Design Equations for a Batch Reactor

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

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 ... 

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

Although semi-analytical solutions are available in some cases [5], these are cumbersome and it is more usual to employ a numerical method. A simple example is presented below which illustrates the solution of the design equation for a batch reactor operated isothermally the adiabatic operation of the same system is then examined. 

Numerical integration of design equation for a batch reactor operated non-isothermally... 

Applying the design equation for a batch reactor with rA = kCA = /cCA0(l — Xa), vA = — 1, we estimate the reaction time needed to convert 90% of the reactant ... 

The longer the reactants are left in the reactor, the greater will be the conversion. Equation (2-6) is the differential form of the design equation, and Equation (2-9) is the integral form of the design equation for a batch reactor. 

We call Equation (2-6) the differential form of the design equation for a batch reactor because we have written the mole balance in terms of conversion. The differential forms of the batch reactor mole balances. Equations (2-5) and (2-6), are often used in the interpretation of reaction rate data (Chapter 7) and for reactCHS with heat effects (Chapters 11-13), respectively. Batch reactors are frequently used in industry for both ga.s-phase and liquid-phase reactions. The lidmratory bomb calorimeter reactor is widely used for ol ning reaction rate data Liquid-phase reactions are frequently carried out in batch reactors when small-scale production is desired or operating difficulties rule out the use of continuous Row systems. 

The design equation for a batch reactor will be integrated for each of the three specified rate equations. The resulting expressions will be linearized and the data will be plotted to test the linearized equadoa If appropriate, the rate constant will be estimated fixnn the slope of the resulting line. 

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