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KINETICS, CATALYSIS, AND REACTION ENGINEERING Use of a Reverse-Flow Chromatographic Reactor To Enhance Productivity in Consecutive Reaction Systems Guillermo A. Viecco and Hugo S. Caram* Department of Chemical Engineering, Lehigh University, 111 Research Drive, Iacocca Hall, Bethlehem, Pennsylvania 18015
A reverse-flow chromatographic reactor can be used to improve the yield and selectivity for a consecutive reaction system (A f B f C) beyond the values obtained from conventional plugflow reactors (PFRs) in the case where the reactants are more strongly adsorbed than the products. It is also simpler than conventional chromatographic, moving, and simulated moving beds and other systems that combine reaction and adsorption separation. The results of the study show the robustness and stability of the system, its capacity to significantly improve the range of yield and selectivity that can be achieved, and the advantage of decoupling the relationship between yield and selectivity found in a PFR. 1. Introduction The reverse-flow chromatographic reactor (RFCR) is a fixed-bed reactor packed with an admixture of adsorbent and catalyst, where at least one of the reactants is fed at the middle of the reactor and where the flow direction of the carrier is periodically switched according to Figure 1. If the adsorbent has a high adsorption capacity toward the reactants, and a low one toward the products, the periodic switching of the carrier can be used to trap the strongly adsorbed reactant inside the reactor. Agar and Ruppel1 and Falle et al.2 have previously studied the RFCR with the objective of complete reactant conversion. Their study was limited to a first-order irreversible reaction, the selective catalytic reduction of NOx by NH3, where only ammonia is adsorbed and is the reactant fed at the middle of the reactor. By using the RFCR, complete conversion of NOx was predicted with little or no slip of ammonia from the system. More recently, Jeong and Luss3 revisited this problem, while Viecco and Caram4 have shown that the RFCR can significantly improve conversion for equilibrium-limited reactions. Little or no experimental information is available for the RFCR. Consecutive reactions systems of the type A f B f C or of the type S + A f B and S + B f C, where S is in excess, are of interest when the desired product is the intermediate, B. Only Hattori and Murakami,5 Takeuchi et al.,6 Schweich and Villermaux,7 and Liden and Vamling8 have considered a chromatographic reactor to carry out consecutive reactions. Of these four studies, three focused on a pulsing chromatographic reactor, while Takeuchi et al.6 considered using the countercurrent moving-bed chromatographic reactor (CMCR). Hattori and Murakami5 considered the reaction system S + A f B and S + B f C and found that an improvement in selectivity was possible by pulsing * To whom correspondence should be addressed. E-mail:
[email protected].
Figure 1. Schematic representation of a RFCR.
both reactants but no improvement was possible when only A was pulsed. Schweich and Villermaux7 studied the same system with pulsing of only A and found no improvement in selectivity, while Liden and Vamling8 only considered adsorption of B and found the same results as those in both previous investigations although with better selectivity. Takeuchi et al.6 found that the reaction system A f B f C shows improved selectivity and conversion in a CMCR when the reactant is fed somewhere in the middle of the bed and when the reactant is more strongly adsorbed than the product. The present work studies the use of a RFCR to increase the yield and selectivity in consecutive reaction systems of the type A f B f C. The yield, or productivity, is defined as the amount of desired product obtained divided by the total amount of reactant, and the selectivity is defined as the amount of desired product obtained divided by the total product obtained according to
yield ) CB,exit/CA,feed selectivity )
CB,exit CB,exit + CC,exit
(1) (2)
