"Laboratory Catalytic Reactors: Aspects of Catalyst

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Handbook of Heterogeneous Catalysis, 2nd Ed. Edited by G. Ertl, H. Kn ..... tory riser reactor for fluid catalytic cracking (FCC) [30, 31]. It consists of a folded ...
2019

9

Laboratory Testing of Solid Catalysts 9.1

Laboratory Catalytic Reactors: Aspects of Catalyst Testing1

In the development of catalysts for new processes or the improvement of existing catalytic systems, various stages can be distinguished, as exemplified by Fig. 1. This development process covers the whole range from the new idea for a process or catalyst via catalyst preparation, catalyst screening, establishing reaction networks, kinetic studies and life tests to scale-up to pilot-plant level before a new or modified process is introduced. During the development, there will be continuous feedback from one activity to another to optimize the catalyst and/or the process. The number of catalyst formulations will decrease during development, but the equipment size and man-hours required increase and thus the costs involved. This demands for an efficient and proper approach for laboratory-scale experimentation. The objectives of the different development stages vary:

automation and miniaturization of the test equipment. This field is often referred to as ‘‘combinatorial chemistry’’ or ‘‘high-throughput experimentation’’. It started in the pharmaceutical industry, but in the past decade also has proven to be a useful approach in catalyst development studies. • Establishing the reaction network by the wealth of techniques at the disposal of catalyst researchers gives insight into how the catalyst works and provides the basis for the kinetic modeling studies. • The time-consuming kinetic studies are indispensable for process design, operation and control. A description is needed of the reaction rate as a function of the process variables, i.e. temperature, pressure and composition of the reaction mixture. • Life studies are intended to test the catalysts during a longer time-on-stream, often on a bench or pilot scale, with real feed and recycle streams. The latter are included to investigate the effect of trace impurities or accumulated components, not observed in laboratoryscale experiments. It is often desired to test the catalyst in the shape used for practical application. Here the need exists for experimental results that can be directly linked to commercial applications.

• Screening must provide the first, rough data on the activity and selectivity of the various catalyst formulations as a function of their composition and preparation and pretreatment history. As there are many variables, a large number of catalysts should be screened at a high throughput rate. The catalysts can then be compared based on their activity per unit mass, active phase or volume, depending on the specific goals. Often a first insight into the deactivation behavior, i.e. The catalyst stability, is obtained simultaneously. In this stage, potentially interesting catalysts are identified. Because of the large number of measurements that must be carried out, there is a continuing trend towards

Although they may be part of a catalyst testing [1–3] program, investigations focused on revealing the reaction mechanism, e.g. in situ FTIR in transmission or reflection mode, NMR, XRD, EXAFS, XPS, EM, ESR, UV–visible, and the reaction cells used are not treated in this chapter. For the correct interpretation of the results, however, this chapter may also provide a worthwhile guide. Various types of reactors can be applied and it is of primary importance to select the proper reactor to obtain the required information, which generally means that one should not mimic the reactor type in which the process will be carried out (no ‘‘Dinky

1 A list of symbols used in the text is provided at the end of the chapter. ∗ Corresponding author.

References see page 2043

Freek Kapteijn and Jacob A. Moulijn∗

9.1.1

Introduction

Handbook of Heterogeneous Catalysis, 2nd Ed. .. .. Edited by G. Ertl, H. Knozinger, F. Schuth, and J. Weitkamp Copyright  2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-31241-2

2020

9.1 Laboratory Catalytic Reactors: Aspects of Catalyst Testing

Mechanism Combinatorial stage

Screening

n tio iza tim Op

Prepration

Kinetics

Quantification stage

Reaction network Kinetics Increasing: Time Money Reality Fig. 1

Stability

Catalytic reaction engineering

Stability tests Scale-up

Stages in a catalyst development program.

Reactor engineering

Transport phenomena Catalyst

Toy’’ approach). The criteria for the selection of a reactor for catalyst testing are different from those for the selection of an industrial reactor. Scaling down as far as possible is desirable for reasons of lower equipment costs, lower materials consumption, less waste formation, lower utility requirements, reduced demands on laboratory infrastructure and increased intrinsic safety (reduced hazards of toxic emissions, explosions and fires). A smaller scale, however, requires a more accurate experimentation and the use of representative (catalyst) samples. In the laboratory, catalysts are often tested using a packed bed contained in a reactor through which a reaction mixture flows (Fig. 2). On the reactor level the fluid seems to flow as a front through the bed (‘‘plug flow’’), but due to the flow around the catalyst particles mixing (‘‘dispersion’’) may occur on the particle size level. This may affect the reactor performance. Along the length of the bed, reactants will be gradually converted. Reactants have to diffuse from the bulk of Mixing dispersion

Plug flow

Diffusion Reaction Transport phenomena

Transport phenomena in a catalytic packed bed reactor on different levels.

Fig. 2

Fig. 3

Catalytic reaction engineering.

the fluid through a stagnant layer around the particles to the exterior surface and subsequently through the pore system to an active site where they can react. Products proceed in the opposite way. Heat produced or consumed will have to be removed or supplied at a sufficient rate, otherwise temperature gradients may develop locally to an undesired level. The description of these phenomena is the subject of catalytic reaction engineering [4–10], which integrates catalysis, reactor analysis and transport phenomena to aid in procuring and interpreting data on catalyst activity, stability, kinetics and reaction mechanisms (Fig. 3). With the goal of obtaining intrinsic catalyst properties (reaction kinetics and selectivities) from experimental data without being disguised by the above-mentioned phenomena, the following conditions should be fulfilled: • effective contact between reactants and catalyst • absence of mass and heat transport limitations inside and outside the catalyst particles • good description of reactor characteristics, with welldefined residence time distributions under isothermal conditions (ideal systems). Generally, this implies the use of ideal reactor types such as the plug-flow reactor (PFR) and the continuously stirred tank reactor (CSTR). By-passing of part of the catalyst by channeling in a packed bed or uneven flow distributions must be avoided. In three-phase systems (gas–liquid–solid), the even distribution of both fluid phases over the catalyst is crucial, while the gas to liquid mass transfer should not be limiting.

9.1.2 Reactor Systems

In this chapter, criteria will be derived that can be used to check whether one operates under conditions that result in deviations of not more than 5% in reaction rate from the ideal situation. This can be expressed as follows: rateobserved = 1 ± 0.05 rateideal

(1)

The various aspects that are to be considered to achieve a proper and efficient catalyst testing approach are presented for heterogeneous systems in which the catalyst is the solid phase and the reactants are in the gaseous and/or liquid phase. The presence of a solid phase introduces complicating phenomena on which this chapter focuses. The solid catalyst can be present in a variety of forms. Fixed-bed configurations are often the most convenient. They can be based on random packings or on structured packings, such as washcoated monoliths. Systems in which the catalyst is not in a fixed position are also widely applied. The most commonly used reactors of this type in catalyst testing are slurry reactors.

2021

Classification Catalytic reactors can globally be classified according to their mode of operation: under steady-state or transient conditions, as indicated in Fig. 4, or according to the contacting/mixing mode, as indicated in Fig. 5 for a fluid–solid system. In both schemes good contact between catalyst and reaction mixture is assumed. Figure 4 represents a classical classification based on mode of operation. Steady-state reactors, especially packed-bed reactors, are most widely used in catalyst testing, predominantly because of the ease of operation and the low costs. Transient operation is less common and has some disadvantages for the mere goal of catalyst testing. In batch reactors, possible deactivation during the extent of the experiment cannot be established, except by verification afterwards by repeating the experiment. Pulse reactors, such as the TAP (temporal analysis of product) and the Multitrack, operate under catalyst conditions that are completely different from those in steady-state operation. An exception is transient operation by using isotopically labeled species under steady-state 9.1.2.1

9.1.2

Laboratory catalytic reactors

Reactor Systems Transient

Steady state

Various laboratory reactors have been described in the literature [3, 11–14]. They depend mainly on the type of reaction system that is investigated: gas–solid (GS), liquid–solid (LS), gas–liquid–solid (GLS), liquid (L) and gas–liquid (GL) systems. The first three are intended for solid or immobilized catalysts, whereas the last two refer to homogeneously catalyzed reactions, which will not be discussed here. The presence of two reaction phases (gas and liquid) should be avoided as much as possible for ease of data interpretation and experimentation. Premixing and saturation of the liquid phase with gas can be an alternative in this case. One must be sure that in the analysis, the catalyst does not further affect the composition of samples taken from the reactor contents or product stream.

Fig. 5

Batch

Continuous flow

Mixed flow

Plug flow Integral

Semi-batch

Discontinuous Step

Pulse

Differential

Single pass

Recycle

External Riser reactor

Fluidization Internal

Berty reactor

Thermobalance Packed bed

Fluid bed Slurry

TAP Multitrack

Classification of laboratory reactors according to mode of operation.

Fig. 4

References see page 2043

1

2

3

4

5

6

7

8

Classification of laboratory reactors according to contacting mode.

