Optimal Distribution of Catalyst and Adsorbent in an Adsorptive

Simulation and optimization studies have been carried out using Claus process and its parametric variants as test cases. The study indicates the condi...
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Ind. Eng. Chem. Res. 2006, 45, 4911-4917

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Optimal Distribution of Catalyst and Adsorbent in an Adsorptive Reactor at the Reactor Level† Praveen S. Lawrence, Marcus Gru1newald, Wulf Dietrich, and David W. Agar* Department of Biochemical and Chemical Engineering, Institute of Chemical Reaction Engineering, UniVersity of Dortmund, Emil-Figge-Strasse 66, D-44227 Dortmund, Germany

The concept of adsorptive reactors has attracted considerable attention as a hybrid process to enhance reaction selectivity and conversion for heterogeneously catalyzed gas-phase reactions. The performance of adsorptive reactors may be enhanced by the nonuniform distribution of catalyst and adsorbent particles within the reactor and general guidelines for determining a suitable distribution are provided in this article. Simulation and optimization studies have been carried out using Claus process and its parametric variants as test cases. The study indicates the conditions under which a nonuniform distribution of catalyst and adsorbent is favorable for adsorptive reactor performance. It also shows that a nonuniform distribution is not always essential for the optimal adsorptive reactor performance and that under certain conditions a simple homogeneous distribution may well suffice. Introduction The concept of adsorptive reactors has attracted considerable attention as a hybrid process to enhance reaction selectivity and conversion for heterogeneously catalyzed gas-phase reactions. An adsorbent is employed as a selective mass source or sink for a particular reaction species (adsorbate) to create favorable concentration profiles within the reactor. Various reaction schemes have been studied experimentally and using numerical simulations to demonstrate the potential of adsorptive reactors. Table 1 presents a summary of recent work that has been carried out on adsorptive reactors. In addition to these studies, in which adsorbent is employed as mass sink/source, adsorptive reactors have also been employed to manipulate temperature profiles by using desorptive heat sinks.1 Several pioneering studies have been carried out to ascertain strategies for improving the performance of adsorptive reactors. For example, Yongsunthon and Alpay10 have studied the concept of feeding and withdrawing inlet and outlet streams at intermediate axial positions for a reaction taking place in a temperature swing reactor. They demonstrated that process performance may be improved by allowing intermediate feed introduction and product removal. The research group of Rodrigues (University of Porto, Portugal) has published many papers on methods to enhance the performance of adsorptive reactors based on their studies of the sorption-enhanced steamreforming process. They have examined the possibility of reactive regeneration techniques,11 removal of a product stream from the middle of a pressure swing adsorptive (PSA) reactor,12 and temperature profiling and nonuniform catalyst/adsorbent distribution along the reactor length to improve the utilization of the adsorbent.3 In addition to the strategies described above, some attention has also been devoted to the appropriate distribution of the catalytic and adsorptive functionalities within an adsorptive reactor. For example, in the Claus process, an optimal uniform * Corresponding author. Tel: +49(231)755-2697. Fax: +49(231)755-2698. E-mail: [email protected]. † Originally submitted for the “CAMURE” special issue, published as the December 7, 2005, issue of Ind. Eng. Chem. Res. (Vol. 44, No. 25).

catalyst to zeolite adsorbent ratio is employed along the reactor length to maximize the breakthrough time of the reactant.6 For sorption enhanced steam-reforming, a reactor with three subsections, each with a different ratio of adsorbent to catalyst, has been employed to improve the reactor performance.3 Though an improved performance is claimed, in conjunction with temperature profiling, little information is provided on the basis for choosing the different compositions and the design thus appears somewhat arbitrary. In both the above-mentioned publications, the distribution of the catalytic and adsorptive functionalities is such that finite quantities of both catalyst and adsorbent are present throughout the reactor. Recently though, a pressure swing adsorption process has been proposed for the isomerization of n-paraffin,5 in which, in contrast to the previously mentioned works,3,6 there is no overlap of the functionalities that are segregated in adjacent zones. As nparaffins adsorb more strongly than iso-paraffins, catalyst and adsorbent are employed in distinct beds, and the reactor size is minimized by varying the individual bed lengths. Thus a review of literature suggests that much effort has been expended to identify the optimal distribution of catalyst and adsorbent within the reactor, but the results have been different for each case studied, and general guidelines are lacking in this area. Though a few attempts have been made in this direction,13 so far the results seem inconclusive. The primary intention of this article is to fill these gaps and to develop some generally valid structuring guidelines. Model Reaction System The single-stage Claus process, an adsorptive reactor concept proposed previously6 by our group, has been chosen as a reference system for this study. The Claus process involves the conversion of sour gases (H2S and SO2) into elemental sulfur and water by a reversible chemical reaction. In this case, byproduct adsorption results in conversion enhancement of the equilibrium reaction according to Le Chatelier’s principle. The reaction kinetics over an γ-Al2O3 catalyst has been described with the simple power law expression given below:

