Experiment 03Bioprocess EngineeringFermentation Kinetics
Bioprocess Engineering: Batch Microbial Fermentation Kinetics ($X, S, P$), Specific Growth Rate ($mu$) & Monod Yield Coefficients ($Y_{X/S}$)
Duration: 8 Hours • Pilot Plant Bioreactor Lab
🎯 Experimental Aim & Learning Objectives
To operate a 5-liter stirred-tank bioreactor (CSTR) for aerobic batch cultivation of Saccharomyces cerevisiae or E. coli; monitor real-time online variables (dissolved oxygen, pH, temperature, agitation); perform offline assays of biomass ($X$), limiting substrate ($S$, glucose), and product ($P$, ethanol); and determine the maximum specific growth rate ($mu_{max}$), saturation constant ($K_s$), and yield coefficients ($Y_{X/S}, Y_{P/S}$) using the Monod kinetic model.
🔬 Theoretical Foundation & Bioprocess Equations
Microbial batch fermentation exhibits distinct growth phases (lag, exponential, stationary, and death):
- Specific Growth Rate ($mu$): During exponential growth, biomass increases autocatalytically:
$$frac{dX}{dt} = mu X implies lnleft(frac{X_t}{X_0}right) = mu cdot t implies t_d = frac{ln(2)}{mu} approx frac{0.693}{mu}$$ - Monod Kinetic Model: Relates growth rate to limiting substrate concentration ($S$):
$$mu = mu_{max} frac{S}{K_s + S}$$
where $mu_{max}$ is the maximum specific growth rate ($text{h}^{-1}$) and $K_s$ is the substrate affinity saturation constant ($text{g/L}$, substrate concentration at which $mu = 0.5 mu_{max}$). A linearized Lineweaver-Burk plot yields:
$$frac{1}{mu} = left(frac{K_s}{mu_{max}}right) frac{1}{S} + frac{1}{mu_{max}}$$ - Yield Coefficients:
• Biomass yield on substrate: $Y_{X/S} = frac{Delta X}{Delta S} = frac{X_{text{final}} – X_0}{S_0 – S_{text{final}}} quad (text{g dry cell weight / g glucose})$.
• Product yield on substrate: $Y_{P/S} = frac{Delta P}{Delta S} = frac{P_{text{final}} – P_0}{S_0 – S_{text{final}}}$. - Bioreactor Aeration & Volumetric Mass Transfer ($K_L a$): Oxygen transfer rate ($text{OTR} = K_L a cdot (C^* – C_L)$) must balance microbial oxygen uptake rate ($text{OUR} = q_{O_2} cdot X$) to maintain dissolved oxygen $> 20%$ saturation.
Figure 1.3: 5-Liter stirred-tank bioreactor instrumentation (CSTR) and microbial batch fermentation kinetic curves ($X, S, P$) governed by the Monod growth model.
🧪 Bioreactor Hardware & Analytical Reagents
- Equipment: 5 L autoclavable glass stirred-tank bioreactor with dual 6-blade Rushton impellers, rotameter air sparger, polarographic DO probe, sterilizable pH electrode, water heating jacket, and peristaltic acid/base pumps.
- Media Formulation (per Liter): $20text{ g Glucose}$, $10text{ g Yeast Extract}$, $20text{ g Peptone}$ (YPD medium), $0.1text{ mL Antifoam A}$.
- Analytical Assays: Spectrophotometer (600 nm) for optical density; analytical balance and $0.45text{ mu m}$ membrane filters for dry cell weight (DCW); Dinitrosalicylic acid (DNS) reagent for residual glucose assay; enzymatic assay kit for ethanol.
📋 Step-by-Step Bioprocess Protocol
- Vessel Sterilization & Calibration: Assemble the bioreactor with 3.5 L medium. Autoclave in situ at $121^circtext{C}$ for 30 minutes. Calibrate pH electrode (buffers 4.0 and 7.0) and polarographic DO probe (sparge $N_2$ for 0%, sparge air at 500 rpm for 100%).
- Inoculation & Control Setup: Inoculate with 200 mL of active S. cerevisiae seed culture ($5%text{ v/v}$). Set operating parameters: Temperature = $30^circtext{C}$, Agitation = $400text{ rpm}$, Aeration = $1.0text{ vvm } (3.5text{ L/min})$, pH maintained at $5.5$ via automated $2text{ M } NaOH$ addition.
- Kinetic Sampling: Draw 15 mL sterile samples every 60 minutes over an 8-hour fermentation cycle.
- Offline Measurements:
• Measure $OD_{600}$ and dry cell weight ($X$, $text{g/L}$).
• Centrifuge sample, collect supernatant, and quantify residual glucose ($S$, $text{g/L}$) via the DNS colorimetric method at 540 nm.
• Quantify ethanol concentration ($P$, $text{g/L}$). - Kinetic Parameter Modeling: Plot $ln(X)$ vs time during the log phase to extract $mu_{max}$. Plot $frac{1}{mu}$ vs $frac{1}{S}$ to determine $K_s$. Calculate $Y_{X/S}$ and $Y_{P/S}$.
📊 Representative Fermentation Kinetic Data
| Time (h) | Biomass $X$ (g/L) | Glucose $S$ (g/L) | Ethanol $P$ (g/L) | Dissolved $O_2$ (%) |
|---|---|---|---|---|
| 0.0 | 0.45 | 20.00 | 0.00 | 100% |
| 2.0 | 0.92 | 18.50 | 0.25 | 78% |
| 4.0 | 2.45 | 13.80 | 1.80 | 42% |
| 6.0 | 5.80 | 4.20 | 6.20 | 22% |
| 8.0 | 7.65 | 0.40 | 8.10 | 55% (Recovering) |
Calculated Kinetic Constants:
• Maximum Specific Growth Rate: $mu_{max} = mathbf{0.412text{ h}^{-1}}$ • Doubling Time: $t_d = frac{0.693}{0.412} = mathbf{1.68text{ hours}}$
• Monod Affinity Constant: $K_s = mathbf{0.85text{ g/L}}$
• Biomass Yield: $Y_{X/S} = frac{7.65 – 0.45}{20.00 – 0.40} = frac{7.20}{19.60} = mathbf{0.367text{ g DCW / g glucose}}$
• Product Yield: $Y_{P/S} = frac{8.10}{19.60} = mathbf{0.413text{ g ethanol / g glucose}}$ ($80.9%$ of theoretical Gay-Lussac yield).
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