Anammox Kinetics at Low Temperature: Modelling the Arrhenius Correction for Northern European Works

Why the standard temperature correction fails below 15 °C

Anaerobic ammonium oxidation has moved from sidestream reject-water duty into mainstream deammonification. The engineering constraint that remains is temperature. UK works run at 8–14 °C for a large part of the year, and the growth rate of Candidatus Brocadia and Candidatus Kuenenia over that range is not well described by a correction fitted at 30–35 °C.

Growth is conventionally written as a dual-substrate Monod expression with multiplicative correction functions:

μ = μ_max · [S_NH4 / (K_NH4 + S_NH4)] · [S_NO2 / (K_NO2 + S_NO2)] · f(T) · f(pH) · f(I)μ = specific growth rate (d⁻¹); S = substrate concentration; K = half-saturation coefficient; I = inhibitor

The temperature term is almost always taken as a single-parameter Arrhenius form:

f(T) = θ^{(T − T₀)}θ ≈ 1.12 for nitrification, 1.06–1.09 commonly assumed for Anammox

That form has no mechanism in it. It cannot represent the thermodynamic penalty on an endergonic step at low temperature, nor the loss of conformational flexibility in the enzyme complex. Extrapolated downwards from mesophilic calibration it fails in the direction that matters: it is optimistic.

A cardinal-temperature model for the 8–20 °C range

A cardinal temperature model with inflection (CTMI) is bounded by a minimum, an optimum and a maximum temperature, so it goes to zero at a real physiological limit instead of decaying exponentially towards it. Fitting compiled Anammox datasets across 8–37 °C gives the following cardinal parameters.

Why the activation energy is high

The catabolic reaction is strongly exergonic:

NH₄⁺ + 1.32 NO₂⁻ + 0.066 HCO₃⁻ + 0.13 H⁺ → 1.02 N₂ + 0.26 NO₃⁻ + 0.066 CH₂O_0.5N_0.15 + 2.03 H₂OΔG°′ ≈ −357 kJ mol⁻¹

A favourable free-energy change says nothing about rate. The apparent activation energy for the hydrazine synthase and hydrazine dehydrogenase route is around 68 kJ mol⁻¹, against roughly 44 kJ mol⁻¹ for aerobic ammonia oxidation. That difference is the whole problem: the higher the activation energy, the steeper the rate collapse as temperature falls.

What it costs in sludge age and tank volume

Suspended growth

Design sludge age follows from the growth rate with a safety factor:

SRT_design = SF / μ_max(T)SF = safety factor, typically 1.5–2.0 for mainstream duty

At 12 °C the cardinal model gives μ_max ≈ 0.025 d⁻¹. Taking a factor of 3 on the inverse growth rate — that is, holding three times the minimum retention needed to avoid washout — gives:

SRT_design = 3 / (0.025 × 1.5) = 80 days

Against 25–30 days at 25 °C. Volume scales with retention, so a 50,000 PE works at 12,000 m³/d holding 3,500 mg/L MLVSS needs of the order of 2,700 m³ — roughly 2.7 times the 25 °C requirement.

Biofilm

For attached growth the controlling parameter is areal loading on the protected surface:

B_A,N = Q (S_in − S_eff) / A_protectedB_A,N = areal nitrogen loading (g N m⁻² d⁻¹)

The maximum areal removal rate for Anammox biofilm falls from about 2.5 g N m⁻² d⁻¹ at 25 °C to about 0.8 at 12 °C. For 1,200 kg N/d that is 1.5 × 10⁶ m² of protected area; at 500 m²/m³ media that is 3,000 m³ of reactor, against 960 m³ at 25 °C.

The real control problem is NOB, not Anammox

It is tempting to assume cold water selects against nitrite-oxidising bacteria and therefore helps. It does not. Compare the apparent activation energies:

NOB and Anammox have essentially the same temperature sensitivity, so cooling does not open a selection window between them. Low-temperature mainstream deammonification therefore stands or falls on deliberate NOB suppression, using three levers:

• Intermittent aeration. Set the aerated fraction from the AOB ammonia oxidation rate and the anoxic fraction from the Anammox nitrite demand, so nitrite is consumed as fast as it is made and never accumulates for NOB to harvest.
• Differential sludge age. NOB washes out below roughly 1.5 days at 12 °C; Anammox must be held above 60 days. Achieving both in one reactor requires selective wasting or membrane retention.
• Free nitrous acid transients. NOB inhibition sets in around 0.02–0.05 mg HNO₂-N/L, roughly an order of magnitude below the Anammox inhibition threshold. Brief FNA peaks in the anoxic phase suppress NOB without touching Anammox.

The related chemistry of nitrogen removal routes is covered in Anammox deammonification and biological nutrient removal; the reactor configurations in MBBR design and sequencing batch reactor design.

Reference installation: mainstream PN/A at 10–14 °C

Two-stage mainstream partial nitritation–Anammox has been demonstrated at Dokhaven-Sluisjesdijk (Rotterdam) at temperatures representative of a UK winter.

The operative detail is the 85-day sludge age. Performance is not bought with a clever aeration recipe; it is bought by holding biomass long enough that a low growth rate stops mattering. Everything else — the short aerated fraction, the low DO setpoint — exists to keep NOB out of that inventory.

Design rules

• Do not extrapolate θ = 1.08 below 15 °C. Use a cardinal-temperature fit, or apply the Arrhenius form with a floor at 15 °C and treat anything below as unquantified.
• Design for SRT above 60 days at 12 °C. That means membrane retention, granular sludge, or biofilm — not conventional clarification.
• Budget for roughly three times the mesophilic reactor volume if the works must meet consent through winter.
• Treat NOB suppression as the primary control objective. Anammox activity is a design input; NOB is the thing that will actually take the process down.
• Prefer biofilm or IFAS to suspended growth at low temperature — the biomass inventory per unit volume is higher and it is not lost on a clarifier upset.