/mL liquid density 0.386 cP liquid viscosity 1.05 g/mL solid density 52.86 1/min mass-transfer coefficient (A) 62.51 1/min mass-transfer coefficient (B) 920.0 J/kg‚K solid heat capacity 2243.9 J/kg‚K fluid heat capacity

Operating Parameters feed rate (cm3/min) feed concentration for each component (g/L) switching time (min) recycle rate (cm3/min) desorbent rate (cm3/min) flow rate in zone I (cm3/min) flow rate in zone II (cm3/min) flow rate in zone III (cm3/min) flow rate in zone IV (cm3/min) raffinate rate (cm3/min) extract rate (cm3/min)

32.8 0.008 14 133 164 133 198 165.2 297 65 131.8

and 7). Because the solute A velocity in zone I decreases as the temperature drops, it is less likely to get into zone IV to contaminate the B product. After port switching, the column in zone I becomes the column in zone II (see Figure 2). For a short period, this column is operated at lower temperature, which makes solute B less likely to break through to contaminate A product, and the raffinate purity also increases. A synergistic effect occurs if the cooler 1 temperature is decreased and the heater temperature is increased (runs 8 and 9), but the increases in purities are rather small. Economically, it may not pay to increase the heater temperature from 50 to 80 °C. From the solute movement diagram in Figure 3, increasing solute velocities in zone III will help to remove solute A from the column, which gives a better extract purity. On the other hand, the leading edge of solute B wave in zone III moves faster and more solute B may get into zone II to contaminate the A product. However, lowering the temperature of zone III may not help to increase the raffinate purity. When the temperature of cooler 3 drops, the solute velocities are decreased and the trailing edge of the solute A wave may not break through in zone III. It will be carried over to the next step after port switching to contaminate B product. Solute B also moves slower in zone III, and in return, less B is removed from the system. The simulation results are shown in Table 2 (runs 10-13). Comparing runs 2 and 10 to 13, we see that the raffinate purities drop and extract purities increase with increases in the cooler 3 temperature. Cooler 3 was also intentionally run at a low temperature in run 14, and as expected, both raffinate and extract purities decrease. Since the decrease in the raffinate purity by heating zone III is mainly due to more solute B going into zone II, decreases in the zone I temperature increase the raffinate purity by a small amount. In runs 15-17, the cooler 1 temperature is decreased. As expected, both raffinate and extract purities increase modestly compared to run 11. The decrease in the raffinate purity by heating zone III can be compensated for by decreasing solute velocities in zone II, which can be achieved by cooling this zone. The simulation results are shown as runs 18-20. Raffinate purity increases tremendously with decreases in the cooler 2

Ind. Eng. Chem. Res., Vol. 46, No. 22, 2007 7211 Table 2. Simulation Conditions and Results for the Separation of Toluene/p-Xylene with a Thermal Four-Zone SMB with One Column per Zone and Four Heat Exchangers at D/F ) 5.0a temperature (°C)

purity (%)

recovery (%)

run

cooler 1

cooler 2

cooler 3

heater

raffinate

extract

average

raffinate

extract

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

25 25 25 25 25 10 0 0 0 25 25 25 25 25 20 10 0 0 0 0 0

25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 20 15 10 6

25 25 25 25 25 25 25 25 25 30 33 35 40 20 33 33 33 33 33 33 54

25 50 80 100 150 25 25 50 80 50 50 50 50 50 50 50 50 50 50 50 60

84.9 87.1 87.5 87.5 87.6 88.1 88.9 89.0 89.1 86.8 85.6 84.4 79.3 86.3 86.0 86.6 87.5 95.5 98.1 98.7 99.0

84.8 87.0 87.2 87.3 87.3 87.9 88.4 88.6 88.6 92.5 93.0 93.0 97.5 74.1 95.6 95.9 96.3 94.5 85.3 63.8 99.4

84.8 87.1 87.3 87.4 87.4 88.0 88.7 88.8 88.9 89.7 90.3 90.2 88.4 80.2 90.8 91.3 91.9 95.0 91.7 81.2 99.2

84.7 87.4 87.6 87.6 87.7 88.0 88.6 88.8 88.8 92.3 95.6 96.6 98.1 70.2 96.1 96.4 96.7 94.8 82.4 41.6 99.99

85.0 86.7 87.2 87.9 88.1 88.2 88.5 88.5 89.1 86.0 93.9 82.2 74.4 85.1 84.3 85.1 86.2 94.3 98.4 99.5 99.99

a

Flow rates are shown in Table 1, and all the flow rates are constant.

temperature compared to run 17. Unfortunately, extract purity also decreases significantly because solute A moves slower in zone III after port switching and may not break through, which contaminates the B product. The average purity can be tuned by optimizing the temperature profile of the system. Run 21 is close to optimum with an average purity of 99.2%. If it is desirable to achieve higher purities, multiple columns per zone can be used. Another benefit in thermal operation with multiple columns per zone is that, after port switching, at least one of the columns in the zone is already at the desired temperature. Thus, it takes less time for thermal waves to break through. Figure 4 shows a complete cycle for a thermal fourzone SMB with two columns per zone and four heat exchangers. The system and operating conditions are listed in Table 1, except, to keep the same productivity for both SMB systems, the column length and switching time are half of those of the one column per zone system. The simulation results (Table 3) are qualitatively the same as the one column per zone results, but higher purities and recoveries are achieved. This is true comparing the two base cases (runs 1 in Tables 2 and 3), the intermediate cases (runs 2 and 3 in both tables, run 9 in Table 2, and run 6 in Table 3), and the two best runs (run 21 in Table 2 and run 10 in Table 3), which are at different conditions. In run 10 in Table 3, both raffinate and extract purities of 99.99% are achieved. In previous simulations, the flow rates are kept constant while the temperatures are changed. The purities can be further improved by changing operating conditions. As shown in Tables 2 and 3, average purities are greater than 99.9% for the best runs; it may not be justified to show the effect of further optimization of operating conditions at D/F ) 5. Thus, simulations were run for both one and two columns per zone systems at D/F ) 1. The operating temperatures were also limited to limit the purity increase. The operating conditions and simulation results with varying flow rates are shown in Table 4. The base case for the four-zone SMB with one column per zone is run 1 in Table 4, which is operated isothermally at 25 °C. As expected, the purities are increased significantly when the temperatures of different zones are changed properly while the flow rates are kept constant, as shown in run 2 in Table 4. The purities are further improved modestly by adjusting the flow

