Analysis of Semibatch Reactors

The zeroth moment 2g gives the total moles of polymer at any time, whereas 2] gives the total count of repeat units, which can be shown to be time invariant. 

Equations (4.2.1a) and (4.2.1b) are suitably added to determine the generation relation of the zeroth moment Xq and first moment 2] as 

Equation (4.2.3b) implies that the first moment X is time invariant and its value can be obtained from the feed conditions. 

In order to solve for the molecular-weight distribution (MWD) of the polymer, as given by Eqs. (4.2.1) and (4.2.2), we must know the volume, V, of the liquid phase of the reactor and the rate of vaporization, Q . The rate of change of volinne V is given by 

In this development, there are seven unknoAvns [pi, p n 2), W, /Iq, Xi, V, and Q ], but we have only six ordinary differential equations [(4.2.1a)-(4.2.1c), (4.2.3a), (4.2.3b), and (4.2.4)] connecting them. Thus, one more equation is required. This is found by using the appropriate vapor-liquid equilibrium condition. Herein, to keep the mathematics simple, we assume the simplest relation given by Raoult s law. 

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We shall use concentration as our variable, leaving the analysis of semibatch reactors using the number of moles, /V,. and convei ion X to the DVD-ROM and Web. 

The design and analysis of semibatch reactors is mote complicated than the design and analysis of batch reactors. Example 7-5 will illustrate the procedure for solving problems involving semibatch reactors. 

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