First-order reactions batch operations

The fed-batch scheme of Example 14.3 is one of many possible ways to start a CSTR. It is generally desired to begin continuous operation only when the vessel is full and when the concentration within the vessel has reached its steady-state value. This gives a bumpkss startup. The results of Example 14.3 show that a bumpless startup is possible for an isothermal, first-order reaction. Some reasoning will convince you that it is possible for any single, isothermal reaction. It is not generally possible for multiple reactions. 

This preliminary study suggests that mass transfer models could describe many features of xylan hydrolysis with accuracy similar to that of conventional first-order reaction-only models that have been long used to describe such systems. For example, a simple leaching model can describe release of xylan into solution as the product of a concentration gradient times a mass transfer coefficient. This model predicts that flowthrough operation could improve xylan release compared to a batch system by reducing the concentration in solution and thereby increasing the concen-... 

In this chapter, we have already discussed the unsteady operation of one type of reactor, the batch reactor. In this section, w C discuss two other aspects of unsteady operation startup of a CSTR and seniibatch reactors. First, the startup of a CSTR is examined to determine the time necessary to reach steady-state operation [see Figure 4-14(a)], and then semibaich reactors are discussed, in each of these cases, we are interested in predicting the concentration and conversion as a function of lime. Closed-form analytical solutions to the differential equations arising from the mole balance of the.se reaction types can be obtained only for zero- and first-order reactions. ODE solvers must be used for other reaction orders. 

Three-phase reactors are operated in either the semibatch or continuous mode, and batch operation is almost never used because the gas phase is invariably continuous. The general principles of design are the same for all types of reactors for a given mode of operation, semibatch or continuous. They differ with respect to their hydrodynamic features, particularly mass and heat transfer. Thus, for simple first-order reactions. Equation 17.8 is valid for any reactor. The rate constant ky,i would be the same for all of the reactors, but specific to each reactor type is the mass transfer term k/. Hence we consider first the design of... 

It is important to emphasize the fact that even for first order reactions the density change influences the performance of continuously operated reactors in contrary to batch reactors. In Figure 2.8 the influence of the expansion factor on the conversion of first order reactions is demonstrated. 

The most limiting factor for enzymatic PAC production is the inactivation of PDC by the toxic substrate benzaldehyde. The rate of PDC deactivation follows a first order dependency on benzaldehyde concentration and reaction time [8]. Various strategies have been developed to minimize PDC exposure to benzaldehyde including fed-batch operation, immobilization of PDC for continuous operation and more recently an enzymatic aqueous/octanol two-phase process [5,9,10] in which benzaldehyde is continuously fed from the octanol to the enzyme in the aqueous phase. The present study aims at optimal feeding of benzaldehyde in an aqueous batch system. 

Determine the time required for 80% conversion of 7.5 mol A in a 15-L constant-volume batch reactor operating isothermally at 300 K. The reaction is first-order with respect to A, with kA = 0.05 min-1 at 300 K. 

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. 

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. 

Both batch and continuous stirred tank reactors are suitable for reactions that exhibit pseudo-zero-order kinetics with respect to the substrate concentration. In other words, under operating conditions the rate is more or less independent of the concentration of the substrate. However, for reactions where pseudo-first-order kinetics with respect to the concentrations of the substrates prevail, a batch tank reactor is preferred. Batch tank reactors are also ideally suited when there is a likelihood of the reactant slowly deactivating the catalyst or if there is a possibility of side product formation through a parallel reaction pathway. 

You are operating a batch reactor and the reaction is first-order, liquid-phase, and exothermic. An inert coolant is added to the reaction mixture to control the temperature. The temperature is kept constant by varying the flow rate of the coolant (see Figure P9-6). 

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. 

Both reactions are assumed to be endothermic with first-order kinetics. The heat required for the reactions is supplied by steam which flows through the jacket around the reactor (Figure 1.10). The desired product is B C is an undesired waste. The economic objective for the operation of the batch reactor is to maximize the profit over a period of time tR that is,... 

A solution polymerization is to be carried out to 95% conversion in a series of stirred-tank reactors, all operating at the same temperature. Batch tests show that the reaction is first order to monomer, and 95% conversion is reached in 6 hours. 

Finally a fourth boundary condition shall be valid to support the worst case character of the procedure. The reaction order necessary for the formal kinetic description of a process has a severe influence on the pressure/time and respectively the tempera-ture/time-profiles to be expected. Industrial experience has shown that approximately 90% of all processes conducted in either batch or semibatch reactors can be described with a second order formal kinetic rate law. But it remains uncertain whether this statement, which is related to isothermal or isoperibolic operation with a rather limited overheating, remains valid if the reaction proceeds adiabatically and if side reactions contribute to the gross reaction rate at a much higher degree. In consequence, it shall be assumed for a credible worst case evaluation that the disturbed process follows a first order kinetics. Any reactions occurring in reality will almost certainly proceed at a much lower rate. 

Viewed from the perspective of ethylene oxide, these reactions are competitive by contrast, from the perspective of the amines, they are consecutive. Consider a research scale batch reactor operating at 60°C and 20 bar to maintain all species in the liquid phase. Actual production of these commodity products on a large scale would be conducted in flow reactors, as described in Illustration 9.5. The rate laws are of the mixed second-order form (first-order in each reactant), with hypothetical rate constants ki, k2, and equal to 1,0.4, and 0.1 L-moCV min, respectively. MEA and DEA are both high-volume chemicals, while TEA is less in demand. The distribution of alkanolamine products obtained under the specified conditions can be influenced by controlling the initial mole ratio of EO to A and the time of reaction. 

The ability of Monod s empirical relation to fit kinetic data for biochemical reactions has its foundations in generalizations of two phenomena frequently observed for fermentation processes (1) nature places a cap on the quantity of microorganism that can be achieved during the exponential phase of growth in a bioreactor operating in a batch mode and (2) as the concentration of the limiting substrate approaches zero, the rate laws for biochemical reactions approach pseudo-first-order behavior with respect to that substrate. The cap indicated on the cell growth rate has been associated with the natural limit on the maximum rate at which replication of DNA can be achieved. 

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

The operational conditions, that is, the concentration of substrate and enzyme, the temperature range, and the reactor configuration are summarized in Table 13.2. The activation energy of the reaction, E, was typically obtained for a batch reactor and compared with that calculated for a CSMR. The data obtained in the CSMR at steadystate enabled us, by using a semi-log plot of reaction rate versus time, to identify a first-order mechanism of enzyme deactivation and to determine both its first-order deactivation constant, kj, and the reaction rate at time zero, r, for each substrate and temperature. It was thus possible to compare the effect of the operational parameters on the activity and stability of these two enzymes. From the Arrhenius plot of these Tq, the E,-values were determined for each substrate, and were found to match the values obtained in the batch reactors. 

For a zero-order reaction (rA = /c in mol m s ), the heat released by the reaction does not depend on the concentration and conversion. Thus the simplification of a negligible influence of the conversion on the runaway (to derive simple runaway criteria as shown above) is now not needed. Instead of Eqs. (4.10.53) and (4.10.55) we obtain for the first and second condition of a stable operation of a cooled batch reactor ... 

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. 

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