Enzymatic Reaction in a Batch Reactor
Enzymatic Reaction in a Batch Reactor
Consider the following reaction scheme: , where is the substrate, is an enzyme catalyst, is the enzymesubstrate complex, which decomposes to give the product , and is the enzyme. This enzymatic reaction takes place in a batch reactor and the governing differentialalgebraic system of equations is:
S+EE.SE+P
k
2
⇆
k
1
k
3
→
S
E
E.S
P
E
d
c
S
dt
k
1
c
S
c
E
k
2
c
E.S
d
c
E.S
dt
k
1
c
S
c
E
k
2
c
E.S
k
3
c
E.S
d
c
P
dt
k
3
c
E.S
c
E0
c
E
c
E.S
3
dm
The initial conditions are: =1mol/, =0.001mol/, =0, and =0.
c
S0
3
dm
c
E0
3
dm
c
P0
c
E.S0
These equations can be solved using the Mathematica builtin function, NDSolve. This approach is the rigorous one.
Another method, called the quasisteadystate assumption, considers that =0. The resulting governing equations are:
d
c
E.S
dt
d
c
S
dt
d
c
P
dt

k
3
c
E0
c
S
K+
c
S
K=+
k
2
k
3
k
1
This model is referred to as MichaelisMenten kinetics. An analytical solution is possible for this model and is given by: t=+Kln.
k
3
c
E0
c
S0
c
S
c
S0
c
S
The reaction rate constants , , and are expressed in /(mol.hr),, and , respectively.
k
1
k
2
k
3
3
dm
1
hr
1
hr
This Demonstration shows the substrate concentration, [S], (red curve) and the product concentration, [P], (blue curve) versus time obtained using the exact approach. The bold dots correspond to the quasisteadystate approach. Agreement between both methods is obtained and justifies the utilization of the pseudosteadystate hypothesis, which is also called the quasisteadystate approach.