In a RFCR, when an adsorbent that strongly adsorbs the main reactant A is chosen, its residence time can be increased with respect to the residence time of the less adsorbed desired product B, thereby increasing the productivity of the reaction over that of conventional plug-flow reactors (PFRs). At the same time, smaller
10.1021/ie049536+ CCC: $30.25 © 2005 American Chemical Society Published on Web 04/15/2005
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reactors, or smaller amounts of catalyst (lower Damko¨hler number), are required in order to obtain the same productivity when compared to a PFR without axial dispersion being used as a reference. Also, because of the nature of the RFCR, it is possible to change the ratio of the catalyst to adsorbent, structuring the reactor packing to optimize the performance. 2. Mathematical Model A preliminary evaluation of the performance of the reactor can be obtained by modeling the RFCR as a chain of N (odd) continuous stirred tank reactors (CSTRs), as is shown in Figure 2. The tank-in-series model is used to represent two effects, the axial mixing and the interfacial mass-transfer resistance between the solid and fluid phases. Although significant effort has been devoted to relating the number of stages to physical parameters for chromatography, the number of stages will be left as an adjustable parameter. The model assumes that the reactor is isothermal, with negligible pressure drop, and the reactant is fed at the (N + 1)/2 stage. It will be assumed that the reactant concentration will be small enough that the overall flow rate will not be affected by the addition. The complete cycle is split into a forward cycle, where carrier fluid enters at the first CSTR and leaves at the Nth CSTR, and a reverse cycle. For consecutive reack1
k2
tions of the type A 98 B 98 C (C is the final product), the material balances for components A and B in the forward cycle are
Vi
Vi
dCA,i dnA,i + (1 - )Vi ) dt dt q(CA,i-1 - CA,i) - Vik1CA,i (3) dCB,i dnB,i + (1 - )Vi ) dt dt q(CB,i-1 - CB,i) + Vik1CA,i - Vik2CB,i (4)
eqs 6 and 7 can be written in dimensionless variables as
dCA,i Da C ) CA,i-1 - CA,i dτi N A,i
dCB,i Da ) γ(CB,i-1 - CB,i) + γ (CA,i - κCB,i) (14) dτi N For N stages with the same volume (V ) NVi), the resulting system of ordinary differential equations (ODEs) can be written in matrix form as
dC/dτi ) AC + F
j ) A, B; i ) 1, N
(5)
(15)
where the coefficient matrix A and the feed vector F are given in Chart 1, where CA0 is the molar feed of reactant A at the (N + 1)/2 equilibrium stage (CA0 ) nA/q). For initial conditions given by C0, the solution to this problem is widely known:
C(τi) ) eAτiC0 + [eAτi - I]F
(18)
Equation 18 only describes the system within half a cycle, when the flow direction is from the first stage to the Nth stage. Unfortunately, the initial conditions are still unknown. However, at the cyclic steady state, the concentration at the beginning of the cycle is the mirror image of the concentration at the end of half the cycle, as Figure 3 shows. Therefore
C0(τi) ) MC0(τi+δτi)
(19)
where δτi is the dimensionless half cycle time defined as
If local adsorption equilibrium between the two phases exists at each CSTR and if the adsorption equilibrium can be described by linear adsorption isotherm
nj,i ) KjCj,i
(13)
δτi )
tsq tsqN ) K′AVi K′AV
(20)
and M is the mirror matrix for a two-component system:
then the concentration in the stationary phase can be eliminated from eqs 3 and 4, yielding
K′AVi K′BVi
dCA,i ) q(CA,i-1 - CA,i) - Vik1CA,i dt
(6)
dCB,i ) q(CB,i-1 - CB,i) + Vik1CA,i - Vik2CB,i dt (7)
Defining
K′j ) + (1 - )Kj γ)
K′A + (1 - )KA ) K′B + (1 - )KB
(8) (9)
κ ) k2/k1
(10)
Da ) k1V/q
(11)
τi )
tq tqN ) K′AVi K′AV
(12)
When eq 19 is substituted into eq 18 and the resulting equation is rearranged, the initial dimensionless concentration at the cyclic steady state is then given by
C0 ) [M - eAδτi]-1A-1[eAδτi - I]F
(22)
Finally, the average concentration of the reactor can be obtained by
CA,average )
1 δτi
∫0δτ C(τi) dτ ) i
A-1 Aδτi A-2 Aδτi [e - I]C0 + [e - I]F - A-1F (23) δτi δτi
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Figure 2. RFCR represented as a series of CSTRs.
Figure 3. Reactant concentration profile as a function of the reactor number at the start (t ) τi) and at the end of half a cycle (t ) τi + δτi).