rate. Further changes of operating temperatures at optimal flow rates did not improve the separation, which indicates that the current temperature profile is close to optimal. The qualitative effects of temperature changes and flow rate changes for the four-zone SMB with two columns per zone are exactly the same as those for four-zone SMB with one column per zone. The increases in purities are insignificant when the flow rates are further optimized at the optimal operating temperature profile. This probably occurs because the solute velocities are already close to optimal after temperatures change. The simulations show that the duration of initial transients of SMB systems for isothermal and thermal operations are identical. Both reach cyclic steady state after 50 cycles. Thermal Four-Zone SMB with No Heat Exchangers. To simplify the design and avoid additional dead volume, we also designed a thermal SMB without external heat exchangers. The traveling thermal waves are produced by changing the feed and desorbent temperatures. As in the analysis in the previous section, each zone in each step in a four-zone SMB has to be operated at appropriate temperatures. Without heat exchangers between columns, thermal waves will travel throughout the columns and can enter the wrong zones. Although heat exchangers or heated/cooled supply tanks have to be used to change the feed and desorbent temperatures, these systems are external to the SMB and do not introduce additional dead volume. For a four-zone SMB with one column per zone, when only the desorbent temperature is increased, the raffinate purities decrease and the extract purities go through a maximum (compare runs 2-6 to run 1 in Table 5). Since the thermal wave breaks through into zones III and II, solute B moves faster and more B will exit with the A product. Therefore, the raffinate purity decreases. Initially, the increase of the extract purity occurs because more B is removed from zone IV. With further increases in the desorbent temperature, solute A in the recycle stream will break through and exit with the B product, decreasing the extract purity. The increase of solute B velocity in zone II can be compensated for by decreasing the feed temperature. Comparing runs 7 to 10 in Table 5, we see that both raffinate and extract purities increase with decreases in feed temperature. The increase in the extract purity occurs because less solute A is

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Figure 4. Complete cycle for a thermal four-zone SMB with two columns per zone and four heat exchangers. Table 3. Simulation Conditions and Results for the Separation of Toluene/p-Xylene with a Thermal Four-Zone SMB with Two Columns per Zone and Four Heat Exchangers at D/F ) 5.0a temperature (°C)

purity (%)

recovery (%)

run

cooler 1

cooler 2

cooler 3

heater

raffinate

extract

average

raffinate

extract

1 2 3 4 5 6 7 8 9 10

25 25 25 15 5 0 0 0 0 0

25 25 25 25 25 25 15 15 5 5

25 25 25 25 25 25 25 35 35 45

25 50 80 80 80 80 80 80 80 80

92.0 94.8 95.3 95.7 95.9 96.2 99.97 99.98 99.99 99.99

92.1 95.0 95.2 95.7 96.0 96.0 75.5 99.94 98.8 99.99

92.0 94.9 95.3 95.7 95.9 96.1 87.7 99.96 99.4 99.99

92.2 95.9 96.0 96.6 97.0 97.0 72.1 99.99 99.8 99.99

92.1 95.1 95.9 96.0 96.6 96.9 99.99 99.99 99.99 99.99

a

Flow rates are shown in Table 1, and all the flow rates are constant.

carried over to zone IV in the recycle stream since the solute A velocity is lower in zones II and I. The average purity is further improved by tuning the temperature profile. In run 11, the average purity is 93.2%, more than 8 percentage points higher than the base case (run 1 in Table 5). The purity changes with respect to the temperature changes for a four-zone SMB with two columns per zone and no heat exchangers are qualitatively similar to those for a four-zone SMB with one column per zone. The simulation results are shown in Table 6. The near-optimal average purity is 99.3%, more than 9 percentage points higher than the base case of the two columns per zone system (run 1 in Table 6).

For the toluene/p-xylene separation, thermal operation with no heat exchangers improves the separation for four-zone SMBs significantly, but the temperatures, particularly the hot temperature, need to be selected carefully. Equation 9, which balances the increased energy in the desorbent with the decreased energy in the feed, can be used as a rule of thumb for initial temperature selection.