2H2S + SO2 h 3/nSn + H2O ∆Had )-108 kJ/mol

10.1021/ie0502842 CCC: $33.50 © 2006 American Chemical Society Published on Web 06/06/2006

(1)

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Table 1. Compendium of Recent Publications on Reaction Schemes for Adsorptive Reactors reaction scheme A+BTC steam-reforming of methane total isomerization process (n-C5 to i-C5) Claus process HCN synthesis dehydrogenation of methylcyclohexane A+DfB+DfC

component adsorbed/ desorbed

reference

either C or A & B is adsorbed adsorption of CO2 on potassium carbonate promoted hydrotalcite adsorption of n-C5 on 5A zeolite adsorption of H2O on 3A zeolite adsorption of CO2 on LiZrO3 clay-based adsorbents desorption of reactant D

Arumugam et al.2 Xiu et al.,3 Hufton et al.4

Table 2. Model Parameters and Correlations Used in the Case Study component pH2S pSO2 pN2  p Di L u

Table 3. Combination of Rate Constants and Equilibrium Constants for Different Data Sets Analyzed in This Study

inlet composition 0.1 bar 0.05 bar 0.85 bar 0.4 0.5 0.2 m2/h 1.5 m 0.15-0.35 m/s

Here, n ≈ 8:

rV,i )

(

250 °C 1.013 bar 2-8 mm 0.06 m Wakao and Funazkri14

T P dp D kfilm & Dax

νik1 pH0.95 p0,22 2S SO2

)

pH0.99 2O mmol Keq s kgcat

case

k1, mmol/ (s kgcat mbar1.17)

k2, mmol/ (s kgcat mbar0.99)

Keq, mbar-0.18

equilibrium conversion, Xeq (%)

A (Claus) B C D E F

0.0303 0.0309 0.0303 0.0113 0.0845 0.1888

0.0010 0.5957 0.0484 0.0484 0.0177 0.1321

29.28 0.052 0.626 0.234 4.76 1.429

96.9 8.9 51.7 29.4 86.8 69.4

propriate k2 values so as to give lower reaction equilibrium constant values (Keq).

(2)

where Keq ) k1/k2 is the reaction equilibrium constant. The water vapor formed is adsorbed on a 3A zeolite with the adsorption equilibrium being described using a Freundlichtype isotherm:

∆Had ) -30.5 kJ/mol qH2O ) KF,H2OcH0.75 2O

Al-Juhani and Loughlin5 Elsner et al.6 Elsner et al.6 Alpay et al.8 Kodde et al.9

(3)

The model parameters required have been obtained from literature data6,15 or calculated using empirical correlations and

Figure 1. Variation of Thiele modulus with particle diameter at reactor entrance conditions for constant diffusivity.

are summarized in Table 2. As our interest in this work is to develop generic guidelines for the distribution of catalyst and adsorbent particles, we have used the Claus kinetics as the base case and extended the study by varying the kinetic parameters (k1 and k2) and other process parameters. Table 3 indicates the various combinations of kinetic parameters used in this work. Figure 1 shows the effect of particle diameter on Thiele modulus (φ) for the Claus reaction at reactor inlet conditions. The low Thiele modulus values suggest that the reaction kinetics are not particularly fast. Considering the reaction kinetics and high reaction equilibrium values for Claus process (equilibrium conversion is 96.9%), we focused our additional studies on reaction systems with higher (or similar) k1 values and ap-