The dimensionless switching time used in the development of the model, δτi, can be more conveniently written as
tsq tsq δτi ) δτ* ) ) K′AV K′ANVi N
(24)
which allows for direct comparison regardless of the number of stages and keeps the dimensionless switching time as an independent dimensionless variable. The linear model for consecutive reaction systems has five dimensionless parameters: the Damko¨hler number, Da, the switching time, δτ*, the number of equilibrium stages, N, the reaction rate ratio, κ, and the separation factor, γ. 3. Simulation Results 3.1. Overall Conversion. The conversion of A for this consecutive reaction system is plotted in Figure 4 as a function of the switching time for several Damko¨hler numbers (N ) 51, κ ) 0.5, and γ ) 5). Damko¨hler numbers were chosen in the range 0.1-5 because they approximately correspond to conversions between 10 Chart 1
Figure 4. Average conversion of A in a RFCR as a function of the switching time for different Damko¨hler numbers (N ) 51, κ ) 0.5, and γ ) 5).
and 99% in a PFR with a first-order reaction. As the switching time decreases, the conversion increases until it reaches a plateau at very small switching times. At long switching times, conversion is very poor. Notice that a transition window, within 0.1 < δτ* < 1.0, appears between two limiting cases at long and short switching times. From the definition of the dimensionless switching time (δτ* ) tsq/VK′A), an order of magnitude analysis can be made to indicate that switching times smaller than 0.5 trap the reactant, while a switching time of 1 will allow a pulse of reactant fed at the end of the reactor to exit at the other end before reversing the flow direction. 3.2. Yield (Productivity). Figure 5 shows the yield as a function of the switching time for different Damko¨hler numbers for a RFCR. The maximum yield for the RFCR is obtained at an intermediate Damko¨hler number and switching time. At the same time, there is a wide range of Damko¨hler numbers (0.1 < Da < 2) and switching times (0.1 < δτ* < 0.7) where the maximum PFR yield is exceeded, showing the robustness and
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Figure 5. Average yield as a function of the switching time for different Damko¨hler numbers (N ) 51, κ ) 0.5, and γ ) 5).
Figure 6. Selectivity as a function of the switching time (N ) 51, κ ) 0.5, and γ ) 5).
Figure 7. Reactant (a) and product (b) concentration profiles as a function of time (N ) 51, Da ) 0.5, δτ* ) 0.2, γ ) 5, and κ ) 0.5). The arrow indicates the carrier flow direction. t1 ) 0 δτ*, t2 ) 0.25 δτ*, t3 ) 0.5 δτ*, t4 ) 0.75 δτ*, and t5 ) δτ*.
stability of the RFCR system. When the switching time is large (δτ* f ∞), the effect of adsorption and flow reversal is not important and the reactor behaves as CSTRs in series. If the switching time is too small (δτ* f 0), both A and B are trapped, resulting in the formation of the undesired product C, instead of B. The cause for the range of useful Damko¨hler numbers is simple because it is the same as that for conventional reactors. For large Damko¨hler numbers, both reactions tend to go to completion, finally decreasing the amount of B produced, while if the reactor is too small (Da f 0), then the production of B is limited by incomplete conversion of A. However, because of the trapping of the reactant inside the reactor, smaller Damko¨hler numbers than those for a PFR are required to obtain a maximum yield. In this case (N ) 51, κ ) 0.5, and γ ) 5), the optimum Damko¨hler number for a PFR is 1.38, while from Figure 5, the optimum yield for the RFCR is obtained at a Damko¨hler number of 0.5. 3.3. Selectivity. The performance of a reactor with respect to consecutive reaction systems is determined not only by the yield but also by the selectivity. In a RFCR, the selectivity is very similar to that of a PFR when only the Damko¨hler number varies. The effect of the switching time on the selectivity is seen in Figure 6. It shows that, at low switching times, because both the reactant and desired product are trapped, the selectivity is very low. As the switching time increases and it reaches the point where the product is able to escape the reactor, it starts to dramatically increase, until it reaches a value very similar to that of a PFR. When both the selectivity and yield are compared against the switching time, it can be concluded that a small increase in the switching time provides a small reduction in the yield but a large improvement in the selectivity. This is another huge potential advantage of
the RFCR because the selectivity is not dependent on the yield, and conditions (given by the Damko¨hler number and the switching time) can be chosen that either maximize the yield or minimize the formation of the undesired product C or any other function. 