Batch reactors reversible reactions

Table 4.10.3 gives the conversion in a batch reactor, a PFR, and a CSTR for different values of 8v for the example of Do = 1. The data indicate that, in contrast to a batch reactor, Xa decreases for a reaction with increasing volume both in a CSTR and in a PFR, which is in general true for a reaction order >0 [see Levenspiel (1996, 1999)]. For a reaction with decreasing volume rate, this is reversed. In both flow reactors (PFR, CSTR), the residence time changes compared to a constant volume reaction, while in a batch reactor the reaction time does not. Thus for reactions with changing volume, the batch and the plug flow performance equations are different. 

Determine the maximum batch reactor yield of B for a reversible, first-order reaction ... 

The results of Example 5.2 apply to a reactor with a fixed reaction time, i or thatch- Equation (5.5) shows that the optimal temperature in a CSTR decreases as the mean residence time increases. This is also true for a PFR or a batch reactor. There is no interior optimum with respect to reaction time for a single, reversible reaction. When Ef < Ef, the best yield is obtained in a large reactor operating at low temperature. Obviously, the kinetic model ceases to apply when the reactants freeze. More realistically, capital and operating costs impose constraints on the design. 

At a fixed temperature, a single, reversible reaction has no interior optimum with respect to reaction time. If the inlet product concentration is less than the equilibrium concentration, a very large flow reactor or a very long batch reaction is best since it will give a close approach to equilibrium. If the inlet product concentration is above the equilibrium concentration, no reaction is desired so the optimal time is zero. In contrast, there will always be an interior optimum with respect to reaction time at a fixed temperature when an intermediate product in a set of consecutive reactions is desired. (Ignore the trivial exception where the feed concentration of the desired product is already so high that any reaction would lower it.) For the normal case of bin i , a very small reactor forms no B and a very large reactor destroys whatever B is formed. Thus, there will be an interior optimum with respect to reaction time. 

The reaction between ethyl alcohol and formic acid in acid solution to give ethyl formate and water, C2H5OH + HCOOH HCOOC2H5 + H20, is first-order with respect to formic acid in the forward direction and first-order with respect to ethyl formate in the reverse direction, when the alcohol and water are present in such large amounts that their concentrations do not change appreciably. At 25°C, the rate constants are kf = 1.85 xlO-3 min 1and kr = 1.76 xlO-3 min-1. If the initial concentration of formic acid is 0.07 mol L-1 (no formate present initially), calculate the time required for the reaction to reach 90% of the equilibrium concentration of formate in a batch reactor. 

The hydrolysis of methyl acetate (A) in dilute aqueous solution to form methanol (B) and acetic acid (C) is to take place in a batch reactor operating isothermally. The reaction is reversible, pseudo-first-order with respect to acetate in the forward direction (kf = 1.82 X 10-4 s-1), and first-order with respect to each product species in the reverse direction (kr = 4.49 X10-4 L mol-1 S l). The feed contains only A in water, at a concentration of 0.050 mol L-1. Determine the size of the reactor required, if the rate of product formation is to be 100 mol h-1 on a continuing basis, the down-time per batch is 30 min, and the optimal fractional conversion (i.e., that which maximizes production) is obtained in each cycle. 

A rate equation is required for this reaction taking place in dilute solution. It is expected that reaction will be pseudo first-order in the forward direction and second-order in reverse. The reaction is studied in a laboratory batch reactor starting with a solution of methyl acetate and with no products present. In one test, the initial concentration of methyl acetate was 0.05 kmol/m3 and the fraction hydrolysed at various times subsequently was ... 

A reversible reaction, At= B, takes place in a well-mixed tank reactor. This can be operated either batch-wise or continuously. It has a cooling jacket, which allows operation either isothermally or with a constant cooling water flowrate. Also without cooling it performs as an adiabatic reactor. In the simulation program the equilibrium constant can be set at a high value to give a first-order irreversible reaction. 

Continuous Multicomponent Distillation Column 501 Gas Separation by Membrane Permeation 475 Transport of Heavy Metals in Water and Sediment 565 Residence Time Distribution Studies 381 Nitrification in a Fluidised Bed Reactor 547 Conversion of Nitrobenzene to Aniline 329 Non-Ideal Stirred-Tank Reactor 374 Oscillating Tank Reactor Behaviour 290 Oxidation Reaction in an Aerated Tank 250 Classic Streeter-Phelps Oxygen Sag Curves 569 Auto-Refrigerated Reactor 295 Batch Reactor of Luyben 253 Reversible Reaction with Temperature Effects 305 Reversible Reaction with Variable Heat Capacities 299 Reaction with Integrated Extraction of Inhibitory Product 280... 

