4.1. Can apparent half-saturation coefficients lump reaction and diffusion inside granules?
Effect of the substrate concentration
The dependency of aerobic growth rates on the bulk oxygen concentration is displayed in Figure 4.4 for the steady-state microbial population distribution under the reference conditions (Figure 4.5). An increasing bulk oxygen concentration resulted in an initial steep increase of the growth rate, followed by a slower increase towards the maximal specific growth rate. This saturation behaviour could be described reasonably well with Monod kinetics upon calibration of the apparent half-saturation coefficient. The fit for NOO was almost perfect. For OHO, Monod kinetics seemed the least appropriate, but still the qualitative
behaviour was the same. This could be sufficiently accurate, given the comparison was now made with another model (a 1D biofilm), with its own uncertainty. In practice, OHO also only play a secondary role for the total COD removal and oxygen consumption in an aerobic granular sludge reactor, given the high abundancy of PAO (Pronk et al., 2015). Overall, Monod kinetics with apparent half-saturation coefficients seem suitable approximations.
Apparent half-saturation coefficients have been used before to model granular sludge reactors. For example, Zhou et al. (2013) and Lübken et al. (2005) used ASM3 without explicit consideration of diffusion. Since stable granules were already formed in the modelled reactors and no significant unidirectional changes in the influent composition or reactor temperature occurred during the studied time-frame, a steady microbial population distribution was probably present throughout their experiments. This corresponds with our results, that for a fixed microbial population distribution, constant apparent half-saturation coefficients could indeed be used to incorporate diffusion resistances.
Figure 4.4. The total specific growth rates of OHO (A), PAO (B), NOO (C) and AOO (D) inside aerobic granules as a function of the bulk oxygen concentration. The trends were approximated by Monod kinetics with apparent half-saturation coefficients. The graphs show the behaviour for the steady-state microbial population under the reference conditions (Figure 4.5; granule radius 0.55 mm, temperature 20 °C, oxygen set-point 2 g O2.m-3 and the influent contains 396 g COD.m-3, 50 g N.m-3 and 20 g P.m-3).
Figure 4.5. Microbial population distribution at steady state for the reference operating conditions, predicted by the 1D biofilm model (granule radius 0.55 mm, temperature 20 °C, oxygen set-point 2 g O2.m-3 and the influent contains 396 g COD.m-3, 50 g N.m-3 and 20 g P.m-3). AOO and NOO are shown on the right axis. Inert particulate organics were not shown and make up the largest fraction near the core.
The dependencies of the total specific growth rates on the other limiting substrates were also calculated and fitted with Monod kinetics for the reference conditions (Figure 9.3).
The ratio of the estimated apparent over the assumed intrinsic half-saturation coefficient varied between 1 and 6 (Figure 4.6). This wide range can be explained by different substrate diffusivities, microbial population distributions and intrinsic kinetics (Pérez et al., 2005). For example, for OHO, the same intrinsic kinetics were used for fermentable substrate (F) and VFA (KVFA,OHO = KF,OHO = 4 g COD.m-3; Table 9.5), but the effective diffusion coefficient of F is lower (De,20,F = 1.6 10-5 m2.d-1 < De,20,VFA = 2.6 10-5 m2.d-1; Table 9.6), leading to more diffusion resistance and thus a higher apparent saturation coefficient. The same intrinsic half-saturation coefficient for O2 was used for OHO and PAO (KO2,PAO = KO2,OHO = 0.20 g O2.m-3), yet the apparent coefficients are different because the intragranule distribution (Figure 4.5) and maximal oxygen uptake rate of these microbial groups was different (Table 9.4 and Table 9.5). Finally, a similar effective diffusion coefficient of O2 and NHx was used (De,20,O2 = 1.37 10⁻4 m2.d-1 and De,20,NHx = 1.45 10-4 m2.d-1), but the ratio of the apparent to the intrinsic half-saturation coefficient of OHO differs strongly for these substrates because of the different intrinsic half-saturation coefficient (KO2,OHO = 0.2 g O2.m-3 and KNHx,OHO = 0.05).
