Comments on Productivity of Batch & Continuous Bioreactors (Chapter 9)

Transcription

1 Comments on Productivity of Batch & Continuous Bioreactors (Chapter 9) Topics Definition of productivity Comparison of productivity of batch vs flowing systems

2 Review Batch Reactor Cell Balances (constant volume): dnx dx VR dt dt dx dx netx g kd X net dt X dt Cycle time for a batch system (lump non-productive time as lost ): X ln m t t t t t t t t m X Productivity (average rate of production): c lag growth harvest prep growth lost lost N X X X m X/ b VR t tc mlnxm X tlost r Y 3 Review teady tate Chemostat (CTR) Cell balance: k D net g d ubstrate balance: D D q m X Y Y Y g P app X/ X/ P/ Rate of cell production: N FX V DX X Productivity is the DX term R 4

3 Chemostat Productivity with onod Kinetics From onod expression: m K g g K ubstrate balance (net = growth): D KD X Y Y X Y D Productivity: m g g X/ X/ X/ m KD r DX D Y D Y C X/ X/ m D 5 Chemostat Productivity with onod Kinetics What happens with increasing D? At small D the cell mass concentration is at its maximum KD X Y Y X/ X/ m D As D increases X always decreases, but the productivity will increase since the increase in D is faster than the decrease in X As D approaches µ m the cell concentration goes to zero (cell mass washout) & the productivity DX will also go to zero m Dmax K There will be an optimum productivity in between 6 3

4 Chemostat Productivity with onod Kinetics Optimal productivity when d(dx)/dd = D X opt opt X/ Y m K K K K K r Y K K K K Copt, X/ m K 7 Chemostat Productivity with onod Kinetics Normally in chemostat >> K so: Usually greater productivity in chemostat than batch system Typically X m /X to & t lost 3 to hours Example in text, X m /X =, t lost = 5 h, µ m = h -, then ratio is 8 r Y K K K K Y C, opt X / m X / m K r Copt, r b X ln X m t m lost 8 4

5 Productivity Chemostat with Recycle Cell balance: net D C ubstrate balance in growth phase: Productivity is DX : g YX/ X X YX/ C D r C DX D Y X/ X C X Y X/ 9 Productivity Chemostat with Recycle onod growth kinetics: C K KD g C m g m D r C D D Y X/ KD C C YX/ m D athematically similar to non-recycle case D KD r C YX/ where D DC C m D 5

6 Productivity Chemostat with Recycle Washout dilution rate m D max Dmax C K Optimum at dr C /dd = also dr C /dd = K m K D opt m Dopt K C K X Y K K K, opt X/ r D K K K K Y Copt, X/ C K Productivity Chemostat with Recycle 6

7 Productivity ulti-tage Chemostat st reactor looks like a single reactor. Great deal of flexibility in operating the nd reactor Additional substrate added? Different concentration added? Different volumes? Remember that the downstream material balances must incorporate the cell mass entering from the upstream reactors Productivity must include the contribution of both volumes F N X FX r X stage V V 3 Productivity ulti-tage Chemostat Example Does order make a difference? ometimes Example two vessels, 8 L & L g/l L/h ax yield.5 g cell mass/g substrate onod growth, µ m = h & K =.75 g/l st reactor, 8 L: g, D / 8.5 KD m D.5 X Y X/ 4 7

8 Productivity ulti-tage Chemostat Example nd reactor, L: X g, D.5 X X m g, K.75 olving iteratively: X Y X X/.56,.389, X g, F rc X V V 8 5 Productivity ulti-tage Chemostat Example What if we change the order? st reactor, L: g, D /.5 KD m D.5 X Y X/ nd reactor, 8 L: X 4.65 g, D.5 X X g,.99 m g,.74 K.75 X X YX/ X

9 Productivity ulti-tage Chemostat Example What if we make the reactor sizes different? st reactor, 9 L: g, D / 9. KD m D. X Y X/ nd reactor, L: X g, D. X X g,.87 m g,.66 K.75 X X YX/ X Productivity ulti-tage Chemostat Example What if we switch the order of these reactors? st reactor, L: g, D /. KD.75.. m D This is a washout condition this configuration will not work properly! 8 9

10 ummary Definition of productivity gives us a quantitative means to decide how to size & operate a bioreactor Not just what can be done but also what should be done ome of the simple configurations have simple relationships for optimal productivity some are much more complicated 9 upplemental lides

11 Other Configurations ulti-tage Chemostat aterial Balances ulti-tage Chemostat Only growth & X = Cell balance transient to steady state dx F V FX net,xv g, dt V dx F F F X V FX FF X net,xv g, dt V V X ubstrate balance transient to steady state FV d X V F F V g, g, dt YX/ X YX/ X d X FV F V V FF FF dt Y X X Y g, g, X/ X/

12 aterial Balances ulti-tage Chemostat For onod growth m g, g, K m g, m g, g, K m g, K K where µ g, is more complicated than just the dilution factor 3