2022

9.1 Laboratory Catalytic Reactors: Aspects of Catalyst Testing

conditions, such as the positron emission profiling technique (see Chapter 6.5). Transient operation is mainly applied for obtaining mechanistic information and for establishing reaction networks [15], but the steadystate isotope transient kinetic analysis (SSITKA) [16–21] approach yields both steady-state information and that of individual reaction sequences. The classification in Fig. 5 serves for the description of the reactors used. Here two ideal contacting types are used, the plug-flow mode and the ideally mixed mode, both for the fluid and the solid phase. By application of the design equations of these ideal reactor types, the experimental results are interpreted in a straightforward manner. For two phases, two contacting types and two operation modes (batch and flow), eight combinations arise. Some laboratory reactors are easily recognized; the packed-bed plug-flow reactor (PFR) (type 1), the internalor external-recirculation reactor (CSTR) with fixed catalyst bed (type 2), the (circulating) fluid-bed reactor (FBR) (type 3), the fluid bed with recycle (type 4), the slurry reactor (type 4), the riser reactor (type 5), the riser reactor with recycle (type 6), the (circulating) fluid bed reactor with continuous catalyst feed (type 7) and the slurry reactor or fluid bed with recycle of fluid and continuous catalyst feed (type 8). Types of Laboratory Reactors There is usually no single best laboratory reactor that could be used for all types of reactions and catalysts. In this section, we discuss the various types of reactors that can be chosen for catalyst screening and/or obtaining the kinetic parameters for a specific reaction system. Table 1 gives 9.1.2.2

Tab. 1

a generalized comparison of frequently used laboratory reactors. More advanced laboratory reactor systems are discussed in Section 9.1.8. 9.1.2.2.1 Gas–Solid and liquid–Solid Reactions The most commonly used (‘‘the workhorse’’) and simplest type of laboratory reactor for gas–solid reaction systems is the packed-bed tubular reactor (Fig. 6). It consists simply of a reaction tube in which the catalyst is held between plugs of quartz wool on a sintered frit or wire mesh gauze. Depending on the reaction conditions, the tube consists of glass, quartz, steel or ceramic (SiC, alumina). For low temperature and pressure glass can be used, high pressure requires steel, high temperature requires quartz or ceramics. The latter are especially suited for high-pressure–high-temperature applications [22] where most steel alloys lose their strength. Its optimal internal diameter amounts to 4–6 mm, predominantly to ensure good heat transport to or from the catalyst [23]. The reactor may have a straight or U-shape or a concentric geometry, with the catalyst in the inner tube [22]. The porous catalyst may be diluted with an inert material with good heat conductivity (SiC) to improve heat transfer and to satisfy plug flow criteria; see Section 9.1.2.5. An inert material may be placed before and after the bed for preheating the fluid phase and avoiding fluidization in up-flow configurations. The packed-bed reactor can also be used for liquid–solid reactions. For low conversions, the packed-bed reactor is operated in the differential mode, and for high conversions in the integral mode. By recirculation of the reactor exit flow one can approach a well-mixed reactor system, the CSTR.

Summary of relative reactor ratings (L = low, M = medium, H = high)

Aspect

Ease of use Ease of construction Cost Ease of sampling and analysis Approach to ideal type Fluid−catalyst contact Isothermicity Temperature measurement Kinetics Deactivation noticed GLS use

Reactor type PFR Differential fixed bed

PFR Integral fixed bed

PFR Solids transport (riser)

CSTR External recirculation

CSTR Internal fluid recirculation

CSTR Spinning catalyst basket

Batch Internal fluid recirculation

H H L M

H H L H

H L H L

M−H M L−M H

M M M−H H

L−M L−M M−H H

M M M M

H H H H

H H M−H H

M M H H

H H M−H H

M−H M−H H M−H

L−M L−M M L

H H H H

H H L−M

H H M−H

M L L

M M M−H

M−H M M−H

L−M M M

M L H

9.1.2 Reactor Systems

2023

Union

O-ring seal

Ceramics coupling

Nut

Swagelok coupling

Inert Catalyst

Quartz wool

Thermocouple

Quartz tube U-shaped Fig. 6

Concentric

Packed bed reactor designs. Examples of geometries and connections.

Internally mixed

Externally mixed

(a) Berty-type

(b)

Carberry-type

Basket designs for Carberry-type reactors: (a) flat blade; (b) pitched blade.

Fig. 8

Schematics applications.

Fig. 7

of

CSTRs

for

heterogeneous

catalysis

An interesting concept is the catalytic wall reactor, in which – as the name suggests – the catalyst is applied to the reactor wall [24, 25]. This type of reactor is particularly suitable for kinetic studies of fast, highly exothermic (or endothermic) reactions, because rapid heat removal (or addition) is possible, ensuring isothermal conditions. A disadvantage of the catalytic wall reactor may be the existence of radial mass transport limitations, which can partly be solved by filling the reactor tubes with inert particles of good heat conductivity [25]. Various designs exist to approach the ideal CSTR or gradientless reactor (Fig. 7) for gas–solid and liquid–solid reactions [4, 11, 26, 27]. A number of configurations are commercially available. Two approaches are followed: either the catalyst is placed in baskets and rotated, the Carberry type [4], or the fluid phase is circulated internally at a high rate, the Berty type [11], or externally by means of a gas pump (membrane, piston, plunger or centrifugal types) or liquid pump [11]. A major problem in gas–solid reactors is achieving good contact between the two phases.

Various basket designs have been proposed to optimize gas–catalyst contact. Figure 8 shows the original Carberry basket in the form of a four-bladed stirrer and a more recent pitched-blade stirrer, claimed to have good mixing properties [7, 26, 28]. The temperature of the catalyst bed cannot be measured in the Carberry-type reactor and highly endo- or exothermic reactions are to be avoided. Figure 9 shows an example of the Berty-type reactor, the RotoBerty reactor. The catalyst is packed in the inner tube to avoid local maldistribution and catalyst by-passing. Monolithic catalysts are ideal for use in these reactors because of their intrinsic low pressure drop. Various stirrer designs exist to create good mixing and even twostage impellers are applied. These stirrers, with speeds up to 10 000 rpm, are usually actuated by feedthrough of the stirrer axis or by magnetic coupling. Since most magnets have their Curie point, i.e. lose their magnetism, at relatively low temperatures, this coupling occurs outside the oven section. Feedthroughs may result in leakages, References see page 2043

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9.1 Laboratory Catalytic Reactors: Aspects of Catalyst Testing

Riser oven Products

Catalyst N2

Oil heating

Oil feed

Preheating catalyst Fig. 10 Schematic of a laboratory-scale microriser reactor set-up for FCC investigations.

Two-stage rotor

Shaft Feed

Fig. 9

Product

Layout of the RotoBerty reactor.

and magnetic coupling may give rise to non-ideal mixing due to the presence of areas without convection. As a result of the low conversion over the catalyst bed, isothermal conditions are approached more easily than in packed-bed reactors. In LS systems, mixing is less problematic and the catalyst is not necessarily held in a packed bed, but can be suspended in the fluid with measures to prevent washing out of the reactor and accumulation at the exit: the slurry reactor (see Section 9.1.2.2.2). Compared with the simple packed-bed reactor, the reactor volume of CSTRs is much larger, often >100 mL, while the amount of catalyst per unit volume is at least two to three times smaller. This implies that on changing the conditions, one should take into account the physical residence time of the reactor before considering the system to have reached a new steady state. This may be appreciable, depending on the pressure and feed flowrates used. Also, deactivation of the catalyst is not so directly noticed for the same reason. It is self-evident that all CSTR systems may operate as batch reactors, in which the composition changes as a function of time (transient operation), when the inlet and outlet lines are closed. An example is the determination of the cis–trans equilibrium for 2-butene by means of the metathesis reaction in an externally recirculated (membrane pump) system [29].

A disadvantage of batch operation is that catalyst deactivation cannot be followed, unless the experiment can be repeated with the same catalyst sample. A special case in kinetic studies is the modeling of catalyst deactivation. For moderately decaying systems, sequential experimental design is recommended (see Chapter 6.1). Here, new experiments are carefully planned on the basis of previous results, using a packedbed reactor. In the case of rapidly deactivating catalysts, these have to be fed continuously to the reactor together with the feed. A relatively new development is the laboratory riser reactor for fluid catalytic cracking (FCC) [30, 31]. It consists of a folded tubular reactor to which the catalyst and evaporated reactants are co-fed and both travel through the system in plug flow (Fig. 10). Various reactor elements can be connected to vary the length. This system results in more representative data than the so-called micro-activity test (MAT) of ASTM [3], in which a certain amount of liquid feed is pushed through a packed bed of catalyst. The reason is that the time-scale of the reactions and especially that of coke deposition – in the order of milliseconds – is much better mimicked in the riser reactor than in the fixed-bed reactor. Another approach for FCC kinetic studies was described by Kraemer et al. [32]. They use an internally recirculated reactor containing the catalyst in a basket, in which it is fluidized by the recirculating gas. A small pulse of reactant is allowed to react for a short time, after which the reactor is purged. This procedure is repeated a number of times to map the catalyst activity as a function of time. The aim is to give a mapping along the length of a riser reactor. 9.1.2.2.2 Gas–Liquid–Solid Reactions Under conditions of good wetting (see Section 9.1.2.5 and Ref. [33]), a packed-bed reactor can be used in trickle flow, i.e. with downflow of gas and liquid, for gas–liquid–solid systems.

