Substrate flows through a packed bed of immobilized-enzyme beads; each bead converts substrate to product following Michaelis–Menten kinetics, limited by diffusion (mass transfer) into the bead and by gradual loss of enzyme activity over time.
v = Vmax·[S] / (Km + [S])
Vmax ∝ enzyme loading × residual activity
activity(t) = exp(-k_d · t) (first-order deactivation)
- Substrate flow rate — higher flow shortens contact time with the beads, lowering per-pass conversion but raising throughput.
- Enzyme loading — the fraction of each bead's surface occupied by immobilized enzyme, setting Vmax.
- Substrate concentration [S] — feed concentration; conversion follows Michaelis–Menten saturation kinetics.
- Operating time — simulates cumulative reactor run-time; enzyme activity decays, reducing rate — motivating bead regeneration/replacement schedules.
Real-world application: continuous biocatalysis with immobilized enzymes is used industrially for making pharmaceuticals, sweeteners (e.g. immobilized glucose isomerase for high-fructose corn syrup) and biodiesel, because it enables reuse of expensive enzymes and steady, scalable production.