Choice of Reactor performance

Choice of Reactor performanceBy JuwariSourceRobin Smith1

Since process design starts with the reactor, the first decisions are to the choice of reactor. These decisions are amongst the most important in the whole process design.

Reactors can be broadly classified as chemical or biochemical.

The issues that must be addressed for reactor design include: Reactor type Catalyst Size Operating conditions (temperature and pressure) Phase Feed conditions (concentration and temperature).2

5.1 REACTION PATHReaction paths that use the cheapest raw materials and produce the smallest quantities of byproducts are to be preferred.

There are many other factors to be considered in the choice of reaction path. Some are commercial, such as uncertainties regarding future prices of raw materials and byproducts. Others are technical, such as safety and energy consumption.3

Example 5.1

Given that the objective is to manufacture vinyl chloride, there are at least three reaction paths that can be readily exploited.

The market values and molar masses of the materials involved are given in Table 5.1.

Oxygen is considered to be free at this stage, coming from the atmosphere. Which reaction path makes most sense on the basis of raw material costs, product and byproduct values?4

Solution Decisions can be made on the basis of the economic potential of the process. At this stage, the best that can be done is to define the economic potential (EP) EP = (value of products) (raw materials costs)

Path 1EP = (62 0.46) (26 1.0 + 36 0.39) = 11.52 $kmol1 vinyl chloride product

Path 2EP = (62 0.46 + 36 0.39) (28 0.58 + 71 0.23) = 9.99 $kmol1 vinyl chloride productThis assumes the sale of the byproduct HCl. If it cannot be sold, then:EP = (62 0.46) (28 0.58 + 71 0.23) = 4.05 $kmol1vinyl chloride product

Path 3EP = (62 0.46) (28 0.58 + 36 0.39)= 1.76 $kmol1vinyl chloride product5

Paths 1 and 3 are clearly not viable. Only Path 2 shows a positive economic potential when the byproduct HCl can be sold. In practice, this might be quite difficult, since the market for HCl tends to be limited. In general, projects should not be justified on the basis of the byproduct value.

The preference is for a process based on ethylene rather than the more expensive acetylene, and chlorine rather than the more expensive hydrogen chloride. Electrolytic cells are a much more convenient and cheaper source of chlorine than hydrogen chloride. In addition, it is preferred to produce no byproducts.6

Example 5.2 Devise a process from the three reaction paths in Example 5.1 that uses ethylene and chlorine as raw materials and produces no byproducts other than water4. Does the process look attractive economically?Solution A study of the stoichiometry of the three paths shows that this can be achieved by combining Path 2 and Path 3 to obtain a fourth path.

Now the economic potential is given by:

EP = (62 0.46) (28 0.58 + 1/2 71 0.23) = 4.12 $kmol1 vinyl chloride product

In summary, Path 2 from Example 5.1 is the most attractive reaction path if there is a large market for hydrogen chloride. In practice, it tends to be difficult to sell the large quantities of hydrogen chloride produced by such processes. Path 4 is the usual commercial route to vinyl chloride.7

5.2 TYPES OF REACTION SYSTEMSReaction systems can be classified into six broad types:Type General equationExample 1. Single reactions.FEED PRODUCT orFEED PRODUCT + BYPRODUCT orFEED1 + FEED2 PRODUCT2. Multiple reactions in parallel producing byproducts.FEED PRODUCTFEED BYPRODUCTorFEED PRODUCT + BYPRODUCT1FEED BYPRODUCT2 + BYPRODUCT3orFEED1 + FEED2 PRODUCTFEED1 + FEED2 BYPRODUCT

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Type General equationExample 3. Multiple reactions in series producing byproductsFEED PRODUCTPRODUCT BYPRODUCTorFEED PRODUCT + BYPRODUCT1PRODUCT BYPRODUCT2 + BYPRODUCT3orFEED1 + FEED2 PRODUCTPRODUCT BYPRODUCT1 + BYPRODUCT24. Mixed parallel and series reactions producingbyproducts.FEED PRODUCTFEED BYPRODUCT PRODUCT BYPRODUCTOrFEED PRODUCTFEED BYPRODUCT1 PRODUCT BYPRODUCT2OrFEED1 + FEED2 PRODUCTFEED1 + FEED2 BYPRODUCT1 PRODUCT BYPRODUCT2 + BYPRODUCT3

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Type Example 5. Polymerization reactionsThere are two broad types of polymerization reactions, those that involve a termination step and those that do not.