9.1.2 Reactor Systems

Laboratory trickle-flow reactors are not very good tools for quantifying reaction kinetics, because fluid dynamics and reaction kinetics are so closely interlinked that their effects on conversion are practically inseparable [34]. Stirred-tank reactors are the predominant reactors used for studying heterogeneously catalyzed gas–liquid reactions. Stirred-tank slurry reactors (usually autoclaves), in which small catalyst particles (1–200 µm) are suspended in the liquid either by mechanical agitation or by the gas flow, can be operated both batchwise and (semi-)continuously. Temperature control is relatively easy due to the large amount of liquid present. Also, the liquid–solid contact area is relatively large and the intraparticle diffusion distances are small. Disadvantages are the potential non-uniform distribution of the catalyst particles in the reactor and the poor gas–liquid mass transfer. Also, filtering the catalyst from the liquid mixture may be problematic. A commonly used stirred-tank reactor system for studying gas–liquid and gas–liquid–solid reactions is the autoclave equipped with gas-inducing impeller. The gas is sucked in through the impeller, creating gas bubbles in the liquid [35]. Most laboratory units are dead-end autoclaves with only feed of the reactant gas by keeping the pressure constant (semi-batch operation). This implies that it is relatively difficult to determine gas–liquid mass transfer [36–39] (see also Section 9.1.3.4). An elegant solution for internally mixed reactors that avoids the use of feedthroughs or voluminous magnetic couplings is the swinging capillary stirrer [40] (Fig. 11). A capillary is welded to the lid of the reactor and sealed at the bottom and equipped with a stirrer blade. From the top a bent rod (piano string) is inserted in this capillary and turned around. This yields a swinging movement and effective mixing and can be used in LS and GLS reactions under high pressures in autoclave reactors. The compact design reduces the reaction volumes to 10 mL and enhances the safety. An alternative to slurry reactors for solid catalyst particles with sizes suitable to be retained by a wire mesh (>1 mm) are the basket reactors discussed in Section 9.1.2.2.1, but adapted for gas–liquid–solid reactions. A popular gas–liquid–solid gradientless laboratory reactor is the Robinson–Mahoney reactor (Fig. 12), in which the gas–liquid dispersion is forced through a stationary catalyst bed. Impellers draw fluid into the center of an annular catalyst basket. The reactor is suitable for high-pressure and high-temperature reactions. Two alternative types of internal recirculation reactors have been proven successful for kinetic investigations: the turbine reactor, in which the gas–liquid mixture is transported back to the top by turbine blades located in the

Fig. 11

2025

Schematic of a microautoclave with swinging capillary

stirrer.

outer annulus of the reactor (Fig. 13) [41], and the screw impeller stirred reactor, having the screw in the central shaft (Fig. 14) [42]. Design Equations To relate the reaction rate or conversion, pressure drop and temperature variation in a catalytic reactor with the operating variables of a reactor, flow-rate, catalyst amount etc., so-called mass, heat and momentum balances are being used in catalytic reaction engineering [4, 8]. In this chapter, it is assumed that the catalyst bed is isothermal 9.1.2.3

References see page 2043

2026

9.1 Laboratory Catalytic Reactors: Aspects of Catalyst Testing

Fig. 12 Schematic of a Robinson–Mahoney reactor (Autoclave Engineers).

and the pressure drop over the bed is negligible. This leaves only mass balances for each reactant or product to be considered. For a component i this mole balance can be written for part of or the whole catalyst bed as inputi − outputi + productioni = accumulationi

(2)

where the production term refers to both production (positive) and consumption (negative) contributions. Under steady-state conditions, the accumulation term vanishes, simplifying the resulting expression. This approach yields the following expressions for a component i and a single reaction: PFR :

CSTR :

dxi   = −νi r W d Fi0 W Fi0

=

xiout − xiin −νi r

(3)

(4)

As the conditions in the CSTR are the same everywhere, the mass balance is considered over the whole reactor, resulting in an algebraic expression relating the reaction rate directly to the measured conversion. For the PFR, only a small slice of the bed can be considered to have constant conditions, leading to a differential equation which describes the conversion as a function of the amount of catalyst. For low conversions, the rate can be

Fig. 13 Schematic of turbine reactor for multiphase kinetic measurements.

considered to be constant over the bed and the expression can be simplified to that of a CSTR (differential reactor). At high conversion, the rate varies over the bed length and the reactor operates under integral conditions. Variation of the space time W/Fi0 yields the corresponding conversion data. By numerical differentiation, rates can be estimated that can be compared for different catalysts. Differential conditions at high conversions, especially of interest for practical applications, can be achieved by using an upwind reactor to attain the desired conversion level, followed by a differential reactor. This requires highly accurate analyses to determine the minor composition changes over the catalyst bed. In general, catalyst activities are compared by comparison of the conversion levels at equal space times, preferably at low conversion levels (‘‘initial reaction rates’’). At high conversions, the reaction rate is much less sensitive and wrong conclusions may be drawn, especially with respect to selectivities (see later).

9.1.2 Reactor Systems

2027

equation (=W/Fi0 ). This exponential behavior can easily be verified experimentally. In recirculation reactors, frequently a recirculation ratio Rc (ratio of the flow returned to the inlet and the flow leaving the reactor) larger than 20 is recommended [11, 26]. This criterion is not complete, as is apparent from literature [43–45]. One can demand that the rate over the catalyst bed may not change more than 5%, thus for an nth-order isothermal reaction n  r(cin , T in ) cin rate at inlet of bed = = rate at outlet of bed r(cout , T out ) cout  n x = 1+ (1 − x)(1 + Rc ) = 1 ± 0.05

(6)

which yields the following criterion: x 0.05 < (1 − x)(1 + Rc ) n

Fig. 14 Schematic of screw impeller stirred reactor for multiphase kinetic measurements.

The CSTR and PFR are the two extremes of continuous reactor types, one with extremely good mixing and the other without. A number of criteria or methods exist to judge whether one can use one of these reactor models. CSTR The most commonly used CSTRs in heterogeneous catalysis are recirculation reactors (gas–solid, liquid– solid, gas–liquid–solid systems) and well-stirred vessels (liquid–solid, gas–liquid–solid systems). Injection of a δ-pulse of a tracer should produce an exponentially decaying output concentration: 9.1.2.4

c(t) = c0 exp(−t/τ )

This criterion implies that the necessary recirculation ratio is not a fixed value, but depends on the reaction under consideration and the conversion level. At low conversions, the recirculation rate does not need to be high according to this criterion [of course, good mixing, Eq. (5), is still required to avoid dead zones in the reactor] and in fact a differential PFR model can be used. At high conversions, the recirculation rate must increase. It can easily be seen that a recirculation ratio of 20 limits the conversion for a first- and second-order reaction to 50% and 25%, respectively. The problem with verification of these criteria is the calculation of the recirculation ratio. No general relation is valid and it must be estimated for each reactor configuration by experimentation; see, e.g., Refs. [26, 44]. PFR PFR systems can be described by an infinite number of CSTRs in series. A packed bed can be considered as a finite number of CSTRs, each corresponding to a certain height of a slice of the catalyst bed, also referred to as the equivalent height of mixing. Reducing the bed length will increase the deviation from plug flow towards more axial mixing. This is also described by the axial dispersion model, in which the dimensionless P´eclet number, Pe, is used as parameter. The relation between Pe and the number N of mixers in series for large N is 9.1.2.5

(5)

where τ represents the average physical residence time in the reactor system (=Ntot,R /Ftot,out ), which should not be confused with the space-time used in the mass balance

(7)

2N = Pe =

Lb Lb u = Pep Dax dp

References see page 2043

(8)

9.1 Laboratory Catalytic Reactors: Aspects of Catalyst Testing

For a sufficiently close approach to ideal plug flow, N or Pe should exceed a certain value that depends on the degree of conversion and on the reaction order. Gierman [46] refined the criterion of Mears [47] and arrived at Eq. (9), which can also be used for monoliths. In the latter case, the axial dispersion coefficient should be replaced by the smaller molecular diffusivity, thus relaxing the criterion for monolithic elements as compared to packed beds.   1 (9) Pe > 8n ln 1−x Evaluation of literature data on the correlation between the particle P´eclet number (also referred to as the Bodenstein number) and the particle Reynolds number for single-phase and trickle flow yielded Fig. 15. At low Rep ( ln (10) dp Pep 1−x Taking Pep = 0.5 for the low Reynolds region of interest for laboratory-scale operation, it is possible to calculate the minimum reactor length for a given reaction order, conversion and particle size. Alternatively, a maximum allowable particle diameter can be calculated for a reactor of a given length. Figure 16 gives the maximum allowable particle diameters for a first-order reaction and various reactor lengths. For trickle-flow reactors the reactor lengths should be 10 times larger at the same particle diameter, due to the lower Pep value for this case. In PFRs, not only the reactor length but also the diameter plays a role in its plug-flow performance. Close

100

Pep

Single phase flow 10−1

10

dt = 50 mm

dp,max / mm

2028

dt = 5 mm Lb = 10 mm 0.1

dt = 1 mm Lb = 1 mm 0.01 0.01

10−1

100

101

102

103

Rep Fig. 15 Relation between the P´eclet particle and Reynolds particle numbers for single-phase and trickle flow. Adapted from Ref. [46].

