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 enzyme-substrate complex, which decomposes to give the product , and is the enzyme. This enzymatic reaction takes place in a batch reactor and the governing differential-algebraic 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 built-in function, NDSolve. This approach is the rigorous one.
Another method, called the quasi-steady-state 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 Michaelis-Menten 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 quasi-steady-state approach. Agreement between both methods is obtained and justifies the utilization of the pseudo-steady-state hypothesis, which is also called the quasi-steady-state approach.