Batch Reactor - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 161

reactor, T c is the temperature of the environment (surroundings). For an adiabatic

Q

reactor, ¼ 0 .

Example 4-6 H-Factor. A reaction with one single temperature-dependent reaction rate
constant,

r ¼ kðTÞC O RA

A C O RB

v A Aþðv B Þ B ! products (E4-6.1)

B

is carried out in a constant volume batch reactor. Each time when the reactor is loaded and
discharged, the temperature profile, i.e. temperature change with time during the intended
reaction period

T ¼ f ðtÞ (E4-6.2)

is different. For comparison purposes, we would like to develop a method to quantify the
effect so that operators can control the reaction effectively. A concept of H-factor was devel-
oped, which is the effective reaction time equivalent to that at a constant temperature T R .
Figure E4-6.1 illustrates this concept. Derive a formula for the H-factor.
Solution. For reaction occurring in a batch reactor, mole balance of reactant A leads to
0 0

In - Out + Generation = Accumulation

n A
d

d

n A rV ¼ (E4-6.3)

t

At T K for t hours

At T R K for a period of time t R

or H hours

t = ?

t = 0

FIGURE E4-6.1 The concept of H-factors as applied to pulping and reactions involving woodchips.