MBBR process design: biofilm kinetics, surface area loading and aeration

The moving bed biofilm reactor (MBBR) grows biomass as a biofilm on small plastic carriers kept in suspension by aeration or mixing. Because the biomass is attached, the process is sized on the area of biofilm, not on the reactor volume or a suspended solids concentration. This note sets out the diffusion-reaction basis, the surface area loading method, temperature correction, media fill and the oxygen transfer calculation.

Technical note, RB Solutions Ltd, 22 October 2026

Principles of the moving bed biofilm reactor

The MBBR was developed to combine the compactness of a biofilm process with the absence of clogging and backwashing of a fixed bed [1]. Carriers of slightly less than unit density circulate throughout the reactor volume, held in the tank by outlet sieves. Biofilm grows mainly on the protected internal surfaces of the carriers, where abrasion between carriers does not remove it. The process has no sludge recycle, so the solids retention time of the biofilm is uncoupled from the hydraulic retention time; slow-growing nitrifiers can be retained in a small volume provided the organic load to the nitrifying stage is low enough for them to compete with heterotrophs for space and oxygen [2, 4].

A typical carrier, the K1 type, has a protected specific surface area of 500 m² per m³ of carrier bulk volume [3]. The fraction of reactor volume occupied by carriers, the fill fraction, can be varied to suit the load up to an upper limit of about 70 %, beyond which free movement of the carriers is impaired [1, 2]. The biofilm area available in a reactor is therefore:

A_{b} = a_{c} f V_{R}

where A_b is the biofilm (protected carrier) area (m²), a_c the specific protected surface area of the carrier bulk volume (m² m⁻³), f the fill fraction (dimensionless, bulk carrier volume divided by reactor liquid volume) and V_R the reactor volume (m³).

Biofilm diffusion and kinetics

Substrate reaches the biomass by diffusion: first across a liquid boundary layer at the biofilm surface, then into the biofilm, where it is consumed as it diffuses. For a steady, planar biofilm with a Monod-type intrinsic rate, the substrate profile satisfies [5, 6]:

D_{f} \frac{d^{2} S_{f}}{d z^{2}} = \frac{q X_{f} S_{f}}{K + S_{f}}

where D_f is the diffusion coefficient of the substrate in the biofilm (m² d⁻¹), S_f the substrate concentration in the biofilm (g m⁻³), z the depth into the biofilm (m), q the maximum specific substrate utilisation rate (g g⁻¹ d⁻¹), X_f the biomass density in the biofilm (g m⁻³) and K the half-saturation constant (g m⁻³).

Two limiting solutions are useful in design. Where the substrate penetrates only part of a deep biofilm and the intrinsic rate is zero order, the flux into the biofilm is half order in the concentration at the biofilm surface [6]:

J = \sqrt{2 D_{f} k_{0} S_{s}} = k_{1 / 2} S_{s}^{1 / 2}

where J is the flux into the biofilm per unit area (g m⁻² d⁻¹), k₀ the zero-order volumetric reaction rate in the biofilm (g m⁻³ d⁻¹), S_s the substrate concentration at the biofilm surface (g m⁻³) and k_1/2 the half-order rate constant (g^1/2 m^−1/2 d⁻¹).

Where the substrate penetrates the full biofilm depth, the flux is zero order and limited by the active biomass; at low concentration it becomes first order. The practical consequence is that the areal removal rate in an MBBR is a function of the bulk concentration in that reactor, rising towards a plateau as concentration increases. A completely mixed reactor operates at its own outlet concentration, so a single-stage reactor designed for a low effluent concentration operates at a low areal rate throughout; staging in series lets the upstream reactors operate at higher concentration and higher rate.

Rate-limiting substrate in nitrification

In a nitrifying biofilm, either ammonium or oxygen can limit the rate. Oxygen has a lower bulk concentration and a high stoichiometric demand, so at the low ammonium concentrations required in the effluent the rate is commonly ammonium-limited, while at higher ammonium concentrations it becomes oxygen-limited and increases with the bulk dissolved oxygen concentration [4]. Nitrification is also depressed by organic load, because heterotrophs growing in the outer biofilm compete for oxygen and space [4, 7]. A nitrifying MBBR is therefore designed with explicit dissolved oxygen and organic load assumptions, stated alongside the areal rate.

