Oxygen Transfer Rate Calculation

Oxygen Transfer Rate (OTR) Calculator

Calculation Results

Volumetric OTR: mg/L/h

Total Mass Transfer: g O₂/h

Oxygen Transfer Capacity: kg O₂/day

function calculateOTR() { var kla = parseFloat(document.getElementById('klaInput').value); var csat = parseFloat(document.getElementById('csatInput').value); var cact = parseFloat(document.getElementById('cactInput').value); var vol = parseFloat(document.getElementById('volInput').value); if (isNaN(kla) || isNaN(csat) || isNaN(cact)) { alert('Please enter valid numerical values for the concentration and coefficient fields.'); return; } // OTR = KLa * (C* – C) var volumetricOtr = kla * (csat – cact); // Total Mass OTR (mg/h) = OTR (mg/L/h) * Vol (L) // Convert to g/h by dividing by 1000 var massOtrGrams = 0; var capacityKgDay = 0; if (!isNaN(vol) && vol > 0) { massOtrGrams = (volumetricOtr * vol) / 1000; capacityKgDay = (massOtrGrams * 24) / 1000; } document.getElementById('volOTR').innerText = volumetricOtr.toFixed(2); document.getElementById('massOTR').innerText = massOtrGrams.toFixed(2); document.getElementById('otc').innerText = capacityKgDay.toFixed(3); document.getElementById('resultsArea').style.display = 'block'; }

Understanding Oxygen Transfer Rate (OTR)

In biochemical engineering and wastewater treatment, the Oxygen Transfer Rate (OTR) is a critical parameter that determines the efficiency of aerobic processes. It represents the speed at which oxygen moves from the gas phase (air or pure oxygen) into the liquid phase (fermentation broth or wastewater) where it can be utilized by microorganisms.

The OTR Formula

The calculation of OTR is based on the two-film theory of mass transfer. The fundamental equation is:

OTR = K_La × (C* – C)

• K_La: The volumetric mass transfer coefficient (measured in h⁻¹). It combines the liquid-side mass transfer coefficient (K_L) and the gas-liquid interfacial area (a).
• C*: The saturation concentration of dissolved oxygen in the liquid (mg/L). This value depends on temperature, pressure, and salinity.
• C: The actual concentration of dissolved oxygen currently in the liquid (mg/L).

Key Factors Affecting OTR

Several physical and chemical factors influence how effectively oxygen dissolves into a liquid:

1. Temperature: As temperature increases, the solubility of oxygen (C*) decreases, but the mass transfer coefficient (K_La) typically increases due to lower viscosity.
2. Agitation and Aeration: Higher stirring speeds or air flow rates increase the "a" component of K_La by creating smaller bubbles and more surface area.
3. Pressure: Increasing the head pressure in a bioreactor increases C* (Henry's Law), which directly boosts the OTR.
4. Salinity and Impurities: Salts and organic compounds can alter bubble size and oxygen solubility, often decreasing the transfer rate compared to pure water.

Example Calculation

Suppose you are operating a 5,000-liter bioreactor for a yeast fermentation. You have measured the following parameters:

• K_La: 120 h⁻¹
• Saturated DO (C*): 8.2 mg/L
• Operational DO (C): 2.5 mg/L

Using the formula:

OTR = 120 × (8.2 – 2.5) = 120 × 5.7 = 684 mg/L/h.

To find the total oxygen supplied per hour: 684 mg/L/h × 5,000 L = 3,420,000 mg/h or 3.42 kg O₂/h.

OTR vs. OUR

In a steady-state biological system, the Oxygen Transfer Rate (OTR) must equal or exceed the Oxygen Uptake Rate (OUR). If the OUR (the rate at which microbes consume oxygen) is higher than the OTR, the dissolved oxygen levels will drop to zero, potentially leading to cell death or a switch to anaerobic metabolism.