Modeling An unsteady-state heterogeneous two-phase dispersion model with internal pore diffusion describing the dynamic behavior of a fixed-bed adsorptive reactor with separate catalyst and adsorbent phases has been developed. The model is based on the following simplifying assumptions: • the fluid in the particle pores and the internal adsorbent/ catalyst surface are in equilibrium • the adsorption process is assumed to exhibit only macropore and film transport limitations. The effect of micropore transport limitation is neglected. This assumption limits the applicability of the results to adsorbents such as alumina, silica, activated carbon and molecular sieve carbons, though not for zeolites (transport within micropores also needs to be considered for zeolites). • the adsorption process is assumed to be highly selective. It should be noted that this assumption may well not be realistic for physisorption processes, but is probably reasonable for chemisorption processes. • the physical structure of the particles can be idealized as porous spheres with a uniform pore structure • particle size and structure were averaged for all particles in order to permit a direct comparison of different particle and reactor configurations • backmixing in bulk fluid phase flow is lumped into an axial dispersion coefficient term • the gas phase behavior obeys the ideal gas law • heat effects are neglected and the reactor is operated isothermally • the volume change due to reaction is neglected. This is justified due to the high dilution of the reaction system with 85% inert. • the bed is assumed to be free of any adsorbate at the start of the adsorption cycle. Particle Model. Inside the particles the mass transfer is described using an effective pore diffusion model and the following expression gives the mass balance for the adsorbent and catalyst particle:

(

)

∂cp,i ∂cp,i 2 ∂2cp,i ) Deff,i + 2 - (1 - p)rV,ads,i ∂t ∂r r ∂r

p

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Here, for all compounds except H2O, rV,ads,i ) 0:

(

)

∂cp,i ∂cp,i 2 ∂2cp,i ) Deff,i + 2 - (1 - p)rV,cat,i p ∂t ∂r r ∂r

(5)

The boundary conditions for the particle mass balance are derived by assuming a linear concentration profiles in the particle boundary layer (eq 6) and symmetric profiles within the particles (eq 7).

kfilm,i(ci - cp,i|r)Rp) ) Deff,i

∂cp,i | ∂r r)Rp

∂ci | )0 ∂r r)0

(6) (7)

Reactor Model. The particle models are incorporated in a fixed-bed reactor, and a one-dimensional axial dispersion model is used to describe the reactor fluid bulk phase (eq 8). The third term on the right-hand side of eq 8 accounts for the mass transfer from the fluid bulk phase to the catalyst and adsorbent particle each weighted according to the contribution of the volume fractions of the particles in the fixed-bed:

∂2ci ∂ci ∂ci 3  ) -u + Dax 2 - (1 - ) (fx,adskfilm(ci ∂t ∂x R ∂x p cp,ads,i|Rp) + fx,catkfilm(ci - cp,cat,i|Rp)) (8) The reactor boundary conditions have been chosen assuming closed vessel behavior:

u(ci (x ) 0, t) - c0,i) ) Dax

∂ci (x ) 0, t) ∂x

∂ci (x ) L, t) )0 ∂x

(9) (10)

At the outset of each reaction cycle the reactor contains just an inert component:

ci (x, t ) 0) ) 0, cp,i (r, t ) 0) ) 0

(11)

Numerical Solution. The model has been implemented in Aspen Custom Modeler (ACM) with a modular model structure and solved using the method of lines. The spatial domain has been discretised using backward finite difference method with 100 finite elements for the reactor length axis and on 28 elements over the particle dimension, with the central finite difference on the radial axis of the particle being allocated in such a manner so as to obtain an equivalent volume increment grid. This procedure ensured a better numerical resolution of the particle mass balances by using incremental control volumes of equal size. Optimization Procedure As one can see from the equations, this modeling study has been restricted to the adsorption step in an adsorptive reactor process. Any study on the optimal distribution of functionalities in an adsorptive reactor is deemed to be complete if and only if both the adsorption and desorption steps of an adsorptive reactor are considered. It is known from standard works on adsorption processes17 that more than one method is available for regeneration and, very often, a combination of different methods is required for an efficient desorption. In addition to the well-known nonreactive desorption techniques, reactive