Surface area loading rate design basis

MBBR design uses the surface area loading rate (SALR) and the corresponding surface area removal rate (SARR):

SALR = \frac{Q S_{0}}{A_{b}} SARR = \frac{Q (S_{0} - S)}{A_{b}}

where SALR and SARR are in g m⁻² d⁻¹, Q is the flow (m³ d⁻¹), S₀ and S the influent and effluent concentrations of the design substrate (g m⁻³, equal to mg L⁻¹) and A_b the biofilm area (m²).

For carbonaceous (BOD) removal, the SALR is selected for the required effluent quality and for whether the stage is to support nitrification downstream; high-rate stages that remove only soluble BOD can be loaded more heavily than stages that must produce a low effluent BOD or protect a downstream nitrifying stage [2]. For nitrification, the design SARR must be read at the bulk ammonium and dissolved oxygen concentrations of each stage, at the minimum design temperature, and with the organic load to that stage taken into account [4, 7]. Design rates should be supported by pilot data, plant data from a comparable duty, or a carrier-specific rate demonstrated for the stated conditions. RB Solutions does not publish generic SALR values here because the published rates are specific to carrier type, temperature, dissolved oxygen and staging.

Effect of temperature

The temperature dependence of the areal rate is represented by an Arrhenius-type expression:

r_{T} = r_{T ref} θ^{(T - T_{ref})}

where r_T is the areal rate at temperature T (g m⁻² d⁻¹), r_Tref the rate at the reference temperature T_ref (°C), and θ the temperature coefficient (dimensionless).

For tertiary nitrification in MBBRs, temperature coefficients of 1.098 under ammonium-limited conditions and 1.058 under oxygen-limited conditions have been reported, for temperatures above 10 °C [8]. The difference reflects the physics: under oxygen limitation the rate is partly governed by diffusion of oxygen, which is less temperature-sensitive than the biological reaction, and the higher oxygen solubility of cold water partly offsets slower kinetics. The higher coefficient gives the more conservative rate reduction for cooling and is the prudent design basis where the limitation regime is not established. Extrapolation below 10 °C should be supported by data for the duty.

Oxygen transfer and aeration: SOTR, AOTR and the alpha factor

Aeration in an MBBR has two duties: supplying oxygen and keeping the carriers in circulation. Oxygen demand is calculated from a mass balance on the substrate removed. For full oxidation of ammonium to nitrate, the stoichiometric demand is 4.57 g O₂ per g NH₄-N oxidised [7]; the carbonaceous demand is calculated separately from the BOD removed and the biomass produced.

Aeration equipment is rated in clean water at standard conditions, as the standard oxygen transfer rate (SOTR), measured in accordance with BS EN 12255-15 [9]. The actual oxygen transfer rate (AOTR) in process water is lower [7]:

AOTR = SOTR \cdot α F \cdot \frac{β C_{s, T}^{*} - C}{C_{s, 20}^{*}} \cdot θ^{(T - 20)}

where AOTR and SOTR are in kg O₂ h⁻¹; α is the ratio of the process-water to clean-water mass transfer coefficient (dimensionless); F the diffuser fouling factor (dimensionless); β the ratio of oxygen saturation in process water to that in clean water (dimensionless); C*_s,T and C*_s,20 the clean-water saturation concentrations at the process temperature and at 20 °C (mg L⁻¹), here taken at the surface at 101.325 kPa without the depth correction for submerged diffusers; C the operating dissolved oxygen concentration (mg L⁻¹); and θ = 1.024 the temperature coefficient for mass transfer [7].

