[Luyben] Process Mod.. - Student subdomain for University of Bath

245 MATHEMATICAL MODELS OF CHEMICAL ENGINEERING SYSTEMS
and replacing internal energies with enthalpies in the time derivative, the energy
equation of the system (the vapor and liquid contents of the tank) becomes
d@,KH+pV,h)
dt
= F,p,h, - Fph - F,p,H + Q - IVkCA (2.27)
In order to express this equation explicitly in terms of temperature, let us
again use a very simple form for h (h = C, T) and an equally simple form for H.
H = C, T + 1, (2.28)
where 1, is an average heat of vaporization of the mixture. In a more rigorous
model A, could be a function of temperature TV, composition y, and pressure P.
Equation (2.27) becomes
0, KW, T + 4) + PV, C, T3
dt
= F,p,C,T, - F&T
- F,pdC, T + I,) + Q - WkC, (2.29)
Example 2.8. To illustrate the application of the energy equation to a microscopic
system, let us return to the plug-flow tubular reactor and now keep track of temperature
changes as the fluid flows down the pipe. We will again assume no radial
gradients in velocity, concentration, or temperature (a very poor assumption in
some strongly exothermic systems if the pipe diameter is not kept small). Suppose
that the reactor has a cooling jacket around it as shown in Fig. 2.7. Heat can be
transferred from the process fluid reactants and products at temperatur