desorption techniques have also been suggested11 to improve the performance of adsorptive reactor. This provides one with numerous options to consider when studying the optimal distribution of catalyst and adsorbent in an adsorptive reactor. Thus, the choice of a particular regeneration strategy for an overall optimization study to develop the proposed structuring guidelines would have introduced an arbitrary element into the analysis. Furthermore, as any catalyst in an adsorptive reactor acts merely as an inert during the desorption step (unless the catalyst possesses strong adsorbing properties toward the adsorbate or under reactive desorption conditions), the inclusion of the desorption step is not expected to alter the results presented in our article significantly. Moreover, for a given reactor volume and feed conditions, the process cycle time is a direct indication of the productivity of the process. For this reason, the cycle time has been chosen as a suitable indicator of the process performance. As will be explained later, at any given time, the behavior in different sections of an adsorptive reactor are governed either by reaction or sorption. This suggests that the optimal distribution may result in arrangement where the catalyst and adsorbent volume fractions vary with position along the reactor. To calculate the optimal nonuniform distribution in an adsorptive reactor, we have carried out optimization studies by subdividing the optimization space into discrete sections. Though it might be more desirable to obtain a continuous optimal activity distribution profile along the reactor length, the problem is simplified by this discrete approach, which is found to be entirely adequate. It should be noted that comparable studies on catalyst dilution for smoothing reactor temperature profiles have revealed only modest sensitivities for influence of the precise fixed-bed structure on the performance. In this study, the reactor has been divided up into 13 discrete sections. Within any discrete element, the optimizer is given the freedom to choose the fraction of catalyst/adsorbent, subject to process constraints. The definition of the optimization is thus as follows:

objective function: maximum process cycle time, τ variable constraints: 0 < fcatj < 1 fcatj + fadsj ) 1 where j ) 1, 2, 3, ..., 13 (segment number) process constraints: actual conversion, X(t) g desired minimum conversion, Xmin For any given reactor length and feed flow rate conditions, the cycle time is a direct measure of the extent of the adsorbent utilization and thus deemed to be an appropriate optimization criterion for the process. As mentioned above, dynamic simulation studies have been carried out using ACM, while the feasible path successive quadratic programming optimizer, (FEASOPT), which is part of the ACM, has been used to carry out dynamic optimization. FEASOPT employs a reduced space optimization method to arrive at the optimal solution. It evaluates the objective variable (cycle time) at the current point and moves the design variables (catalyst fraction values) to take the objective variable toward its optimum value. After solving with the new values of the

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Figure 2. Influence of catalyst volume fraction on process cycle time under homogeneous distribution condition.

design variables, FEASOPT re-evaluates the objective variable. In this way, it steps toward the optimum solution. FEASOPT solves the simulation at each step subject to simulation equations, variable bounds, and any constraints applied to the optimization. Results and Discussion As the primary aim of this paper is to demonstrate the importance of the distribution of catalyst and adsorbent particles in an adsorptive reactor, we shall deal with the process architecture at three different levels: • A constant volume of catalyst and adsorbent (uniform distribution) at every location in reactor. Here, the catalyst and adsorbent are present in separate particles (conventional adsorptive reactor). This is termed homogeneous axial distribution. • A variable volume of catalyst and adsorbent (nonuniform distribution) at every location in reactor. Here again, the catalyst and adsorbent are present in separate particles (conventional adsorptive reactor). This is termed a macrostructured distribution. • A combination of catalyst and adsorbent within the same particle is referred to as micro-integrated particles. A macrostructured distribution of micro-integrated particles can be envisaged, as can the microstructuring of the adsorptive and catalytic functionalities within the particle. In this paper, we shall confine our discussions to the first two levels alone. The third level will be the subject of a future article. We shall use one of the test cases (case E) to study the performance improvements that may be achieved by carrying out structuring at different levels. The following considerations are based on the following operating point: Xequ ) 86.8%, u ) 0.3 m/s, dp ) 2 mm, Xmin ) 96%. Level 1: Homogeneous Axial Distribution of Catalyst and Adsorbent Particles. This is the simplest method of distributing catalyst and adsorbent within a reactor. The catalyst and adsorbent are present in separate particles and the same volume fraction of catalyst (and adsorbent) is present at every location in reactor. The optimal catalyst fraction is the value, which for minimum conversion level desired, offers the longest cycle time. Figure 2 shows the existence of such an optimal catalyst fraction in this test case. Essentially, when too little catalyst is present in the reactor, reaction ceases to occur resulting in the early breakthrough of the reactants resulting in a lower cycle time. On the other hand, when the catalyst fraction is too high, the reaction is pushed toward equilibrium and with too little adsorbent in the reactor, the reaction ceases to occur beyond equilibrium and the conversion quickly drops to equilibrium value upon adsorbent saturation. By choosing the optimal ratio,

Figure 3. Variation of approach to equilibrium along the axial space at different process time for the test case.

