Formula sheet

Sidestream Deammonification Formula Sheet

Formula sheet for sidestream PN/A deammonification with ammonia load, nitrite target, oxygen saving, alkalinity, nitrate byproduct, inhibition and validation checks.

Branch: Environmental Engineering
Content: Formula sheet
Updated: Jul 03, 2026
Revision: v1.1.0 · reviewed

This formula sheet collects screening equations for sidestream deammonification and partial nitritation-anammox validation. It is intended for engineering review, startup checks, troubleshooting and teaching. It is not a design standard, kinetic model or substitute for site-specific wastewater process engineering.

State the process boundary before using any equation: centrate, filtrate, digester supernatant, reactor influent, reactor effluent, bypass flow or return to the main plant. Many sidestream errors come from mixing concentration values with different flow windows.

Use and Reporting Basis

Use one reporting basis through the calculation. Nitrogen species should normally be reported as nitrogen, for example $\text{mg/L as N}$ , $\text{kg NH}_4\text{-N/d}$ , $\text{kg NO}_2\text{-N/d}$ and $\text{kg NO}_3\text{-N/d}$ . Do not mix as-nitrogen values with as-ion values unless the conversion is explicit.

Use one time basis through the calculation. A daily sidestream average is useful for plant-load screening, but a dewatering batch, centrate pump cycle or reactor-feed pulse may control inhibition and biomass response. For startup release, pair every concentration with the flow and time window that produced it.

The equations below are first-pass screens. They help identify whether a trend is chemically plausible, whether a load step is aggressive, and whether a release package needs more evidence. They do not predict microbial kinetics or guarantee performance.

Required Boundary Set

Before calculating, state:

\{\text{sidestream source},\ Q,\ NH_4-N,\ NO_2-N,\ NO_3-N,\ pH,\ alkalinity,\ temperature,\ DO,\ time\ window\}

If the boundary changes during dewatering, use interval calculations rather than one daily average.

Sidestream Ammonia Load

Ammonia nitrogen load is:

L_{NH4}=Q_{side}C_{NH4-N}(0.001)

where $Q_{side}$ is in $\text{m}^3/\text{d}$ , $C_{NH4-N}$ is in $\text{mg/L as N}$ and $L_{NH4}$ is in $\text{kg N/d}$ .

Mini check:

L_{NH4}=120(850)(0.001)=102\ \text{kg N/d}

Use flow-weighted data where possible. A high concentration grab sample does not define load unless the matching flow is known.

Equalized Load Pulse

For a batch sidestream volume (V_b) released over time (t_b):

\displaystyle Q_{pulse}=\frac{V_b}{t_b}

Pulse ammonia load rate is:

\dot{L}_{NH4,pulse}=Q_{pulse}C_{NH4-N}(0.001)

If (V_b=180\ \text{m}^3), (t_b=12\ \text{h}=0.5\ \text{d}) and (C=850\ \text{mg/L as N}):

Q_{pulse}=360\ \text{m}^3/\text{d}

\dot{L}_{NH4,pulse}=360(850)(0.001)=306\ \text{kg N/d}

The daily average may be (102\ \text{kg N/d}), but the reactor experiences the pulse rate during feed. Equalization and control tuning should be checked against the pulse.

PN/A Nitrite Target

For a simplified PN/A balance, define the target nitrite-to-ammonia ratio:

\displaystyle R_{NO2/NH4}=\frac{L_{NO2,target}}{L_{NH4,rem}}

If $R_{NO2/NH4}=1.32$ , the ammonia fraction oxidized to nitrite is:

\displaystyle f_{PN}=\frac{R_{NO2/NH4}}{1+R_{NO2/NH4}}

So:

\displaystyle f_{PN}=\frac{1.32}{1+1.32}=0.569

The target nitrite production is:

L_{NO2,target}=f_{PN}L_{NH4}

For the mini check:

L_{NO2,target}=0.569(102)=58.0\ \text{kg NO}_2\text{-N/d}

Measured Nitrite Ratio

For measured loads:

\displaystyle R_{meas}=\frac{L_{NO2,meas}}{L_{NH4,rem,meas}}

If (R_{meas}) is far above target, nitrite may be accumulating. If it is far below target while ammonia remains high, partial nitritation may be weak or sampling may be mismatched.

Residual Ammonia for Anammox

The remaining ammonia load is:

L_{NH4,rem}=L_{NH4}-L_{NO2,target}

Using the same basis:

L_{NH4,rem}=102-58.0=44.0\ \text{kg N/d}

The ratio check is:

\displaystyle \frac{L_{NO2,target}}{L_{NH4,rem}}=\frac{58.0}{44.0}=1.32

This is a target balance, not proof of biological conversion. The measured reactor must still show nitrite consumption, nitrate byproduct and total nitrogen reduction.

