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Calculating Growth Kinetics in a Batch Reactor

Bacteria used to degrade a contaminant in a bacth reactor are found to grown on the contaminant with Monod Kinetics. Assuming Umax (the max specific growth rate)=10 per day, and Ks (called half velocity constant)=5mg/L and Kd (the decay constant)=0.05 per day.

At what value of S (the substrate concentration) will dX/dt=0. (X is the biomass concentration).

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I am not sure how to find X and S:
dx/dt=(Umax)(X)=0
Umax(X)=0
Umax(S/Ks+S)X=0
Monod model assumes that the test chemical is the sole growth limitinG compound in system.

Need S and X for the formula. Please help!

Solution Summary

One solution to pollution is bioremediation using strains of pollution-destroying bacteria. We can study this process by using a batch reactor system to measure the growth rates of bacteria in the presence of specific contaminants. The solution presented here calculates the substrate (the contaminant) concentration when the rate of biomass accumulation (aka bacterial growth) reaches steady state equilibrium (dx/dt = 0).

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