1

Fig. 16 Maximum allowable particle diameter as a function of (1 − x) for plug-flow behavior (first-order reaction, single phase) at different bed lengths and for a flat velocity profile for different reactor diameters.

to the wall the packing density is lower than that in the interior because of the presence of a flat wall surface. The higher voidage implies a lower resistance to flow and higher local velocities are to be expected. On the other hand, the radial mixing effects in the packed bed may relax this influence. To avoid these phenomena, as a rule of thumb the following condition should be satisfied [48]: dt > 10 dp

(11)

The maximum allowable particle diameters for typical reactor diameters are included in Fig. 16. Especially at low conversion levels, the last criterion is more severe at a given reactor length, while with increasing conversion the axial dispersion criterion should be satisfied. In ideal trickle-flow reactors, all particles in the catalyst bed take part in the overall reactor performance, since each is surrounded, ‘‘wetted’’, by the liquid phase that flows around it. Situations in which the liquid preferentially flows through a certain part of the bed, while the gas phase predominantly flows through another part, should be avoided [34]. In such cases, part of the bed is not contacted by the liquid reactant at all and does not contribute to the overall conversion. To avoid this maldistribution, Gierman [46] proposed the following criterion for the wetting number Wtr for concurrent downflow operation: Wtr =

10−2

0.1

(1– x)

Trickle flow 10−2 −3 10

Lb = 100 mm

1

vl u l > 5 × 10−6 dp 2 g

(12)

The main variables that dictate the uniformity of catalyst irrigation are the liquid velocity, the particle diameter and the kinematic viscosity of the liquid. Figure 17 shows the maximum allowable particle diameter for several reactor

9.1.2 Reactor Systems

of the reaction rate constant from the ideal situation:

10

≡ Lb = 1000 m

1

=

Lb = 100 m Lb = 10 m

0.1 10−7

10−6

10−5

nl /m2 s−1 Fig. 17 Maximum allowable particle diameter as a function of the kinematic viscosity for complete wetting in trickle-flow reactors.

lengths as a function of the kinematic viscosity at constant liquid hourly space velocity. From the foregoing, it will be clear that the particle size is a major factor to be considered in the application of small reactors. Obviously, catalysts in the commonly used form of extrudates of e.g. 1–3 mm in diameter can only be tested in a large reactor at the pilot-plant scale. Although these particles can be crushed to the size suitable for testing in laboratory reactors, this is not always desired. Sometimes performance data are needed under conditions where internal diffusion gradients exist, to be able to predict industrial operation. The catalyst may also be of the eggshell type or have another defined concentration profile of the active phase that is not to be destroyed. A way to satisfy the criteria of small particle size and yet to use the full-size catalyst is to dilute the large catalyst particles with fine inert particles. In this way, the hydrodynamics and kinetics are decoupled [34]. The fine particles dictate the hydrodynamic performance, i.e. The plug-flow and wetting behavior, while the catalyst particles determine the kinetic behavior. Needless to say that bed dilution is also applicable in the case of small catalyst particles to obtain a sufficient bed length. This dilution technique has been successfully applied for years in hydrotreating research using trickle-flow reactors [34]. The optimal and most reproducible way of packing a reactor with large and fine particles is according to the dry method. First, the reactor is packed with the large particles, followed by packing this prepacked bed with the fine particles while vibrating the reactor, using a sufficiently low flow-rate to avoid segregation [49]. One should be careful, however, with the degree of dilution. A too dilute system, especially in the case of equal sized particles, may lead to uneven distribution and bypassing of the catalyst. Berger et al. [50] evaluated this problem and derived an expression to estimate the deviation ()

xundiluted bed − xdiluted bed b nxdp ≈ xundiluted bed 1 − b 2Lb bnxdp < 0.05 2L0

(13)

where L0 is the undiluted bed length and b the volume fraction of diluent. This criterion is valid at low conversion (x < 0.5) and reaction orders n ranging from 0 to 1. It imposes constraints on the maximum particle size as a function of bed dilution and vice versa, as represented graphically in Fig. 18 for various bed lengths. In general, samples should not be diluted more than 5–10-fold. In kinetic investigations, the measured conversions are used to calculate the rate coefficient, e.g. to determine the apparent activation energy of the catalytic reaction. For an irreversible first-order reaction, the reaction coefficient can be calculated directly from the conversion using   1 1 (14) ln k= 1−x (W/Fi0 ) pi,0 Therefore, in most cases it is more useful to calculate the deviation of this k instead of the deviation of xi . If this is done using Eq. (13), the following expression for the deviation of the rate coefficient (k ) is obtained, defined similarly to  in Eq. (13): kundiluted bed − kdiluted bed kundiluted bed   1 − x(1 − ) ln 1−x   = 1 ln 1−x

k =

(15)

10

dp,max / mm

dp,max / mm

2029

Lb = 1000 mm

1

Lb = 100 mm Lb = 10 mm

0.1

0.01 1

0.1

Fraction of catalyst (1 – b) Fig. 18 Maximum allowable particle diameter as a function of the catalyst fraction (1 − b) in a diluted bed; nx = 0.2. References see page 2043

2030

9.1 Laboratory Catalytic Reactors: Aspects of Catalyst Testing

This imposes limits on the particle size at large fractions of inerts. It is recommended, however, that the preparation method should be improved. Visual inspection of the sample batches often already indicates its (in)homogeneity.

0.99 Axial dispersion criterion 0.20

0.98

b

0.95

0.10

0.90

0.05

0.80 0.50

∆k = 0.005

0.00 0

0.2

0.4

0.6

Summary of Laboratory Systems Usually small amounts of catalyst are applied in laboratory reactors, ranging from 10 to 1000 mg, with gas flow-rates between 10 and 1000 mL min−1 (STP). This depends largely on the reactor type used. PFRs cover the whole spectrum with diameters ranging from a few to 20 mm, while CSTRs generally need more catalyst and higher flow-rates due to their dimensions. Using packed beds in the latter necessitates the use of larger particles to overcome the pressure drop problem to obtain high recirculation rates [42]. This is not always acceptable. In this respect, monolithic catalysts are easier to use in CSTRs due to their intrinsic low pressure drop. Some practical advantages/disadvantages of commonly used reactors are: 9.1.2.6

0.02 0.01

0.8

1

x Calculated effect of conversion and dilution on k , the relative deviation in the first-order rate coefficient calculated from the conversion, using Eq. (15) for an Lb /dp ratio of 100. Dashed lines represent the criterion for neglecting the effect of axial dispersion at Wcat /F 0 = 5.58 × 105 g s mol−1 and Wcat + Wdil = 400 mg.

Fig. 19

Figure 19 shows the results of this calculation for several selected values of k as a function of the dilution and the conversion for a constant Lb /dp = 100. The figure should be read as follows: an experiment at x = 0.5 and b = 0.95 (and Lb /dp = 100) will result in a deviation of the calculated rate coefficient due to the dilution (k ) of approximately 7%. The shaded area in Fig. 19 corresponds to conditions where the deviation exceeds the criterion of 5% deviation and it should be avoided in particular if the aim is to measure intrinsic reaction kinetics. Generally, one should try to avoid the combination of a high degree of bed dilution and high conversion levels. It should be noted that Eq. (13) and hence also Eq. (15) have not been validated at conversion levels above 0.75 and dilutions below 0.8, but they can be used as a safe rule of thumb. The plug-flow criterion for 5% deviation of the conversion due to axial dispersion is also included in Fig. 19. The small dark shaded area corresponds to conditions where this deviation exceeds the criterion of 5%. This criterion is easily satisfied due to the high Lb /dp ratio used as a consequence of the application of a high degree of dilution. This is not generally valid; dilution is used to satisfy this criterion, amongst other uses, but on the other hand it creates a deviation in the observed conversion. Hence there should be a dilution degree at which both criteria will yield similar constraints. This dilution degree depends strongly on the system in question. One should also be cautious with too much dilution for reasons of sample inhomogeneity. Catalyst batches may contain particles of different activities, due to incomplete wetting during preparation or, more frequently, during impregnation. If too few particles are being used, the sample may not be statistically representative.