The clean-water oxygen saturation concentration at 101.325 kPa is 11.29 mg L⁻¹ at 10 °C and 9.09 mg L⁻¹ at 20 °C [10]. The alpha factor depends on the diffuser type, the airflow per diffuser, the concentration of surfactants and the treatment stage; it is lower for fine-bubble diffusers in poorly treated water and rises along the treatment train as surfactants are removed [11, 12]. Published alpha values for activated sludge are not directly transferable to an MBBR, where the carriers alter bubble break-up and residence time. Alpha for a specific design should come from data for the diffuser and carrier combination, and the sensitivity of the blower duty to alpha should be shown.

The air required for carrier circulation can exceed the air required for oxygen transfer, particularly in lightly loaded polishing stages. The blower duty is the larger of the two, and both are calculated.

Worked example: nitrifying MBBR area, volume and oxygen

Stated inputs. Flow Q = 2000 m³ d⁻¹; NH₄-N reduced from 30 to 2 mg L⁻¹; low organic load to the stage; design nitrification SARR of 0.6 g N m⁻² d⁻¹ at 15 °C, taken here as an illustrative pilot result for the stated conditions rather than a recommended value; minimum design temperature 10 °C; K1-type carrier with a_c = 500 m² m⁻³ [3]; fill fraction f = 0.60, within the 70 % limit [1, 2]; operating dissolved oxygen 4.0 mg L⁻¹; β = 0.95 and F = 1.0 (stated inputs).

Biofilm area and reactor volume

Ammonium removed: 2000 × (30 − 2) = 56 000 g N d⁻¹. Rate at 10 °C with the conservative coefficient: 0.6 × 1.098⁻⁵ = 0.376 g N m⁻² d⁻¹ [8]. Biofilm area A_b = 56 000/0.376 = 148 950 m². Carrier bulk volume = 148 950/500 = 297.9 m³; reactor volume = 297.9/0.60 = 496.5 m³.

Second route, by volumetric rate: the reactor provides a_cf = 500 × 0.60 = 300 m² of biofilm per m³, so the volumetric nitrification rate is 0.376 × 300 = 112.8 g N m⁻³ d⁻¹, and V_R = 56 000/112.8 = 496.5 m³. The routes agree.

Sensitivity: with the oxygen-limited coefficient of 1.058 [8], the 10 °C rate would be 0.453 g N m⁻² d⁻¹ and the area 123 700 m², 17 % less. The choice of temperature coefficient is therefore a sizing decision, not a detail. Because the effluent target of 2 mg L⁻¹ NH₄-N would hold a single completely mixed reactor in the ammonium-limited regime throughout, the stage is divided into at least two reactors in series, and the illustrative rate must correspond to the bulk concentration in each.

Oxygen demand and required transfer capacity

Nitrification oxygen demand: 4.57 × 56.0 = 255.9 kg O₂ d⁻¹ = 10.66 kg O₂ h⁻¹ [7]. Field correction excluding α and F: (0.95 × 11.29 − 4.0)/9.09 × 1.024^{(10 − 20)} = 0.584 [7, 10]. Required αF·SOTR = 10.66/0.584 = 18.3 kg O₂ h⁻¹. With F = 1.0, the clean-water SOTR is 18.3/α kg O₂ h⁻¹; for an alpha of 0.5, for example, it would be 36.5 kg O₂ h⁻¹. Check by direct substitution: 18.3 × 0.584 = 10.7 kg O₂ h⁻¹, which recovers the demand. The carbonaceous oxygen demand of any residual BOD, the depth correction for the diffuser submergence, and the carrier circulation air are added before the blower is sized.

