Insights from Mathematical Modelling into Energy Requirement and Process Design of Continuous and Batch Stirred Tank Aerobic Bioreactors
Abstract
:1. Introduction
2. Mathematical Modelling
2.1. Bioreaction Kinetics
2.2. Bioreactor Working Volume and Substrate Utilisation
2.2.1. Continuous Bioreactor
2.2.2. Batch Bioreactor
2.3. Oxygen Transfer and Detrmination of Agitator Power Requirement
2.4. Flooding and Phase Equilibrium Constraints
2.5. Aeration System Power Requirement
2.6. Refrigeration Power Requirement for Cooling
3. Results and Discussion
3.1. Bioreaction Kinetics
3.2. Bioreactor Volume and Feed/Wasted Sugar Substrate
3.2.1. CSTB
3.2.2. Batch
3.2.3. Effect of KS and Sugar Concentration
3.3. Electrical Power Requirement for Oxygen Transfer
3.3.1. CSTB—Effect of vvm, Agitator Mechanical Power and Steady-State Sugar Substrate Concentration
3.3.2. CSTB—Agitator and Compressor Power Requirement that Minimises Total Electrical Power for Aeration
3.3.3. CSTB—Effect of Steady-State Oxygen Concentration (COL)
3.3.4. Batch—Agitator and Compressor Power Requirement
3.4. Refrigeration Electrical Power Requirement for Cooling
3.5. Process Design Optimisation/Trade-Offs and Comparison of Batch and CSTB
- Working volume of the bioreactor
- Amount of feed sugar required
- Amount of wasted or unutilised sugar leaving the bioreactor
- Electric energy requirement for oxygen transfer and cooling
- Greenhouse gas emissions associated with electric energy supply
- Cost
4. Conclusions
Funding
Conflicts of Interest
Abbreviations
AT | cross-sectional area of bioreactor (m2) |
COG | oxygen concentration in air bubble (mg L−1) |
COGI | oxygen concentration in air entering bioreactor (mg L−1) |
COGO | oxygen concentration in air leaving bioreactor (mg L−1) |
COL | oxygen concentration in the bioreaction liquid (mg L−1) |
CSTB | continuous stirred tank bioreactor |
D | impeller diameter (m) |
DR | dilution rate (h−1) |
F | volumetric flowrate of feed entering bioreactor (m3 h−1) |
FG | inlet air volumetric flowrate (m3 h−1) |
FS0 | mass flowrate of sugar entering bioreactor (kg h−1) |
FSW | mass flowrate of wasted sugar exiting bioreactor (kg h−1) |
kLa | volumetric oxygen mass transfer coefficient (h−1) |
KO | Monod kinetic constant for oxygen (g L−1) |
KS | Monod kinetic constant for sugar (g L−1) |
M | Henry’s Law constant |
mS | specific maintenance coefficient (h−1) |
N | agitator rotational speed (s−1) |
NA | aeration number |
NFr | Froude number |
NP | agitator power number (ungassed) |
NPG | agitator power number (gassed) |
OUR | oxygen uptake rate (g L−1 h−1) |
OTR | oxygen transfer rate (g L−1 h−1) |
Pag | agitator mechanical power input in gassed bioreactor (kW) |
Patm | atmospheric pressure (Pa) |
Pb | product concentration in batch bioreactor when bioreaction is completed (g L−1) |
PC | compressor mechanical power input (kW) |
Pf | steady-state product concentration in CSTB (g L−1) |
Pi | atmospheric pressure + static head in bioreactor (Pa) |
P0 | concentration of any product in the feed (g L−1) |
PR | product production rate (kg h−1) |
Ptot | sum of compressor and agitator electrical power inputs (kW) |
Sb | sugar concentration in batch bioreactor when bioreaction is completed (g L−1) |
Sf | steady-state sugar concentration in CSTB (g L−1) |
S0 | concentration of sugar in the feed (g L−1) |
tb | bioreaction time in batch bioreactor (h) |
td | down time between batches in batch operation (h) |
T | bioreactor diameter (m) |
VL | bioreactor working volume (m−3) |
vs | air superficial velocity (m h−1) |
vvm | volume of air per minute per unit bioreactor working volume (min−1) |
Xf | steady-state cell concentration in CSTB (g L−1) |
YXS | Yield coefficient for biomass (g dry cell weight per g sugar) |
YPS | Yield coefficient for product (g product per g sugar) |
α, β | bioreaction model kinetic constants |
δ, Φ | OUR model constants |
µ | specific growth rate (h−1) |
µmax | maximum specific growth rate (h−1) |
ηC | compressor isentropic efficiency |
ηm | electric motor efficiency |
ηr | refrigeration efficiency |
γ | isentropic exponent of compression |
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μmax (h−1) | KS (g·L−1) | KO (g·L−1) | α | β (h−1) | YXS | YPS | mS (h−1) |
---|---|---|---|---|---|---|---|
0.25 | 0.005 | 0.000363 | 2.9220 | 0.1314 | 0.55 | 1 | 0.025 |
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Fitzpatrick, J.J. Insights from Mathematical Modelling into Energy Requirement and Process Design of Continuous and Batch Stirred Tank Aerobic Bioreactors. ChemEngineering 2019, 3, 65. https://doi.org/10.3390/chemengineering3030065
Fitzpatrick JJ. Insights from Mathematical Modelling into Energy Requirement and Process Design of Continuous and Batch Stirred Tank Aerobic Bioreactors. ChemEngineering. 2019; 3(3):65. https://doi.org/10.3390/chemengineering3030065
Chicago/Turabian StyleFitzpatrick, John J. 2019. "Insights from Mathematical Modelling into Energy Requirement and Process Design of Continuous and Batch Stirred Tank Aerobic Bioreactors" ChemEngineering 3, no. 3: 65. https://doi.org/10.3390/chemengineering3030065