6. Biochemical reactions.can be divided into two broad types. 1) the reaction exploits the metabolic pathways in selected microorganisms yeasts, moulds and algae) to convert feed to product2) the reaction is promoted by enzymes.

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5.3 REACTOR PERFORMANCEFor polymerization reactors, the main concern is the characteristics of the product that relate to the mechanical properties. The distribution of molar masses in the polymer product, orientation of groups along the chain, cross-linking of the polymer chains, copolymerization with a mixture of monomers, and so on, are the main considerations.Ultimately, the main concern is the mechanical properties of the polymer product.

For biochemical reactions, the performance of the reactor will normally be dictated by laboratory results, because of the difficulty of predicting such reactions theoretically. There are likely to be constraints on the reactor performance dictated by the biochemical processes. For example, inthe manufacture of ethanol using microorganisms, as the concentration of ethanol rises, the microorganisms multiply more slowly until at a concentration of around 12% it becomes toxic to the microorganisms.11

For other types of reactors, three important parameters are used to describe their performance:

stoichiometric factor is the stoichiometric moles of reactant required per mole of product12

Example 5.3

Benzene is to be produced from toluene according to the reaction.

Some of the benzene formed undergoes a number of secondary reactions in series to unwanted byproducts that can be characterized by the reaction to diphenyl, according to the reaction:

Table 5.2 gives the compositions of the reactor feed and effluent streams.

Calculate the conversion, selectivity and reactor yield with respect to the:a. toluene feedb. hydrogen feed.13

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The principal concern is performance with respect to toluene, since it is more expensive than hydrogen.16

5.4 RATE OF REACTIONThe rate of reaction is the number of moles formed with respect to time, per unit volume of reaction mixture:If the volume of the reactor is constant (V = constant):

The rate is negative if the component is a reactant and positive if it is a product. For example, for the general irreversible reaction:

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Rate reaction for Elementary reaction

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Rate reaction for Nonelementary reaction

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5.5 IDEALIZED REACTOR MODELS

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Example 5.4 Benzyl acetate is used in perfumes, soaps, cosmetics and household items where it produces a fruity, jasmine like aroma, and it is used to a minor extent as a flavor. It can be manufactured by the reaction between benzyl chloride and sodium acetate in a solution of xylene in the presence of triethylamine as catalystThe reaction has been investigated experimentally by Huang and Dauerman in a batch reaction carried out with initial conditions given in Table 5.3

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The solution volume was 1.321 103m3 and the temperature maintained to be 102C. The measured mole per cent benzyl chloride versus time in hours are given in Table 5.4.

Derive a kinetic model for the reaction on the basis of the experimental data. Assume the volume of the reactor to be constant25

Solution The equation for a batch reaction is given by Equation 5.38

Initially, it could be postulated that the reaction could be zero order, first order or second order in the concentration of A and B. However, given that all the reaction stoichiometric coefficients are unity, and the initial reaction mixture has equimolar amounts of A and B, it seems sensible to first try to model the kinetics in terms of the concentration of A. This is because, in this case, the reaction proceeds with the same rate of change of moles for the two reactants. Thus, it could be postulated that the reaction could be zero order, first order or second order in the concentration of A. In principle, there are many other possibilities. Substituting the appropriate kinetic expression into Equation 5.47 and integrating gives the expressions in Table 5.5:

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The experimental data have been substituted into the three models and presented graphically in Figure 5.5. From Figure 5.5, all three models seem to give a reasonable representation of the data, as all three give a reasonable straight line.

