Instrumented 3.0 L Glass Stirred-Tank Bioreactor
2.0 L working volume vessel with 4 vertical baffles, ring sparger, and Rushton turbine.
Chemical & Process Engineering / Bioreactor Oxygen Transfer k_L a
FREE TO EXPLORELABORATORY 31 · CHEMICAL & PROCESS ENGINEERING
Aerated Stirred-Tank Bioreactor Oxygen Mass Transfer Coefficient k_L a
Determine the volumetric gas–liquid oxygen mass transfer coefficient k_L a in an aerated, agitated stirred-tank fermenter using the dynamic gassing-out method with a fast-response dissolved oxygen probe as a function of impeller agitation speed N. Explore interactive transport phenomena, unit operations simulation, and chemical engineering telemetry.
TRANSPORT PHENOMENA · UNIT OPERATIONS · PROCESS CONTROL · REACTION ENGINEERING
Your virtual chemical and process engineering laboratory.
MASS TRANSFER FACTOR (K_L A)—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Agitation N = 300.0 RPM.
Adjust Agitation N, then execute chemical process trial.
Chemical and process engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity transport phenomena and unit operations modeling.
Process engineering assumptions and boundary condition limits
The transport and thermodynamic models apply within the specified calibrated operating window (100.0 to 600.0 RPM). Evaluated using a 3.0 L glass fermenter (liquid volume V_L = 2.0 L, Rushton turbine D_i = 45 mm, ring sparger) sparged with air at 1.0 vvm (2.0 L/min) and 25.0 °C. Linear regression models k_L a versus N^1.2 to extract slope S = 0.0240 h^-1/RPM^1.2.
Process apparatus & industrial sensors.
Fast-Response Polarographic Dissolved Oxygen (DO) Probe
Measures dissolved oxygen percentage from 0 to 100% saturation with 0.1% accuracy and t_90 < 2 s.
Dual-Gas Mass Flow Metering Manifold
Switches instantaneously between nitrogen gas (deoxygenation) and clean compressed air (reoxygenation).
Digital Variable-Speed Overhead Impeller Motor
Maintains precise agitation speeds from 100 to 600 RPM with ±1 RPM accuracy.
Circulating Thermostatic Water Jacket
Maintains aqueous broth at constant temperature 25.00 ± 0.05 °C.
Real-Time Bioprocess Data Acquisition Module
Logs DO reoxygenation curves at 5 Hz and computes k_L a via real-time linear regression.
FOLLOW THE METHOD
A reason behind every step.
Determine the volumetric gas–liquid oxygen mass transfer coefficient k_L a in an aerated, agitated stirred-tank fermenter using the dynamic gassing-out method with a fast-response dissolved oxygen probe as a function of impeller agitation speed N. Standardized parameter settings: 100.0, 200.0, 300.0, 400.0, 500.0, 600.0 RPM.
01
DO Probe 2-Point Calibration
Calibrate the DO probe at 0% saturation using zero-oxygen sodium sulfite solution (0.1 M Na2SO3 with CoCl2 catalyst) and 100% saturation in air-saturated water at 25.0 °C.
02
Bioreactor Charging & Thermostating
Fill reactor with 2.0 L of deionized water; set water jacket to 25.0 °C and turn on Rushton impeller at target test speed.
03
Nitrogen Deoxygenation Phase
Sparge nitrogen gas at 2.0 L/min through the ring sparger until dissolved oxygen C_L drops below 1.0% saturation.
04
Air Sparging & Reoxygenation Initiation
Instantly switch gas supply from nitrogen to compressed air at 2.0 L/min (1.0 vvm, t = 0); log transient DO percentage C_L(t) at 5 Hz.
05
Dynamic k_L a Regression Analysis
Plot ln[(C* - C_L) / C*] versus time t over the 20% to 80% DO window to extract volumetric mass transfer coefficient k_L a.
06
Agitation Speed Progression Protocol
Repeat dynamic reoxygenation procedure at impeller speeds N = 100, 200, 300, 400, 500, and 600 RPM; plot k_L a versus N^1.2 to determine slope S.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates Bioreactor Oxygen Transfer k_L a mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
k_L a = S · N^1.2 = 0.0240 · N^1.2
| # | Impeller Agitation Speed N (RPM) | Mass Transfer Factor (k_L a) (h^-1) | Agitation speed factor N^1.2 (RPM^1.2) | Volumetric oxygen mass transfer coefficient k_L a (h^-1) | Remove |
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CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
In the dynamic gassing-out method for determining k_L a, the liquid is first deoxygenated by sparging:
According to the van't Riet correlation for aerated water, k_L a scales with agitation speed N approximately as:
The units of the volumetric mass transfer coefficient k_L a are:
Adding surfactant antifoam agents to a bioreactor typically causes k_L a to:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
In industrial bioprocess engineering, aerobic fermentation (e.g., antibiotic synthesis, monoclonal antibody production, yeast cultivation, and wastewater bio-oxidation) requires continuous delivery of dissolved oxygen to metabolizing microbial cells. Because oxygen is sparingly soluble in aqueous nutrient broths (saturation concentration C* is only ~8.0 mg/L at 25 °C), the rate of biological oxygen consumption by dense cultures can deplete dissolved oxygen in seconds unless oxygen is continuously transferred across the gas-liquid interface. The volumetric rate of oxygen transfer (OTR) is governed by two-film mass transfer theory: OTR = k_L a · (C* - C_L), where k_L is the liquid-side film mass transfer coefficient, 'a' is the specific gas-liquid interfacial area per unit liquid volume, C* is saturation dissolved oxygen concentration, and C_L is bulk dissolved oxygen concentration. The lumped parameter k_L a (units h^-1) represents the aeration capacity of the bioreactor. In the dynamic gassing-out method, liquid is first deoxygenated by sparging nitrogen gas until C_L = 0; nitrogen is then shut off, air sparging is initiated, and the transient reoxygenation curve C_L(t) is recorded using a fast-response polarographic dissolved oxygen (DO) probe: dC_L / dt = k_L a · (C* - C_L) -> ln[(C* - C_L(t)) / C*] = -k_L a · t. According to van't Riet's classical correlations for aerated stirred tanks, volumetric mass transfer coefficient k_L a scales with mechanical agitation speed as N^1.2 and superficial gas velocity as v_s^0.5: k_L a ∝ (P_g / V)^0.4 · v_s^0.5 ∝ N^1.2. In this laboratory investigation, an instrumented 3.0-liter glass stirred-tank bioreactor is operated across impeller speeds from 100 to 600 RPM at constant air sparging rate to measure reoxygenation curves, verify N^1.2 scaling, and determine the aeration scaling slope S = 0.0240 h^-1/RPM^1.2.
k_L a = S · N^1.2 = 0.0240 · N^1.2
Evaluated using a 3.0 L glass fermenter (liquid volume V_L = 2.0 L, Rushton turbine D_i = 45 mm, ring sparger) sparged with air at 1.0 vvm (2.0 L/min) and 25.0 °C. Linear regression models k_L a versus N^1.2 to extract slope S = 0.0240 h^-1/RPM^1.2.