• PFR: deactivation noted directly, small amounts of catalyst needed, simple, yields primarily conversion data not rates • CSTR: larger amounts of catalyst and flows needed, deactivation not immediately determined, direct rate from conversions • FBR: no ideal reactor behavior, continuous handling of solids possible • batch: catalyst deactivation hard to detect, yields quickly conversion and selectivity data over wide conversion range. More detailed discussions of laboratory reactors can be found elsewhere [3, 12, 13, 51]. 9.1.3

Mass and Heat Transfer

Due to the consumption of reactants and the production or consumption of heat, concentration and temperature profiles can develop in the stagnant zone around the catalyst particle and in the particle itself (Fig. 20). In this section, criteria are derived to ensure that the effect of these gradients on the observed reaction rate is negligible [4, 23, 52]. In gas–liquid–solid slurry reactors the mass transfer between the gas and liquid phase also has to be considered [9, 53]. Here, the focus will be on solid-catalyzed single-phase reactions. Extraparticle Gradients Extraparticle mass and heat transfer are most conveniently analyzed by means of the so-called film model, in which 9.1.3.1

9.1.3 Mass and Heat Transfer

orders and exothermic reactions. For an isothermal, nthorder irreversible reaction, this results in the following criterion:

Gas film

Ts T c

Cs

Ca < Tb

T

Cb

0.05 |n|

(20)

Analogously to mass transfer, the following equation is used for external heat transfer:

c

Bulk gas Exothermic

2031

− a  h(Tb − Ts ) = rv,obs (−Hr )

(21)

Endothermic

Combination with Eq. (17) yields Temperature and concentration gradients in and around a catalyst particle for exo- and endothermic reaction. Fig. 20

the flux from the bulk fluid to particle is defined in terms of mass and heat transfer coefficients kf and h, respectively. A mass balance over the film layer yields Ap kf (cb − cs ) = Vp rv

(16)

This expression shows that the mass transfer rate is proportional to the concentration difference over the film. The observed reaction rate can then be expressed as follows: rv,obs = r(cs ) = a  kf (cb − cs )

(17)

where a  = Ap /Vp is the specific particle area (m−1 ). No transport limitations exist if cs ≈ cb . But how can we determine the concentration at the surface cs ? In order to relate cs to observable quantities, a dimensionless number Ca, the Carberry number [8], is introduced as follows: Ca =

rv,obs a  kf (cb − cs ) cb − cs = =  a kf cb a  kf cb cb

(18)

where a  kf cb is the maximum mass transfer rate, which is obtained when the surface concentration equals zero (this corresponds to the best catalyst possible). Ca relates the concentration difference over the film to procurable quantities and is therefore a so-called observable [4]. A criterion for the absence of extraparticle gradients in the rate data can be derived from the definition of an effectiveness factor for a particle. This should not deviate more than 5% from unity as criterion: observed reaction rate rate at bulk fluid conditions rv,obs (cs , Ts ) = = (1 − Ca)n = 1 ± 0.05 rv,chem (cb , Tb )

ηe =

(19)

The − sign applies to positive reaction orders and endothermic reactions and the + sign to negative reaction

Ts − Tb kf cb (−Hr ) cb − cs = = βe Ca Tb hTb cb

(22)

where βe is called the external Prater number. This represents the maximum relative temperature difference over the film or the ratio between the maximum heat production and heat transfer rates. For rather general kinetics, the effectiveness factor definition can be approximated as rv (cs , Ts ) kv (Ts ) f (cs ) kv (Ts ) = · ≈ rv (cb , Tb ) kv (Tb ) f (cb ) kv (Tb )    Ea Tb = exp − − 1 = 1 ± 0.05 RTb Ts

ηe =

(23)

with the assumption that heat effects dominate the transport limitations, so for small Ca values. Series expansion of the exponential leads to a simple result:      Ea rv,obs  (−Hr )kf cb  |γb βe Ca| =  < 0.05 RTb hTb kf a  cb  (24) A result like this is rather logical since it contains the three groups that determine the overall process. The Carberry number determines the concentration drop over the film, the Prater number determines the maximum temperature rise or drop (exothermic or endothermic reaction) and the dimensionless activation energy expresses the sensitivity of the reaction towards a temperature change. Both criteria for extraparticle gradients contain observables and can be calculated based on experimental observations of reaction rates. For heat and mass transfer coefficients in packed beds, various correlations exist in terms of dimensionless numbers. Table 2 summarizes the most appropriate ones for laboratory reactors [5, 7, 54, 55]. Values of kf and h for gases in laboratory systems range between 0.1 and 10 m s−1 and between 100 and 1000 J K−1 s−1 m−2 , respectively. In References see page 2043

2032

9.1 Laboratory Catalytic Reactors: Aspects of Catalyst Testing Correlations to calculate mass and heat transfer coefficients in packed beds [5, 7, 54, 55] and monoliths [56–58]

Tab. 2

Packed beds: Mass transfer

Heat transfer

Sh =

kf dp D1f

Nu =

Sc =

µf ρf D1f

Pr =

Range of validity

hdp λf

Rep =

ρf udp µf

µf Cˆ pf λf

Gases Sh =

1 0.357 Rep 0.641 Sc 3 εb

Sh ≈ 0.07Rep

Nu =

1 0.428 Rep 0.641 Pr 3 εb

Nu ≈ 0.07Rep

3 < Rep < 2000 0.1 < Rep < 10

Liquids Sh =

1 0.250 Rep 0.69 Sc 3 εb

Nu =

1 0.300 Rep 0.69 Pr 3 εb

55 < Rep < 1500

Sh =

1.09 13 1 Rep Sc 3 εb

Nu =

1.31 13 1 Rep Pr 3 εb

0.0016 < Rep < 55

Monoliths:   dH 0.45 Sh = Nu∞ 1 + B1 ReSc L   dH 0.45 Nu = Nu∞ 1 + B1 RePr L where ρ udH Re = f µf √ εM δ w 4Ach dH = = √ 1 − εM Och and Nu∞ = 2.976(square) 3.657 (circular) 3.660 (hexagonal) B1 = 0.095 (catalytic monoliths)

the case of monoliths, other correlations should be used because of the different geometry [56–58]. Intraparticle Gradients Since the reactants have to diffuse to the active sites in the interior of the catalyst particles and meanwhile they can react, a concentration profile can develop over the particle diameter. Mathematically, this is described by a differential equation derived from a mass balance over a small shell of the catalyst particle. This reads, for a slab geometry and first-order irreversible reaction: 9.1.3.2

Deff

d2 c − kv c = 0 dz2

(25)

where Deff is the effective diffusivity and kv the rate constant based on unit volume of catalyst. The effective diffusivity depends on the morphology of the porous material. For large pores (>∼10 nm) the diffusivity is determined by the molecular diffusivity (∼10−4 − 10−5 m2 s−1 for gases), and in the case of small pores by the Knudsen diffusivity (∼10−6 − 10−7 m2 s−1 ). The molecular diffusivity of species i in the fluid can be calculated by correlations [5, 6] or by extrapolation from a known value at other conditions of temperature and pressure, using the dependence Df ,i ∝

T 1.75 ptot

(26)

9.1.3 Mass and Heat Transfer

The Knudsen diffusivity of species i in a cylindrical pore of radius r0 equals  T (27) DK,i = 97r0 Mi In the transition region, the Bosanquet equation, which accounts for both contributions, can be used: 1

1 1 = + D D D K,i f ,i

(28)

In zeolitic materials, in which the molecules are of pore size dimensions, activated configurational diffusion takes place, for which even lower diffusivity values, below 10−8 m2 s−1 , hold [59]. In this case, the diffusion description resembles that of surface diffusion – migration over the surface in the adsorbed phase – which explains the sometimes unexpected high diffusional flux [60]. A more rigorous approach for the combined effect of the various diffusion modes is based on the Maxwell–Stefan approach [60], for porous materials often referred to as the ‘‘dusty gas model’’. In addition, due to the presence of solid material, the volume in which diffusion can take place is reduced by a factor εp , the particle porosity. The tortuous path increases the diffusion length for a molecule relative to the spatial coordinate by a factor τp . The effective diffusivity can then be expressed as Deff =

εp ≈ 0.05 − 0.1D D τp

(29)

The form of the steady-state mass balance [Eq. (25)] will depend on the particle shape (sphere, cylinder, trilobe, slab, etc.). For any geometry, the characteristic length should be defined as L=

Vp 1 =  Ap a

(30)

to obtain essentially the same result as for the slab geometry of thickness 2L given below. The solution of the concentration profile is z

cosh φ c L = (31) cs cosh(φ) in which φ is known as the Thiele modulus and is the square root of the ratio of the reaction rate and the diffusional rate in the particle:  kv (32) φ=L Deff When the Thiele modulus is small, no internal concentration profile exists. In the case of large values,

2033

due to the existence of a concentration profile, the catalyst is not effectively used and an effectiveness factor is defined as observed reaction rate rate without internal gradients rv (c, T ) dV rv,obs = = rv,chem (cs , Ts ) rv,chem (cs , Ts ) Vp

ηi =

(33)

Only for simple reaction kinetics can an analytical expression for the effectiveness factor be given, such as for a first-order reaction in a slab, Eq. (34). In comparing catalyst activities and in kinetic studies, one needs data that are not disguised by concentration gradients. For a 5% tolerance level, the criterion for the effectiveness factor for the absence of internal diffusion limitations reads ηi =

tanh(φ) = 1 ± 0.05 φ

(34)

