Ideal reactors

By comparing the design equations of batch, CFSTR, and plug flow reactors, it is possible to establish their performances. Consider a single stage CFSTR. 

Conversion versus V/F for the dehydrogenation of benzene using the Runge-Kutta fourth order method 

At constant density, the material balance is uCA0 = uCA + (-rA)Vr and the volume of the reactor is 

For a well-mixed batch reactor, the design equation is 

Time must be included for emptying, cleaning, and filling the batch reactor (=30 min). 

Introduction to Reactor Design Fundamentals for Ideal Systems 389 

The kinetics of reactions has been studied for different reaction systems in liquid or gas phase, simple and multiple reactions, taking into account volume variation for different cases, and an important conclusion is that the understanding of kinetics is fundamental to the design of reactors. 

To design reactors, we have to calculate molar and energy balances considering that reactions can also take place under nonisothermal conditions. These balances contain always the generation term due to the chemical reaction, which is represented by the reaction rate. 

The conventional ideal reactors are batch, continuous, and semibatch. The conditions established for ideal reactors were shown in the previous section, and recapping, tanks should have perfect mixture and tubular reactors should have plug flow. 

Number of mol of reactant that becomes product I Formation rate of product rj [mol/(h.vol)]  

Molar flow of - Molar flow of + Generation or - Accumulation rate 

In practice, conditions in a reactor are usually quite different than the ideal requirements used in the definition of reaction rates. Normally, a reactor is not a closed system with uniform temperature, pressure, and composition. These ideal conditions can rarely if ever be met even in experimental reactors designed for the measurement of reaction rates. In fact, reaction rates cannot be measured directly in a closed system. In a closed system, the composition of the system varies with time and the rate is then inferred or calculated from these measurements. 

There are several questions that can be put forth about the operation of reactors and they can be used to form the basis of classifying and defining ideal conditions that are desirable for the proper measurements of reaction rates. 

The first question is whether the system exchanges mass with its surroundings. If it does not, then the system is called a batch reactor. If it does, then the system is classified as a flow reactor. 

The second question involves the exchange of heat between the reactor and its surroundings. If there is no heat exchange, the reactor is then adiabatic. At the other extreme, if the reactor makes very good thermal contact with the surroundings it can be held at a constant temperature (in both time and position within the reactor) and is thus isothermal. 

Mechanical variables Constant volume Constant pressure 

For the reaction A — P differential Equation (2.2-4) can be replaced by algebraic Equation (2.2-8)  

V = volume flow (no change due to reaction) Vr = effective reactor volume A = concentration of A in mol L .  

Hence the change in the molar flux of starting material A is equal to the amount of 

For a reaction that is nth order in starting material A A = -kA and the mean residence time r = Vr/V is given by Equation (2.2-9a) 

in a bimolecular reaction of A with B, the starting material B is present in excess E, then B = A + and Equation (2.2-8) then reads  

Defining the operation of a chemical reactor is done by writing the equations of conservation of mass, energy and momentum for each element of volume of the reactor, as follows 

Ideal reactors work under very simple limiting conditions, mainly concerning the residence time distribution. The operation of an ideal reactor is essentially controlled by chemical kinetics and thus the kinetic analysis of a chemical reaction is facilitated by the use of such a reactor. Furthermore, most laboratory and industrial reactors operate under conditions very near to ideality or may be modelled by simple combinations of ideal reactors. There are three main types of ideal reactors  

Rate of production due to chemical reaction within the element of volume 

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How a differential equation is formulated for some lands of ideal reactors is described briefly in Sec. 7 of this Handbook and at greater length with many examples in Walas Modeling with Differential Equations in Chemical Engineering, Butterworth-Heineman, 1991). 

For the ideal reactors considered, the design equations are based on the mass conservation equations. With this in mind, a suitable component is chosen (i.e., reactant or product). Consider an element of volume, 6V, and the changes occurring between time t and t + 6t (Figure 5-2) ... 

Adesina [14] considered the four main types of reactions for variable density conditions. It was shown that if the sums of the orders of the reactants and products are the same, then the OTP path is independent of the density parameter, implying that the ideal reactor size would be the same as no change in density. The optimal rate behavior with respect to T and the optimal temperature progression (T p ) have important roles in the design and operation of reactors performing reversible, exothermic reactions. Examples include the oxidation of SO2 to SO3 and the synthesis of NH3 and methanol CH3OH. 

Table 8-1 gives tlie relationships between tlie age distribution functions and Figure 8-6 shows the age distribution functions of ideal reactors. 

Non-ideal reactors are described by RTD functions between these two extremes and can be approximated by a network of ideal plug flow and continuously stirred reactors. In order to determine the RTD of a non-ideal reactor experimentally, a tracer is introduced into the feed stream. The tracer signal at the output then gives information about the RTD of the reactor. It is thus possible to develop a mathematical model of the system that gives information about flow patterns and mixing. 

To design a chemical reactor, the average concentrations, d,b,c,..., or at least the spatial distribution of concentrations, must be found. Doing this is simple for a few special cases of elementary reactions and ideal reactors that... 

Chapter 1 treated single, elementary reactions in ideal reactors. Chapter 2 broadens the kinetics to include multiple and nonelementary reactions. Attention is restricted to batch reactors, but the method for formulating the kinetics of complex reactions will also be used for the flow reactors of Chapters 3 and 4 and for the nonisothermal reactors of Chapter 5. 

Compare this result with that for a single, ideal reactor having the same input concentration, throughput, and total volume. Specifically, compare the outlet concentration of the composite reactor with that from a single CSTR having a... 

Reactor models consisting of series and parallel combinations of ideal reactors... 

This chapter treats the effects of temperature on the three types of ideal reactors batch, piston flow, and continuous-flow stirred tank. Three major questions in reactor design are addressed. What is the optimal temperature for a reaction How can this temperature be achieved or at least approximated in practice How can results from the laboratory or pilot plant be scaled up ... 

The above computation is quite fast. Results for the three ideal reactor t5T)es are shown in Table 6.3. The CSTR is clearly out of the running, but the difference between the isothermal and adiabatic PFR is quite small. Any reasonable shell-and-tube design would work. A few large-diameter tubes in parallel would be fine, and the limiting case of one tube would be the best. The results show that a close approach to adiabatic operation would reduce cost. The cost reduction is probably real since the comparison is nearly apples-to-apples. ... 

TABLE 6.3 Comparison of Ideal Reactors for Consecutive, Endothermic Reactions... 

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