## Surface-Immobilized Enzyme CSTR with Product Inhibition

### Biochemical Engineering

Problem Statement: Consider a continuous bioreactor in which a product-inhibited enzyme is immobilized on the surface of carrier beads through covalent chemical bonding. The surface area of immobilized beads is A, and the beads are completely fluidized. Substrate of concentration sf is continuously fed into the reactor of void volume V at a flow rate of F, and the reactor fluid content is also continuously removed at the same rate. List all the applicable equations to be solved to find the steady-state rate of conversion in the reactor.

Solution:

```   The substrate and product concentration at the reacting surface satisfy
the following relationship:

rate of mass flux = rate of reaction at the surface
kLs*(sb-s) = vm*s/(Km+s+Kp*p)
kLp*(p-pb) = vm*s/(Km+s+Kp*p)

Another way of expressing the above relationship is to say that the
substrate and product concentrations at the surface are functions of
that in the bulk.
s = s(sb,pb)
p = p(sb,pb)

Furthermore, in a continuous reactor operated at steady-state, the
substrate and product concentrations in the bulk are described by the
following coupled set of algebraic equations:

V*d(sb)/dt = 0 = F*(sf-sb) - A*kLs*(sb-s(sb,pb))

V*d(pb)/dt = 0 = -F*pb + A*kLp*(p(sb,pb)-pb)
```

Steady-State, Surface-Immobilized Enzyme CSTR with Product Inhibition. A series of Mathcad files contain the solution to this problem.

See here when an enzyme is entrapped inside gel beads of radius R.