Batch reactors irreversible reactions

One irreversible chemical reaction occurs in a constant-volume batch reactor. The reaction is exothermic and a digital controller removes thermal energy at an appropriate rate to maintain constant temperature throughout the course of the reaction. Sketch the time dependence of the rate of thermal energy removal, d 2/t< f)removai vs. time, for isothermal operation when the rate law is described by ... 

EP.ll The consecutive reaction is A—KR S performed in a batch reactor. The reaction rates are first order and irreversible. The ratio at 50°C is known as ... 

Can an irreversible elementary reaction go to completion in a batch reactor in finite time ... 

The reaction is essentially irreversible, and its rate in a constant volume batch reactor is given by... 

For the case where all of the series reactions obey first-order irreversible kinetics, equations 5.3.4, 5.3.6, 5.3.9, and 5.3.10 describe the variations of the species concentrations with time in an isothermal well-mixed batch reactor. For series reactions where the kinetics do not obey simple first-order or pseudo first-order kinetics, the rate expressions can seldom be solved in closed form, and it is necessary to resort to numerical methods to determine the time dependence of various species concentrations. Irrespective of the particular reaction rate expressions involved, there will be a specific time... 

The following problem is formulated as an optimization problem. A batch reactor operating over a 1-h period produces two products according to the parallel reaction mechanism A — B, A — C. Both reactions are irreversible and first order in A and have rate constants given by... 

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. 

Investigate an isothermal, batch reactor (Set batch=l und isothermal=l) with an irreversible first-order (k1 k2). For this purpose set REST to a very high value, say le20. Determine the necessary reaction time to achieve a fraction conversion, XA, of 90, 95 und 99%. Determine also the cycle time and the productivity. For this assume the down-time between batches is 30 min (1800 s). Perform this for two different temperatures between 300K and 320K. 

Fig. 3 The batch reactor with irreversible reaction and cooling water flow at 0.023 m3/s gave these results.

An isothermal, first-order, Kquid-phase, irreversible reaction is conducted in a constant volume batch reactor. 

The following data on an irreversible reaction are obtained with decaying catalyst in a batch reactor (batch-solids, batch-fluid) What can you say about the kinetics... 

We need reaction-rate expressions to insert into species mass-balance equations for a particular reactor. These are the equations from which we can obtain compositions and other quantities that we need to describe a chemical process. In introductory chemistry courses students are introduced to first-order irreversible reactions in the batch reactor, and the impression is sometimes left that this is the only mass balance that is important in chemical reactions. In practical situations the mass balance becomes more comphcated. 

Figure 2-5 Plots of Ca(1) und Cg(t) versus kt for the first-order irreversible reaction A— B,r = kCA in a batch reactor.

One measures Cj (t, T) for given Cjo and then finds a suitable method of analyzing these data to find a suitable rate expression that will fit them. For liquid solutions the typical method is to obtain isothermal batch-reactor data with different Cjo and continues to gather these data as a function of temperature to find a complete rate expression. For a simple irreversible reaction we expect that the rate should be describable as... 

Assuming that we have an irreversible reaction with a single reactant and power-law kinetics, r = kC, the concentration in a constant-volume isothermal batch reactor is given by integrating the expression... 

An irreversible aqueous reaction gave 90% conversion in a batch reactor at 40°C in 10 min and required 3 min for this conversion at 50°C. 

Therefore, to find the behavior of a PFTR for kinetics that we have solved in a batch reactor, all we have to do is make the transformation tbatch —> tpFTR- The solution for the th-order irreversible reaction fi om Chapter 2 is... 

An irreversible first-order reaction gave 95% conversion in a batch reactor in 20 min. 

For a first-order irreversible reaction in an isothermal batch reactor X(t) = 1 — e (Chapter 2) so the average value of X is... 

At the same time, as a chemist I was disappointed at the lack of serious chemistry and kinetics in reaction engineering texts. AU beat A B o death without much mention that irreversible isomerization reactions are very uncommon and never very interesting. Levenspiel and its progeny do not handle the series reactions A B C or parallel reactions A B, A —y C sufficiently to show students that these are really the prototypes of aU multiple reaction systems. It is typical to introduce rates and kinetics in a reaction engineering course with a section on analysis of data in which log-log and Anlienius plots are emphasized with the only purpose being the determination of rate expressions for single reactions from batch reactor data. It is typically assumed that ary chemistry and most kinetics come from previous physical chemistry courses. 

