function calculateOTR() {
// Get input values
var kla = document.getElementById('otr_kla').value;
var cStar = document.getElementById('otr_c_star').value;
var cL = document.getElementById('otr_c_l').value;
var volume = document.getElementById('otr_volume').value;
// Validation
if (kla === "" || cStar === "" || cL === "") {
alert("Please fill in kLa, Saturation Concentration, and Current Dissolved Oxygen fields.");
return;
}
var klaVal = parseFloat(kla);
var cStarVal = parseFloat(cStar);
var cLVal = parseFloat(cL);
var volVal = parseFloat(volume);
if (isNaN(klaVal) || isNaN(cStarVal) || isNaN(cLVal)) {
alert("Please enter valid numbers.");
return;
}
// Core Calculation: OTR = kLa * (C* – C_L)
var drivingForce = cStarVal – cLVal;
// Handle negative driving force (physically implies desorption, but usually we cap at 0 for standard OTR reqs)
if (drivingForce 0) {
var totalTransfer = otrGlh * volVal; // g/h
document.getElementById('res_total_transfer').innerHTML = totalTransfer.toFixed(2) + " g/h";
totalRow.style.display = "flex";
} else {
totalRow.style.display = "none";
}
// Show results container
document.getElementById('otr_result_container').style.display = "block";
}
How to Calculate Oxygen Transfer Rate (OTR) in Bioprocesses
The Oxygen Transfer Rate (OTR) is a critical parameter in aerobic fermentation, wastewater treatment, and cell culture engineering. It quantifies the rate at which oxygen is transferred from the gas phase (usually air bubbles) into the liquid phase where microorganisms can utilize it. Understanding how to calculate OTR is essential for scaling up bioreactors and optimizing yield.
The Fundamental OTR Formula
The calculation of OTR relies on the "driving force" principle of mass transfer. The standard equation used in biochemical engineering is:
OTR = kLa × (C* – C_L)
Where:
OTR: Oxygen Transfer Rate (typically expressed in mg/L/h or mmol/L/h).
kLa: The volumetric mass transfer coefficient (h⁻¹ or s⁻¹). This represents the efficiency of the reactor's aeration and agitation system.
C*: The saturation concentration of oxygen in the liquid phase (mg/L). This is the maximum amount of oxygen the liquid can hold at equilibrium.
C_L: The actual dissolved oxygen concentration currently in the liquid (mg/L).
Detailed Breakdown of Variables
1. Volumetric Mass Transfer Coefficient (kLa)
This is the most complex variable. It combines the liquid film mass transfer coefficient (kL) and the interfacial area per unit volume (a). Factors influencing kLa include:
Air Flow Rate: Increased aeration increases gas holdup and surface area.
Fluid Viscosity: More viscous fluids generally result in lower kLa values.
Antifoam Agents: These often reduce kLa by affecting bubble surface properties.
2. The Driving Force (C* – C_L)
Mass transfer occurs because there is a concentration gradient. Oxygen moves from areas of high concentration (the interface of the air bubble, assumed to be at saturation C*) to areas of low concentration (the bulk liquid, C_L).
To maximize OTR, you generally want to maximize the difference between these two values. Since C* is fixed by temperature and pressure (according to Henry's Law), operators usually try to keep C_L low (by consumption) or increase C* by increasing reactor pressure or oxygen enrichment.
Why Calculate OTR?
Calculating OTR helps engineers ensure that the Oxygen Supply Rate matches the Oxygen Uptake Rate (OUR) of the culture.
If OTR < OUR: The culture is oxygen-limited. Cell growth may stall, or the organisms may switch to anaerobic metabolism, producing unwanted byproducts like ethanol or organic acids.
If OTR > OUR: The system is sufficient, and dissolved oxygen levels (DO) will rise until a steady state is reached.
Common Units and Conversions
While this calculator uses standard engineering units, you may encounter variations:
kLa: Often in s⁻¹. To convert to h⁻¹, multiply by 3600.
Concentration: Often in mmol/L. To convert O2 mmol to mg, multiply by 32 (molecular weight of O2).
Example Calculation
Imagine a bioreactor with the following parameters:
kLa: 50 h⁻¹
Saturation (C*): 7.8 mg/L (typical for water at 25°C)
Current DO (C_L): 1.5 mg/L
The calculation would be:
OTR = 50 × (7.8 – 1.5) = 50 × 6.3 = 315 mg/L/h
This means every hour, 315 milligrams of oxygen are transferred into every liter of the liquid.