Membrane Bioreactor for BOD, Ammonia and Nitrates Handbook

Design tool for wastewater treatment biological reactors


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 and NO3 as target contaminants. It should be used when the treatment objective is convert Ammonia to Nitrates, Nitrates to N2 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 pre-anoxic tank.

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 reactors.

Design tool

Web Based Excel Interface



Quick calculation instructions

  1. Plant design inputs: Flow, temperature and altitude (impacts the oxygenation rate).
  2. Biological reactor 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 [2].
    • Aerator height: How high is the aerator from the bottom of the tank.
    • 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 [2]:
      • 2500 to 4000mg/L for SRT between 20 and 30 days
    • Dissolved oxygen concentration typical values are between 1.5 and 2mg/L.
    • Safety factor for TKN: Accounts for the variation of the Ammonia concentration in the wastewater. Recommended value: 1.5[1]
  3. Membrane design 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 manufacturer.
    • 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 [7]:
      • 6000 to 14000mg/L
  4. Wastewater quality inputs:
    • 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 biodegradability [2]:
      • 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.
  5. Biochemical 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.
  6. Aeration constants (advanced)
    • Use this section do adjust the aeration devices efficiency and parameters.
    • Default aerator: Fine bubble for the biological process and coarse bubble for the membrane scouring.

Calculation model description

    1. Membrane operational time is calculated based on the cleaning intervals and duration.
    2. Instantaneous product flow is calculated dividing the average wastewater flow by the fraction of time the membranes will be in filtration mode.
    3. 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.
    4. Instantaneous membrane flux is calculated from the membrane area and the instant flow.
    5. Membrane tank size is calculated from the packing density. If the user defined a minimum volume, this will be used.
    6. The average aeration flow for the membranes tank is calculated.
    7. Average flux is calculated from the membrane area and design flow.
    8. bCOD, nbCOD, nbsCODe, nbVSS and iTSS parameters are calculated according to the wastewater inputs.
    9. Endogenous decay coefficient and maximum specific growth rates correction for the design temperature [1].
    10. Calculation of the specific growth rate for AOB and NOB [1];
    11. The program will pick the lower specific growth rate and use to calculate the SRT.
    12. Final SRT is adjusted with the safety factor.
    13. Soluble bCOD calculation from the SRT and coefficients [1].
    14. Effluent soluble BOD calculation from bCOD.
    15. Biomass production is calculated. An optimization algorithm is used to find the exact NOX production for the calculated SRT.
    16. Production of TSS and VSS is calculated [1].
    17. 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 specified volume.
    18. HRT, MLVSS, FM, BODload and yields are determined from mass balance relations.
    19. Oxygen consumption for the aerobic treatment is calculated [1]
    20. The desired effluent Nitrates concentration is calculated using the MBR recirculation ratio [1].
    21. Nitrate concentration feeding the anoxic compartment is then determinated.
    22. An optimization model is used to adjust the hydraulic retention time of the anoxic tank to the desired Nitrate removal rate. The Standard Denitrification Rate (SDNR) is calculated using the Food-to-Microorganism ration and the fraction of readily biodegradable COD in the wastewater [1].
    23. If the user defined the tank volume, the SDNR will be calculated and the difference between the input nitrates concentration and the nitrates removed will be displayed to the user. Ideally this number should equal zero or be negative.
    24. Oxygen credits from the denitrification subtracted from the oxygen requirements in the aeration tank [1].
    25. Oxygen credits from the membrane aeration are subtracted from the oxygen requirements in the aeration tank [7].
    26. Alpha coefficient for the aerator is calculated from the MLSS in the tank [5].
    27. Atmospheric pressure [1] and oxygen saturation [3,4] determination.
    28. Standard Oxygen Transfer Rate determination [1].
    29. Air flow calculation from the air density[1].
    30. Activated sludge return rate and waste flow by mass balance relations.
    31. Clarifier area determination
    32. Final BOD from effluent suspended solids and soluble BOD [1].
    33. Alkalinity requirements check [1].
    34. 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 [6]. 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.

Literature references

[1] Metcalf & Eddy, AECOM - Wastewater Enginering: Treatment and Resource Recovery, 5th Edition, McGraw-Hill 2014.
[2] Marcos Von Sperling, Lodos Ativados, 2ed, Departamento de Engenharia Sanitária e Ambiental - UFMG, Belo Horizonte - MG - Brasil 2002.
[3] 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.
[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.
[5] 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.
[6] EPA/600/R-10/100 EPA Nutrient Control Design Manual, August 2010.
[7] Simon Judd, The MBR Book, 2nd edition, Elsevier - Oxford - UK 2011.