Batch equation

Most kinetic experiments are run in batch reactors for the simple reason that they are the easiest reactor to operate on a small, laboratory scale. Piston flow reactors are essentially equivalent and are implicitly included in the present treatment. This treatment is confined to constant-density, isothermal reactions, with nonisothermal and other more complicated cases being treated in Section 7.1.4. The batch equation for component A is... 

A simpler method arbitrarily picks values for oq and reacts this material in a batch reactor at constant V and T. When the reaction is complete, P is calculated from the molar density of the equilibrium mixture. As an example, set = 22.2 (P=l atm) and react to completion. The long-time results from integrating the constant-volume batch equations are a = 5.53, 5 = c= 16.63, = 38.79mol/m, and y =0.143. The pressure at equili-... 

Alternatively, the residence time in the plug-flow reactor could be calculated from the batch equations given in Table 5.10. This... 

Section P2.4 has integrals of many batch equations. Numerical integration sometimes is more convenient than analytical. 

We next turn to process feedback. W e mentioned earlier that a plug-flow reactor can be viewed as a string of small batch reactors. We also pointed out that the result of each batch is uniquely determined by the fresh feeds since the solution to the batch equations is a forward integration in time. A plug-flow7 reactor cannot by itself show output multiplicity or open-loop instability. This picture changes when we... 

PVA accompanying the permente is lost permanently, since it leaves with tbe fabric, and reduces the quality of the removal siep. Yield is based on membrane retention and concentration factor. In practice, the process is tun in contlnuons stages, so yield must be calculated from a siage-by-siage computation, but the batch equations (18.1-6) and (18.1-7) give a reasonable approximation. 

Similarly, using the technique described in Sec. 7, the general batch equation is obtained ... 

To find X5, which is a combination of the reaction product from reaction 4 and Cj, we must first run a batch using X4 as the initial concentration. We can integrate the batch equation for the batch reaction time of t=0.15 h. 

Note that all three component batch equations must also be integrated since the system depends on all three components. Integrating Equation 3.1 for Cg, Cg, and Og, after t = 0.15 h, we find that the concentration of the fifth batch is Cg = 0.1697 mol/L, Cg = 0.4577 mol/L, and Cg = 0.0623 mol/L, which is the concentration of y4- Since we are only interested with plots in Cg-Cg space, we can ignore the ethylene concentration, giving y4 = [0.1697, 0.0623] mol/L. 

When a = 0 in a fed-batch reactor, Equation 7.21 reduces to the standard batch equation, which is identical to the PFR equation under continuous operation. 

It has already been established that, at equilibrium, the fed-batch equation reduces to the CSTR equation. Thus, the value of a in the fed-batch may be computed from the CSTR residence time by... 

Basically, the simple batch equation predicts the behavior when recirculation occurs because of low conversion per pass through the reactor. If we use the data in Example 4.2, the conversion per pass will be 1 — exp[—less than 0.3%. Working below the limiting current density it will be even smaller. It is immaterial in practice whether in a batch recirculation system the reactor is operating in a plug-flow or stirred-tank mode. Therefore, we can use the model equations derived for the batch reactor unless there are special circumstances such as, for example, the use of a three-dimensional electrode cell with a high active specific electrode area. 

Q Evaluate the algebraic (CSTR) or integral (tubular, batch) equations either numerically or analytically to determine the reactor volume, processing time, or conversion... 

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