Equations for a batch reactor

From the mass balance equation for a batch reactor... 

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

By considering the small region in the emulsion phase where the distribution of the gas concentration can be regarded as flat, the equation for a batch reactor can be adapted and the following relationship is finally obtained. 

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. 

Integrate the Performance Equation. For a reversible first-order reaction, the performance equation for a batch reactor is... 

If we now write the equation for a batch reactor (Chapter 5, Section 5.2.2) with deactivating enzyme over time, we obtain Eq. (17.20), or after separation of variables Eq. (17.21), and after integration Eq. (17.22). 

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 ... 

Batch Reactor Since there is no addition or removal of reactants, the mass and energy conservation equations for a batch reactor with a constant reactor volume are... 

The CSTR operator, Rc, has an identical term to describe accumulation under transient operation. The algebraic sum of the two other terms indicates the difference of in-flow and out-flow of that species. This operator also describes semibatch or semicontinuous operation in cases where the volume can be assumed to be essentially constant. In the more general case of variable volume, V must be included within the differential accumulation term. At steady state, it is a difference equation of the same form as the differential equation for a batch reactor. 

FIGURE 6 Solution to the difFerential equation for a batch reactor with aggregation (i.e., equation (6.132)). (a) Variation in [Pg.242]

Interval III is characterized by polymerization in a constant number of latex particles in the absence of monomer droplets. The concentration of monomer in the latex particles thus declines as polymerization progresses. The principal modification required for the application ofEq. (S) in modeling Interval III is its coupling with a monomer balance equation and the modification of the growth factor K to incorporate the declining monomer concentration. A full monomer balance equation for a batch reactor demands the consideration of the monomer consumed in both the aqueous phase and the particles iMin and Ray, 1974). Frequently, however, the aqueous phase consumption is relatively small so that only consumption in the latex phase is significant. The latter is given by... 

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. 

This is the equation for a batch reactor, a constant volume of reaction mixture, and we see that it corresponds to the rate definition given in equation (1-12). A similar expression, of course, would apply for molal units. 

This is the energy balance equation for a batch reactor, in which T is the temperature of reaction, Tj is the temperature of the cooling/heating coil, and To is the initial temperature of the system. All other parameters have already been defined. 

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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