Stoichiometric Closure Screen

A simplified closure error can be written as:

\displaystyle e_N=\frac{|L_{DIN,in}-L_{DIN,out}-L_{N2,screen}|}{L_{DIN,in}}

Use it only as a plausibility check. A large closure error may indicate biomass storage, unmeasured nitrogen species, bad flow data, inconsistent sampling times or laboratory uncertainty.

Oxygen Screen

Full nitrification oxygen demand can be screened as:

O_{conv}=4.57L_{NH4}

For partial nitritation to nitrite:

O_{PN}=3.43L_{NO2,target}

Using the mini check:

O_{conv}=4.57(102)=466\ \text{kg O}_2/\text{d}

O_{PN}=3.43(58.0)=199\ \text{kg O}_2/\text{d}

Screened oxygen reduction is:

S_O=O_{conv}-O_{PN}=466-199=267\ \text{kg O}_2/\text{d}

This is not automatically blower energy saving. Field oxygen transfer, mixing, turndown, pressure, control stability and reactor configuration determine actual power.

Aeration Margin

For available oxygen transfer:

\displaystyle M_{O2}=\frac{OTR_{available}-O_{PN}}{O_{PN}}

A positive margin is not enough if DO exposure drives NOB growth. In PN/A, oxygen must be sufficient for AOB but controlled enough to avoid full nitrification drift.

Alkalinity Screen

Partial nitritation alkalinity demand is:

A_{PN}=7.14L_{NO2,target}

For the same target:

A_{PN}=7.14(58.0)=414\ \text{kg/d as CaCO}_3

Available sidestream alkalinity load is:

L_{Alk}=Q_{side}Alk(0.001)

If $Alk=3800\ \text{mg/L as CaCO}_3$ :

L_{Alk}=120(3800)(0.001)=456\ \text{kg/d as CaCO}_3

Screened margin:

M_{Alk}=L_{Alk}-A_{PN}=456-414=42\ \text{kg/d as CaCO}_3

A positive screen does not guarantee stable pH. Trend pH, alkalinity and load during the actual dewatering schedule.

pH Guard Screen

For release, use a guarded pH:

pH_{guard}=pH_{obs}-U_{pH}

where (U_{pH}) is measurement or operating uncertainty. If inhibition, alkalinity or biology is sensitive near the observed pH, the guarded value should be used in FNA and FA screens.

Nitrate Byproduct

A simplified anammox nitrate byproduct screen is:

L_{NO3,exp}=R_{NO3/NH4}L_{NH4,rem}

With $R_{NO3/NH4}=0.11$ :

L_{NO3,exp}=0.11(44.0)=4.84\ \text{kg NO}_3\text{-N/d}

Higher nitrate may indicate NOB activity, ordinary nitrification drift or oxygen exposure. Very low nitrate with high ammonia and nitrite may indicate limited anammox conversion rather than perfect performance.

NOB Drift Screen

A simple nitrate drift ratio is:

\displaystyle D_{NOB}=\frac{L_{NO3,meas}-L_{NO3,exp}}{L_{NH4,in}}

If (D_{NOB}>0), measured nitrate exceeds the simplified anammox byproduct expectation. Interpret it with DO history, temperature, SRT, NOB suppression strategy and sampling uncertainty before calling the process failed.

Nitrogen Removal Screen

For a simplified load balance:

L_{DIN,out}=L_{NH4,out}+L_{NO2,out}+L_{NO3,out}

Apparent dissolved inorganic nitrogen removal is:

L_{DIN,rem}=L_{DIN,in}-L_{DIN,out}

For a complete PN/A target screen, nitrogen converted to gas can be approximated as:

L_{N2,screen}=L_{NH4,rem}+L_{NO2,target}-L_{NO3,exp}

Using the mini check:

L_{N2,screen}=44.0+58.0-4.84=97.2\ \text{kg N/d}

Use this as a plausibility screen. Real systems include biomass assimilation, dissolved nitrogen species, storage, sample timing and measurement uncertainty.

Main-Plant Return Impact

The residual sidestream nitrogen returned to the main process is:

L_{return}=L_{DIN,out}+L_{bypass}

Return fraction against main influent load is:

\displaystyle f_{return}=\frac{L_{return}}{L_{main}+L_{return}}

This tells whether a sidestream unit that looks acceptable locally is still materially loading the main plant.

Free Nitrous Acid

Free nitrous acid fraction is:

\displaystyle f_{HNO2}=\frac{1}{1+10^{pH-pK_a}}

Free nitrous acid on an as-nitrogen basis is:

C_{FNA,N}=C_{NO2-N}f_{HNO2}

Example:

C_{NO2-N}=190\ \text{mg/L as N},\quad pH=6.65,\quad pK_a=3.25

f_{HNO2}=0.000398

C_{FNA,N}=190(0.000398)=0.0756\ \text{mg/L as N}

Treat this as an inhibition screen, not as a universal threshold. Biological response depends on organisms, exposure time, temperature, acclimation and process state.

Use guarded pH when FNA is near an action threshold. Because FNA rises sharply as pH falls, a small pH measurement error can change the inhibition interpretation.