27It is difficult to tell from the graph which line gives the best fit. The fit can be better judged by carrying out a least squares fit to the data for the three models. The difference between the values calculated from the model andthe experimental values are summed according to:

28However, the most appropriate value of the rate constant for each model needs to be determined. This can be determined, for example, in a spreadsheet by setting up a function for R2 in the spreadsheet and then using the spreadsheet solver to minimize R2 by manipulating the value of kA. The results are summarized in Table 5.6.

From Table 5.6, it is clear that the best fit is given by a first order reaction model: rA = kACA with kA = 0.01306 h1.

29Example 5.5 Ethyl acetate is widely used in formulating printing inks, adhesives, lacquers and used as a solvent in food processing. It can be manufactured from the reaction between ethanol and acetic acid in the liquid phase according to the reaction

Experimental data are available using an ion-exchange resin catalyst based on batch experiments at 60C. These data are presented in Table 5.7.

30Molar masses and densities for the components are given in Table 5.8.

Initial conditions are such that the reactants are equimolar with product concentrations of initially zero. From the experimental data, assuming a constant density system:

a. Fit a kinetic model to the experimental data.b. For a plant producing 10 tons of ethyl acetate per day, calculate the volume required by a mixed-flow reactor and a plug-flow reactor operating at 60C. Assume no product is recycled to the reactor and the reactor feed is an equimolar mixture of ethanol and acetic acid. Also, assume the reactor conversion to be 95% of the conversion at equilibrium.

31Solutiona. To fit a model to the data, first convert the mass percent data from Table 5.7 into molar concentrations. Volume of reaction mixture per kg of reaction mixture (assuming no volume change of solution)

Molar concentrations are given in Table 5.9

A reaction rate expression can be assumed of the form

32Substituting the kinetic model and integrating give the results in Table 5.10 depending on the values of the order of reaction. The integrals can be found from tables of standard integrals.

33Note in Table 5.10 that many of the integrals are common to different kinetic models. This is specific to this reaction where all the stoichiometric coefficients are unity and the initial reaction mixture was equimolar. In other words, the change in the number of moles is the same for all components. Rather than determine the integrals analytically, they could have been determined numerically. Analytical integrals are simply more convenient if they can be obtained, especially if the model is to be fitted in a spreadsheet, rather than purpose-written software. The least squares fit varies the reaction rate constants to minimize the objective function

34Again, this can be carried out, for example, in spreadsheetsoftware, and the results are given in Table 5.11

From Table 5.11, there is very little to choose between the best two models. The best fit is given by a second-order model for the forward and a first-order model for the reverse reaction withHowever, there is little to choose between this model and a second-order model for both forward and reverse reactions

35b. Now use the kinetic model to size a reactor to produce 10 tons per day of ethyl acetate. First, the conversion at equilibrium needs to be calculated. At equilibrium, the rates of forward and reverse reactions are equal.

Substituting for the conversion at equilibrium XE gives:

Rearranging gives:

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37Alternatively, the residence time in the plug-flow reactor could be calculated from the batch equations given in Table 5.10. This results from the residence time being equal for both. Thus the final concentration in a plug-flow reactor is given by (Table 5.10):

The final concentration of CA from the conversion is 8.33 0.395 = 3.29 kmolm3 (assuming no volume change). Thus, the above equation can be solved by trial and error to give the residence time of 120.3 min.As expected, the result shows that the volume required by a mixed-flow reactor is much larger than that for plug-flow

38A number of points should be noted regarding Examples 5.4 and 5.5

The kinetic models were fitted to experimental data at specific conditions of molar feed ratio and temperature. The models are only valid for these conditions. Use for nonequimolar feeds or at different temperatures will not be valid.

