Lecture 19: Oxygen Transfer in Fermentors

10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 19: Oxygen transfer in fermentors This lecture covers: Applications of gas-liquid transport with reaction Gas-liquid mass transfer in bioreactors Microbial cells often grown aerobically in stirred tank reactors -oxygen supply is often limiting μ X X X X X X X X X X critical value ≈ 0.01 mM D.O. Figure 1. μ vs dissolved oxygen. D.O. = dissolved oxygen Equilibrium solubility of O2 ≈ 1 mM bubble 4 O2 cell 1 2 3 Figure 2. Oxygen pathway. 1) 2) 3) 4) Diffusion across stagnate gas film Absorption Stagnate liquid layer (rate-limiting step) Diffusion and convection Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. at equilibrium 3) O2 flux = kl (CO2 − CO2 ) [=] * mass transfer coefficient mol area time bulk liquid concentration What is the value for the interfacial area? Important - system parameters: liquid physical properties (surface tension, viscosity) power input/volume (stirring, propeller size) superficial gas velocity empirical correlations (TIB 1:113 ’83) β ⎛P⎞ kl a = constantU s ⎜ ⎟ where Us is the superficial gas velocity ⎝V ⎠ ⎛ length ⎞ ⎛ area ⎞ −1 kl a[=] ⎜ (s-1) ⎟⎜ ⎟ = time ⎝ time ⎠ ⎝ volume ⎠ α U S [ =] length (m/s) time power P = V volume (W/m3) const. = 0.002 α = 0.2 β = 0.7 @ SS, O2 transport = O2 uptake by biomass biomass growth rate kl a (C − CO2 ) = * O2 μX YX O 2 dX < kl aCO* 2 YX O Crude limit: 2 dt or dX dt yield coefficient ≈ .4-.9 g cell dry wt. g O2 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 19 Page 2 of 4 Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. O2 transport in tissues o o r o R0 o o capillary radius Rc Figure 3. Krogh cylinder model. One-dimensional steady-state diffusion: DO2 ∂ ⎛ ∂CO2 ⎞ ⎜r ⎟ = VO2 r ∂r ⎝ ∂r ⎠  Fick's Law metabolic consumption rate of oxygen, zero-order (cylindrical coordinates) Boundary conditions: symmetry no-flux flux=0 @ r=R0 ∂CO2 = 0 @ r=R0 ∂r CO2 = CO2 , plasma @ r=Rc DO2 Integrate twice: CO2 CO2 , plasma ⎛ r* ⎞ = 1 + Φ ⎜ r *2 − R*2 − 2 ln * ⎟ R ⎠ ⎝ where r * = r R0 , R* = Rc R0 , Φ = 1 VO2 char. rxn rate R2 = 4 CO2 , plasma DO2 char. transport rate 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 19 Page 3 of 4 Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 CO2 Φ decreasing CO2 , plasma r* Figure 4. Dissolved oxygen vs. radius for various values of O2 diffuses further before consumption as When R ≈ 0.05, * decreases. CO2 = 0 @ r * = 1 when Φ ≥ 0.2 ~50-100 o Φ Φ. μm O2 necrotic core Figure 5. Tumor micrometastases. 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 19 Page 4 of 4 Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].