Free Ammonia

For total ammonia nitrogen as N:

\displaystyle f_{NH3}=\frac{1}{1+10^{pK_a-pH}}

C_{FA,N}=TAN_N f_{NH3}

With $pK_a=9.25$ , $TAN_N=500\ \text{mg/L as N}$ and $pH=7.8$ :

\displaystyle f_{NH3}=\frac{1}{1+10^{9.25-7.8}}=0.034

C_{FA,N}=500(0.034)=17.1\ \text{mg/L as N}

Free ammonia may help suppress NOB, but excessive exposure can also inhibit AOB or anammox activity. Always interpret it with pH, temperature, loading and trend evidence.

Biomass Retention Screen

For systems that depend on slow-growing biomass:

\displaystyle \theta_X=\frac{M_X}{Q_{loss}X_{loss}}

where (M_X) is retained active solids or biofilm-equivalent inventory and (Q_{loss}X_{loss}) is biomass loss rate. This is a simplified screen, but it reminds reviewers that hydraulic loading, washout and solids loss can control recovery after an upset.

Reactor Loading and Residence Time

Hydraulic residence time is:

\displaystyle HRT=\frac{V}{Q_{side}}

Volumetric ammonia loading is:

\displaystyle VLR_{NH4}=\frac{L_{NH4}}{V}

If $V=240\ \text{m}^3$ :

\displaystyle HRT=\frac{240}{120}=2.0\ \text{d}

\displaystyle VLR_{NH4}=\frac{102}{240}=0.425\ \text{kg N}/\text{m}^3\text{/d}

Residence time and loading should be checked over the same operating window. Intermittent dewatering can produce high short-term loading even when the daily average looks acceptable.

Temperature Correction Reminder

If a site uses a temperature correction for biological rate:

k_T=k_{20}\theta^{T-20}

This should be used cautiously. Temperature affects AOB, NOB and anammox differently, and a single correction factor can hide community shifts during startup or seasonal change.

Load-Ramp Check

A simple feed-ramp check is:

\displaystyle r_L=\frac{L_{new}-L_{old}}{L_{old}}

If the ammonia load rises from $82$ to $102\ \text{kg N/d}$ :

\displaystyle r_L=\frac{102-82}{82}=0.244

That is a $24.4\%$ step increase. Slow-growing biomass and biofilm systems may need a hold period after each loading step before the next ramp.

Release Gate

A compact release gate is:

G = L \land B \land I \land C \land R

where (L) is load basis, (B) is nitrogen balance, (I) is inhibition screen, (C) is control stability and (R) is return-impact evidence. If any element is false, the result should stay in startup, diagnostic or conditional mode rather than normal release.

Conservative Validation Load

When release criteria are close, include measurement uncertainty:

L_{cons}=Q(1+u_Q)(C+U_C)(0.001)

If:

Q=120\ \text{m}^3/\text{d},\quad u_Q=0.05,\quad C=850\ \text{mg/L},\quad U_C=40\ \text{mg/L}

then:

L_{cons}=120(1.05)(850+40)(0.001)=112\ \text{kg N/d}

Use conservative checks for release decisions, not only for permit reporting. A reactor that barely passes with nominal data may fail after measurement uncertainty and dewatering variability are included.

Validation Checklist

A calculation package should include at least the following checks before a sidestream deammonification result is treated as stable.

Check	Formula Basis	Engineering Use
ammonia load	$Q_{side}C_{NH4-N}(0.001)$	defines the load the reactor must explain
PN/A target	$f_{PN}=R/(1+R)$	checks whether nitrite supply and residual ammonia are balanced
oxygen screen	$O_{conv}$ and $O_{PN}$	separates theoretical oxygen reduction from real blower energy
alkalinity screen	$A_{PN}$ and $M_{Alk}$	flags pH-collapse risk during load increase
nitrate byproduct	$R_{NO3/NH4}L_{NH4,rem}$	distinguishes expected byproduct from NOB drift
FNA/FA screens	acid-base fractions	connects nitrite, ammonia and pH to inhibition risk
mass balance	$L_{DIN,in}-L_{DIN,out}$	prevents false release based on one nitrogen species
uncertainty	conservative load	protects decisions near limits or acceptance gates

Validation should show a coherent pattern: ammonia decreases, nitrite is not persistently accumulated, nitrate is plausible, total nitrogen falls, pH and alkalinity remain stable, and downstream effluent trends do not worsen. If those signals disagree, treat the calculation as a diagnostic lead rather than as release evidence.

Common Formula Mistakes

Common mistakes include mixing as-ammonium and as-nitrogen units, treating target nitrite production as allowed effluent nitrite, using concentration instead of load, claiming oxygen savings as guaranteed energy savings, ignoring alkalinity and pH, using nitrate alone as proof of failure, calculating FNA without pH, and applying daily averages to intermittent centrate feed. A strong calculation states boundary, time window, units, assumptions, uncertainty and validation evidence.

REF

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