3.4. Transient Concentration Profiles. A better understanding of the system is obtained when the concentration profiles in the reactor are studied. Figure 7 shows the reactant and product concentration profiles during the forward half of a cycle. The reactant is clearly trapped inside the reactor, with a concentration much larger than the feed concentration, which accounts for the large conversion. On the other hand, the product travels across the whole reactor before exiting. The product concentration is also higher than the reactant feed concentration, although smaller than the reactant concentration. When both figures are compared, the relative velocity of the wave of the product and reactant given by γ is clearly seen. As the product travels across the reactor, it is initially consumed by the reaction to form the undesired product C. However, continually more B is produced by the trapped reactant, and most of it is able to exit the reactor before forming C. 3.5. Comparison with a PFR. It has already been seen that a RFCR has a better performance than a PFR for a fixed set of values of N, γ, and κ. This behavior was also studied for a wide range of values of reaction rate ratios, κ, showing consistent improvement over the maximum yield obtained by a PFR. Figure 8 shows the optimal performance of a RFCR against that of a PFR for different reaction rate ratios. The Damko¨hler numbers plotted correspond to those which maximized the yield of B, both for the PFR and for the RFCR. For the RFCR, the maximum yield was obtained at slightly different switching times for the different reaction rate ratios considered (0.21 < δτ* < 0.24). The Damko¨hler
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Figure 8. Performance improvement in a RFCR compared to a PFR as a function of the reaction rate ratio κ (γ ) 5 and N ) 51).
Figure 9. Yield as a function of the selectivity for a PFR and a RFCR (κ ) 0.5, N ) 51, and γ ) 5).
number is significantly lower in the RFCR, a potential economic advantage because it will allow reduction of the reactor volume or catalyst inventory. At the same time, as observed before, the selectivity and yield are significantly improved. In summary, not only does the RFCR require much less catalyst, but it also produces more of the desired product or less side product. The performance of a reactor for a consecutive reaction system can be evaluated from a plot of yield versus selectivity. From this plot, operating conditions that satisfy the requirements of the process can de determined. Figure 9 shows this plot for a PFR and for a RFCR. For the PFR, the selectivity and Damko¨hler number have a one-to-one relationship (there is only one Damko¨hler number that yields a given selectivity). For the RFCR, there is a new degree of freedom, given by the switching time, which allows one to obtain a given selectivity for multiple Damko¨hler numbers. In Figure 9, in which the dotted line shows the performance of the PFR, the Damko¨hler number increases as the selectivity decreases. For any Damko¨hler number for the RFCR, the switching time increases as the selectivity increases until it matches the performance of the PFR at very long switching times (δτ* > 10). Notice the large region of high yield at high selectivity that the RFCR is able to achieve. It is also important to state that if a better separation factor or a larger number of equilibrium stages describes the RFCR, this high yield and high selectivity region expands to higher values. However, it is not possible to obtain 100% yield and selectivity. The relationship between the performance of the system and the separation factor and the number of stages is complex. An increase in the difference of the
Figure 10. Yield as a function of the separation factor for different numbers of equilibrium stages (Da ) 0.5, δτ* ) 0.2, and κ ) 0.5).
residence time of the species, determined by the separation factor, inhibits the rate of the second reaction by removing B fast enough to prevent significant conversion of B to C while maintaining the same conversion of A. The degree of dispersion of the different chemical species is determined by the number of equilibrium stages. Increasing the number of equilibrium stages reduces the dispersion, which increases the conversion of A to B and of B to C. However, because A is trapped better than B, this results in a net increase in the exit concentration of B. These considerations are validated by the results shown in Figure 10. An important observation is that there is a significant improvement in the yield when the separation factor increases from 2 to 5, and for separation factors greater than 5, this improvement is not as significant. Also, a similar behavior is observed for the number of equilibrium stages. It was also observed that if the number of equilibrium stages is increased, the optimal conversion was obtained at smaller Damko¨hler numbers and longer switching times. The effect of the separation factor on the Damko¨hler number for optimal conversion is similar to the effect of the number of stages, but it decreases the switching time at the optimal conversion. These results can be explained by a steeper front and higher concentration of reactants within the front, caused by the decrease in the dispersion as the number of stages increases. The higher reactant concentration results in faster reaction rates for the formation of desired product, B. This allows for a smaller reactor and with it a decrease in the residence time of B, with a corresponding increase in the yield and selectivity. An increase in the separation factor results in shorter switching times due to the easier removal of the desired product, B, and therefore the flow direction can be reversed earlier, allowing a smaller amount of B to escape while A is still trapped. 4. Conclusions Reverse flow of the carrier is a convenient way of trapping an adsorbate in a packed bed with adsorbent. When that adsorbate reacts to form a product that is less strongly adsorbed, the observed conversion is much higher than the conversion obtained by conventional reactors. For consecutive reaction systems, improvement in the yield is observed over the maximum PFR yield, and at the same time, the selectivity is improved under the conditions at which the maximum yield is obtained.
