Batch reactors first order irreversible reaction

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. 

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.

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

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 ... 

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. 

Turning to some design considerations, we now utilize a simple first-order irreversible reaction, with kV/F = ZO, and the conversion will be = 0.667 from Eq. 10.2.b-3 or 4 or from Fig. 10.2.b-l (the ordinate corresponding to the intersection of kV/F = 2JD and the ii = 1 line). In a plug flow or batch reactor, the conversion would be... 

ILLUSTRATIVE EXAMPLE 8.14 Product B is being produced from reactant A in a batch reactor in a first order irreversible reaction. The materials are aUowed to react for a period of 30 minutes at which time the batch (products) are removed. This shutdown period lasts approximately 15 minutes. Calculate the size of the reactor necessary to yield J at a rate of 250 Ib/h. Assume the temperature and pressure of the reaction to be constant. The following data is given ... 

TABLE 11.2 Ratio of Residence Times to Reaction Times in Batch Reactors vs CSTRs vs Conversion for a First-Order Irreversible Reaction... 

In order to calculate the exit reactant concentration for a first-order irreversible reaction in a reactor of known RTD, one must find the reactant concentration in a fluid element of residence time t, i.e. in a batch reactor after time t, multiply it by the fraction of fluid elements of that residence time and sum (integrate) over all permissible residence times. This gives ... 

Another problem that arises in batch operations is the question. What is the optimal time to run a particular operation For exanple, consider the sinple case of a batch reactor producing a product via a first-order, irreversible reaction. The conversion of product follows a single e q)onential relationship, as shown in Figure 14.11. 

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... 

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

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... 

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... 

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,... 

For the plug-flow reactor there is a formal analogy with the batch reactor equations derived in Chapter 1 if there is no volume change on reaction. As an example, consider the PFR design equation, (4-45), written for first-order irreversible kinetics (A B). 

In a batch reactor, a first-order, irreversible, liquid-phase reaction, A B occurs. The initial concentration is Qto-... 

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... 

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. 

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

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

Note that the uniform conditions in the reactor equal those at the reactor outlet, which implies that the production rate of A is also determined by the outlet conditions. The mass balance for a component in a CSTR is an algebraic equation, in contrast to the case of reactions in a batch or a plug flow reactor. For a single, irreversible first-order reaction and constant density, Eqn. 7.32 becomes ... 

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 ... 

Stability and dynamics of chemical reactions within batch systems date back to the pioneering work of Russian scientist Nikolay Semenov on chain reactions and combustion, for which he shared the 1956 Nobel Prize with Sir Cyril Hinshelwood. There have since been considerable literature contributions, the most widely studied system being the irreversible first order reaction A B with Arrhenius kinetics k T) = kot p —E/RT). The mass balance (in dimensionless variables) within the reactor yields ... 

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. 

The influence of heat transfer on yield and selectivity in scaling up batch and semibatch reactors will be illustrated using a series reaction, taking place in an ideal jacketed stirred-tank reactor. This reaction is composed of two irreversible elementary steps, both exothermic and both with first order kinetics ... 

When a reactor is charged with liquid A and B is a gas that is added continuously, it becomes a semibatch reactor. The rates of reaction depend on the concentration of B in the liquid phase, which is a function of gas solubility, pressure, and agitation conditions. However, we are often concerned with the relative reaction rates and the selectivity, which do not depend on Cb if the reaction orders are the same for both reactions. The reactions are treated as pseudo-first-order, and equations are developed for an ideal batch reactor with irreversible first-order kinetics... 

ERA The reaction was performed in a batch reactor and in the gas phase. 10% N2 was introduced in the reactor at 2 atm and 450°C. After 50 min, the pressure was 3.3 atm. The reaction is irreversible and of first order. Calculate the specific reaction rate constant. If the same reaction would be performed in a piston system with variable volume, how volume changes keeping pressure constant at 2 atm and considering the same conversion as before Calculate the initial concentration ... 

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 ... 

Program to design batch reactor/CSTR/PFR for first-order exothermic irreversible reaction operating at adiabatic condition... 

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