Table 1. Design quantities and their sources used in the worked example
Quantity	Value	Status
Carrier protected specific area (K1 type)	500 m² m⁻³	Published [3]
Maximum fill fraction	about 70 %	Published [1, 2]
Temperature coefficient, ammonium-limited / oxygen-limited	1.098 / 1.058	Published [8]
Oxygen for nitrification	4.57 g O₂ g⁻¹ N	Stoichiometric [7]
Oxygen saturation, 10 °C / 20 °C, 101.325 kPa	11.29 / 9.09 mg L⁻¹	Published [10]
Mass transfer temperature coefficient	1.024	Published [7]
Nitrification SARR at 15 °C	0.6 g N m⁻² d⁻¹	Illustrative input only
β, F, operating DO	0.95, 1.0, 4.0 mg L⁻¹	Stated inputs

Solids separation downstream of the MBBR

The MBBR has no sludge recycle, so all biomass produced leaves in the effluent as detached biofilm at a concentration set by the yield and the load. A yield of about 0.5 g suspended solids per g of filtered COD removed has been reported for carbonaceous MBBR treatment [2]. The detached solids are typically more dilute than activated sludge and can have poorer settling properties, so the separation stage is designed on the solids load and settling behaviour of the actual biofilm sludge. Options include conventional settlement, coagulation followed by a lamella clarifier, dissolved air flotation, or filtration, the choice depending on the effluent standard. In England and Wales, the discharge standards for urban waste water treatment plants are set out in the Urban Waste Water Treatment (England and Wales) Regulations 1994 and applied through the environmental permit [13]; fixed-film reactors for wastewater treatment plants are covered by BS EN 12255-7 [14].

Design sequence

An MBBR process design proceeds as follows: define the design loads and minimum temperature; divide the duty into carbonaceous and nitrifying stages; select areal rates for each stage at the stated bulk concentration, dissolved oxygen and temperature, from pilot or comparable data; calculate biofilm area, carrier volume and reactor volume by two routes; set the number of reactors in series; calculate oxygen demand and convert to SOTR with a stated alpha; check carrier circulation air; and size the solids separation stage on the detached biofilm load.

References

Ødegaard, H., Rusten, B. and Westrum, T. (1994) A new moving bed biofilm reactor: applications and results. Water Science and Technology, 29(10–11), 157–165.
Ødegaard, H. (2006) Innovations in wastewater treatment: the moving bed biofilm process. Water Science and Technology, 53(9), 17–33.
Rusten, B., Eikebrokk, B., Ulgenes, Y. and Lygren, E. (2006) Design and operations of the Kaldnes moving bed biofilm reactors. Aquacultural Engineering, 34(3), 322–331.
Hem, L.J., Rusten, B. and Ødegaard, H. (1994) Nitrification in a moving bed biofilm reactor. Water Research, 28(6), 1425–1433.
Williamson, K. and McCarty, P.L. (1976) A model of substrate utilization by bacterial films. Journal of the Water Pollution Control Federation, 48(1), 9–24.
Harremoës, P. (1978) Biofilm kinetics. In: Mitchell, R. (ed.) Water Pollution Microbiology, vol. 2, 71–109. New York: Wiley.
Metcalf & Eddy, AECOM (2014) Wastewater Engineering: Treatment and Resource Recovery, 5th ed. New York: McGraw-Hill.
Salvetti, R., Azzellino, A., Canziani, R. and Bonomo, L. (2006) Effects of temperature on tertiary nitrification in moving-bed biofilm reactors. Water Research, 40(15), 2981–2993.
BS EN 12255-15:2003, Wastewater treatment plants. Part 15: Measurement of the oxygen transfer in clean water in aeration tanks of activated sludge plants. London: BSI.
Benson, B.B. and Krause, D. (1984) The concentration and isotopic fractionation of oxygen dissolved in freshwater and seawater in equilibrium with the atmosphere. Limnology and Oceanography, 29(3), 620–632.
Rosso, D., Larson, L.E. and Stenstrom, M.K. (2006) Surfactant effects on alpha factors in full-scale wastewater aeration systems. Water Science and Technology, 54(10), 143–153.
Gillot, S. and Héduit, A. (2008) Prediction of alpha factor values for fine pore aeration systems. Water Science and Technology, 57(8), 1265–1269.
The Urban Waste Water Treatment (England and Wales) Regulations 1994, SI 1994/2841. legislation.gov.uk.
BS EN 12255-7, Wastewater treatment plants. Part 7: Biological fixed-film reactors. London: BSI.

Related technical notes

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