Energy Balance—Reactor

For reactions involving heat effects, the total and component mass balance equations must be coupled with a reactor energy balance equation. Neglecting work done by the system on the surroundings, the energy balance is expressed by... 

The component mass balance equation, combined with the reactor energy balance equation and the kinetic rate equation, provide the basic model for the ideal plug-flow tubular reactor. 

When the process occurs nonisothermally in the reactor, energy balances must be used in conjunction with material balances. The general expression for energy balance is ... 

Note that now Tj is a variable that is a function of position Zc in the cooling coif while T, the reactor temperature in the CSTR reactor, is a constant. We can solve this differential equation separately to obtain an average coolant temperature to insert in the reactor energy-balance equation. However, the heat load on the cooling coil can be comphcated to calculate because the heat transfer coefficient may not be constant. 

The obvious way to heat or cool a chemical reactor is by heat exchange through a wall, either by an external jacket or with a cooling or heating coil. As we discussed previously, the coolant energy balance must be solved along with the reactor energy balance to determine temperatures and heat loads. 

Calculate the inlet reactor temperature and the recycle flowrate from a reactor energy balance. 

The temjperature and energy loads are matched as cIoseTy as possible. Styrene reactors typically operate i abaticalfy (no heat is added), causing the temperature to drop as the endothermic reaction proceeds. The teactor-inlet temperature required to adiieve the specified outlet temperature is calculated from a reactor energy balance,... 

Component A balance around reactor Energy balance on reacting mixture Energy balance on the coolant in the jacket... 

Liquid-phase reactions often are carried out in batch reactors. Equation 6.15 is therefore a common batch-reactor energy balance. Two cases where Equation 6.15 can be simplified include the case of adiabatic operation (Q = p) and the case of heat transfer through a jacket or cooling coil... 

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. 

Finally we require a boundary condition for the reactor energy balance, which we have from the fact that the heating fluid enters the reactor at = 0,T(0) = r (0). Combining these balances and boundary con-didons and converting to reactor length in place of volume gives the model... 

The reader has met examples of reactor energy balances in Chapter 2 and this chapter. It may be useful to consider this a little further with reference to optimization. Inclusion of a substantial electrical term makes the energy balance, and therefore the calculation of the cooling or heating requirements, somewhat different from that of other chemical plants. 

The straight line in Figure 8-15 is the overall reactor energy balance, Eqa (8-40). This equationserves to locate the value of Tq that corresponds to a givenoutletcondition, (xa(Z),7XZ)). 

The intersection of the curve and the straight line is the only point at which die reactor energy balance, the design equation, and the F/P exchanger energy balance are satisfied simultaneously. The point of intersection gives the values of xaCZ) and T 2) that result from a specified value of Tin. 

MacGregor, J.F. (1986) Online Reactor Energy Balances via Kalman Eiltering. lUPAC Conference on Instrumentation and Automation in Rubber, Plastic and Polymerization Industries, Akron, OH. 

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