we strike a balance between breakthrough of reactant due to lack of reaction beyond equilibrium due to absence of adsorbent (right of the optimal point in Figure 2) or too little reaction (left of the optimal point). Since the homogeneous distribution is deemed to be the simplest of structuring approaches, we shall take this optimal cycle time to be the benchmark value and compare the performance obtained at the next level against this result. Level 2: Nonuniform Axial Distribution. At the previous level, though the choice of the optimal value results in the longest possible cycle time, the results provides very little clue as to the utilization of the catalyst and adsorbent functionalities. Any tool that might indicate the extent of utilization of functionalities may help us ascertain the true optimal nature of the result. One approach to indicate their utilization is to use the approach to equilibrium parameter (Λ), a direct measure of the reaction driving force at any spatial location within reactor defined by

Λ)

∏i ciυ Keq

i

)

pH0.99 2O

k2

pH0.95 p0.22 k1 2S SO2

(12)

For Λ ) 1, the reaction is at thermodynamic equilibrium; Λ > 1, forward reaction occurs; Λ < 1, backward reaction occurs. Figure 3 shows the variation of the approach to equilibrium parameter for the test case at its optimal homogeneous distribution for different process times prior to breaching the process constraint. This graph is typical for any reversible reaction taking place in an adsorptive reactor. To obtain useful information from the variation of Λ in the reactor, the reactor is divided in to 3 segments and each segment analyzed separately. Segment 1. In this segment, the value of Λ is always greater than 1 and is virtually a constant with time. The meagre product concentration in this segment exerts a negligible influence on the reaction rate, and the segment is kinetically controlled. Thus, any adsorbent present in this segment plays only a passive role in its performance. Segment 2. In this segment, the value of Λ is a function of position and time. At any point, while the adsorbent is unsaturated, Λ is greater than 1. Upon adsorbent saturation, however, the value of Λ attains 1, and this indicates reaction equilibrium. Though the zone is kinetically governed initially, the imposition of the sorption regime renders any catalyst present in this segment ineffective. This ineffective utilization of the catalyst further strengthens the case against the global nature of the optimal homogeneous axial distribution results.

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Figure 4. Comparison of the optimal catalyst functionality distribution in the case of homogeneously distributed adsorptive reactor (filled points) and the optimally macrostructured adsorptive reactor.

Segment 3. The behavior of this segment is similar to segment 2 and may be considered as its extension. What distinguishes these two segments is that, unlike segment 2, the adsorbent in segment 3 remains unsaturated even up to the breach of the process constraint. Hence, this section is kinetically controlled throughout the process cycle. The existence of the third segment is attributed to the minimum conversion constraint imposed on the process, and such a constraint is a logical criterion for industrial applications. For example, in the Claus process, the desired conversion is determined by environmental legislation, which typically demands a minimum sulfur recovery of 99.5% (German environmental standards).16 Similarly, in the case of hydrogen production for fuel cells by sorption enhanced steamreforming process, Xiu et al.3 impose a minimum methane conversion of 50%. It is thus clear from the previous discussion that, at any time, different regimes govern an adsorptive reactor. This leads one to question the true optimal nature of the results from the homogeneous distribution studies. This warrants a macrostructuring optimization study where the catalyst and adsorbent particles are nonuniformly distributed along the reactor. To carry out this level 2 optimization study, the reactor is divided into 13 segments, and catalyst fraction in each segment is assigned to be a design variable, which may be altered by the optimizer to arrive at the optimal value of the objective variable (process cycle time). Figure 4 shows the nonuniform distribution derived for the discussed test case. The result shows a distribution where a pure layer of adsorbent is sandwiched between layers of catalyst at the reactor exit and entrance corresponding to the existence of kinetic regimes at the reactor entrance and exit, and an intermediate sorption regime between them, strongly reflecting the conclusions drawn from the approach to equilibrium study (Figure 3). This optimal distribution of catalyst and adsorbents yields an increase in the process cycle time over the homogeneous distribution (level 1). The improvement in process cycle time over homogeneous distribution is significant and may be as high as 150%. It should be noted that this performance gain is dependent on the desired minimum conversion, an aspect which will be discussed later. As indicated earlier, the increase in the performance may be attributed to a more effective allocation of catalyst and adsorbent within reactor. For the test case, when the desired minimum conversion is set to 96%, macrostructuring results in a 30% reduction in the catalyst consumption over the uniform axial distribution case. Though this reduction in the catalyst amount may appear significant, owing to its low absolute value (change from 0.19 to 0.14 volume fraction of bed), this would correspond