∆Tfeed ≈

D ∆Tdesorbent F

(9)

Since the isotherms change with temperature, this estimation is

Ind. Eng. Chem. Res., Vol. 46, No. 22, 2007 7213 Table 4. Simulation Conditions and Results for the Separation of Toluene/p-Xylene with a Thermal Four-Zone SMB with One and Two Columns per Zone and Four Heat Exchangers with Adjusted Flow Rates at D/F ) 1.0 temperature (°C) run

cooler 1

1 2 3

25 15 15

4 5 6

25 20 20

cooler 2

Table 7. Simulation Conditions and Results for the Separation of Toluene/p-Xylene with a Thermal Four-Zone SMB with One and Two Columns per Zone and No Heat Exchangers with Adjusted Flow Rates at D/F ) 5.0

purity (%)

cooler 3

heater

raffinate

extract

temperature (°C) desorbent

run

feed

Four-Zone SMB with One Column per Zone 25 25 25 77.2 74.0 17 34 35 97.5 96.2 17 34 35 96.5 97.8

75.6 96.8 97.2

1 2 3

25 0 0

Four-Zone SMB with One Column per Zone 25 84.9 84.8 84.8 32 92.2 94.2 93.2 32 93.9 93.6 93.8

Four-Zone SMB with Two Columns per Zone 25 25 25 83.6 83.3 21 29 30 98.4 98.1 21 29 30 98.1 99.1

83.5 98.3 98.6

4 5 6

25 0 0

Four-Zone SMB with Two Columns per Zone 25 92.0 92.1 92.0 30 99.5 98.4 99.0 30 99.9 98.2 99.1

Operating Conditions (cm3/min)

flow rate

feed raffinate extract desorbent recycle tsw (min)

run 1

run 2

run 3

run 4

run 5

run 6

32.8 31 34.6 32.8 103 14

32.8 31 34.6 32.8 103 14

32.8 36 29.6 32.8 103 14

32.8 31 34.6 32.8 103 7

32.8 31 34.6 32.8 103 7

32.8 36 29.6 32.8 103 7

temp (°C)

purity (%)

recovery (%)

run

feed

desorbent

raffinate

extract

average

raffinate

extract

1 2 3 4 5 6 7 8 9 10 11

25 25 25 25 25 25 20 15 5 0 0

25 30 31 32 33 35 33 33 33 33 32

84.9 76.9 75.1 72.6 69.2 63.2 73.1 78.9 87.6 90.7 92.2

84.8 93.3 93.9 93.8 93.5 91.3 94.6 95.6 95.6 95.2 94.2

84.8 85.1 84.5 83.2 81.4 77.2 83.8 87.2 91.6 93.0 93.2

84.7 93.8 94.0 94.2 93.9 91.4 95.0 96.1 96.1 95.6 94.5

85.0 74.0 72.6 68.4 55.2 41.1 70.1 76.6 88.0 91.1 93.0

Flow rates are shown in Table 1, and all the flow rates are constant.

Table 6. Simulation Conditions and Results for the Separation of Toluene/p-Xylene with a Thermal Four-Zone SMB with Two Columns per Zone and No Heat Exchangers at D/F ) 5.0a temp (°C)

purity (%)

recovery (%)

run

feed

desorbent

raffinate

extract

average

raffinate

extract

1 2 3 4 5 6 7 8 9 10 11

25 25 25 25 25 25 25 15 5 0 0

25 30 31 32 33 34 35 31 31 31 30

92.0 82.5 79.3 75.6 77.7 67.2 63.1 92.2 98.3 99.3 99.5

92.1 99.7 99.8 99.8 99.8 99.6 99.2 99.7 99.5 99.2 98.4

92.0 91.1 89.6 87.7 85.7 83.4 81.2 95.9 98.9 99.3 99.0

92.2 99.99 99.99 99.99 99.99 99.99 99.99 99.99 99.99 99.99 99.4

92.1 82.0 75.9 72.9 74.7 51.6 40.5 92.9 99.6 99.99 99.99

a

raffinate

extract

average

Operating Conditions

Table 5. Simulation Conditions and Results for the Separation of Toluene/p-Xylene with a Thermal Four-Zone SMB with One Column per Zone and No Heat Exchangers at D/F ) 5.0a

a

purity (%)

average

Flow rates are shown in Table 1, and all the flow rates are constant.

not exact. For example, for run 10 in Table 6 according to eq 9, the desorbent temperature should be 30 °C for a feed temperature of 0 °C. When this prescription is followed, the average purity is 99.0% compared to the optimized average purity of 99.3%. This operation is simple, since only the feed and desorbent temperatures need to be changed accordingly, and thus should be useful for retrofitting an existing unit. Unfortunately, as will be shown later, it does not work for all separation systems.

flow rate (cm3/min)

run 1

run 2

run 3

run 4

run 5

run 6

feed raffinate extract desorbent recycle tsw (min)

32.8 65 131.8 164 133 14

32.8 65 131.8 164 133 14

32.8 55 141.8 164 139 14

32.8 65 131.8 164 133 7

32.8 65 131.8 164 133 7

32.8 55 141.8 164 139 7

In the previous simulations, only the temperatures changed. The separation can be further improved by changing the flow rates. The simulation results are shown in Table 7. The results are very similar for both one and two columns per zone systems. Further optimizing the flow rate does improve the separation, but the increases in purities are very modest. At optimal flow rates, further changes of operating temperatures did not improve the separation, which indicates the that current temperature profile is close to optimal. Dead Volume Effects. Dead volume effects can be important in SMB systems, especially for systems producing high-purity products.9,27,44,47,70,71 Dead volumes are always present due to tubes, valves, and pumps and may account for up to 3% of the unit volume in industrial- or pilot-scale plants.70 Mixing in the dead volume causes spreading of the concentration profile in the SMB unit, and dead volume causes a lag time in SMBs, which can be compensated for by adjusting flow rates.44,47 Since we assume that dead volume was included in the original isothermal design, only the additional dead volumes introduced by external heat exchangers are studied. A shell and tube heat exchanger is used with the streams from the columns flowing through the tubes. The flow in the tube is described with a second-order model.44

