Question

Calculate concentrations of nutrient, S and biomass, X at the outlet of the chemostat of sterile feed, So 20 8 dm2 Kinetics of cell grows is represented by the Monod model: u(S) a mar K +S Consider 2 cases: a) D 0.5 h b) D-1.5 h where D is dilution rate D F/V. Please discuss the results. Calculation should be performed for Hx1.0h, Ky 10- dm YX/s 0.3 3

Answer 1

S₀= 20 g/dm³

μ_max= 1 hr^-1

K_m= 10 g/dm³

Y_X/S= 0.3

Two cases are there where,

i) D= 0.5 hr^-1

ii) D= 1.5 hr^-1

we lnow in chemostat Y/s (Soung DZ we also know, D

Awa cases have Here we when D- 0.5 h row km+S MKm S= 0.5x 10 10 S lo gm 3 KnD max 10x0-5 1-05 O.3 11 Substoute 3 when D= 1.5 hn"ニu MEmay. S KmtS Aen 15 1-5 XI0 -30 M.KM -0.5 g1-1a m3 30 Sチ Kn D Amay-D Loxl-5 20 O.3 1-15 15 m sabtate An3

now, we can see that when D>μ_max (case ii), then S is negative, which is theoritically absurd.

The actual thing is that if dilution rate (D) is greater than the maximum growth rate (μ_max) then itexceeds critical dilution rate and as a result "wash out" occurs. So in practical D should always less than or equal to the maximum growth rate.

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