Figure 5. Comparison of progression of adsorbate concentration fronts in a macrostructured adsorptive reactor and homogeneously distributed adsorptive reactor. The filled data points correspond to the homogeneous distribution case and the empty ones correspond to the macrostructured adsorptive reactor.

to only a 6% increase in adsorbent volume in the reactor bed. This marginal increase in adsorbent volume does not allow one to claim that performance improvement by macrostructuring is due to an increase in the adsorbent volume in reactor. The progression of the adsorbate concentration fronts provides a more plausible explanation for the differences in performance. It is known from the literature17 that the shape of an adsorbate concentration front is primarily governed by the sorption isotherm and to a lesser extent by the transport limitations and axial dispersion in an absorber bed. These hydrodynamic parameters tend to widen the adsorbate concentration front and, hence, accelerate front breakthrough. In the case of a nonuniform distribution (Figure 4), the adsorbent section is essentially decoupled from the catalyst beds, and its performance is governed only by adsorption separation principles. Under homogeneous distribution conditions, there is a simultaneous formation of adsorbate in segment 1 and segment 2. Though the reaction occurring in segment 2 is much less than in segment 1, it influences the adsorbate concentration front in a fashion similar to transport resistances resulting in a widening of the front and culminates in the early breakthrough of the front. Figure 5 compares the development of adsorbate concentration fronts in the two functionality distributions. This analysis confirms that the process improvement by macrostructuring is not due to the increase of adsorbent volume in bed, but rather due to the more effective utilization of individual functionalities. It is thus obvious that macrostructuring of adsorptive reactors is crucial for its optimal performance. As a consequence of structuring, the adsorbent is well-utilized without any additional complication in the reactor design. So far, we have demonstrated the impact of structuring using a test case. Now, to generalize the results of this study, we will present similar structuring studies for different combinations of kinetic parameters, under different desired minimum process conversion constraints and process parameters. Figure 6 shows the influence of structuring an adsorptive reactor for different equilibrium constants. The continuous solid line shows the variation of equilibrium conversion against the reaction equilibrium constant. For any desired conversion below the equilibrium line, there is little justification for employing an adsorptive reactor and a conventional heterogeneously catalyzed gas-phase reactor is adequate. The data points correspond to the case studies that have been studied, and the adjoining numbers indicate the increase in the performance of a macrostructured adsorptive reactor over homogeneously distributed adsorptive reactor. Optimal Macrostructuresalternate Catalyst and Adsorbent Layers? It is interesting to note that structuring has the

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Figure 6. Influence of structuring on the performance of an adsorptive reactor for different values of reaction equilibrium constant. The numbers indicate the increase in performance of macrostructured adsorptive reactor over homogeneously distributed adsorptive reactor.

Figure 7. Effect of minimum conversion on the optimal macrostructure for the case, k1 ) 0.447 and Keq ) 0.23.

Figure 8. Development of adsorbate concentration fronts in the case of multiple alternate layer catalyst and adsorbent arrangement for 55% minimum conversion for case D.

potential to enhance the process performance in excess of 100% when desired conversions are close to reaction equilibrium values, while it loses its relevance as more stringent conversion demands are made, with greater deviations from the equilibrium value. For a low desired minimum conversion, a macrostructured reactor resembles a reactor-in-series arrangement, where an adsorber bed is sandwiched between two catalyst beds. The volume of these catalyst beds is fixed by the reaction kinetics and mass transport limitations of the system. The total volume of the catalyst is divided between the two beds, and it is known from the approach to equilibrium studies that the catalyst is divided such that the beds are kinetically controlled throughout the process. Moreover, as the desired minimum conversion is increased, additional catalyst is required to meet the stricter reactant breakthrough requirements. This results in the loss of the reactor-in-series structure and the actual structure tends toward a homogeneous distribution, rendering macrostructuring irrelevant. Figure 6 shows the gradual transition of functionality distribution in macrostructured reactors for the test case with