We shall now proceed to compare the three basic types of reactor—batch, tubular and stirred tank—in terms of their performance in carrying out a single first order irreversible reaction ... 

This is the most common mode of addition. For safety or selectivity critical reactions, it is important to guarantee the feed rate by a control system. Here instruments such as orifice, volumetric pumps, control valves, and more sophisticated systems based on weight (of the reactor and/or of the feed tank) are commonly used. The feed rate is an essential parameter in the design of a semi-batch reactor. It may affect the chemical selectivity, and certainly affects the temperature control, the safety, and of course the economy of the process. The effect of feed rate on heat release rate and accumulation is shown in the example of an irreversible second-order reaction in Figure 7.8. The measurements made in a reaction calorimeter show the effect of three different feed rates on the heat release rate and on the accumulation of non-converted reactant computed on the basis of the thermal conversion. For such a case, the feed rate may be adapted to both safety constraints the maximum heat release rate must be lower than the cooling capacity of the industrial reactor and the maximum accumulation should remain below the maximum allowed accumulation with respect to MTSR. Thus, reaction calorimetry is a powerful tool for optimizing the feed rate for scale-up purposes [3, 11]. 

Fig. 2.4 Time histories of Ca (continuous line), Cpi (dotted line), and Cp2 ( dashed line) in a batch reactor for parallel reactions of A producing Pi, via an equilibrium limited reaction, and P2, via an irreversible reaction. Initial conditions are Cao = 1 molm-3,...

To this goal, let us consider a cooled batch reactor in which the following network of irreversible reactions takes place ... 

Consider a jacketed batch reactor in which the same network of irreversible exothermic reactions adopted in Chap. 5 takes place. In order to design the FD framework, the state-space model (5.15) is rewritten in a slightly different form, i.e.,... 

We begin by considering the simple chemistry of a liquid-phase, first-order, irreversible, exothermic reaction occurring in a batch reactor ... 

This case was analyzed in 1968 by Aris, based on a formalism introduced more generally in an earlier paper (1965a). Essentially the same problem was analyzed again by Bailey in 1972. Because the reactions are irreversible, c x,t) is negative unless c(x,r) is zero. Because the reactions are first order, the only relevant parameter of any species x is the kinetic constant k(x), and this has been reduced by renormalization to k x. Hence, the kinetic equation in a batch reactor has the form ... 

The time necessary to achieve 90% conversion in a batch reactor for an irreversible first-order reaction in which the specific reaction rate is 10 s is 6.4 h. For second-order reactions we have... 

We make the assumption that the reaction is first order and irreversible, so that if N is the number of moles of A in the batch reactor at time t and V is its volume. 

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). 

The reaction is carried out in a well-stirred batch reactor at 40°C. Under these conditions, the esterification reaction can be considered as irreversible at conversions less than 70%. The following data were obtained using identical sulfuric acid concentrations in both runs. 

This lime is the reaction time t (i.e., Jr) needed to achieve a conversion X for a second-order reaction in a batch reactor. It is important to have a grasp of the order of magnitudes of batch reaction times. Jr, to achieve a given conversion, say 90%, for different values of the product of specific reaction rate. k. and initial concentration. AO-. Table 4-1 shows the algorithm to find the batch reaction limes. Jr. for both first- and a second-order reactions carried out isothermaliy. We can obtain these estimates of Jr by considering the first- and second-order irreversible reactions of the form... 

The optimal temperature policy in a batch reactor, for a first order irreversible reaction was formulated by Szepe and Levenspiel (1968). The optimal situation was found to be either operating at the maximum allowable temperature, or with a rising temperature policy, Chou el al. (1967) have discussed the problem of simple optimal control policies of isothermal tubular reactors with catalyst decay. They found that the optimal policy is to maintain a constant conversion assuming that the decay is dependent on temperature. Ogunye and Ray (1968) found that, for both reversible and irreversible reactions, the simple optimal policies for the maximization of a total yield of a reactor over a period of catalyst decay were not always optimal. The optimal policy can be mixed containing both constrained and unconstrained parts as well as being purely constrained. 

Economic optimum almost always exists, while process-based optimum may not exist in some cases. To clarify this point, let us consider the simplest possible problem (which is certainly not a fixed bed catalytic reactor), an isothermal batch reactor, where an irreversible first order reaction,... 

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