2. Given that kinetic models are only valid for the range of conditions over which they are fitted, it is better that the experimental investigation into the reaction kinetics and the reactor design are carried out inparallel. If this approach is followed, then it can be assured that the range of experimental conditions used in the laboratory cover the range of conditions used in the reactor design. If the experimental programme is carried out and completed prior to the reactor design, then there is no guarantee that the kinetic model will be appropriate for the conditions chosen in the final design.

3. Different models often give very similar predictions over a limited range of conditions. However, the differences between different models are likely to become large if used outside the range over which they were fitted to experimental data.

5.6 CHOICE OF IDEALIZED REACTOR MODELSingle reactions.

The highest rate of reaction is maintained by the highest concentration of feed .In the mixed-flow reactor the incoming feed is instantly diluted by the product that has already been formed. The rate of reaction is thus lower in the mixed-flow reactor. Thus, For single reactions, an ideal-batch or plug-flow reactor is referred.39

2. Multiple reactions in parallel producing byproducts.

The ratio of the rates of the secondary and primary reactions givesMaximum selectivity requires a minimum ratio r2/r1A batch or plug-flow reactor maintains higher average concentrations of feed. Thus, if a2 < a1, use a batch or plug-flow reactor. a2 > a1, use a mixed-flow reactor.Case 140

Case 2

Given this reaction system, the options are: Keep both CFEED1 and CFEED2 low (i.e. use a mixed flow reactor). Keep both CFEED1 and CFEED2 high (i.e. use a batch or plug-flow reactor). Keep one of the concentrations high while maintaining the other low (this is achieved by charging one of the feeds as the reaction progresses).41

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3. Multiple reactions in series producing byproducts.

In the mixedflow reactor, FEED can leave the instant it enters or remains for an extended period. Similarly, PRODUCT can remain for an extended period or leave immediately. Thus, the mixed-flow model would be expected to give a poorer selectivity or yield.A batch or plug-flow reactor should be used for multiple reactions in series.43

4. Mixed parallel and series reactions producing byproducts.

As far as the parallel byproduct reaction is concerned, for high selectivity, if: a1 > a2, use a batch or plug-flow reactor a1 < a2, use a mixed-flow reactor

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The series byproduct reaction requires a plug-flow reactor. Thus, for the mixed parallel and series system above, if: a1 > a3, use a batch or plug-flow reactor

But what is the correct choice if a1 < a3? Now the parallel byproduct reaction calls for a mixed-flow reactor. On the other hand, the byproduct series reaction calls for a plugflow reactor. It would seem that, given this situation, some level of mixing between a plug-flow and a mixed-flow reactor will give the best overall selectivity. This could be obtained by a:

series of mixed-flow reactors (Figure 5.7a) plug-flow reactor with a recycle (Figure 5.7b) series combination of plug-flow and mixed-flow reactors(Figures 5.7c and 5.7d).

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5. Polymerization reactionsPolymers are characterized mainly by the distribution of molar mass about the mean as well as by the mean itself. Orientation of groups along chains, cross-linking of the polymer chains, and so on, also affect the properties. The breadth of molar mass has an important influence on the mechanical and other properties of the polymer, and this is an important factor in the choice of reactor.Two broad classes of polymerization reactions can be identified2:(a) In a batch or plug-flow reactor, all molecules have the same residence time, and without the effect of termination (see Section 5.2) all will grow to approximately equal lengths, producing a narrow distribution of molar masses. By contrast, a mixed-flow reactor will cause a wide distribution because of the distribution of residence times in the reactor.(b) When polymerization takes place by mechanisms involving free radicals, the life of these actively growing centers may be extremely short because of termination processes such as the union of two free radicals (see Section 5.2). These termination processes are influenced by free-radical concentration, which in turn is proportional to monomer concentration. In batch or plug-flow reactors, the monomer and free-radical concentrations decline. This produces increasing chain lengths with increasing residence time and thus a broad distribution of molar masses. The mixed-flow reactor maintains a uniform concentration of monomer and thus a constant chain-termination rate. This results in a narrow distribution of molar masses. Because the active life of the polymer is short, the variation in residence time does not have a significant effect46