increasing levels of minimum conversion. So far, we have demonstrated that the macrostructuring results in a reactor-inseries arrangement where an adsorbent bed is sandwiched between two catalyst beds. From one point of view, this optimal macrostructure is nothing more than the simplest arrangement of alternative layers of catalyst and adsorbent in a reactor. At this juncture, the natural question that arises is whether multiple alternating layers of catalyst and adsorbent would yield an optimal solution to the problem of macrostructuring. The following analysis provides an answer to this question and describes the conditions under which such a structure is appropriate. To explain this phenomenon, we shall take the results from the test case D, where the reaction equilibrium constant is fairly low (Keq ) 0.23) limiting the equilibrium conversion to 29.4%. A nonuniform distribution of catalyst and adsorbents results in an improvement in performance up to a desired minimum conversion of around 75%. Beyond this conversion, the macrostructuring loses its efficacy, and a macrostructured distribution performs as well as a homogeneous distribution. For a desired conversion of 40%, the optimal nonuniform distribution is found to be reactor-in-series arrangement where a single adsorbent bed is sandwiched between two catalyst beds. As the desired minimum conversion is increased to 55%, a nonuniform distribution is still found to be the optimal distribution. However, the more stringent process constraints demand a higher volume of catalyst, and the two catalyst bed distribution can no longer be structured such that they both operate under kinetically controlled regimes throughout the process cycle. This constrains the optimizer to distribute the catalyst in more than two beds. For the case of 55% desired conversion, the optimizer suggests the distribution of catalyst in three beds with two adsorbent beds sandwiched between them (Figure 7). Figure 8 illustrates the development of the adsorbate concentration front when the desired conversion is set to 55%. On further increase in the desired conversion to 75%, a macrostructured distribution tendstowardahomogeneousdistributionwithcomparableperformance. It should be noted here that this multiple alternate catalyst and adsorbent beds are found to be optimal only for low equilibrium constant values (typically less than one), and at high reaction equilibrium values this gradual transition is less conspicuous. Conclusions and Future Work In this work, we have attempted to understand the influence of the distribution of catalyst and adsorbent particles on the performance of an adsorptive reactor. Parametric studies were carried out using the kinetics of the Claus process as the reference case. A simplified model was used to carry out the simulations. Using numerical simulations and optimization studies, we first demonstrated the need to employ an optimal ratio of catalyst to adsorbent in an homogeneously distributed adsorptive reactor. Subsequently, we identified the shortcomings of a homogeneous distribution in an adsorptive reactor and showed that the optimal solution commonly lies in a nonuniform distribution of catalyst and adsorbent in the reactor. We have identified conditions under which macrostructuring is appropriate and the conditions under which it would lose its efficacy. This paper thus provides some generic guidelines for the distribution of catalyst and adsorbent functionalities within an adsorptive reactor. It is known that the performance of any heterogeneously catalyzed reaction system is usually subject to transport resistances and adsorptive reactors are no exception to this rule.

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One possible approach to reduce transport limitations is to locate the catalyst and adsorbent activities within the same particle. In the future, we intend to analyze the benefits of this microintegration approach to improve the performance of an adsorptive reactor. In the case of micro-integration, the catalyst and adsorbent are uniformly distributed within a multifunctional adsorptive catalyst particle. It is also known from the literature18 that a prudent nonuniform distribution of catalytic activity within a particle can perform better than a uniform distribution. Thus, instead of a simple micro-integration of catalyst and adsorbents, the catalyst and adsorbent may also be nonuniformly distributed within the particle to further enhance the performance of the adsorptive reactor. This microstructuring will also be the subject of future work. Acknowledgment We would like to thank Deutcshe Forshungsgemeinschaft (DFG) for their support to this work through the “Integrierte Reaktions- und Trennoperationen” project (DFG/ FOR 344). Nomenclature ci ) bulk phase concentration [mol/m3] c0,i ) reactor inlet concentration [mol/m3] cp,i ) particle concentration [mol/m3] Di ) molecular diffusion coefficient [m2/s] Dax ) axial dispersion coefficient [m2/s] Deff,i ) effective pore diffusion coefficient Deff,i ) Di/τ [m2/s] fx,ads ) adsorbent particle fraction in conventional reactor [-] fx,cat ) catalyst particle fraction in conventional reactor [-] KF,i ) Freundlich constant [(mol/m3)0.25] Keq ) equilibrium constant, water-gas shift reaction [-] k1 ) forward reaction rate constant, Claus reaction [mol/bar1.25 m3 s] k2 ) reverse reaction rate constant, Claus reaction [mol/bar m3 s] kfilm,i ) external particle mass transfer coefficient [m/s] L ) reactor length [m] pi ) partial pressure [bar] qH2O )mol of adsorbate per volume of adsorbent [mol/m3] Rp ) particle Radius [m] r ) radial coordinate [m] rV,ads,i ) adsorption rate [mol/m3 s] rV,cat,i ) reaction rate [mol/m3 s] t ) time [h] τ ) cycle time [h] u ) superficial gas velocity [m/s] Vp ) particle volume [m3] X ) conversion x ) axial coordinate [m] Greek Letters  ) reactor void fraction [-] p ) particle porosity [-] ν ) stoichiometric coefficient [-]

