Q.58
The amount of biomass in a reactor at the end of the batch process is 50 g.
Fed-batch operation is initiated by feeding the substrate solution at a constant rate of
1 L h−1. The concentration of substrate in the feed is
50 g L−1. The maximum biomass yield
(YXSM) is
0.4 g biomass / g substrate.
Assuming the system is at quasi-steady state, the maximum amount of biomass after
5 h of feeding is __________________ g.
Fed-batch processes enable controlled substrate addition to maximize biomass growth while avoiding limitations like substrate inhibition. At quasi-steady state, biomass increases linearly with the amount of substrate fed, based on the yield coefficient. After 5 hours of feeding, the maximum biomass reaches 150 g.
Problem Breakdown
The reactor starts with 50 g biomass after batch phase. Substrate feeds at 1 L h-1 with 50 g L-1 concentration, so substrate addition rate equals 50 g h-1. Maximum yield YX/Smax = 0.4 g biomass per g substrate means all fed substrate converts to biomass at quasi-steady state (constant specific growth rate, no accumulation). After 5 h, total substrate fed = 50 g h-1 × 5 h = 250 g, yielding extra biomass = 0.4 × 250 g = 100 g.
Calculation Steps
This assumes negligible maintenance, death rates, volume change impact on concentration (focus on total mass), and quasi-steady state where μ ≈ D (dilution rate) balances growth.
Common Distractors Explained
GATE numerical answer type (no options), but typical distractors include:
Exam Strategy
Quasi-steady state fed-batch simplifies to linear biomass growth: dX/dt = YX/S F Sf (total mass basis). Common in GATE BT for bioprocess engineering. Practice Monod kinetics tie-ins for variable μ cases. For your biotechnology studies, this concept optimizes high-density cultures in bioreactors.
