Energy balances semi batch reactors

The development of the semi-batch reactor energy balance follows directly from the CSTR energy balance derivation by setting Q = 0. The main results are summarized in Table 6.9 at the end of this chapter. Note in particular that Equations 6.81-6.83 in the semi-batch reactor Table 6.9 are identical to the corresponding Equations 6.72-6.74 in the CSTR Table 6.8. 

It is good practice to enumerate the unknowns and applicable equations when setting up a model for the noni so thermal semi-batch reactor. As discussed in Chapter 4, for a single-phase system, the molar concentrations of the components, and the temperature and the pressure specify all Intensive variables of the reactor. If we use the reactor volume as the single extensive variable, then we have + 3 unknowns. As in Chapter 4, we have n.s equations from the material balances and one equation of state. The energy balance of this chapter provides an additional equation. Finally, we must specify the reactor pressure or some other/System. coBStraint. that. determines the reactor pressure. 

Table 6.9 Energy balances for the semi-batch reactor.

Derive the CSTR energy balance given by Equation 6.72 in Table 6.8 by making the assumptions listed in the table. Now derive the semi-batch reactor Equation 6.81 in Table 6.9. Why are these two energy balances identical even though they apply to different reactor types . ... 

Note, however, that the temperature of the liquid inside the batch or semi-batch reactor changes with time. The energy balance for the liquid inside the batch or semi-batch reactor is... 

Section 13.3 shows how to apply the energy balance to a semi-batch reactor with a variable ambient temperature. 

In this chapter, we first consider uses of batch reactors, and their advantages and disadvantages compared with continuous-flow reactors. After considering what the essential features of process design are, we then develop design or performance equations for both isothermal and nonisothermal operation. The latter requires the energy balance, in addition to the material balance. We continue with an example of optimal performance of a batch reactor, and conclude with a discussion of semibatch and semi-continuous operation. We restrict attention to simple systems, deferring treatment of complex systems to Chapter 18. 

The condition for the practical implementation of such a feed control is the availability of a computer controlled feed system and of an on-line measurement of the accumulation. The later condition can be achieved either by an on-line measurement of the reactant concentration, using analytical methods or indirectly, by using a heat balance of the reactor. The amount of reactant fed to the reactor corresponds to a certain energy of reaction and can be compared to the heat removed from the reaction mass by the heat exchange system. For such a measurement, the required data are the mass flow rate of the cooling medium, its inlet temperature, and its outlet temperature. The feed profile can also be simplified into three constant feed rates, which approximate the ideal profile. This kind of semi-batch process shortens the time-cycle of the process and maintains safe conditions during the whole process time. This procedure was shown to work with different reaction schemes [16, 19, 20], as long as the fed compound B does not enter parallel reactions. 

For liquid-phase isothermal semi-batch operations with uniform injection rate, we can use the energy balance equation (Eq. 3.1.38) to determine the needed heating (or cooling) load and to estimate the isothermal HTN. Recall that the first term in Eq. 9.1.38 expresses the rate of heat transfer to the reactor... 

For multiple reactions occurring in either a semi batch or batch reactor. Equation (9-21) can be generalized in the same manner as the steady-state energy balance, to give... 

Nonisothermal reactor design requires the simultaneous solution of the appropriate energy balance and the species material balances. For the batch, semi-batch, and steady-state plug-flow reactors, these balances are sets of initial-value ODEs that must be solved numerically, in very limited situations (constant thermodynamic properties, single... 

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