∂ci ∂ci ∂2ci + Vs ) DD 2 ∂t ∂z ∂z

(10)

where DD is the axial dispersion coefficient in the tube. Axial mixing in tubes has been throughoutly studied for both laminar and turbulent flows.72-76 In this study, Levenspiel’s method75 is adopted by correlating the term DD/Vsdtube to Reynolds number, where dtube is the tube diameter. DD/Vsdtube was determined from Levenspiel’s figure.75 First, a thermal four-zone SMB with two columns per zone and four heat exchangers is studied. The base case is run 10 in Table 3. The tubes in the heat exchangers are assumed to be 2 cm in diameter. The average overall heat transfer coefficient is 100 Btu/hr‚ft2‚oF, which is reasonable for liquid-liquid heat transfer in shell and tube heat exchangers.77 The minimum approach temperature is 10 °C. The flow rates for each heat exchanger are listed in Table 8. Because smaller heat exchangers

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Table 8. Simulation Results for Heat Exchangers in a Thermal Four-Zone SMB Separating Toluene/p-Xylene with Two Columns per Zone for Run 10 in Table 3

cooler 1 cooler 2 cooler 3 heater

temperature change (°C)

flow rate (mL/min)

heat duty (kcal/h)

surface area (cm2)

5f0 45 f 5 80 f 45 0 f 80

133 165.2 165.2 133

-13.45 -133.70 -121.37 236.09

23.70 235.67 213.93 416.13

will minimize dead volume effects, the feed and desorbent temperatures are changed externally (Figure 4), and these flows do not go through the heat exchangers. Table 8 contains the simulation results from the HeatX block of Aspen Plus 2004. To simplify the SMB analysis, the average values for dead volumes and fluid velocities are used. The average surface area for each heat exchanger is 222.36 cm2. For a 2 cm i.d. tube, the average length is 35.4 cm. The tube volume of each heat exchanger is 17.7% of the total column volume. According to the flow rates in Table 8, the average superficial fluid velocity is 0.79 cm/s. The Reynolds number is

Re ) VsFf dtube/µ ) 0.79(cm/s) × 6.84(g/cm3) × 2 (cm)/0.00386(g/cm‚s) ) 2800 (11) According to Levenspiel’s figure,75 the flow is in the turbulent region and DD/Vsdtube ) 1.5. The corresponding tube Peclet number, NPe ) VsLtube/DD ) 11.8. Simulations were run for a thermal four-zone SMB with two columns per zone with additional dead volume equal to 17.7% of the column volume. Initially, to minimize the axial mixing effect, NPe was set to a large value (400). The simulation results are shown in runs 1 and 2 in Table 9. With constant flow rates, the raffinate purity decreases slightly and the extract purity decreases enormously because of the increase in lag time caused by the additional dead volume. This effect can be corrected by adjusting the flow rates (run 3). Compared to the base case (run 1 in Table 9), the decreases in product purities are very small. This effect is consistent with the dead volume results reported for isothermal four-zone SMBs.44,47 Next, dispersion is increased by decreasing the tube Peclet number. The simulation results are shown in runs 4-6 in Table 9. Both raffinate and extract purities drop slightly with NPe ) 11.8. With NPe ) 1, a larger but still modest reduction in purities is observed. Simulations were also done for a dead volume of 50% of column volume (runs 9-15 in Table 9). Again, the lag time effect can be corrected by adjusting the raffinate and extract flow rates (compare runs 9 and 10). With a larger dead volume, axial dispersion effects are somewhat more significant but they still are not large. Therefore, for this example, the dead volume effects caused by external heat exchangers are small. In addition, there may be mixing volumes caused by gaps between the outlet of the heat exchanger and inlet of the column. These volumes are modeled as fully mixed tanks. We assume there is a 2-4 cm gap between the connections, which is approximately 1-2% of the total column volume. The simulation results are shown in runs 7 and 8 in Table 9. Compared to run 5, the changes in product purities are small. Energy Comparison for Isothermal and Thermal Operations. Thermal SMB operation can increase the product purities significantly with constant D/F when each zone is operated at an appropriate temperature. Thermal operation can also be used to reduce desorbent usage if product purities are acceptable. Solvent is usually removed by evaporation or distillation. Compared to the latent heat involved in evaporation or distillation, the sensible heat required for heating and cooling in a

thermal SMB is much smaller. For example, the latent heat of vaporization of n-heptane is 315 kJ/kg at its boiling point, whereas the specific heat capacity is 2.0 kJ/kg‚°C.77 Energy consumption is compared for an isothermal SMB (D/F ) 5.0) and a thermal SMB (D/F ) 0.0). Both SMBs have two columns per zone. Thermal SMBs with very dilute feeds can operate with no additional desorbent because the energy input essentially produces pure desorbent from the dilute feed.64 The system and operating conditions for both SMBs are shown in Tables 1 and 10, except that the column length and switching time are half of the values in Table 1. The isothermal system is operated at 25 °C. The raffinate and extract purities for the isothermal four-zone SMB with D/F ) 5.0 are 92.0 and 92.1%, respectively. The flow rates and temperatures for the thermal four-zone SMB at D/F ) 0.0 are shown in Table 10. As expected, there is no separation for isothermal operation at D/F ) 0.0 (run 1). The temperature of each zone is adjusted to obtain a similar average purity as the isothermal four-zone SMB at D/F ) 5.0. The absolute values of heat duty

