Page 1
Marc Deront (Sirous Ebrahimi)
The job to be done: Design and operate Bioprocesses towards best
efficiency and productivity, at minimal cost!
Biomass, which plays the key role inside bioreactors, if formed of
microorganisms requiring an optimal microenvironment!
Requirement of efficient transport processes in bioreactors
#5_Kla 1
Bioprocesses in Bioreactors
Transports
Consumption
(..) substrate
+ (..) O2
+ (..) N-source
+ …
Production
Biomass
+ (..) CO2
+ (..) H+
+ (..) heat
+ …
Page 2
Marc Deront (Sirous Ebrahimi)#5_Kla 2
WHAT, is Transported/Transferred into or from bioreactors:
• Gas : O2, CO2 …
• Fluids: Organic pollution, medium and substrates (or products)
• Solids: Organic matter (which must dissolved), minerals
• Heat
1. Mass transfer (liquid and gas): by means of Convection due to
Diffusion and Advection (mass displacement, f(density), f(T))
2. Heat transfer : Radiation (space), Conduction (solid), Convection
(fluid, density), Advection
Transport process, is an interdependent chain/network of 3 types of
transports mechanisms.
Rate limitation of one transport mechanism governs the overall transport
process.
Fundamentals of Transport processes
Page 3
Marc Deront (Sirous Ebrahimi)#5_Kla 3
1. Transport: FAST in ONE phase
Feeding, liquid pump, Aeration compressor
Mixing of stirred vessels or bubble columns
2. Transfer: SLOW between TWO phases
O2 and CO2 gas-liquid transfer in bioreactor
heat transfer in bioreactor
3. Transfer (Fick Diffusion) very SLOW in ONE phase
in biofilms
immobilized enzymes/organisms
in stagnant films at surfaces
In WWTP bioprocess, the most important nutriment, after substrate, is O2
O2 transfer is the most important transport process to provide!
3 types of transport in bioprocess
C
QQ.C
KLA(C*– C)
dC-AD -—
dX
Page 4
Marc Deront (Sirous Ebrahimi)#5_Kla 4
Many environmental bioprocesses are aerobic bioprocesses which
REQUIRE oxygen transfer for biomass respiration (electron acceptor
requirement, see COD balance). At steady state:
Biomass respiration Oxygen transfer rate
rO2 = qO2 . CX [gO2 .m-3.hr-1] OTR= kLa (CO2,L*- CO2,L)
Optimal dissolved O2 concentration
Optimization
• Oxygen transfer is expensive… about 20 to 60% WWTP operating energy
• Maximal dissolved oxygen is low, and in the range of mg O2/L. (About 8.6, 9,1 or 11
mg O2/L for 25, 20 or 10°C which be compared to 102 to 105 mg COD/L of electron
donor (substrate or organic pollutant)
CO2,L
[mg/L]
qO2 [gO2 .gX-1.hr-1]
0 1 2 3 4 … 11
Optimal range
qO2max
Critical CO2,L
O2 transfer for biomass respiration
Page 5
Marc Deront (Sirous Ebrahimi)
In air, XO2g molar fraction of O2 in gas = 0.21
PO2 = XO2g. P = 0.21*1= 0.21 [atm]
From Ideal Gas Law: PO2.V = nO2.R.T
As CO2g = nO2/V =PO2/(R.T)=mO2.C*O2L
As C*O2L= PO2/HO2,pc mO2 and HO2,pc are linked:
Calculate C*O2L, at T=298°K ; HO2,pc =780 [atm.mole-1.L]
HO2,pc Henry’a law : C*O2L=(0.21/780)*32*1000=8.6 [mg.L-1]
Ideal gas law : CO2g=0.21/(0.08205*298)=0.0086 [mole.L-1]
mO2 Partion C*O2L=(0.0086/32)*32*1000=8.6 [mg.L-1]
OP2
#5_Kla 5
mO2 partition coefficient = 32 at 298K(Thermodynamic parameter)
