Page 190 - Modelling in Transport Phenomena A Conceptual Approach

170 CHAPTER 6. STEADY-STATE MACROSCOPIC BALANCES

Dividing Ea. (6.3-37) by the volumetric flow rate, &, gives

where r is the residence time defined by

(6.3-39)

Partial molar heat capacity of species i, Cpi, is related to the partial molar
enthalpy as
aHi
G i = (w) (6.3-40)
P
If cpi is independent of temperature, then integration of Eq. (6.3-40) gives

Hi(Tin) - Hi(2') = Cpi(Tin - T) (6.3-41)
Substitution of Eqs. (6.3-40) and (6.3-41) into Eq. (6.3-38) yields

(6.3-42)

where
(6.3-43)
i
It should be noted that the reaction rate expression in Eq. (6.3-42) contains a
reaction rate constant, k, expressed in the form

]c = Ae-&/a* (6.3-44)

Therefore, Eq. (6.3-42) is highly nonlinear in temperature.
Once the feed composition, stoichiometry and order of the chemical reaction,
heat of reaction, and reaction rate constant are known, conservation statements for
chemical species and energy contain five variables, namely, inlet temperature, T,,,
extent of reaction, E, reactor temperature, T, residence time, 7, and interphase heat
transfer rate, Qint. Therefore, three variables must be known while the remaining
two can be calculated from the conservation of chemical species and energy. Among
these variables Tin is the variable associated with the feed, [ and T are the variables
associated with the product, r and Qint are the variables of design.

Example 6.6 A liquid feed to a jacketed CSTR consists of 2000mol/m3 A and
2400 mol/ m3 B. A second-order irreversible reaction takes place as
A+B-t2C