28.16 Bacteria growing in a batch reactor utilize a soluble food source (substrate) as depicted in Fig. P28.16. The upta

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28 16 Bacteria Growing In A Batch Reactor Utilize A Soluble Food Source Substrate As Depicted In Fig P28 16 The Upta 1 (114.42 KiB) Viewed 32 times

28.16 Bacteria growing in a batch reactor utilize a soluble food source (substrate) as depicted in Fig. P28.16. The uptake of the substrate is represented by a logistic model with Michaelis-Menten limitation. Death of the bacteria produces detritus which is subse- quently converted to the substrate by hydrolysis. In addition, the bacteria also excrete some substrate directly. Death, hydrolysis and excretion are all simulated as first-order reactions. Mass balances can be written as dX S = μmax 1 (₁-X) ( x + ² + 5 ) X - ² X-kaX-keX dt K Ks+S dC =kdX - knC dt dS S =k₂X+knC-max 1 - (1₁-X) (K, $s) X dt K + S where X, C, and S = the concentrations [mg/L] of bacteria, detritus, and substrate, respectively; max = maximum growth rate [/d], K = the logistic carrying capacity [mg/L]; Ks = the Michaelis-Menten half-saturation constant [mg/L], ka = death rate [/d]; k₂ = excretion rate [/d]; and kn = hydrolysis rate [/d]. Simulate the concentrations from t = 0 to 100 d, given the initial conditions X(0) = 1 mg/L, S(0) = 100 mg/L and C(0) = 0 mg/L. Employ the following parameters in your calculation: µmax = 10/d, K = 10 mg/L, Kç = 10 mg/L, kd 0.1/d, ke 0.1/d, and kn = 0.1/d. =