Since during a kinetic study one measures the observed reaction rate and not the intrinsic rate, one cannot determine whether this criterion is satisfied. Therefore, the so-called Wheeler–Weisz modulus is introduced, which yields a procurable quantity [4, 8]. From series expansion and since ηi is close to 1, the following criterion follows for an nth-order reaction [23]:   rv,obs L2 n + 1 < 0.15 (35) = ηi φ 2 = Deff cs 2 Note that cs is not an observable quantity. However, its value may be calculated from Eq. (18). Alternatively, using cb instead is often justified. Here, the generalized form of the Thiele modulus is used, in order to be independent of the reaction kinetics and which is defined such that for the limit φ → ∞, ηi → 1/φ [8, 61] Lrv (cs ) φ=

cs

2 D r (c) dc  eff v

(36)

ceq

For an nth-order irreversible reaction, Eq. (36) yields  kv n−1 φ=L · n+1 (37) 2 cs Deff Figure 21 shows the effectiveness factor as a function of the Wheeler–Weisz modulus for a number of reaction orders, indicating that criterion (35) holds for the References see page 2043

2034

9.1 Laboratory Catalytic Reactors: Aspects of Catalyst Testing

profiles over a particle:

1st order 1

T − Ts cs − c = βi Ts cs

0th order 3rd order

with

hi

2nd order

βi =

0.1 0.1

1

10

hif2 Fig. 21 Isothermal internal effectiveness factor as a function of the Wheeler–Weisz modulus for different reaction orders.

generalized Thiele modulus. Due to the definition of L, it is fairly independent of the catalyst geometry. The derivation of the internal temperature gradient can only be performed numerically, even for simple kinetics. Again, the 5% criterion is used for the internal effectiveness factor. Assuming that the rate can be simplified into a temperature- and a concentrationdependent part, this yields rv (c, T ) kv (T ) f (c) kv (T ) = ≈ rv (cs , Ts ) kv (Ts ) f (cs ) kv (Ts )    Ea Ts = exp − − 1 = 1 ± 0.05 RTs T

ηi =

(38)

where the concentration effects are assumed to be negligible in order to derive a criterion for the temperature effects only. In the non-isothermal case, the reaction temperature in the center of the particle will be higher than Ts at the external surface for exothermic reactions and lower for endothermic reactions. Since we focus on small deviations from the isothermal behavior, the rates in the particle center will be higher or lower, respectively, than at the surface. An expression for the temperature rise in the particle is obtained from the mass [Eq. (25)] and heat balance for a particle: − λp,eff

d2 T = rv (−Hr ) dz2

(40)

(39)

Effective thermal conductivity values of porous materials, λp,eff , in gaseous atmospheres range from 0.1 to 0.5 J s−1 K−1 m−1 [6] and are only slightly larger than those of the gas phase. Straightforward combination of Eqs. (25) and (39) and integration lead to a simple general result that relates the temperature and concentration

(−Hr )Deff cs Tmax = λp,eff Ts Ts

(41)

the internal Prater number, which represents the maximum relative temperature difference across the particle or the ratio of the heat production rate and the heat conduction rate in the particle. Series development and combination of Eqs. (38) and (39) yield the criterion for absence of temperature effects on the experimental data [47, 23]:       E  (−H )D c a r   eff s 2 γs βi ηi φ  =   RTs λp,eff Ts   rv,obs L2  ×  < 0.1 Deff cs 

(42)

This criterion also contains ‘‘observables’’ and so an estimation can be made of the presence of temperature gradients. This result is not unexpected and is similar to that for external transport. The Wheeler–Weisz parameter represents the concentration profile, the Prater number the maximum heat production relative to heat removal by conduction and the dimensionless activation energy the sensitivity of the rate towards a temperature change. It can be shown that |βi |ηi φ 2 represents the relative temperature gradient over the particle, just as |βe |Ca represents the relative temperature gradient over the film. When using the criterion, cs and Ts are not always known. Then, using the values for the bulk phase generally yields a good estimate. They can also be calculated from the external transport balances, Eqs. (18) and (22). It will be clear that in the case of exothermic reactions, the effectiveness factor can become larger than one. This is indicated by the numerical solution for the effectiveness factor in Fig. 22 for various values of βi and γs . Situations may arise in which concentration effects counterbalance the temperature effect, resulting in an effectiveness factor of around one. On the other hand, the temperature effect in the case of endothermic reactions only adds to the lowering of the effectiveness factor by a concentration profile. Catalyst Bed Gradients In the catalyst bed, temperature gradients may develop, analogously to those in a particle. In the axial direction 9.1.3.3

9.1.3 Mass and Heat Transfer

where the reaction rate rV ,obs based on the whole bed volume can be expressed as

10 bi

rV ,obs = rv,obs (1 − εb )(1 − b)

0.6 hi

0.4 1 0.2 −0.2 0.1 0.1

1 f

2035

10

Fig. 22 Internal effectiveness factor as a function of the Thiele modulus for non-isothermal reactions at different values for the Prater number and γs = 10 (numerical solutions for a first-order reaction).

the conversion increases, causing a temperature gradient. These temperature gradients should be kept as small as possible, because otherwise the rate data may not have the value attributed to them. The heat produced or consumed by the reaction can be removed or supplied, respectively, by the fluid phase flowing through the bed or by axial and radial conduction through the bed itself. Especially in the case of gas-phase reactions, the heat capacity of the fluid may be insufficient to keep the temperature change within acceptable limits. Axial conduction contributions are negligible in the case of packed beds due to the large length-to-diameter ratio imposed by the various criteria. Radial conduction to the wall of the reactor has the largest effect in minimizing temperature gradients. Heat conduction through packed beds, however, is poor. The porous particles themselves have poor conductivity and heat transfer between the particles occurs only through their contact points and via the fluid phase. Radiation is only important at very high temperatures, in reactions such as the reforming of methane by steam or carbon dioxide or the methane coupling reaction. Additionally, due to the lower porosity in the wall region the heat transfer from the bed to the reactor wall might be even worse. Mears analyzed this problem for a plug-flow reactor [52] and obtained an approximate solution for the maximum temperature rise in the catalyst bed. Based on this result, a criterion for a (T − grad)ext > (c − grad)int , (T − grad)int > (c − grad)ext

(56)

Effect of Transport Limitations on Observed Behavior

Bim = 10–104 Bih = 10−4 –10−1

gas–solid

The observed reaction rate can be expressed as follows: rv,obs = ηrv,chem (cb , Tb ) = ηe ηi rv,chem (cb , Tb )

gas–liquid

This indicates that for liquid–solid reactions, the external gradient is negligible, whereas in gas–solid reactions it will depend on the specific parameter values. Unlike in industrial operation (high flow-rates, relatively large particles), where as a rule of thumb the internal temperature gradient is assumed to be the largest [66], in laboratory operation the external gradient usually is the largest. Comparing the criteria for intraparticle and for bed behavior, Eqs. (42) and (43), neglecting the wall contribution and bed dilution, one sees immediately that their ratio results in   rv,obs (−Hr )dt 2 (1 − εb ) γw 32λb,eff Tw  ≈

γb βe Ca 2   2  λp,eff dt s (1 − εb ) dp

λb,eff

8

>> 1

(55)

The criterion for a flat velocity profile requires that the first term be >100. The second term is >1 since the effective conductivity of the bed is smaller than that of a particle and the last term is only slightly < 1. Therefore, the temperature gradient in the catalyst bed will be the first to develop to an unacceptable extent and should be verified first. In the case of too large temperature gradients, bed dilution with a wellconducting chemically inert material will improve the situation considerably. Whether the criteria for intra- or extraparticle heattransport limitations are more severe than the corresponding ones for mass transport depends on the absolute values of the products γs βi and γb βe . In some cases the former product exceeds unity but more often it does

(57)

If external mass transport limitations strongly dominate, the rate becomes equal to the mass transfer rate, Eq. (17), with cs = 0. Hence a first-order dependence is observed. Furthermore, the mass transfer coefficient is fairly independent of temperature. On the other hand, the observed rate constant does depend on the flow-rate and particle size (through correlations in Table 2). If internal diffusion limitations dominate ηi → 1/φ, so for an nth-order reaction:    n+1 Ea rv,obs ∝ L−1 kv Deff cs n+1 ∝ L−1 c 2 exp − 2RTs (58) Then the reaction is dependent on the particle size, has an apparent order of (n + 1)/2 and an apparent activation energy that is half the true activation energy. At low temperatures reaction rates are generally kinetically controlled. With increasing temperature, one first enters the diffusion-limited region and at still higher temperatures the film (extraparticle) diffusion-limited region. In so-called Arrhenius plots this is nicely seen as a changing slope of the rate versus 1/T plot, which can be used as an indication for the presence of limitations. A number of examples of this behavior can be found in the literature, e.g. for the Fischer–Tropsch synthesis of middle distillates [67] and the catalytic gasification of carbon [68]. These examples also prove the applicability of the theory. Changing activation energies, however, are not always indicative of the presence of limitations. The approach of thermodynamic equilibrium in the case of exothermic reactions can cause this phenomenon, References see page 2043

2038

9.1 Laboratory Catalytic Reactors: Aspects of Catalyst Testing Tab. 4

Apparent catalyst rate behavior depending on rate-controlling regime (isothermal case)

Controlling process Kinetics Internal diffusion External mass transfer a

Apparent order

Apparent activation energy

Dependency L

Dependency u

n

Ea (true)