∆Hcolumnj ) |(QjFfCP,f + VjFsCP,s/tsw)∆Tj|

(12)

are shown in Table 10. The total absolute heat duty is 77.50 kcal/h. Equation 12 assumes that heat exchangers are operated with constant inlet and outlet temperatures; therefore, no additional energy is required to heat or cool the heat exchangers themselves. The implementation of heat exchangers will be discussed later. The n-heptane is recovered from the raffinate and extract streams by distillation. The distillation columns were designed with the RADFRAC block of Aspen Plus 2004 using the PengRobinson vapor-liquid equilibrium (VLE) correlation. The feeds to the distillation columns are saturated liquids, and the pressure drop is 0.0056 bar/stage. We specify the external reflux ratio as Rreflux ) 1.15Rreflux,min, which is reasonable in engineering practice.77 The product purities and recoveries are both set to >99.9% in the distillates of the columns. The heat duties of the distillation columns are listed in Table 11. If we do not consider the cost differences for cooling and heating in the thermal four-zone SMB and simply add duties, the total heat requirement (reboiler duties plus SMB requirements) for the thermal SMB and its distillation columns is 583.3 kcal/h, which is 28.6% of the total (2040.7 kcal/h) for the isothermal SMB distillation columns. The total energy consumption of the thermal SMB is much lower than the isothermal SMB because the thermal SMB uses less desorbent. Simulation Results for Nonlinear Isotherms The separation of C8 aromatics is used as an example for thermal operation with nonlinear isotherms. Typically, high purity (>99.7%) p-xylene is required. Because the p-xylene purification requires high purity and recovery, multiple columns per zone SMBs are usually used in large-scale applications. The feed is a C8 aromatics mixture with 23.6% p-xylene, 49.8% m-xylene, 12.7% o-xylene, and 14% ethylbenzene.79 The desorbent is p-diethylbenzene (PDEB). The adsorbent is Baexchanged faujasite-type zeolite. Adsorption equilibrium follows the Langmuir isotherm.

qmKici 1 + Kici

(13)

Ki ) K∞,ieAi/T

(14)

q/i )

Ind. Eng. Chem. Res., Vol. 46, No. 22, 2007 7215 Table 9. Dead Volume Effects for a Thermal Four-Zone SMB Separating Toluene/p-Xylene with Two Columns per Zonea flow rate (cm3/min) run

NPe

additional mixing

1 2 3 4 5 6 7 8

400 400 40 11.8 1 11.8 11.8

0% 0% 0% 0% 0% 0% 1% 2%

9 10 11 12 13 14 15

400 400 40 20 10 1 0.1

0% 0% 0% 0% 0% 0% 0%

a

raffinate

extract

purity (%) raffinate

Dead Volume ) 17.7% of Column Volume 65 131.8 99.99 65 131.8 99.8 85 111.8 99.97 85 111.8 99.97 85 111.8 99.9 85 111.8 99.8 85 111.8 99.9 85 111.8 99.98 Dead Volume ) 50% of Column Volume 65 131.8 99.8 125 71.8 99.97 125 71.8 99.96 125 71.8 99.8 125 71.8 99.7 125 71.8 99.5 125 71.8 98.9

recovery (%)

extract

average

raffinate

extract

99.99 65.7 99.95 99.93 99.9 98.6 99.9 99.8

99.99 82.7 99.96 99.95 99.9 99.2 99.9 99.9

99.99 50.1 99.99 99.99 99.99 99.9 99.99 99.99

99.99 99.99 99.99 99.99 99.99 99.99 99.99 99.99

50.5 99.94 99.94 99.8 99.1 97.7 96.0

75.2 99.96 99.95 99.8 99.4 98.6 97.5

20.2 99.99 99.99 99.99 99.99 99.9 98.4

99.99 99.99 99.99 99.99 99.99 99.95 99.9

The operating temperatures are the same as run 10 in Table 3.

Table 10. Simulation Conditions and Results for a Thermal Four-Zone SMB Separating Toluene/p-Xylene with Two Columns per Zone and Four Heat Exchangers at D/F ) 0.0a inlet temp (°C) flow rate (cm3/min) feed switching time (min) recycle desorbent zone I zone II zone III zone IV raffinate extract raffinate purity (%) extract purity (%) average purity (%)

32.8 17.475 90 0 90 112 79.2 90 22 10.8

run 1

run 2

heat (abs)b (kcal/h) 3.62

25 25 25 25

20 20 34 43

9.945 12.38 15.75 35.8

49.9 50.1 50.0

92.1 91.1 92.1

All flow rates are constant. b CP,f ) 2243.9 J/kg‚K ) 0.5385 kcal/ kg‚K and CP,f ) 920 J/kg‚K ) 0.2208 kcal/kg‚K are used to calculate the absolute heat duties.

adsorption equilibrium on faujasite-type zeolites such as oxylene (OX),81 the isotherm for MX is assumed to be the same that for OX. Since PX/PDEB selectivity on Ba-exchanged faujasite zeolite is approximately constant in the temperature range of 130-175 °C,82 the same values of Ai are used for PDEB and PX. The system and operating conditions at 180 °C for an industrial-scale SMB for the separation of C8 aromatics79 are shown in Table 13. A 24-column isothermal SMB and a thermal four-zone SMB with two columns per zone are simulated and compared. This system is modeled with a variable dispersion coefficient estimated with the Chung and Wen correlation.68 The kinetic model is a linear lumped parameter with ∆q as the driving force. For the ∆q driving force, if film diffusion is neglected, the mass transfer coefficient is66

kmap )

a

Table 11. Operating Conditions and Heat Duties for Distillation Columns for Solvent Recovery in Toluene/p-Xylene Separation thermal SMB D/F ) 0.0 (cm3/min)

feed flow rate feed stage total stages reflux top pressure (bar) bottom pressure (bar) condenser duty (kcal/h) reboiler duty (kcal/h) total reboiler duty (kcal/h)

extract

raffinate

extract

10.8 71 142 5.66 1.2 2.0 447.33 447.83 505.77

22 15 39 0.82 1.2 1.44 58.44 59.86

65 73 142 5.69 1.2 2.0 1327.65 1328.03 2040.74

131.8 15 39 0.82 1.2 1.44 713.09 713.59

qm (kg/kg) K∞,i (m3/kg) Ai (K)

