Keep the Bioreactor at 37 °C

E. coli respire glucose aerobically and release heat as they grow, so the broth must be cooled to stay between 36 and 38 °C for the whole 24 h batch. First run a batch yourself by adjusting the cooling water. Then compare three ways of running the cooling to see why the pump must be sized for the peak heat output, not the average. Finally, test your knowledge with the four steps from Lecture 2: moles of glucose, heat released, mass of cooling water and flow rate. Work through the three stages in order.

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Where does 2,802.8 kJ mol⁻¹ come from?

Δ_rH° = ΣnΔ_fH°(products) − ΣmΔ_fH°(reactants)

C₆H₁₂O₆(s) + 6O₂(g) → 6CO₂(g) + 6H₂O(l)

Δ_rH° = [6 × (−393.5) + 6 × (−285.8)] − [(−1,273) + 6 × (0)]
= −4,075.8 − (−1,273) = −2,802.8 kJ mol⁻¹

The value is per mole of glucose, because the equation has one glucose on the left. O₂ is an element in its standard state, so Δ_fH° = 0. Enthalpies of formation are in kJ mol⁻¹.

5 kg of glucose is consumed by E. coli over a 24 h batch. Cooling water enters at 20 °C and leaves at 30 °C.

Predict first. The average flow needed for this batch is 1.3 L/min (Lecture 2). If the flow is left at 1.3 L/min for the whole run, will the broth stay between 36 and 38 °C?

Cooling water 0.30 L/min

Run the batch with:

Cooling	In range	Broth	Water used	Largest flow

Remember

Aerobic respiration of glucose: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O, Δ_rH° = −2,802.8 kJ mol⁻¹ (Lecture 2). The negative sign means that heat is released; the calculations use its size.
Heat released, q = n × 2,802.8 kJ mol⁻¹, where n = mass ÷ 180 g mol⁻¹.
Cooling water: q = m × C × ΔT, so m = q ÷ (C ΔT), with C = 4.18 kJ kg⁻¹ K⁻¹ and 1 L of water ≈ 1 kg. Divide by the time in minutes to get a flow in L/min, or by the time in seconds to get a rate in kW (kJ s⁻¹).
The model assumes that all of the glucose is completely oxidised to CO₂ and H₂O, and that all of the heat goes into the broth (5 kg of glucose in about 500 kg, or 0.5 m³, of broth). In a real culture some of the carbon is converted to biomass, so the heat calculated here is an upper estimate. The stirrer also adds heat, and some heat is lost through the walls and in the exhaust gas.