F/M and F/V

Organic loading rate is an important design and controlling parameter in biological wastewater treatment process. It is measured by the amount of food provided to a unit amount of biomass (or reactor volume) for a unit period of time. Food-to-microorganisms (F/M) ratio is based on the amount of biomass while Food-to-volume (F/V) ratio is based on reactor volume.

The F/M and the F/V are calculated using the following equations.

1               ———————————–(1)

1                        ———————————–(2)
F/M  = food-to-microorganism ratio (g BOD/g MVLSS/day)
F/V   = food-to-volume ratio (g BOD/g MLVSS/day)
Q       = influent flow rate (m3/day)
S0     = influent BOD (mg/L)
X       = MLSS in aeration tank (mg/L)
V       = tank volume (m3)

Four different F/M ratio exist depending on the unit used for food and microorganisms. Those four are inter-convertible using the ratio of COD/BOD and MLVSS/MLSS as shown in Table 1, where COD/BOD and MLVSS/MLSS were assumed at 2.0 and 0.8, respectively, for municipal wastewater.

Typically MBR runs at lower F/M ratio than conventional activated sludge (CAS) process in order to mitigate membrane fouling and maintain high oxygen transfer efficiency. The preferred F/M ratio range in MBR is approximately a third to a half of that in CAS, i.e. 0.05-0.15 g BOD/g MVLSS/day or 0.1-0.3 g COD/g MLVSS/day in municipal MBR.

It is noticeable that nitrogen is not taken into consideration when F/M and F/V are calculated, but it contributes to the oxygen demand significantly. One example for municipal wastewater here shows the oxygen demand for COD removal approximately equals to that for nitrogen oxidation (nitrification) before considering the oxygen recovery (or credit) from denitrification.

Table. 1. Comparison of preferred ranges of operating parameters in MBR and CAS

Design Parameter Unit MBR CAS


g BOD/g MLSS/day 0.04-0.12 0.16-0.24
g COD/g MLSS/day 0.08-0.24 0.32-0.48
g BOD/g MLVSS/day 0.05-0.151), 2) 0.2-0.3
g COD/g MLVSS/day 0.1-0.303) 0.4-0.6
F/V g BOD/L/day 0.5-1.5 0.6-0.9
g COD/L/day 1.0-3.0 1.2-1.8
MLSS g/L 8-121) 2-4
MLVSS g/L 6-10 1.7-3.4
SRT days 10-30 5-10
SOUR mg O2/g MVLSS/hr 2-54) 6-12
OUR mg O2/L/hr 15-50 20-40
DO mg/L 1-2 1-2

1) Judd, 2006
2) Brepols, 2010
3) Converted from the BOD based F/M assuming COD/BOD=2.0 for municipal wastewater
4) Ng, 2006


© Seong Hoon Yoon