With the system of Example 9.2 and starting with an R-free solution, kinetic experiments in a batch reactor give 58.1% conversion in 1 min at 65°C, 60% conversion in 10 min at 25°C. Assuming reversible first-order kinetics, find the rate expression for this reaction and prepare the conversion-temperature chart with reaction rate as parameter. 

Integrate the Performance Equation. For a reversible first-order reaction, the performance equation for a batch reactor is... 

If the reactor is to be operated isothermally, the rate of reaction diA can be expressed as a function of concentrations only, and the integration in equation 1.24 or 1.25 carried out. The integrated forms of equation 1.25 for a variety of the simple rate equations are shown in Table 1.1 and Fig. 1.8. We now consider an example with a rather more complicated rate equation involving a reversible reaction, and show also how the volume of the batch reactor required to meet a particular production requirement is calculated. 

The design of chemical reactors encompasses at least three fields of chemical engineering thermodynamics, kinetics, and heat transfer. For example, if a reaction is run in a typical batch reactor, a simple mixing vessel, what is the maximum conversion expected This is a thermodynamic question answered with knowledge of chemical equilibrium. Also, we might like to know how long the reaction should proceed to achieve a desired conversion. This is a kinetic question. We must know not only the stoichiometry of the reaction but also the rates of the forward and the reverse reactions. We might also wish to know how much heat must be transferred to or from the reactor to maintain isothermal conditions. This is a heat transfer problem in combination with a thermodynamic problem. We must know whether the reaction is endothermic or exothermic. 

The various types of reactors employed in the processing of fluids in the chemical process industries (CPI) were reviewed in Chapter 4. Design equations were also derived (Chapters 5 and 6) for ideal reactors, namely the continuous flow stirred tank reactor (CFSTR), batch, and plug flow under isothermal and non-isothermal conditions, which established equilibrium conversions for reversible reactions and optimum temperature progressions of industrial reactions. 

Methanol reacts with limonene over acidic catalysts in a batch reactor to 1-methyl-4-[alpha-methoxy-isopropyl]-l -cyclohexene (alpha-terpinyl methyl ether) as the main reaction product (see Eq. 15.3.3 R- = CH3-). Besides the desired methoxylation, isomerisation reactions leading to terpinolene and traces of alpha-and gamma-terpinene can be observed. Furthermore, the addition of methanol to the methylterpinylether leads to the undesired cis- or trans-1,8-dimethoxy-p-menthane. The amount of unidentified products does not exceed 1%. At high temperatures and long reaction times the reverse reaction of the alpha-terpinyl methyl ether and the other addition products to limonene and its isomers can be observed. The reaction scheme of the alkoxylation oflimonene is illustrated in Equation 15.3.5. 

Desorbed species are not removed and are allowed to accumulate in the inherently closed system of the batch reactor. Thus, unless a unidirectional reaction is being studied, reverse reactions must be taken into account in Ihe data analysis. The accumulation of desorbed... 

Below, we describe tbe design formulation of isothermal batch reactors with multiple reactions for various types of chemical reactions (reversible, series, parallel, etc.). In most cases, we solve the equations numerically by applying a numerical technique such as the Runge-Kutta method, but, in some simple cases, analytical solutions are obtained. Note that, for isothermal operations, we do not have to consider the effect of temperature variation, and we use the energy balance equation to determine tbe dimensionless heat-transfer number, HTN, required to maintain the reactor isothermal. 

We start the analysis with single reversible reactions. When a reversible reaction takes place, there is only one independent reaction hence, only one design equation should be solved. However, the rates of both forward and backward reactions should be considered. Tbe design procedure is similar to the one discussed in Section 6.2. To illustrate the effect of the reverse reaction, consider the reversible elementary isomerization reaction A B in a constant-volume batch reactor. We treat a reversible reaction as two chemical reactions ... 

Figure 6.8 shows the reaction operating curve for different values of 2/ 1 Note that the design equation for batch reactors with single reversible reactions has two parameters ( 1 and 2). whereas the design equation for reactors with an irreversible reaction has only one parameter. Also note that for an irreversible reaction, 2 = 0, and, from Eq. 6.3.3, Zi q = aCO). 

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