(n + 1)/2

1 Ea (true) 2

1/L



1

∼0

Lm−2[a]

um[a]

m represents the power of the Reynolds number in the Sherwood correlation in Table 2.

for example in hydrogenation reactions [68]. A change in rate-determining steps or deactivation of the catalyst might also be causes. The same holds for reaction orders. Table 4 surveys the various observations that can be made when mass transfer affects the isothermal kinetic behavior of catalyst particles. Temperature gradients in endothermic reactions amplify the effects of concentration gradients. In exothermic reactions the thermal effects can compensate the concentration effects or dominate completely. In the latter cases the apparent activation energy may become higher than the true one due to a kind of ‘‘light-off’’ [5]. 9.1.6

Diagnostic Experimental Tests

Apart from the criteria based on the observable quantities derived in Section 9.1.4, some other experimental tests exist to verify the presence or absence of transport limitations. Extraparticle Concentration Gradients Figure 23a shows a test to determine whether external mass transport limitations exist. The test consists of varying the flow-rate and amount of catalyst simultaneously, while keeping the space-time W/Fi0 constant. As the mass transfer coefficient kf depends on the fluid velocity in the catalyst bed, external limitations show by a change in conversion. If no external limitations exist, the resulting conversions should be the same. However, if temperature effects also interfere, these might (over)compensate for concentration effects, so this method should be used with caution. 9.1.6.1

Intraparticle Concentration Gradients More attention should be paid to the diffusion limitations, as was shown before. Under strongly limited conditions, the observed rate becomes particle size dependent, ∝1/L. Variation of the particle size, e.g. by crushing and sieving the catalyst and performing the tests 9.1.6.2

under identical conditions, should give a proper answer to whether diffusion interferes or not. Figure 23b exemplifies this. At small particle size, the reaction is chemically controlled and independent of the particle size. Only for larger particles does a decrease in the observed rate occur. One should be aware of the fact that extraparticle limitations also induce a particle size dependence. The flow-rate through the bed should not have any effect (Table 4). Also in this case temperature effects should be avoided. Koros and Nowak [69] designed a more complex test based on the fact that the intrinsic reaction rate is proportional to the concentration of active sites in the kinetic regime, to its square root in the diffusion-limited regime and independent of this concentration in the external transport-limited regime. The idea is to crush a catalyst and dilute it with inert support to various concentrations and pelletize to identical particle sizes. The observed rate as a function of the site concentration should indicate the regime in which one operates. This test is not always conclusive: some reactions are structure sensitive or diffusion limitations occur on a very small scale, as in zeolite crystals. Madon and Boudart discussed this test in detail [70]. Temperature Gradients The best way to investigate the possible disguise by temperature gradients is to dilute the catalyst bed with an inert material with good heat conduction properties such as SiC. Upon dilution, lower conversions should result for exothermic reactions and higher for endothermic reactions, if gradients are present. The presentation of crude rate data in ‘‘Arrhenius plots’’ to inspect the temperature behavior can give indications of the presence of limiting transport processes by the changing slope (∝ activation energy). However, one should be aware of the fact that other phenomena can also induce this. Examples are a changing rate-determining step, catalyst deactivation or fouling, approach of thermodynamic equilibrium and ignition phenomena. 9.1.6.3

9.1.7 Proper Catalyst Testing and Kinetic Studies

F 0A

F 0A1

F 0A5

F 0A

F 0A

F 0A

Increasing flow rate

W1

Wi /F A0 i constant

X1

Increasing dp1 particle size

W5

X5

dp5

X1

X

2039

X5

X

X5 X1

X1 X5 F 0A1

(a)

Fig. 23

F 0A5 Flow rate

dp1 Reference catalyst (b)

dp5 Particle size

Diagnostic tests for (a) extraparticle limitations and (b) intraparticle limitations.

9.1.7

1

During the experimental investigations, one should carry out a proper testing of the catalysts, in order to obtain the relevant information with regard to intrinsic activity, selectivity, deactivation and kinetic behavior. The following guidelines should be applied: • adhere to criteria: ideal reactor behavior: plug flow or CSTR; isothermal bed; absence of limitations: observables, diagnostic tests • compare at low conversions to get insight in real activity differences (PFR) • compare selectivities at same conversion levels • make sure steady-state catalysis is really achieved. In diagnostic tests, crushing of the particles will not always be conclusive. Eggshell catalysts or other types, zeolites and washcoated monoliths are examples. In washcoated monoliths, the layer thickness is generally already small (1. This problem especially occurs at low reactant concentrations (e.g. exhaust catalysis, water purification) and/or low flowrates. The number of molecules passed over the catalyst per unit time may be much smaller than the number of available active sites in the catalyst. It may take a long time before each site has converted sufficient molecules to consider it as catalysis. Sometimes, the occurrence of a temperature profile along the reactor axis cannot be avoided, as in the study of exhaust gas monolithic catalysts. A possible approach can be to measure the temperature profile along the catalyst length and to use this for the data interpretation. It requires, however, a complete analysis of the mass and heat balances for a correct interpretation [71]. 9.1.8

Current Trends in Catalyst Testing

Figure 25 illustrates the historical trends towards scaling down and automation in catalyst development in terms of manpower needed since the 1960s [72]. The conventional approach towards solid catalyst development involved the evaluation of a single or a few catalyst compositions over a range of reaction conditions in a single dedicated reactor system, first in pilot plants, later in non-automated, then semi-automated bench-type reactor systems. Further benefit came from scaling down to micro- and nano-flow with full automation. In the past decade, further improvements have resulted from so-called parallelization or highthroughput experimentation (HTE) and from the development of so-called microchannel reactors or microreactors. Parallelization/High-Throughput Experimentation Although since the early days of catalyst development test rigs have been used in parallel for screening series of new catalysts [73, 74], the first reference in the open literature referring to the use of a single dedicated setup using parallel reactors to study solid catalysts appeared in 1980 [75]. In 1986, Creer et al. [76] published a detailed account of the design, implementation and verification of a system for testing of solid catalysts with six microreactors 9.1.8.1

2 Pilot plant (non-automated)

1

Manhour per reactor hour

2040

Bench scale (non-automated)

0.5

Bench scale (semi-automated)

0.1 Micro-and nano-flow (automated)

0.05

Parallellization

0.01

1960

1970

1980

1990

2000

Year Fig. 25 Manpower needed for different reactor units as a function of the approximate introduction year for general use in oil processing research.

in parallel. Several parallel catalyst testing systems have now been commercialized. In the early days of HTE, experimentation was mainly aimed at a qualitative comparison of activities of a large number of catalyst compositions to obtain ‘‘hits’’, socalled primary screening. However, the development of new and better experimental methods and techniques to control gas supply, fast analysis and computerization has led to more quantitative results, similar to or better than those of conventional laboratory reactors [77, 78]. A typical setup of the so-called six-flow reactor for catalyst comparison is shown in Fig. 26 [78–80]. Basically, a feed, a reactor and an analysis section are required. The six parallel reactors are placed in one oven. Nowadays, mass flow controllers for both liquid and gas result in stable molar flow-rates, ideal for kinetic studies. Pressure controllers maintain a constant feed pressure for the flow controllers, while backpressure controllers maintain the pressure in the reactors. Various methods of product analysis are available, which depend considerably on the system under investigation. An example of the successful implementation of the sixflow reactor was the kinetic study of the selective catalytic reduction of NO over alumina-supported manganese oxide [80]. One reactor served as the reference filled with inert particles, the others being filled with different amounts of catalyst. Product analysis was performed with a mass spectrometer. This yielded data at five different space times. The equipment was PC-controlled and predesigned kinetic runs (pressure and temperature variation) could be carried out automatically within a short period. The feed composition to all reactors is the same and only the cost of additional flow controllers to divide the feed mixture and a selection

9.1.8 Current Trends in Catalyst Testing

Feed control

Reactor

2041

Analysis

P MFC MFC MFC

Vent

MFC

SV

MFC MFC MFC MFC

BPC

MFC

BPC

Fig. 26

Six-flow reactor setup for simultaneously testing of different catalyst samples.

