Design tool for wastewater treatment biological
Membrane bioreactors (MBR) are a combination of membrane filtration
processes with activated sludge biological treatment processes. MBR
systems can produce high quality effluents with a smaller footprint
than conventional activated sludge processes.
This model sizes the biological reactor for MBR with submerged
membranes using NH4 as target contaminant. It should be
used when the treatment objective is convert Ammonia to Nitrates and
remove BOD at the same time. The algorithm considers both AOB and
NOB kinetics for Nitrification instead of the "AOB only" approach
commonly used before 2015. The denitrification occurs in a
Since there are several types of membranes in the market, this
model was conceived as being "membrane agnostic". The membrane can
be elaborated separately according to the manufacturer requirements
and the biological model design, goal of this tool, will require the
minimum parameters just to estimate the mass balance in the
Quick calculation instructions
- Plant design inputs: Flow, temperature and altitude (impacts the
- Biological reactor design inputs:
Membrane design inputs:
- Tank depth: Higher will improve the oxygen transfer but is
limited by construction costs. Typical depths are between 4 and
5.5m for diffused aerators .
- Aerator height: How high is the aerator from the bottom of the
- Aeration tank volume: If a number is set the value will be
used as the tank volume and the MLSS will be adjusted according
to the SRT. If this is set to false the volume will
be determined by the algorithm (recommended).
- Mixed Liquor Suspended Solids (MLSS): This is the most
important design parameter for the reactor and together with the
SRT, define the reactor volume. Typical values :
- 2500 to 4000mg/L for SRT between 20 and 30 days
- Dissolved oxygen concentration typical values are between 1.5
- Safety factor for TKN: Accounts for the variation of the
Ammonia concentration in the wastewater. Recommended value:
Wastewater quality inputs:
- Membrane design flux: This should be the flux at the average
plant flow. In case of peak flows, the average flux must be
reduced to respect the maximum allowed flux by the membrane
- Membrane specific air demand is the average quantity per
membrane area in one hour. Example: If the system only aerates
the membranes for 10 minute every 60 minutes, the SAD input
must be the instant flow (m³/h)/m² divided by 6.
- Typical values for the MLSS in the membrane tank :
- Sludge recirculation ratio (RAS) is the flow that returns from
the membrane tank to the aerobic reactor. Set the RAS to 0 if
the membranes are placed inside the biological reactor.
Biochemical constants (advanced)
- All parameters from this list are the minimum required for
sizing the plant.
- TDS impacts the aeration efficiency.
- Minimum recommended nutrient concentrations BOD:N:P (mg/L) for
- 100:5:1 for SRT lower than 10 days
- 100:3:0.5 for SRT between 20 and 30 days
- Effluent Nitrite concentration: The Nitrite (NO2)
concentration in the treated effluent is very low but in some
cases the nitrification is limited by NOB and this concentration
can be high even with low Ammonia in the product. If there are
no regulations for Nitrites it is advised to keep the same value
as set for Ammonia in the product.
- You can use the default values for the "Expected Suspended
solids in the product" and "bCOD to BOD ratios" unless you have
more accurate values.
Aeration constants (advanced)
- Use this section to adjust the biochemical/kinetic constants.
- Actual values are valid for domestic and municipal wastewater.
- Coefficients are based in bCOD instead of BOD for maximum
compatibility with dynamic computation models. Be aware that
several constants reported in the literature are BOD based and
need to be converted before use.
- To prevent the model from using the NOB route for
nitrification calculations, set the maximum specific growth for
NOB bacteria to 100.
- Use this section do adjust the aeration devices efficiency and
- Default aerator: Fine bubble for the biological process and
coarse bubble for the membrane scouring.
Calculation model description
- Membrane operational time is calculated based on the cleaning
intervals and duration.
- Instantaneous product flow is calculated dividing the average
wastewater flow by the fraction of time the membranes will be in
- Number of membrane elements and membrane area are determined
by the desired flux and the instant product flow. Quantity of
elements is rounded to the higher integer.