6. Biochemical reactions.(a) Reactions that exploit the metabolic pathways in selected microorganisms. Consider microbial biochemical reactive of the type:

where A is the feed, R is the product and C represents the cells (microorganisms). The kinetics of such reactions can be described by the Monod Equation

where rA = rate of reactionk = rate constantCC = concentration of cells (microorganisms)CA = concentration of feedCM = a constant (Michaelis constant that is a function of the reaction and conditions)The rate constant can depend on many factors, such as temperature, the presence of trace elements, vitamins, toxic substances, light intensity, and so on. An excess of feed material or microorganisms can slow the rate of reaction. Thus, depending on the concentration range, mixed-flow, plug-flow, a combination of mixed-flow and plug-flow or mixed-flow with separation and recycle might be appropriate.47

(b) For enzyme-catalyzed biochemical reactions

The kinetics can be described by the Monod Equation in the form

where CE = enzyme concentrationThe presence of some substances can cause the reaction to slow down. Such substances are known as inhibitors.

High reaction rate in Equation 5.71 is favored by a high concentration of enzymes (CE) and high concentration of feed (CA). This means that a plug-flow or ideal-batch reactor is favored if both the feed material and enzymes are to be fed to the reactor.48

5.7 CHOICE OF REACTOR PERFORMANCESingle reactions.

with single reactions the goal is to minimize the reactor capital cost, which often (but not always) means minimizing reactor volume, for a given reactor conversion. Increasing the reactor conversion increases size and hence cost of the reactor but, decreases the cost of many other parts of the flowsheet. Because of this, the initial setting for reactor conversion for single irreversible reactions is around 95%and that for a single reversible reaction is around 95% of the equilibrium conversion.

2. Multiple reactions in parallel producing byproducts.

when dealing with multiple reactions, whether parallel, series or mixed, the goal is usually to minimize byproduct formation (maximize selectivity) for a given reactor conversion. Chosen reactor conditions should exploit differences between the kinetics and equilibrium effects in the primary and secondary reactions to favor the formation of the desired product rather than the byproduct, that is, improve selectivity. Making an initial guess for conversion is more difficult than with singlereactions, since the factors that affect conversion also can have a significant effect on selectivity.49

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Consider the system of parallel reactions from Equations 5.64 and 5.65.

A high conversion in the reactor tends to decrease CFEED. Thus: a2 > a1 selectivity increases as conversion increases a2 < a1 selectivity decreases as conversion increases

If selectivity increases as conversion increases, the initial setting for reactor conversion should be in the order of 95%, and that for reversible reactions should be in the order of 95% of the equilibrium conversion.

If selectivity decreases with increasing conversion, then it is much more difficult to give guidance. An initial setting of 50% for the conversion for irreversible reactions or 50% of the equilibrium conversion for reversible reactions is as reasonable as can be guessed at this stage. However, these are only initial guesses and will almost certainly be changed later.

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3. Multiple reactions in series producing byproduct.

Consider the system of series reactions from Equation 5.68.

Selectivity for series reactions of the types given in Equation 5.7 to 5.9 is increased by low concentrations of reactants involved in the secondary reactions. In the preceding example, this means reactor operation with a low concentration of PRODUCT, in other words, with low conversion. For series reactions, a significant reduction in selectivity is likely as the conversion increases.Again, it is difficult to select the initial setting of the reactor conversion with systems of reactions in series. A conversion of 50% for irreversible reactions or 50% of the equilibrium conversion for reversible reactions is as reasonable as can be guessed at this stage. Multiple reactions also can occur with impurities that enter with the feed and undergo reaction. Again, such reactions should be minimized, but the most effective means of dealing with byproduct reactions caused by feed impurities is not to alter reactor conditions but to carry outfeed purification.

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