Design equation batch reactor

In general, when designing a batch reactor, it will be necessary to solve simultaneously one form of the material balance equation and one form of the energy balance equation (equations 10.2.1 and 10.2.5 or equations derived therefrom). Since the reaction rate depends both on temperature and extent of reaction, closed form solutions can be obtained only when the system is isothermal. One must normally employ numerical methods of solution when dealing with nonisothermal systems. 

Design of a Batch Reactor. As seen above, for a batch reactor the design equation estimates only the time required for a reaction to proceed to a desired conversion level. If we want to design a batch reactor, i.e. estimate its volume, we have to consider other factors such as production rate, as demonstrated in the following example. 

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). 

Equations 14.1-13 and 14.1-16 are used by chemical engineers for the design of batch reactors. 

From diese various estimates, die total batch cycle time t(, is used in batch reactor design to determine die productivity of die reactor. Batch reactors are used in operations dial are small and when multiproducts are required. Pilot plant trials for sales samples in a new market development are carried out in batch reactors. Use of batch reactors can be seen in pharmaceutical, fine chemicals, biochemical, and dye industries. This is because multi-product, changeable demand often requues a single unit to be used in various production campaigns. However, batch reactors are seldom employed on an industrial scale for gas phase reactions. This is due to die limited quantity produced, aldiough batch reactors can be readily employed for kinetic studies of gas phase reactions. Figure 5-4 illustrates die performance equations for batch 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. 

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

Example 2.2 Derive the batch reactor design equations for the reaction set in Example 2.1. Assume a liquid-phase system with constant density. 

Example 2.10 Suppose 2A —> B in the liquid phase and that the density changes from po to Poo = Po + Ap upon complete conversion. Find an analytical solution to the batch design equation and compare the results with a hypothetical batch reactor in which the density is constant. 

Using V, we can write the design equations for a batch reactor in very compact form ... 

Chapter 2 developed a methodology for treating multiple and complex reactions in batch reactors. The methodology is now applied to piston flow reactors. Chapter 3 also generalizes the design equations for piston flow beyond the simple case of constant density and constant velocity. The key assumption of piston flow remains intact there must be complete mixing in the direction perpendicular to flow and no mixing in the direction of flow. The fluid density and reactor cross section are allowed to vary. The pressure drop in the reactor is calculated. Transpiration is briefly considered. Scaleup and scaledown techniques for tubular reactors are developed in some detail. 

Chapter 1 treated the simplest type of piston flow reactor, one with constant density and constant reactor cross section. The reactor design equations for this type of piston flow reactor are directly analogous to the design equations for a constant-density batch reactor. What happens in time in the batch reactor happens in space in the piston flow reactor, and the transformation t = z/u converts one design equation to the other. For component A,... 

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. 

The design equations for a nonisothermal batch reactor include A-fl DDEs, one for each component and one for energy. These DDEs are coupled by the temperature and compositional dependence of 91/. They may also be weakly coupled through the temperature and compositional dependence of physical properties such as density and heat capacity, but the strong coupling is through the reaction rate. 

The design equations for a chemical reactor contain several parameters that are functions of temperature. Equation (7.17) applies to a nonisothermal batch reactor and is exemplary of the physical property variations that can be important even for ideal reactors. Note that the word ideal has three uses in this chapter. In connection with reactors, ideal refers to the quality of mixing in the vessel. Ideal batch reactors and CSTRs have perfect internal mixing. Ideal PFRs are perfectly mixed in the radial direction and have no mixing in the axial direction. These ideal reactors may be nonisothermal and may have physical properties that vary with temperature, pressure, and composition. 

Multiphase reactors can be batch, fed-batch, or continuous. Most of the design equations derived in this chapter are general and apply to any of the operating modes. Unsteady operation of nominally continuous processes is treated in Chapter 14. 

Equating the time of passage through the tubular reactor to that of the time required for the batch reaction, gives the equivalent ideal-flow tubular reactor design equation as... 

A simulation model needs to be developed for each reactor compartment within each time interval. An ideal-batch reactor has neither inflow nor outflow of reactants or products while the reaction is carried out. Assuming the reaction mixture is perfectly mixed within each reactor compartment, there is no variation in the rate of reaction throughout the reactor volume. The design equation for a batch reactor in differential form is from Chapter 5 ... 

Thus within each time interval, the batch reactor can be modeled using Equation 5.39. This differential form of the design equation reflects the fundamental dynamics of a... 

The starting point for the development of the basic design equation for a well-stirred batch reactor is a material balance involving one of the species participating in the chemical reaction. For convenience we will denote this species as A and we will let (— rA) represent the rate of disappearance of this species by reaction. For a well-stirred reactor the reaction mixture will be uniform throughout the effective reactor volume, and the material balance may thus be written over the entire contents of the reactor. For a batch reactor equation 8.0.1 becomes... 

For constant fluid density the design equations for plug flow and batch reactors are mathematically identical in form with the space time and the holding time playing comparable roles (see Chapter 8). Consequently it is necessary to consider only the batch reactor case. The pertinent rate equations were solved previously in Section 5.3.1.1 to give the following results. 

In this chapter, we first consider uses of batch reactors, and their advantages and disadvantages compared with continuous-flow reactors. After considering what the essential features of process design are, we then develop design or performance equations for both isothermal and nonisothermal operation. The latter requires the energy balance, in addition to the material balance. We continue with an example of optimal performance of a batch reactor, and conclude with a discussion of semibatch and semi-continuous operation. We restrict attention to simple systems, deferring treatment of complex systems to Chapter 18. 

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