. gasmoleO m 3
2
. liquidmoleO m 3
2*
O lC2
2O gC
,O pc OH m RT2 2
2
1273 333
8391 24 23 24323 167 2367
-
O ,pc
[ atm.mole .L ] ;T [ - K ]
H exp(- . / T - . ln(T ) . )
R Values Unités
8,314472 J⋅mole-1⋅K-1
0,0820578437 L⋅atm⋅K-1⋅mole-1
Henry’s law
Henry’s law HO2
2
*
O lC. liquidmoleO L
1
2
atm
2 2 2
O g O O lC m C
,pc .O O O lP H C22 2
,cp .O l O OC H P 22 2
O2 Gas-liquid partition
“cp” vs. “pc”
c: O2 Concentration in liquid
p: O2 partial Pressure in gas
Page 6
Marc Deront (Sirous Ebrahimi)#5_Kla 6
spent air out
[molegas.h-1]
In WATER: Max. dissolved O2 (Saturation in
water) below 9 [mg.L-1] 0.3 [mole.m-3]
In GAS: O2 concentration (Air) : 0.3 [g.L-1] =
9.37 [mole.m-3]
Biomass consumes ONLY dissolved oxygen !
XO2gin > XO2g and CO2g
in > CO2g
Often in bioreactor CO2g CO2gin
O2
XO2gin inlet molar fraction of O2
CO2gin inlet O2 gas concentration [moleO2.m
-3gas]
O2 transfer for biomass respiration
fresh air in
XO2g outlet ( reactor) molar fraction of O2
CO2g outlet O2 gas concentration [moleO2.m-3
gas]
Page 7
Marc Deront (Sirous Ebrahimi)#5_Kla 7
gasAir bubble
Air in (21% O2)
Air out
LIQUID
GAS
R2
R4 R5
R6
R1Gas film
R3
Liquid film
Transport of oxygen, so crucial for biomass of aerobic bioprocesses, from
gas bubble to microorganisms through medium, is hindered by
several transfer resistances !
O2 transfer. A chain transport mechanisms
R1 R3 R5
R2
R4
R6
Gas Phase
Bubble
liquid Phase Cell
CO2
DiffusionConvection
Page 8
Marc Deront (Sirous Ebrahimi)#5_Kla 8
Bubbles side:
• R1, Within the gas film itself
• R2, At the gas-liquid interface
• R3, Within the liquid film itself
In the medium: R4, Liquid bulk resistance
Microorganisms side
• R5, Within the liquid film surrounding the microorganism
• R6, At the liquid-microbe interface
Which is the greatest resistance limiting overall transfer rate?
Negligible Quantities:• Gas phase diffusivity >> Liquid phase diffusivity, hence, R1 << R3
R1 usually negligible
• Assuming Gas/Liquid interface is in partition equilibrium Cgi = mi.Cli
R2 Interfacial resistance is small to be neglected
• In well mixed , inviscid systems, there is no resistance through the liquid phase R4 bulk resistance negligible (specially under
good mixing)
• The liquid-microbe interfacial resistance is small (particularly face to liquid-bubble interface) R6 can be neglected
• For small sized cells (e.g yeast and bacteria), Cell. diam. (~1-10µm) << Bubble diam. (~1-5 mm) it results in a larger cellular
interfacial area, hence, R5 <<R3 R5 negligible
Diffusion inside liquid film of gas bubble R3 is the rate controlling for overall transfer resistance.
Note: For large microbial pellets [(4-5 mm) relative to the size of a bubble (4-5mm)] e.g. microbial pellets or
fungi, the liquid film surrounding the pellet can be the rate limiting resistance…
O2 transfer. A chained transport mechanisms
Page 9
Marc Deront (Sirous Ebrahimi)#5_Kla 9
At interfaces, there are always more or less stagnant layers, of thickness where only
diffusion is possible, hindering gas transfer by R1 and R3 resistances.
