Question

Chemical engineering question from Chapter 10 "mass transfer" in Bioprocess Engineering Principles; Pauline M. Doran; 2nd edition, Academic Press, 2012 (ISBN: 978-0-12-220851-5).

Problem:

The specific oxygen demands and critical oxygen concentrations for typical microbial, plant, and animal cell cultures are listed below: C-critical (g/m²) Required cell concentration Cell Culture 0.2624 25 (g/L) E coli Vitis vinifera (grape) Chinese hamster ovary (CHO) qo 8.5 (mmol/g.h) 0.6 (mmol/g.h) 3x10-10 (mmol/cell.h) 1.76 25 (g/L) 0.64 3 x 109 (cells/L) Estimate ka required to achieve the cell concentrations, while maintaining the dissolved oxygen concentration above critical. The oxygen solubility in the media used for the cultures is 7.2 g/m². Assume steady state; no accumulation of oxygen at any location in the fermenter.

Equations from chapter:

Answer 1

Oxygen intake rate per unit volume of broth = Qo = qo * x = specific oxygen uptake rate * cell concentration.

By mass trasfer, rate of oxygen transfer per unit volume = Kla * (Cla* - Cla) = liquid phase mass transfer coefficient * ( oxygen solubility in liquid - oxygen concentration in broth)

at steady state -

qo * x = Kla * (Cla* - Cla)

at Cla = C critical, the minimum value of mass trasfer coefficient can be calculated as -

Kla critical = qo*x / (Cla* - C critical)

oxyfen molecular weight = 32 gm/mol.

for, qo = 8.5 mmol/gmhr = 8.5 mmol O2 / gm cell . hr

= 8.5 mmol O2 / gmcell.hr * 1 mol/1000 mmol * 32gm O2 / 1mol O2

= 0.272 gm O2/ gm cell .hr * 1hr/3600 sec = 7.5556 * 10^-5 fm O2/ gm cell.sec

for microbial cell culture, using the values from the table in the question -

qo = 8.5 mmol/gm.hr * 1mol/1000 mmol * 32 gm/mol * 1hr/3600sec = 7.5556 * 10^-5 gm/gm.sec,

x = 25 g/L * 1000 L/m3 = 25000 gm / m3.

Cla* = 7.2 gm/m3, C critical = 0.2624 gm/m3.  

Kla critical = 7.5556*10^-5 gm/gm.sec * 25000 gm/m3 / (7.2 - 0.2624) gm/m3 = 0.27227 sec^-1

So, for maintaining dissolved oxygen above critical value, the Kla value should be greater than 0.27227 sec^-1 for microbial cell culture.

similarly for plant and animal cell culture -

for plant cell culture, using the values from the table in the question -

qo = 0.6 mmol/gm.hr * 1mol/1000 mmol * 32 gm/mol * 1hr/3600sec = 5.3333*10^-6 gm/gm.sec,

x = 25 g/L * 1000 L/m3 = 25000 gm / m3.

Cla* = 7.2 gm/m3, C critical = 1.76 gm/m3.  

Kla critical = 5.3333*10^-6 gm/gm.sec * 25000 gm/m3 / (7.2 - 1.76) gm/m3 = 0.2451 sec^-1

So, for maintaining dissolved oxygen above critical value, the Kla value should be greater than 0.2451 sec^-1 for plant cell culture.

for animal cell culture, using the values from the table in the question -

qo = 3*10^-10 mmol/cell.hr * 1mol/1000 mmol * 32 gm/mol * 1hr/3600sec = 8/3 * 10^-15 gm/cell.sec,

x = 3*10^9 cells/L * 1000 L/m3 = 3*10^12 cell/ m3.

Cla* = 7.2 gm/m3, C critical = 0.64 gm/m3.  

Kla critical = 8/3 *10^-15 gm/cell.sec * 3*10^12 cell/m3 / (7.2 - 0.64) gm/m3 = 1.2195*10^-3 sec^-1

So, for maintaining dissolved oxygen above critical value, the Kla value should be greater than 1.2195*10^-3 sec^-1 for animal cell culture.