E. coli growth occurs a 5.0 L continuously-stirred tank reactor, the feed only contains glucose as the carbon source, and the glucose is the limiting nutrient. The initial cell concentration in the reactor is 96 g cells/L. The glucose is supplied in a feed stream at 65 g/L, entering the tank at 1.6 L/h (also called the dilution rate, D). The reactor is operated at steady state in terms of flow rate, so the exit stream leaves as 1.6 L/h as well. The specific growth rate in the continuous rector follows the Monod equation, with µmax = 0.42 h-1 and a saturation constant (Ks) of 12.5 g/L. A. Use the Monod equation to determine the specific growth rate, µ, for the cells. (assume the reactor has an initial glucose concentration of 65 g/L, matching the feed concentration, and that the cells are in the exponential growth phase) B. Using the initial concentration of cells and the growth rate found in part A, what is the rate of new cell growth, dX/dt, in the bioreactor (in g/L-h)? C. At what rate do the cells initially consume glucose (in g/h, considering the reactor volume)? (assume the cells are growing in the exponential growth phase and all glucose is used to produce new cells- no product is formed and maintenance energy is negligible).
E. coli growth occurs a 5.0 L continuously-stirred tank reactor, the feed only contains glucose as the carbon source, and the glucose is the limiting nutrient. The initial cell concentration in the reactor is 96 g cells/L. The glucose is supplied in a feed stream at 65 g/L, entering the tank at 1.6 L/h (also called the dilution rate, D). The reactor is operated at steady state in terms of flow rate, so the exit stream leaves as 1.6 L/h as well. The specific growth rate in the continuous rector follows the Monod equation, with µmax = 0.42 h-1 and a saturation constant (Ks) of 12.5 g/L.
A. Use the Monod equation to determine the specific growth rate, µ, for the cells. (assume the reactor has an initial glucose concentration of 65 g/L, matching the feed concentration, and that the cells are in the exponential growth phase)
B. Using the initial concentration of cells and the growth rate found in part A, what is the rate of new cell growth, dX/dt, in the bioreactor (in g/L-h)?
C. At what rate do the cells initially consume glucose (in g/h, considering the reactor volume)? (assume the cells are growing in the exponential growth phase and all glucose is used to produce new cells- no product is formed and maintenance energy is negligible).
D. Determine which of these three events will occur in the reactor: (i) the cell concentration will stay the same (it is at steady state), (ii) the cell concentration will increase (cells are growing faster than they are leaving the reactor), or (iii) the cell concentration in the bioreactor will decrease (cells are leaving the reactor faster than they can grow with the given feed stream) Note that the initial conditions given in the problem do not necessarily indicate that the reactor is at steady state, and the cell growth may need to adjust to the actual concentration of glucose in the reactor with time.
E. What flowrate of 65 g/L glucose feed is needed to run the chemostat bioreactor at steady state with a constant cell concentration of 96 g cells/L?
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