The interfacial equilibrium constant mO2, is determined by the solubility of the gas in the
liquid phase (gas-liquid partition or Henry’s law).
Gas-Liquid Mass Transfer (1)
321 4 5
Bubble area
Astagnant
gasfilm
stagnantliquidfilm
GAS LIQUID
Ideally mixed
gas bulk phase
Ideally mixed
liquid bulk phase
CO2g
g L
CO2gi
CO2Li
R3R1
mO2 coeff.
CO2L
1. Convective transport to gas film
2. Diffusion in gas film over distance g
3. Gas/liquid O2 partition equilibrium at
bubble interface of area A
4. Diffusion in liquid film over distance L
5. Convective transport from liquid film
Page 10
Marc Deront (Sirous Ebrahimi)#5_Kla 10
Assuming steady state along transport chain: rategas= rateliq
3 unknowns (CO2Li, CO2g
i, rate) 3 equations… solving for CO2Li.
If gas diffusion or stagnant layer
If liquid diffusion or stagnant layer
Rate of transfer through a stagnant gas film (Fick)
2 22 2
i g
ga
d
s O g
ei
O g O g
g
g g
g
f
O
g
grate C k CAD D
A eC whC kre
Rate of transfer through a stagnant liquid film (Fick)
22 2 2. O L
l
l
def
iq l O L l
l
il
O
l
i
L O Lrate kAD D
AC wherC eC kC
Equilibrium at interface (Henry’s law)
Gas-Liquid Mass Transfer (2)
2
2
2
*
2
; i O gg
g
g
O L
O
O L CC
Cm
kD
2 2
22 2
2 2
2
2
2
2
2
2
.i i
l O L
lO
O
O
i i
O gg O L
i
O g
O g
Og
g
o g L
L
o
l
O
O
L
k C
Ck
k CC C
k C
kC
A A
mm
Ckm
Cm
2 22 2. ; 32 298i i
o g O o L mO aC tm C K
22; l
l O LO
l
i
LCk CD
Page 11
Marc Deront (Sirous Ebrahimi)
Considering overall transport, from bubble
gas phase to medium liquid phase, each resistant
step rates should be equal, and equal to
an overall gas transfer rate from gas bubble to liquid medium…
Thus overall KL depends on gas-liquid
partition coefficient, and resistances
of gas and liquid stagnant layers :
#5_Kla 11
2
2
2
22 2
2
2
i i
O lg O L
i
O g
i
g O g
O g
O L
l
gO O LL
A A
slo
C Ckk C
C
C
Ce
C k
C kp
22 2 22 2 2 2
* *
2rate = .l O L L O L
i i
O gg O OO L OL OLg O gkA A A withKC C CC Ck C C m C
2
1 1
.
1
L l gO kmK k
2 2 22
2
2
2
2
2
2
2 2
2
* *
O L O L
O
O O
O
i i
O L O L
i
O g i
O L
l
O L
O
O L
gL
L
g
m m
rate
K
C
rate rat
A
C
m A A
C C
CC
C C
C
k
e
C
k
KL overall mass transfer parameter (1)
CO2,gas
[moleO2m-3]
CO2,liq [moleO2m-3]
kL
kg
GASCO2g
C*O2L
CO2gi
CO2LiCO2L
kl
LIQUID
? What at S.S.?
Page 12
Marc Deront (Sirous Ebrahimi)#5_Kla 12
As KL overall transfer coefficient:
In bioprocesses, as Dg >> Dl, then m.kg >> kl
As: O2 diffusion coefficient in water Dl=10-9[m2.s-1]
Stagnant layer thickness : l=10-5[m]
Thus :
[mole.s-1] with : KL [m.s-1]; A [m2];
C*O2L = CO2g/m [mole.m-3] (HO2,pc=m.RT)
2
1 1
.