()( )

T VB Dm ) 4.4 × 10-12 µB V A

PX

MX

OX

EB

PDEB

0.1024 0.001421 3271.4

0.0917 0.006377 2237.1

0.0917 0.006377 2237.1

0.0966 0.004692 2441.5

0.0847 0.001725 3271.4

Values for the constants are in Table 12. The p-xylene (PX), o-xylene (OX), and ethylbenzene (EB) values are based on experimental data.80 Since m-xylene (MX) has a very similar

1/6

∆HB ∆HA

1/2

(16)

The viscosity is correlated with Eyring’s equation84

µB ) B1eB2/T

(17)

where B1 and B2 are constants. Substituting eqs 16 and 17 into eq 15, we obtain

kmap )

Table 12. Isotherm Parameters for the C8 Aromatics Separation79,80

(15)

dp2

where Dmp ) pDm/τ. We assume that the tortuosity factor τ is independent of temperature. The molecular diffusivity is correlated83

isothermal SMB D/F ) 5.0

raffinate

60Dmp(1 - e)Fs

2.64 × 10-10

()( )

60p(1 - e)Fp VB VA τd 2B p

1

1/6

∆HB ∆HA

1/2

T (18) eB2/T

Combining all the constants, eq 18 simplifies to

T kmap ) B B /T e 2

(19)

where B is a constant for each compound. The values of B, B2,

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Ind. Eng. Chem. Res., Vol. 46, No. 22, 2007

Table 13. System and Operating Parameters for a Four-Zone SMB with Two Columns per Zone for the Separation of C8 Aromatics at 180 °C79 L Dcol e p dp FF FD kmap (PX) kmap (MX) kmap (OX) kmap (EB) kmap (PDEB) CP,s CP,f feed rate feed composition desorbent rate raffinate rate extract rate recycle rate switching time D/F

System Parameters 3.42 m column length 4.12 m column diameter 0.39 external void fraction 0.37 internal void fraction 620 µm adsorbent particle diameter 713.7 g/L feed density 722.9 g/L desorbent density 8.1 1/min mass transfer coefficient 8.1 1/min mass transfer coefficient 8.1 1/min mass transfer coefficient 8.1 1/min mass transfer coefficient 6.8 1/min mass transfer coefficient 230 cal/kg‚°C solid heat capacity 610 cal/kg‚°C fluid heat capacity Operating Parameters 87 m3/hr PX 23.6%, MX 49.8%, OX 12.7%, EB 14% 133.06 m3/h 131.41 m3/h 88.65 m3/h 504.32 m3/h 3.45 min 1.53

Table 14. Mass Transfer Coefficients for C8 Aromatics at Different Temperatures kmapa (1/min) temperature (°C) PX MX OX EB PDEB a

B (1/K‚min)

180

160

140

0.2896 0.2896 0.2896 0.2896 0.2431

8.1 8.1 8.1 8.1 6.8

6.81 6.81 6.81 6.81 5.72

5.64 5.64 5.64 5.64 4.73

B2 ) 1262 K.

Table 15. Simulation Conditions and Results for a Thermal Four-Zone SMB with Two Columns per Zone and No Heat Exchangers for the Separation of C8 Aromaticsa temperature (°C)

PX (%)

run

feed

desorbent

purity

recovery

PRI

1 2 3 4 5 6 7 8 9

180 170 160 156.6 150 170 170 160 160

180 170 160 156.6 150 180 190 180 156.6

90.5 98.0 98.9 98.8 98.8 91.6 83.8 93.0 99.1

96.4 96.1 92.5 91.1 88.0 96.9 97.4 97.5 91.0

93.4 97.0 95.7 95.0 93.4 94.2 90.6 95.2 95.1

a

Flow rates are shown in Table 13, and all the flow rates are constant.

and kmap(T) are listed in Table 14. The mass transfer coefficients decrease with decreases in temperature. Thermal Four-Zone SMB with No Heat Exchangers. First, simulations were run for the thermal four-zone SMB without heat exchangers. In Table 15, the purity-recovery index (PRI ) (PX purity + PX recovery)/2) is used to compare different runs. In isothermal operation (runs 1-5), PX purity increases and PX recovery decreases with decreases in temperature. This occurs mainly due to the shift in selectivity, Ri,j ) Ki/Kj shown in Table 16. The R values increase considerably with deceases in temperature. With further decreases in temperatures, mass transfer rates become low, which reduces separation performance. The near-optimal temperature is about 170 °C for this set of data.

