Repeated Medium Replacement Culture Repeated Medium Replacement Culture
(REPLCUL)
(REPLCUL)
Introduction Introduction
V V
RS
0V
RVX VS
Final Conditions Initial Conditions
Replacement
Figure. One cycle for medium replacement culture.
•Each cycle is operated as a constant volume batch culture, in which the concentration of substrate decreases, while that of biomass increases.
VS
FVX
FModel
The equations are for batch culture, where the total masses are used for convenience .
μ = μ
mS / (Ks + S)
Monod kinetics
Model Coding
RS = -RX/Y RX = U*X
U = UM*S /(KS + S)
Coding
xdot(1) = RX*V
xdot(2) = -RS*V
Model
The initial conditions
0
(1 ) (1 )
R
F
F R
f V V
VX f VX
VS f VS V S
=
= -
= - +
Coding
F = VR/V
VX = (1-F) *VXF
VS = (1-F) *VSF + VR*SO
Program I
Symbols
D Dilution rate l/h f Fraction of volume replaced - KS Saturation constant g/m3 S Substrate concentration g/m3 X Biomass concentration g/m3 V Reactor volume m3
V0 Initial volume of liquid m3
VX Biomass in reactor Kg VS Substrate in reactor Kg VR Volume replaced m3 Y Yield coefficient g/g
µ Specific growth rate l/h
Indices
F Refers to final values at end of cycle S Refers to substrate
X Refers to biomass
0 Refers to initial and inlet values
Program II
Exercises
1. Run the program, and observe the number of cycles required to reach the pseudo steady state, for which each cycle becomes identical with the next.
Experiment with the initial conditions to reduce this number.
초기값 : UM=0.8, KS=0.1, Y=0.5, tf=4, VR=5, V=10, VSF=2, VXF=3, S0=5
Exercises
2. Adjust the operation variables so that the substrate is at least 90% consumed.
Does this alter the end biomass concentration?
Is the final substrate concentration in the K
Sregion? Yes
VSF= 1.0
Exercises
2. Vary K
Sto see the influence
KS= 0.1 tf = 4.0
KS= 1.0 tf = 4.0
μ = μ
mS / (Ks + S)
Exercises
2. Vary K
Sto see the influence
μ = μ
mS / Ks + S
KS= 5.0 tf = 4.0
KS= 5.0 tf = 10.0
Exercises 3. Experiment to see the influence of VR on the washout point.
VR= 2.0 VR= 5.0
VR= 8.0
Exercises 4. Revise the program to allow for product production, using kinetics of your choice
µ
M= 0.8µ
M= 0.5µ
M= 1.1μ = μ
mS / Ks + S
Exercises
5. Revise the program to simulate removal of medium without cells.
S0 = 0
Exercises
추가사항 #1. tf의 변화에 따른 biomass와 substrate의 변화
tf = 1.5
tf = 2.0 tf = 4.0
tf = 1.0
Exercises
추가사항 #2. VR에서의 substrate양의 변화에 따른 biomass와 substrate의 변화
S0= 3.0
S0 = 5.0 S0 = 8.0
S0 = 1.0