Supplementary File Nº1.
Mass transfer and oxygen limitation during bioreactor operation.
Oxygen limitation probably occurred in R1 according to a previous study carried out in our laboratory in a very similar experimental set-up [18]. The following calculations confirm the basis of this statement.
Bordel et al. [18] determined a KLa value for oxygen () of 150 h-1 under the same conditions in a very similar experimental system. Using this reference value, the corresponding KLa value for toluene () can be estimated based on the fundamental definition of the volumetric mass transfer coefficient:
(1)
where, DTol and DO2 are the diffusivities of toluene and oxygen in water, respectively; while δ and “a”represent the thickness of the liquid film and the interfacial area for mass transfer, respectively. Since δ and “a” are the same for O2 and toluene, Equation 1 can be reduced to:
(2)
From Eq. 2 and assuming that ≈ 150 h-1, the resulting value is 65 h-1.
Based on these mass transfer coefficients for oxygen and toluene, the maximum VOC and O2 supply rate in each reactor (R1, R2 and R3) can be estimated as follows:
(Eq 3)
(Eq 4)
where C*is the liquid concentration of the target substrate in equilibrium with the gas concentration. In addition, it must be taken into account the stoichiometric value of 1.5 gO2 gToluene-1 consumed, experimentally reported by Bordel et al. [18], and assumed here as a typical yield for the aerobic bacterial degradation of toluene. All data are summarized in table A. The maximum mass transfer rates of toluene (TTRmax) and oxygen (OTRmax) are given in Table A.
Table A. Oxygen needs and oxygen limitation in the three reactors during operation.Reactor / TTRmax
(g m-3 h-1) / OTRmax
(g m-3 h-1) / Theoretical oxygen needs
(g m-3 h-1) / Oxygen Limitation
R1 / 3432 / 1245 / 5148 / YES
R2 / 85 / 1245 / 127 / NO
R3 / 2.6 / 1245 / 3.9 / NO
Reactor 1:
Reactor 1 was fed with an average gas phase concentration of 9.5 g m-3. Based on the modified Henry’s law for toluene (accounting for the biomass concentration), the C*Tol in R1 = 52.8 g m-3. Solving Eq 3 by applying a of 65 h-1the maximum toluene supply to the system will be:
65h-1 × (52.8)g m-3 = 3432 g m-3 h-1
And the oxygen needed to oxidize this toluene will be:
3432gtol m-3 h-1 × 1.5 gO2 gToluene-1 = 5148 g m-3 h-1
Based on the saturation of oxygen at 25ºC, the C*O2 in R1 = 8.3 g m-3. Solving Eq 4 by applying a of 150 h-1, the maximum oxygen supply to the system will be:
150 h-1 × (8.3-0) g m-3 = 1245 g m-3 h-1
Oxygen needs > Oxygen supply. The oxygen supply is four times lower than the needs to degrade the toluene maximum supply, which would likely induce O2 limitation in R1.
Reactor 2:
Reactor 2 was fed with an average gas phase concentration of 0.3 g m-3. Based on the modified Henry’s law for toluene (accounting for the biomass concentration), C*Tolin R2 = 1.3 g m-3. Solving Eq 3 by applying a of 65 h-1the maximum toluene supply to the system will be:
65h-1 × (1.3)g m-3 = 84.5 g m-3 h-1
And the oxygen needed to oxidize this toluene will be:
84.5gtol m-3 h-1 × 1.5 g O2 g-1 toluene = 126.8 g m-3 h-1
Based on the saturation of oxygen at 25ºC, C*O2 in R2 = 8.3 g m-3. Solving Eq 4 by applying a of 150 h-1, the maximum oxygen supply to the system will be:
150 h-1 × (8.3) g m-3 = 1245 g m-3 h-1
Oxygen needs Oxygen supply. The maximum oxygen supply is one order of magnitude higher than the maximum oxygen needs, thus, no oxygen limiting conditions were likely to occur in R2.
Reactor 3:
Reactor 3 was fed with an average gas phase concentration of 0.011 g m-3. Based on the Henry’s law for toluene, C*Tol in R3 = 0.04 g m-3. Solving Eq 3 by applying aof 65 h-1,the maximum toluene supply to the system will be:
65h-1 × (0.04)g m-3 = 2.6 g m-3 h-1
And the oxygen needed to oxidize this toluene will be:
2.6gtol m-3 h-1 × 1.5 gO2 gToluene-1 = 3.9 g m-3 h-1
Based on the saturation of oxygen at 25ºC, C*O2in R3 = 8.3 g m-3. Solving Eq 4 by applying a of 150 h-1 the maximum oxygen supply to the system will be:
150 h-1 × (8.3) g m-3 = 1245 g m-3 h-1
Oxygen needs Oxygen supply. The maximum oxygen supply is more than 300 times higher than the oxygen needs, thus, no oxygen limiting conditions were likely to occur in R3.