Batch reactors design equations for

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. 

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,... 

For batch reactors, time is the key design variable. The batch reactor design equations answer the question How long does it take to obtain a specified conversion or concentration ... 

Separate and integrate the batch-reactor design equation. The reaction time required for any given initial composition and conversion of reactants may now be calculated directly from the preceding expression, once this expression has been integrated and solved for t = f(X). The appropriate... 

These conclusions can be readily quantitatively visualized as shown in Fig. 10.2.b-3, which is based on the geometric nature of the plug flow or batch reactor design equation versus that for the perfectly mixed flow reactor. 

Gas sparged chemical reactors are designed and used in many different geometries. These reactors are usually continuous in gas, and batch or continuous in liquid. Some of the geometries in use are bubble columns, pipe and static mixer reactors, stirred vessels, packed columns, tray columns, spray columns, jet loop reactors, and venturi ejector reactors. Design equations for each geometry are based on correlations and simpUfying assumptions, such as uniform kLa in the stirred vessel. Other gas-Uquid reactors include spray columns and spray combustors. 

Now we need to consider a number of complications. In the discussion that follows, we will analyze the use of the design equation for two made up reactions that incorporate many variations of the batch-reactor design equations. These examples will also permit a more detailed discussion of some of the procedures used in Example 4-1. 

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. 

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. 

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. 

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 ... 

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. 

Fig. 2. Graphical integration of the design equation for a batch reactor, (a) General case [eqn. (5)]. (b) Constant density case [eqn. (6)].

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