Under substrate-limited conditions, a microorganism exhibits Monod growth with a maximum specific growth rate of 0.5 h-1, a saturation constant (Ks) of 0.15 g L-1, and a cell yield on substrate of 0.4 g cell g substrate-1. Endogenous growth and maintenance are negligible. The available growth medium contains 10 g L-1 substrate.
After 6 hours in a batch reactor containing 100 L of the growth medium, the cell density is 0.2 g/L. Estimate the initial mass of cells (g) that were used to inoculate the reactor.
What is the substrate concentration 6 hours after inoculation?
What is the rate of substrate consumption 6 hours after inoculation?
2. You have conducted a series of pilot-scale experiments on a fed-batch reactor for a novel bioproduct. You plan to scale up your reactor to 1000 L and harvest biomass every 10 hours. Your initial culture volume of 400 L has a glucose concentration (So) of 20 g L-1. Glucose is added at a concentration of 200 g/L (SF). The initial biomass concentration is 50 g L-1. The kinetic and yield factors of the organism are mmax = 0.4 h-1, KS = 0.5 g L-1, and Yx/s = 0.3 g cell g glucose-1. Endogenous growth and maintenance are negligible (i.e., kd = 0), and you can use the pseudo-steady-state assumption.
If at 10 hours your reactor is at 90% of capacity, what is the flow rate of nutrient entering the reactor?
What is the glucose concentration (g L-1) after 10 hours?
How much glucose (g) has the organism consumed?
How much biomass (g) was produced?