Table 16. Selectivity r Values for the C8 Aromatics System at Different Temperatures R values temperature (°C)

PX/MX

PX/OX

PX/EB

PX/PDEB

180 170 150 120

2.185 2.300 2.568 3.095

2.185 2.300 2.568 3.095

1.891 1.971 2.153 2.501

0.824 0.824 0.824 0.824

Table 17. Selectivity r Values for the Linear Toluene/p-Xylene System at Different Temperatures temperature (°C)

RTOL/PX

0 20 40 80 160

1.382 1.403 1.422 1.453 1.499

The simulation results with different desorbent and feed temperatures are shown in runs 6-8 in Table 15. When the desorbent temperature is increased (compare runs 2, 6, and 7), PX purity drops significantly while PX recovery increases slightly. Since no heat exchanger is used between zones III and IV, the thermal wave will break through in zone IV and can enter zone III. The higher temperature reduces the selectivity and worsens the separation. The slight increase in PX recovery (or raffinate purity) is due to more thorough cleaning of the columns in zone IV. Cooling zones I and II will help to prevent the breakthrough of the solute waves and achieve better separation. Comparing runs 6 and 8, we see an improvement of both PX purity and recovery by lowering the feed temperature. Since, with a higher desorbent temperature, the separation is not favorable in zone III, we cannot obtain a higher PRI than the base case (run 2 in Table 15). One more simulation was run to balance heating and cooling using eq 9 (run 9 in Table 15). By decreasing the desorbent temperature, PX purity increases and PX recovery decreases (compare runs 3, 6, and 8). A PX purity greater than 99% is achieved in this run, but recovery is low. For systems with large decreases in selectivity with increases in temperature, the thermal SMB without heat exchangers does not work appropriately. The toluene/p-xylene separation worked because its selectivity is almost constant over the temperature range (Table 17). Thermal Four-Zone SMB with Four Heat Exchangers. The simulation results for an SMB with two columns per zone and four heat exchangers for the separation of C8 aromatics are shown in Table 18. In runs 1-4, only the heater temperature is increased. PX purity goes through a maximum value and PX recovery increases with increases in the heater temperature. The decrease in PX purity is due to the breakthrough of other xylene isomers and EB at high temperatures. In runs 3, 5, and 6, only the cooler 1 temperature is decreased. PX purity and recovery increase with decreases in the cooler 1 temperature because the solute velocities decrease as temperature drops in zone I, and thus, less impurities (MX, OX, and EB) are carried around into zone IV and eventually the p-xylene product. In runs 6-8, PX recovery increases and PX purity goes through a maximum value with decreases in the cooler 2 temperature. The increases in both PX recovery and purity are due to the increase in selectivity at lower temperatures. With further decreases in the cooler 2 temperature, PX purity decreases because the mass transfer rate becomes much lower. Unlike the thermal effect for a four-zone SMB, for the separation of toluene and p-xylene with linear isotherms, where the raffinate purities (or B recoveries) increase and extract

Ind. Eng. Chem. Res., Vol. 46, No. 22, 2007 7217 Table 18. Simulation Conditions and Results for a Thermal Four-Zone SMB with Two Columns per Zone and Four Heat Exchangers for the Separation of C8 Aromaticsa temperature (°C) run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 a

cooler 1 170 170 170 170 160 150 150 150 150 150 150 150 148 148 148

cooler 2 170 170 170 170 170 170 160 150 150 150 150 150 150 152 152

cooler 3 170 170 170 170 170 170 170 170 168 165 160 160 160 160 162

PX (%) heater 170 173 175 180 175 175 175 175 175 175 175 174 174 174 174

purity 98.0 98.3 98.0 94.8 99.0 99.4 99.5 99.4 99.5 99.6 99.8 99.8 99.9 99.9 99.9

recovery 96.1 97.5 97.5 97.7 97.6 97.6 97.7 97.9 98.1 98.3 97.8 97.7 98.5 98.4 98.6

PRI 97.0 97.9 97.7 96.2 98.3 98.5 98.6 98.7 98.8 98.9 98.8 98.8 99.2 99.2 99.2

Flow rates are shown in Table 13, and all the flow rates are constant.

purities decrease with decreases in the cooler 3 temperature, the thermal effect in zone III is more complicated for this nonlinear system. Comparing runs 8-11, with decreases in the cooler 3 temperature, PX purity increases and PX recovery goes through a maximum value because of the increase in selectivity. PX recovery decreases with further decreases in the cooler 3 temperature because the mass transfer rates decrease. In run 11, a PX purity >99.7% with PX recovery >97% is achieved, which satisfies the industrial requirement. The temperature profile was tuned in runs 12-15. In run 13, PX purity greater than 99.9% with recovery of 98.5% is achieved by decreasing cooler 1 and the heater temperatures slightly. The best PRI achieved is 99.2% in run 15. Compared to the industrial-scale SMB systems for the p-xylene purification,79 where usually 24 columns or sections are used, the thermal four-zone SMB is a much less complicated system with only eight columns. The D/F ) 1.53 used in this study is similar to the value used in industrial-scale SMB systems. Discussion For one column per zone systems, partial feed operation will increase product purities,25,27,33,34 and shifting heat exchangers before the ports are switched should increase the separation because it will take a shorter time for the column temperatures to reach the desired values. Thermal operations can also be combined with VARICOL operations.36-38 In this study, temperature changes in the heat exchangers are assumed to be instantaneous. In reality, sufficient residence time of fluid in the heat exchangers is required, which will introduce additional lag time and broaden the thermal traveling wave. The lag time can be compensated for by adjusting the fluid flow rates as show previously. The broadening of the thermal traveling wave will reduce the separation efficiency; however, the decrease of product purity and recovery were insignificant. Although the temperature effect on fluid viscosity was included to determine the temperature effect of the mass transfer coefficient, it was not included in the calculation of pressure drops. Viscosity changes will affect the maximum allowed pressure drop for each column and pump. More importantly, viscosity changes can cause viscous fingering instabilities.9,10,85 Large axial dispersion coefficients have been used to model extracolumn dispersion and viscous fingering in isothermal SMBs9,85 and could be employed in thermal SMBs. Density