Tab. 5

Examples of parallel catalyst testing systems

Reactor system

Dimensions

Catalyst

Test reaction

Tubular plug flow (six-flow) Ceramic monolith

6 reactors 2.2 mm diameter, 150 mm length, 16 columns, 16 rows 2.6 mm diameter, 75 mm length, 16 columns, 8 rows 16 teeth 6-mm circular holes 15 autoclaves, 45 mL

Particles Powder, particles

Catalytic reduction of NO Methane oxidation

Catalytic coating

Total oxidations

[82]

Granular Powder

Gas-phase reactions Hydrogenation of citral (G−L reaction)

[83] [84]

Ceramic monolith with impermeable wall Rotating sample wheel Multibatch mini-autoclaves

valve are required. The tremendously increased data generation speed outweighs completely the relatively small additional investment. Since then, this basic approach of parallelization has been extended to multiples of reactors in various forms; see Table 5 for examples. Automated equipment, especially when using a parallel reactor system, yields a wealth of data that should be properly processed and interpreted. The time involved in the latter should not be underestimated and one should not lose oneself in experimentation only. Miniaturization The successful use of parallel multi-tube fixed-bed reactor systems for catalyst optimization has increased the demand for fast primary screening devices and methodologies, with further miniaturization being one of the key issues [77]. Recent advances in automation, robotics, microfabrication and instrumentation have allowed the development of new types of reactors, namely microchannel reactors or microreactors [85–87]. Such 9.1.8.2

References [78–80] [81]

reactors consist of a very large number of parallel channels, having diameters between 10 and several hundred micrometers. These small dimensions result in very high surface-to-volume ratios and thus very large heat and mass transfer rates, so that they are suitable not only for the initial screening of catalysts, but also for catalyst testing under kinetically controlled conditions. In Table 6, a few examples of the use of microreactors in catalyst testing are given. More about microreactors and the microfabrication techniques can be found in, e.g., Refs. [77] and [84–88] and in Chapter 10.8. The disadvantage of microchannels filled with catalyst powder is the large pressure drop in the small-diameter channels. To overcome this problem, cross flow can be used [93, 94] or the catalytic material can be deposited on the channel walls [87, 95]. The latter is most commonly used. The catalytic-wall microreactor is particularly suitable for studying fast, highly exothermic (or endothermic) References see page 2043

2042 Tab. 6

9.1 Laboratory Catalytic Reactors: Aspects of Catalyst Testing Examples of microreactors

Reactor system

Channel dimensions

Catalyst

Test reaction

References

Tubular plug flow

1 mm wide, 0.3 mm deep, 6 mm long, six channels

Granular

CO oxidation

[89]

Tubular plug flow (SWITCH 16)

16 channels

Powder

CO oxidation

[90–92]

Cross-flow packed bed

25.5 mm wide, 500 µm deep, 400 µm long

Particles

CO oxidation

[93, 94]

Stacked plates

300 µm wide, 250 µm deep, 20 mm long, 34 channels/plate, 10 plates

Catalytic coating

Oxidative dehydrogenation of propane

[95]

Cross-flow stacked plates

145 µm wide, 145 µm deep, 6.5 mm long

Catalytic coating

Ammonia oxidation, partial oxidation of methane

[96–98]

Single-bead

7 × 15 channels (or more)

Particles, usually spherical

Partial hydrogenation, partial oxidation

reactions, because very rapid heat removal (or addition) is possible, ensuring isothermal conditions. Microreactors have also been developed for heterogeneously catalyzed gas–liquid reactions. Examples are given by, e.g., Jensen [87]. The operation of many coated channels in parallel assumes that each channel receives equal flows by using special geometries or contains equal amounts of catalyst coating. This is not always the case, however, and one should consider the effect of deviations on the kinetic interpretation of data or on the design of microreactor systems. Delsman et al. [99] present relations to approximate these deviations and showed that especially distributions in the channel diameter (flow-rate) cause the largest deviations. List of Symbols

a a Ap Ach b

c p C p C dH dp

area of gas bubbles per unit volume of liquid specific surface area of catalyst particle external surface area of particle cross-sectional area of monolith channel volume of inert particles as fraction of total solids volume concentration molar heat capacity mass heat capacity hydrodynamic channel diameter monolith particle diameter

m−1

dt Dax DK,i Dif D Deff Ea f (c) Fi0 Ftot g h h0 kv

m−1

kf

m2

kL

m2

L

– mol m−3 J mol−1 K−1 J kg−1 K−1 m

Lb L0 Mi n N Ni Och p

m

diameter of reactor tube axial dispersion coefficient Knudsen diffusivity of component i molecular diffusivity of i in fluid phase f average diffusivity effective diffusivity in particle activation energy concentration function in rate expression molar flow of i at reactor inlet total flow through catalyst bed gravitational acceleration heat transfer coefficient static heat transfer coefficient rate constant per unit particle volume mass transfer coefficient (fluid-to-solid) mass transfer coefficient (gas-to-liquid) characteristic catalyst dimension bed length undiluted bed length molar mass of component i reaction order number of tanks in series number of moles periphery of monolith channel cross section pressure

[77]

m m2 s−1 m2 s−1 m2 s−1 m2 s−1 m2 s−1 J mol−1 mol s−1 mol s−1 m s−2 J m−2 s−1 K−1 J m−2 s−1 K−1 m s−1 m s−1 m m m kg kmol−1 – – mol m Pa

References

r0 rv rv,chem rv,obs rV ,obs rW R Rc s t T u Vp W x y0 z

average pore radius reaction rate per unit particle volume intrinsic reaction rate per unit particle volume observed reaction rate per unit particle volume observed reaction rate per unit bed or liquid volume reaction rate per unit catalyst mass universal gas constant recirculation ratio geometry parameter time temperature superficial velocity particle volume catalyst mass conversion mole fraction of reactant in reactor feed gas coordinate

m mol s−1 m−3 p mol s−1 m−3 p mol s−1 m−3 p mol s−1 m−3 b mol s−1 kg−1 J mol−1 K−1 – – s K m s−1 m3 kg – – m

Dimensionless numbers Bim Biot number of mass Bih Biot number of heat Biot number heat transfer at Biw wall Ca Carberry number Nu Nusselt number Pep P´eclet particle number Pr Prandtl number Re Reynolds number Rep Reynolds particle number Sc Schmidt number Sh Sherwood number Wetting number in trickle Wtr flow Greek letters β Prater number γ dimensionless activation energy wall thickness in monolith δw Hr heat of reaction ε porosity εM porosity of monolith η overall effectiveness factor external effectiveness factor ηe ηi internal effectiveness factor λf thermal conductivity of fluid phase

λeff λ0eff µ νl νi ρ τ τp φ φG ϕ

effective thermal conductivity stationary effective thermal conductivity dynamic viscosity kinematic viscosity of liquid stoichiometric coefficient of i in reaction density average residence time CSTR particle tortuosity factor Thiele modulus generalized Thiele modulus parameter in effective thermal conductivity equation

2043

J m−1 s−1 K−1 J m−1 s−1 K−1 kg m s−1 m2 s−1 – kg m−3 s – – – –

Subscripts app apparent b in bulk phase; also bed chem chemically controlled e external eff effective f fluid phase i intraparticle i of species i M monolith obs observed p particle s at external particle surface t tube w at the reactor wall Superscript eq equilibrium References

– – m J mol−1 – – – – – J m−1 s−1 K−1

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2044

9.1 Laboratory Catalytic Reactors: Aspects of Catalyst Testing

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2045

mixtures is usually carried out on a small scale, in a laboratory apparatus accommodating typically 0.1–10 g of catalyst. To ensure that meaningful and reproducible results are obtained in such laboratory-scale units, they must be properly designed and constructed and parts which are prone to malfunctions should be avoided. It is the intention of the present chapter to discuss critical building blocks of laboratory-scale catalytic units which are frequently designed in an inadequate manner. Since the core part of such units, viz. the catalytic reactor, is the subject of Chapter 9.1, this contribution will focus on the peripheral building blocks, i.e. the devices for the preparation of the feed mixtures to be sent to the reactor and the systems downstream of the reactor for transferring product samples to an analytical instrument. 9.2.2

Overall Equipment

All research in the field of heterogeneous catalysis ultimately aims at a more detailed understanding of the various chemical and mass transfer steps and, based on this knowledge, at the design and preparation of improved catalysts. Testing the performance of a solid catalyst in the conversion of gaseous, liquid or supercritical feed

The overall equipment used for catalytic studies is usually classified into (i) batch methods, (ii) semi-batch methods (e.g. a hydrogenation reaction in which hydrogen gas bubbles continuously through a batch reactor containing the liquid substrate and the suspended catalyst), (iii) transient methods (including pulse reactors) and (iv) continuous flow methods. Although all these methods have their specific advantages and disadvantages [1], continuously operated flow-type units strongly prevail in practice. The reasons are obvious: such units are not only well suited to measure the kinetics of the catalytic reaction, but they also enable the experimentalist to detect readily and quantitatively whether the catalyst, while working, preserves a constant activity, deactivates (which happens frequently) or, conversely, becomes more active (which sometimes happens). A rough scheme of a continuously operated flow-type unit for studying a gas-phase reaction on a solid catalyst is depicted in Fig. 1. Arbitrarily, a fixed-bed reactor (see Chapter 10.1) was chosen. In fact, fixed-bed reactors are most popular in heterogeneous catalysis, because they are easy to construct, relatively inexpensive (even if designed for high pressure), robust (since there are no moving parts) and a downscaled image of the most frequently employed reactor type in industrial catalysis. Ideally, the fixed-bed reactor behaves like a plug-flow (or, synonymously, piston-flow) reactor (PFR) with no radial gradients of partial pressure or gas velocity and with a complete absence of axial mixing. In a PFR, the reactant and product partial pressures are thus only a function of the reactor length. Its antipode is the continuous stirred tank reactor (CSTR), which



References see page 2053

9.2

Ancillary Techniques in Laboratory Units for Testing Solid Catalysts .. Jens Weitkamp∗ and Roger Glaser

9.2.1

Introduction

Corresponding author.