Nitrogen Cycle Kinetics: Nitrification, Denitrification, and Organic N Hydrolysis

QUAL2K models nitrogen using three state variables, following EPA nutrient criteria for rivers and streams: Organic N (index 5), Ammonium NH₄ (index 6), and Nitrate NO₃ (index 7). These interact through hydrolysis, nitrification, denitrification, and settling. Nitrification is a major oxygen sink in the dissolved oxygen balance, while phosphorus dynamics are covered in the Phosphorus Cycle page.

Nitrogen Cycle Diagram

Figure 1: Nitrogen transformations in the water column

Organic Nitrogen

Organic nitrogen (particulate and dissolved) undergoes hydrolysis to release ammonium and settling to remove particles:

\frac{dOrgN}{dt} = -k_{hn} \cdot OrgN - v_{on} \cdot \frac{OrgN}{H}

Where:

$k_{hn}$ — organic N hydrolysis rate (day⁻¹), typically 0.02–0.4
$v_{on}$ — organic N settling velocity (m/d), typically 0.001–0.1
$H$ — stream depth (m)

Ammonium (NH₄)

Ammonium is produced by organic N hydrolysis and consumed by nitrification:

\frac{dNH_4}{dt} = k_{hn} \cdot OrgN - k_n \cdot NH_4

Where:

$k_n$ — nitrification rate (day⁻¹), typically 0.1–1.0

Nitrate (NO₃)

Nitrate is produced by nitrification and consumed by denitrification:

\frac{dNO_3}{dt} = k_n \cdot NH_4 - k_i \cdot NO_3

Where $k_i$ is the denitrification rate (day⁻¹), typically 0.0–0.5.

Denitrification occurs primarily in anoxic zones (DO < 2 mg/L) where facultative bacteria use NO₃ as an electron acceptor instead of O₂.

Typical Nitrogen Rate Constants

Nitrogen-related rate constants at 20°C

Parameter	Symbol	Range	θ	Units
Organic N hydrolysis	khn	0.02 – 0.40	1.047	day⁻¹
Organic N settling	von	0.001 – 0.10	—	m/d
Nitrification	kn	0.10 – 1.00	1.083	day⁻¹
Denitrification	ki	0.00 – 0.50	1.047	day⁻¹
O₂:N ratio	ron	4.57 (fixed)	—	mg O₂ / mg N

Python Implementation

pythonkinetics.py — Nitrogen cycle

# Organic N: hydrolysis + settling
khn = temp_correction(rates.get('khn', 0.02), 1.047, temp)
von = rates.get('von', 0)
loss_on = khn + (von / max(h, 0.01))
orgn_hydrolyzed = khn * conc[5] * dt
conc[5] *= math.exp(-loss_on * dt)

# NH4: gains from hydrolysis, loses to nitrification
kn = temp_correction(rates.get('kn', 0.1), 1.083, temp)
conc[6] += orgn_hydrolyzed                    # source from Org-N
conc[6] *= math.exp(-kn * dt)                 # nitrification sink

# NO3: gains from nitrification, loses to denitrification
ki = temp_correction(rates.get('ki', 0.0), 1.047, temp)
nh4_nitrified = kn * conc[6] * dt
conc[7] += nh4_nitrified                      # source from NH4
conc[7] *= math.exp(-ki * dt)                 # denitrification sink