fingering could also occur in thermal SMBs but can be controlled by operating columns horizontally. Another important practical issue is the implementation of heat exchangers in thermal SMBs. Although it may be easier to couple heat exchangers with the columns, it is advantageous to have each heat exchanger stay in the same zone. Then, the inlet and outlet temperatures of the heat exchangers are constant, the heat exchangers are essentially at steady state, and less energy is used. Since they are not switched from zone to zone, the heat exchangers do not have to be identical and customized designs can be used. However, if heat exchangers stay with zones, will the leftover fluid in the heat exchanger tubes reduce the separation? For example, at the end of step 1 in Figure 2, the leftover fluid in cooler 1 is almost pure solute A plus desorbent. After switching to step 2, this heat exchanger is again used to cool zone I, but it has been switched to a different column. The feed to this heat exchanger is still almost pure solute A plus desorbent, but it may have a slightly different concentration. Cooler 3 is very similar to cooler 1 since almost pure B plus desorbent is processed. In cooler 2, the leftover fluid is a mixture of A, B, and desorbent, and the leftover fluid in the heater is almost pure desorbent. After switching, these streams remix with feed and desorbent streams, respectively. Thus, the negative effects of leftover fluids appear to be limited. The economics of different operating temperatures of the heat exchangers was not considered. For example, in some cases, the outlet temperature of a heat exchanger is zero, which will require refrigeration. A complete economic analysis is required to determine the optimum operating temperatures. Conclusions Thermally assisted SMBs operated in the traveling wave mode can significantly improve the separation, reduce the amount of desorbent, and reduce the number of columns without the limitations of radial heat transfer that occur in the direct mode. For dilute systems with linear isotherms, the SMB separations are improved significantly with thermal operation. The heat exchanger dead volume reduced the separation performance very modestly. If selectivity is approximately constant, thermal SMBs can also be operated without heat exchangers by changing the feed and desorbent temperatures. A considerable increase in separation performance is achieved with this operation mode, although the increase is less than that predicted when heat exchangers are used. For separation of a concentrated mixture of C8 aromatics with nonlinear isotherms, thermal effects are more complicated. A PX purity of 99.9% and recovery of 98.6% are achieved with thermal operation for a four-zone SMB with two columns per zone and four heat exchangers. Thermal SMB operation without heat exchangers was not successful with this system because selectivity drops at higher temperatures. Acknowledgment The assistance of Dr. Jeung Kun Kim is gratefully acknowledged. Discussions with Dr. Nadia Abunasser and Dr. Jin Seok Hur were very helpful in improving this paper. Nomenclature Ac ) cross sectional area of column, cm2 Aw ) surface area of the column wall, cm2 B, B1, B2 ) constant ci ) solute concentration of component i, g/L

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cji,pore ) volume average solute concentration in the liquid phase inside the porous particles, g/L cF ) feed concentration, g/L CP,f ) fluid heat capacity, J/g‚K CP,s ) solid heat capacity, J/g‚K CP,w ) wall heat capacity, J/g‚K dp ) particle diameter, µm dtube ) tube diameter in heat exchangers, cm D ) desorbent flow rate, cm3/min Dcol ) column diameter, cm DD ) axial dispersion coefficient in dead volume, cm2/s Dm ) molecular diffusivity, cm2/s Dmp ) effective molecular diffusivity, cm2/s DT ) thermal diffusivity, cm2/s D/F ) desorbent-to-feed ratio EB ) ethylbenzene ED ) eddy diffusivity, cm2/s EDT ) thermal eddy diffusivity, cm2/s EZ ) axial dispersion coefficient, based on superficial velocity, cm2/s F ) feed flow rate, cm3/min hw ) heat transfer coefficient, W/cm2‚K ∆Hads ) heat of adsorption, J/g ∆HA, ∆HB ) solute and solvent latent heats of vaporization at normal boiling point, kJ/kg‚K ∆Hcolumnj ) absolute heat duty of columns, eq 12 kmap ) mass-transfer resistance, 1/s Kdi ) the fraction of the interparticle volume species can penetrate KPDEB ) adsorption equilibrium constant of p-diethylbenzene, cm3/g KPX(OX, MX, EB) ) adsorption equilibrium constant of xylene isomers, cm3/g KTOL, KPX ) linear equilibrium parameter L ) column length, cm Ltube ) tube length, cm MX ) meta-xylene NPe ) tube Peclet number, ) VsLtube/DD OX ) ortho-xylene Pe ) particle Peclet number, ) Vsdp/Ez, eq 7 PX ) para-xylene q ) solute concentration on the solid phase, g/(cm3 of adsorbent) qji ) the volume average solute concentration on the solid phase inside the porous particles, g/(cm3 of adsorbent) qmPDEB ) adsorbed phase saturation concentration, kg/kg qmPX(MX;OX;EB) ) adsorbed phase saturation concentration, kg/ kg Qj ) volumetric flow rate in zone j, cm3/min Re ) Reynolds number Rreflux ) external reflux ratio of distillation column Rreflux,min ) minimum external reflux ratio of distillation column tsw ) switch time, min T ) temperature, K T h * ) volume average of stagnate fluid temperature, K Tamb ) ambient temperature, K T h s ) volume average of solid temperature, K TC ) cold temperature, K TH ) hot temperature, K TI1, TI2 ) intermediate temperatures, K us,i,j ) solute velocity, cm/s uport ) port velocity ) L/tsw, cm/s uth ) thermal wave velocity, cm/s Vj ) interstitial velocity, cm/s Vs ) superficial velocity, cm/s

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ReceiVed for reView January 9, 2007 ReVised manuscript receiVed July 9, 2007 Accepted July 26, 2007 IE070047U