lecture notes-bioreactor design and operation-2

lecture notes-bioreactor design and operation-2 -...

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Multi-stage Chemostat System In some fermentations, the growth and product- formation steps need to be separated. e.g. secondary metabolite, culture of genetically engineered cells. Growth stage Product formation stage At steady state, V n , X n ,S n, ,P n in the reactor of each stage don’t change with time. P 1 ≈0 P 2
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Multi-stage Chemostat System X 0 =0, V i, i=1,2….n constant. stage. each in rates growth gross specific respective the to equal are they 0, Kd When ely. recspectiv n, and 2,. .., 1, Stage in rates growth specific net are and ... , 2 1 = n μ At steady state Limiting substrate: dt dS V Y X V FS FS M S X 1 1 / 1 1 1 1 0 = - - M S X Y D X S S / 1 1 1 2 1 - = Stage 1: cell growth condition, Kd=0, q p =0 dt dX V V X FX FX 1 1 1 1 1 1 0 = + - Cell mass: ) 1 ( 1 0 1 1 X X D - = At steady state
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Multi-stage Chemostat System ) 1 ( 2 1 2 2 X X D - = μ dt dX V V X FX FX 2 2 2 2 2 2 1 = + - 2 2 V F D where = Stage 2 – product formation conditions, Kd=0, F’=0 At steady state Cell mass: P 1 ≈0 P 2 F V 2 are constant.
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Multi-stage Chemostat System Stage 2 – product formation conditions, Kd=0, F’=0 At steady state Limiting substrate: dt dS V Y X q V Y X V FS FS S P p M S X 2 2 / 2 / 2 2 2 2 1 = - - - μ S P p M S X Y D X q Y D X S S / 2 2 / 2 2 2 1 2 - - = dt dP V X q V FP FP p 2 2 2 2 2 1 = + - At steady state Product: 2 2 1 2 D X q P P p + =
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Multi-stage Chemostat System Stage n – product formation conditions, Kd=0, F’=0 If μ n (e.g. Monod model) and q p are known functions, X n , P n , and S n at nth stage could be determined by the above equations. ) 1 ( 1 n n n n X X D - - = μ S P n n p M S X n n n n n Y D X q Y D X S S / / 1 - - = - n n p n n D X q P P + = - 1 Similarly, equations could be obtained for nth stage.
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Multi-stage Chemostat System To determine the parameters (X, P) graphically when growth kinetics cannot be expressed analytically. With no additional streams added to the second or subsequent units, mass balance around the nth stage on cell, substrate and product yields dt dX V V X FX FX n n n n n n n = + - - μ 1 F: the volumetric flowrate (l/h); Dn=F/Vn: the dilution rate at the nth stage (1/h); Vn: the liquid volume of the nth chemostat (l) , ) ( Since , , n n n x n x X S X r = ) ( ) ( 1 , , - - = n n n n x n x X X D S X r ) ( 1 n n n n n X X D X - = - , 0 state steady at = dt dX n r x,n : cell growth rate at nth stage (g/l-h);
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lecture notes-bioreactor design and operation-2 -...

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