Wastewater Temperature: Predicting It in Sewers and Tanks, and Designing for the Cold Case

Why temperature is a design variable

Biological rates follow an Arrhenius-type relation, r_T = r₂₀ θ^{(T − 20)}. For heterotrophic BOD removal θ is about 1.04; for autotrophic nitrifiers it is 1.07 to 1.10, so the maximum nitrifier growth rate at 8 °C is only about 35 to 40 percent of its value at 20 °C, and the minimum aerobic sludge age for nitrification roughly triples. Oxygen solubility rises in cold water (about 11.3 mg/L at 10 °C against 9.1 at 20 °C), which helps transfer a little, but settling velocities fall as viscosity rises (water is 30 percent more viscous at 10 °C than at 20 °C), and anaerobic digestion heating demand is set directly by the feed temperature. So the design question is: what is the lowest sustained temperature the process will see, and for how long?

Heat balance in a sewer

Wastewater leaves buildings at 15 to 25 °C depending on the share of hot water, and then exchanges heat with the sewer air above it and, through the pipe wall, with the surrounding soil. Treating a reach of length Δx as a steady-state exchanger with lumped thermal resistances gives:

Field calibration on UK sewers gives resistances that vary with season and sewer type. In a collector sewer the water-to-air resistance is small, around 0.02 to 0.03 m·K/W, and the water-to-soil resistance 0.07 to 0.11; in a small residential sewer both are larger, of the order of 0.05 to 0.4 to air and 0.3 to 0.8 to soil, rising in summer as the heat transfer coefficient to the air falls. The soil term depends on the ratio of soil penetration depth to conductivity, which in practice is calibrated rather than measured. Two conclusions from the field work matter for design: in-sewer air temperature, not soil temperature, is the dominant influence on wastewater temperature in most sewers, and it tracks the wastewater closely, so a poorly ventilated sewer loses little heat.

Worked example. A collector carrying 50 L/s at 14 °C runs 3 km through soil at 9 °C with in-sewer air at 12 °C. Take R_wa = 0.025 and R_ws = 0.09 m·K/W. Heat loss per metre = (14 − 12)/0.025 + (14 − 9)/0.09 = 80 + 56 = 136 W/m. Heat capacity flow = 1,000 × 4,186 × 0.05 = 209,300 W/K. Cooling rate = 136 / 209,300 = 0.00065 K/m, i.e. 0.65 K per km, so about 1.9 °C over the reach, falling as the temperature difference closes. A small residential sewer at 5 L/s with the larger resistances loses heat at a similar rate per metre but has one tenth of the heat capacity flow, so it can cool by several degrees in a kilometre. Long trunk sewers and rising mains therefore deliver winter sewage at 8 to 11 °C to UK works even when it left the houses at 15.

Heat loss from treatment tanks

At the works the open water surface, the aeration air and the tank walls all lose heat. Per unit of water surface, the components are:

• Convection and radiation from the surface to the air: of the order of 10 to 30 W/m² per kelvin of water-air difference in wind, a few W/m²K in still air.
• Evaporation: proportional to the vapour pressure difference between the water surface and the air; on a cold dry windy day it can exceed the convective term.
• Aeration air: diffused air leaves the tank saturated at the water temperature. Each cubic metre of air warmed from 2 to 12 °C and saturated carries off about 12 kJ sensible and 20 kJ latent heat; at an air rate of 1 m³ per m³ of tank per hour this is a loss of about 9 W per m³ of tank, comparable with the surface loss on a deep tank.
• Walls and floor to the ground: small for buried concrete; significant for above-ground steel tanks, where insulation or cladding pays back in nitrification capacity.

For a typical activated sludge plant at 12 hours retention the net drop through the works in winter is 1 to 2 °C, more for shallow tanks, lagoons and long open channels, and much more where surface aerators throw water into freezing air. Covering tanks, using fine-bubble rather than surface aeration, deepening tanks and insulating above-ground vessels all raise the winter process temperature by a degree or two, which for a nitrifying plant is worth 10 to 20 percent of reactor volume. For packaged and containerised plant the enclosure itself is the heat retention measure, one reason packaged plant rooms hold temperature better than open civil tanks of the same volume.

The UK design temperature

The Met Office Central England Temperature series and the regional HadUK-Grid series give the air climate: mean January and February air temperatures of about 4 °C in central and eastern England with monthly means below 2 °C in cold years, and soil at 1 m depth lagging the air by a month and damped to a 5 to 10 °C annual range. Wastewater at UK works follows with a further lag; the usual observed minimum is 8 to 10 °C in February and March, with 6 to 7 °C at small rural works, long outfall sewers and in snowmelt. A permit, however, applies every day, so the design temperature is not the monthly mean but the sustained minimum the process must nitrify through, conventionally the temperature exceeded for about 90 percent of the time in winter, which for most of England is 8 to 10 °C and for exposed or upland sites lower.

Design method: establish the winter wastewater temperature from works records or, for a new works, from the sewer heat balance and the regional climate; subtract the heat loss through the works; size the aerobic sludge age and the aeration at that temperature; and check the summer case for oxygen transfer and settling, since the warm case governs air demand while the cold case governs tank volume. Treatment-side sizing is in the activated sludge design guide, and the low-temperature kinetics of newer processes in the anammox low-temperature guide.

Measuring and monitoring

Temperature is cheap to measure and widely neglected. A works should log inlet, aeration tank and final effluent temperature continuously; the difference between inlet and tank is the works heat loss, and its trend tells whether a cover or a change of aeration has paid off. For a sewer study, loggers at manholes a known distance apart over a winter, with air and soil probes, calibrate the two resistances directly and are far more reliable than literature values. Heat is also a resource: a 50 L/s sewer at 14 °C in a 9 °C environment carries recoverable heat of hundreds of kilowatts, and in-sewer or effluent heat recovery to heat pumps is a growing part of the sector's net zero programme, with the heat balance above as its starting point.

How to set the winter design temperature for a sewage works

1. Get the records. Inlet and tank temperature logs for an existing works, or regional air and soil climate series for a new site.
2. Run the sewer heat balance. Reach by reach with calibrated or conservative resistances; residential sewers cool faster per unit flow than collectors.
3. Estimate works heat loss. Surface, evaporation, aeration air and wall terms for each open tank at the winter design air temperature and wind.
4. Choose the design temperature. The sustained winter minimum, conventionally the 90-percentile winter value, not the monthly mean.
5. Size the biology at that temperature. Aerobic sludge age for nitrification with the temperature-corrected growth rate; check settling with the cold-water viscosity.
6. Decide heat retention measures. Covers, fine-bubble aeration, deeper tanks and insulation of above-ground vessels where a degree or two reduces the reactor volume.