τ ) particle tortuosity factor [-] Λ ) approach to equilibrium [-] Φ ) Thiele modulus [-] Subscripts ads ) adsorbent particle cat ) catalyst particle equ ) equilibrium min ) minimum Literature Cited (1) Richrath, M.; Gru¨newald, M.; Agar D. W. Temperaturregelung auf partikula¨rer Ebene durch Kopplung von Reaktion und Desorption: Teil I. Accepted for publication in Chem.-Ing.-Tech. (2) Arumugam, B. K.; Wankat, P. C. Pressure transients in gas-phase adsorptive reactor. Adsorption 1998, 4, 345-354. (3) Xiu G. H.; Li, P.; Rodrigues A. E. New generalized strategy for improving sorption-enhanced reaction process. Chem. Eng. Sci. 2003, 58, 3425-3437. (4) Hufton, J. R.; Mayorga. S.; Sircar. S. Sorption-enhanced reaction process for hydrogen production. AIChE J. 1999, 45 (2), 248-255. (5) Al-Juhani A. A.; Loughlin K. F. Simulation of a combined isomerization reactor and pressure swing adsorption unit. Adsorption 2003, 9, 251-264. (6) Elsner M. P.; Dittrich C.; Agar D. W. Adsorptive reactors for enhancing equilibrium gas-phase reactionssTwo case studies. Chem Eng. Sci. 2002, 57 (9), 1607-1619. (7) Elsner M. P.; Menge M.; Mu¨ller C.; Agar D. W. The Claus process: teaching an old dog new tricks. Catal. Today 2003, 79-80, 487494. (8) Alpay E.; Chatsiriwech D.; Kershenbaum. L. S. Combined reaction and separation in pressure swing processes. Chem. Eng. Sci. 1994, 49 (24B), 5845-5864. (9) Kodde, A. J.; Fokma, Y. S.; Bliek, A. Selectivity effects on series of reactions by reactant storage and PSA operation. AIChE J. 2000, 46 (11), 2295-2304. (10) Yongsunthon, I.; Alpay, E. Design of periodic adsorptive reactors for the optimal integration of reaction, separation and heat exchange. Chem. Eng. Sci. 1999, 54, 2647-2657. (11) Xiu G. H.; Rodrigues A. E. Sorption enhanced reaction process with reactive regeneration. Chem. Eng. Sci. 2002, 57, 3893-3908. (12) Lu Z. P.; Rodrigues A. E. Pressure swing adsorption reactors: Simulation of three-step one-bed process. AIChE J. 1994, 40, 1118-1137. (13) Lee I. D.; Kadlec R. H. Effects of adsorbent and catalyst distributions in pressure swing reactor. AIChE Symp. Ser. 1984, 84, 167176, 264. (14) Wakao, N.; Funazkri, L. T. Effect of fluid dispersion coefficients on particle-to-fluid mass transfer coefficients in packed beds. Chem. Eng. Sci. 1978, 33, 1375-1384. (15) Elsner, M. P. Experimentelle und modellbasierte Studien zur Bewertung des adsorptiven Reaktorkonzeptes am Beispiel der ClausReaktion. Ph.D. Dissertation, University of Dortmund, 2004. (16) TA Luft. 1986, Deutschland, Nr. 2.5.1 (17) Yang, R. T. Gas Separation by Adsorption Processes; Series of Chemical engineering, Vol. I; Imperial College Press: 1997. (18) Morbidelli, M.; Servida, A; Varma, A. Optimal catalyst activity profiles in pellets 1. The case of negligible external mass transfer resistance. Ind. Eng. Chem. Fundam. 1982, 21, 278-284.

ReceiVed for reView March 1, 2005 ReVised manuscript receiVed May 30, 2005 Accepted June 9, 2005 IE0502842