Batch Reactor - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 164

2 L water into an M/K digester, quickly ramped up the temperature to 160 C. After 2 h at
160 C, she then quenched the reaction mixture down to room temperature. After thoroughly
washing the woodchips that were collected from the hot water extraction experiments, Kate
found that the woodchips are weighing 385 g.

a. How much mass loss (in %) for the woodchips occurred in the hot water extraction
experiment?
b. If Kate were to carry out the experiment at 180 C, what is the extraction time she should
keep in order to obtain roughly the same level of extraction?

Solution
a. Initially, the woodchips weigh 500 g and after extraction they weigh 385 g. Therefore,
500

385 g ¼ 115 g of wood was extracted or removed to the liquid phase. The mass loss is

¼

23%.
b. Let us assume that the extraction reaction can be approximated by a single temperature
varying reaction rate constant. That is the rate of mass removal may be approximated
by

thus 115/500

r ¼ kðTÞf ðCÞ (E4-7.1)

where C is the concentration of components inside the wood.
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 (E4-7.2)

t

Since the volume is constant (constant volume batch reactor), we further obtain

d C A
d

n A kf ðCÞ¼ (E4-7.3)

t

Since the rate constant k is only a function of temperature, separation of variables for Eqn
(E4.4-6) leads to

d

d C A

E
RT

f ðCÞ ¼ n A k

d t ¼ n A k 0 exp t (E4-7.4)

For a desired reaction end condition or conversion, the reaction time can be obtained by
integrating Eqn (E4-7.4) .

d

Z C A Z t

d C A

E
RT

E
RT f ðCÞ ¼

n A k 0 exp t ¼ n A k 0 exp t (E4-7.5)

C A0 0