- Instantaneous membrane flux is calculated from the membrane
area and the instant flow.
- Membrane tank size is calculated from the packing density. If
the user defined a minimum volume, this will be used.
- The average aeration flow for the membranes tank is
- Average flux is calculated from the membrane area and design
- bCOD, nbCOD, nbsCODe, nbVSS and iTSS parameters are calculated
according to the wastewater inputs.
- Endogenous decay coefficient and maximum specific growth rates
correction for the design temperature .
- Calculation of the specific growth rate for AOB and NOB ;
- The program will pick the lower specific growth rate and use
to calculate the SRT.
- Final SRT is adjusted with the safety factor.
- Soluble bCOD calculation from the SRT and coefficients .
- Effluent soluble BOD calculation from bCOD.
- Biomass production is calculated. An optimization algorithm is
used to find the exact NOX production for the calculated SRT.
- Production of TSS and VSS is calculated .
- Volume of the reactor is calculated based on the user
specified MLSS. If the user defined the tank volume then the
MLSS will be adjusted to accommodate the biomass into the
- HRT, MLVSS, FM, BODload and yields are determined from mass
- Oxygen consumption for the aerobic treatment is calculated 
- Oxygen credits from the membrane aeration are subtracted from
the oxygen requirements in the aeration tank .
- Alpha coefficient for the aerator is calculated from the MLSS
in the tank .
- Atmospheric pressure  and oxygen saturation [3,4]
- Standard Oxygen Transfer Rate determination .
- Air flow calculation from the air density.
- Activated sludge return rate and waste flow by mass balance
- Clarifier area determination
- Final BOD from effluent suspended solids and soluble BOD .
- Alkalinity requirements check .
- Mixing power to the anoxic tank is calculated. Please not that
this is not the electric power but rather the energy that must
be dissipated in the fluid to perform the mix.
Known limitations and important notes
- This model does not estimate suspended solids removal in the
primary clarifier. It assumes the wastewater inputs already
consider the primary removal.
- Biochemical and aeration constant inputs are assumed at 20°C and
then corrected to the process temperature.
- TDS effects in the biomass are not considered. TDS inputs are
used only for oxygen transfer efficiency calculations.
- This model calculates the rates for AOB and NOB bacteria and
then picks the slower (critical) reaction to calculate the design
SRT . When the design is based in the NOB kinetics, the final
Ammonia concentration will be lower than the desired value
specified in the inputs. When the design is limited by AOB, the
final Nitrite concentration will be lower than the desired value.
- Sludge waste is assumed to extremely low and is not considered
in the membrane flux calculation.
 Metcalf & Eddy, AECOM - Wastewater Enginering: Treatment and
Resource Recovery, 5th Edition, McGraw-Hill 2014.
 Marcos Von Sperling, Lodos Ativados, 2ed,
Departamento de Engenharia Sanitária e Ambiental - UFMG, Belo
Horizonte - MG - Brasil 2002.
 Benson, B.B., and Daniel Krause, Jr, 1980,
The concentration and isotopic fractionation of gases dissolved in
freshwater in equilibrium with the atmosphere. 1. Oxygen: Limnology
and Oceanography, vol. 25, no. 4.
 Benson, B.B., and Daniel Krause, Jr, 1984, The concentration and
isotopic fractionation of oxygen dissolved in freshwater and seawater
in equilibrium with the atmosphere: Limnology and Oceanography, vol.
29, no. 3.
 Racault. Y.A.-E. Stricker. A. Husson, and
S.Gillot (2010) "Effect of Mixed Liquor Suspended Solids on the Oxygen
Transfer Rate in Full-Scale Membrane Biorreactors,"Proceedings of the
WEF 83rd ACE", New Orleans, L A.
 EPA/600/R-10/100 EPA Nutrient Control Design
Manual, August 2010.
 Simon Judd, The MBR Book, 2nd
edition, Elsevier - Oxford - UK 2011.