1
L l gO kmK k
KL overall mass transfer parameter (2)
4 -1 in the order of 10 m.slL
l
L
def DK k
Gas
phase
[mole.m-3]
Interfacial Area A [m2]
Liquid
phase
Transfer
CO2g CO2L[mole.m-3]
22
*· · L L O LOK CR A Cate
Page 13
Marc Deront (Sirous Ebrahimi)
Oxygen Mass Transfer Rate [mole.m-3.s-1]:
• No transfer, if C*O2L = CO2L, no driving force.
• Maximal transfer rate occurs when CO2L= 0. MaxOTR =KLa.C*O2L
(which is thermodynamically determined by solubility, and bioreactor)
• In bioreactor, after inoculation, biomass respiration increases demand,
decreasing CO2L, (C*O2L ̶ CO2L) driving force and O2 transfer rate
increase.
The rate of oxygen mass transfer in fermentation broths is highly influenced
by several physical and chemical factors that change either :
• the value of KL or the value of interfacial area a
• the driving force for mass transfer, (C*O2L ̶ CO2L)
Even if it can estimated, the precise value of gas transfer coefficient KLa for a given
bioprocess often requires Experimental KLa determination!!!
#5_Kla 13
2 2 22
* *
1
.
with Specific gas/liquid surface a a [ ]
· ·
re
O L OLLL O L O L
Ra
a
a
K C KV
Am
V
C CR te A Ce
at
2 2
*. O L O LLK aR COT C
Gas-Liquid Mass Transfer
Page 14
Marc Deront (Sirous Ebrahimi)#5_Kla 14
2. WITH Biomass “Dynamic” method
time
CO2L
CO2Lfinal
Gas flow
ON
2
2 2
*. O L
L O L O L
dCOTR K a C C
dt
1. WITHOUT Biomass
Common absorption method
(pO2 probe)
Experimental Determination of KLa
2 2
2 2
* 0
*ln .
O LO L
L
O L O L
C CK a t
C C
time
Gas flow
ON
2
22 . . . .
. . . :
O L
O x
dCrO q C OU R
dt
OU R OxygenUptake Rate
Gas flow
OFF
2
2 2
*
2. O L
L O L O L
dCK a C C rO
dt
dCO2L/dt
CO2L
KLa.C*O2L- rO2
KLa
CO2L
Page 15
Marc Deront (Sirous Ebrahimi)#5_Kla 15
The volumetric gas mass transfer in bioreactors is determined by agitation
(liquid mixing) and/or the aeration rate :
1. In CSTR bioreactor (Continuously Stirred Tank Reactor)Pg stands for Power [W.m-3] (Agitation)
Vsg stands for superficial gas velocity [m.s-1] (Aeration)
c1, and are constants for given combination
of the fluid and bioreactor geometry
2. In Bubble column of Airlift reactorAgitation term becomes negligible
for commonly gas flow rate
5 < Vsg < 30 [cm.s-1]
one can use for calculations
lK a (agitation,aeration)
1L
g
sg
PVc
VaK
1L sgK c Va
0.7 10.32. [ ] ; [ / ]sg sgL s V sVK ma
Volumetric gas mass transfer coefficient KLa
Page 16
Marc Deront (Sirous Ebrahimi)
Practically, as a general rule of thumb: in bioreactor, KL coefficient liquid
phase depends on bubble diameter:
- For bubbles diameter > 2-3 mm, KL 3-4×10-4 m/s and KL is
relatively constant and insensitive to conditions.
- For smaller bubble diameter KL 1 ×10-4 m/s depending on bubble
rigidity
To substantially improve mass transfer rates, it is usually more
productive to focus on the interfacial area a increase .
In bubble column, specific gas/liquid surface area a is a function of:
• Bubble diameter db (average 6 mm)
• Gas holdup ε (reactor volume expansion – Aeration)
So in bubble column or airlift bioreactor, it’s easy to measure ε gas holdup which
depends on gas superficial velocity Vsg.
#5_Kla 16
6bd
a
4 13 4 10 . if a L LK Kth n am s e How ?
Volumetric gas mass transfer coefficient Kla (2)