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Because the strongest adsorbate is the reactant, the reaction removes the adsorbate and therefore there is no need for a desorption step. The limitation of trapping of the reactant, instead of one of the products, is the fundamental difference between the RFCR and other types of adsorptive reactors, with the advantage that the construction of a RFCR is much simpler than that of other adsorptive reactors. For the consecutive reaction system considered, conversion starts to decrease as the switching time and selectivity increase, until eventually both end at the value obtained for a PFR with half of the Damko¨hler number. This means that there is a maximum in the yield at some intermediate point. This yield is higher than the value obtained in conventional reactors. As in the case of the switching time there is an optimum value of the Damko¨hler number that maximizes yield. Most important is that smaller Damko¨hler numbers are required than those in any other type of reactor reported thanks to the increase in the reaction rate due to the increase in the concentration caused by the trapping of the reactant at the center of the RFCR. For this consecutive reaction system, the difference in the relative residence time between the main reactant and the desired product due to the preferential adsorption of the reactant allows increased yield and selectivity. Another important advantage is that the switching time and Damko¨hler number can be selected to maximize the yield or to maximize the selectivity for a given yield. This is something that cannot be done in conventional steady-state reactors, where the selectivity and yield cannot be independently selected. Notation V ) reactor volume, cm3 q ) carrier flow rate, cm3/min
ts ) half cycle time, min ki ) reaction rate constant of reaction i, s-1 κ ) k2/k1 ) reaction rate ratio Ki ) adsorption equilibrium constant of component i ) void fraction Ki′ ) + (1 - )Ki γ ) KA′/KB′ ) separation factor δτ* ) tsq/VKA′ ) dimensionless switching time Da ) K1V/q ) Damko¨hler number N ) number of equilibrium stages
Literature Cited (1) Agar, D.; Ruppel, W. Extended reactor concept for dynamic DeNOx design. Chem. Eng. Sci. 1988, 43 (8), 2073-2078. (2) Falle, S.; Kallrath, J.; Brockmuller, B.; Shreieck, A.; Griddings, J.; Agar, D.; Watzenberger, O. The dynamics of reverse flow chromatographic reactors with side stream feed. Chem. Eng. Commun. 1995, 135, 185-211. (3) Jeong, Y. O.; Luss, D. Pollutant destruction in a reverseflow chromatographic reactor. Chem. Eng. Sci. 2003, 58 (7), 10951102. (4) Viecco, G. A.; Caram, H. S. The reverse flow chromatographic reactor. AIChE J. 2004, accepted for publication. (5) Hattori, T.; Murakami, Y. Study on the pulse reaction technique. I. Theoretical study. J. Catal. 1968, 10, 114-122. (6) Takeuchi, K.; Miyauchi, T.; Uraguchi, Y. Computational studies of a chromatographic moving bed reactor for consecutive and reversible reactions. Chem. Eng. J. Jpn. 1978, 11 (6), 216220. (7) Schweich, D.; Villermaux, J. The preparative chromatographic reactor revisited. Chem. Eng. J. 1982, 24, 99-109. (8) Liden, G.; Vamling, L. Periodic operation of a tubular reactor: a simulation study of consecutive reactions in a chromatographic reactor. Chem. Eng. J. 1989, 40, 31-37.
Received for review May 28, 2004 Revised manuscript received March 7, 2005 Accepted March 18, 2005 IE049536+