Arnaldos et al. (2015) hypothesized that half-saturation coefficients of organic molecules are more strongly affected by diffusion than inorganic molecules. The results from this study show that many more factors influence the ratio of the apparent to the intrinsic half-saturation coefficient apart from the diffusion coefficient, such as the maximal growth rate, microbial population distribution and the intrinsic half-saturation coefficient. The wide range of values for the Kapp/K ratio (Figure 4.6) also indicates that a reduction of the maximal specific
growth rates of all microbial groups with the same factor, as applied by Pons et al. (2008), is an inadvisable method to account for the effect of diffusion. Further research could investigate the apparent kinetics of the uptake of phosphate and volatile fatty acids, which was not done explicitly in this chapter since these are not growth reactions, but a similar methodology could be used (Figure 4.2).
Figure 4.6. Ratio of the apparent (Kapp) to the intrinsic half-saturation coefficient (K) of different microbial groups for different limiting substrates. Results obtained for the steady-state population under the reference conditions.
Time delay
When the concentration of a limiting substrate changes in the bulk liquid, the rates inside granules do not immediately reach a new steady-state, since the formation of new substrate gradients through simultaneous diffusion and reaction takes time. Consequently, also the total specific growth rates inside granules respond with a delay to changes in the bulk liquid. For example, when the 1D biofilm model was used to predict the apparent half-saturation coefficients of OHO for fermentable substrates, an excess of this substrate was first added (step 2 in Figure 4.2), leading to a fast increase in the bulk liquid concentration from 0 to 400 g COD.m⁻3 (Figure 4.7). Upon this fast change in the concentration, it took 19 seconds to reach 95% of the steady-state growth rate. For all other limiting substrates and microbial groups, the rate reached 95% of the steady-state value even faster. The response times are thus in the order of seconds, while a reactor cycle typically takes several hours. On top of that, sudden big changes in substrate concentrations rarely occur in full scale systems. Even though Monod kinetics with apparent half-saturation coefficients do not predict the time delay, these results indicate that it can be neglected when the macroscale reactor behaviour is of interest. Previous work on apparent half-saturation coefficients did not acknowledge that their use neglects the formation time of substrate gradients (Arnaldos et al., 2015), but this chapter confirms that the time delay can be neglected for aerobic granules in particular.
Figure 4.7. The total specific growth rate of OHO (full line) as a function of time during a fast increase in the bulk liquid concentration of fermentable organic matter (dashed line). Results obtained from 1D biofilm model simulations after reaching a steady-state population under the reference conditions. This was the slowest response observed among all limiting substrates and microbial groups.
4.2. Which factors influence half-saturation coefficients?
Influence of competition
The response of the AOO growth rate to the bulk oxygen concentration was less steep when other aerobic reactions were active simultaneously (Figure 4.8A). This effect was most prominent with aerobic OHO growth, but hardly noticeable with NOO growth, respectively increasing the apparent half-saturation coefficient by 204% and 4% compared to the scenario without competition. The decrease in the AOO growth rate can be explained by the additional oxygen consumption by the competing organisms, leading to lower intragranule oxygen concentrations (Figure 4.8B). When OHO were active, the oxygen concentrations dropped below the intrinsic half-saturation coefficient of AOO at locations where AOO biomass was most abundant, causing a significant reduction of their total growth rate. On the other hand, NOO consume oxygen slower and thus the O2 concentration did not approach the half-saturation coefficient at these locations. In summary, the faster the consumption of a limiting substrate by competing organisms (oxygen in this example), the lower the intragranule profile of this substrate (microscale; Figure 4.8B) and thus the higher the apparent half-saturation coefficient for this substrate becomes (macroscale; Figure 4.8A). Interactions are reciprocal, meaning that AOO will also alter the OHO, PAO and NOO activity through their oxygen consumption.
Figure 4.8. A: The total specific growth rate of AOO inside aerobic granules as a function of the bulk oxygen concentration when other aerobic growth reactions are active simultaneously.
The calibrated apparent half-saturation coefficients KO2,AOO,app are shown at the corresponding curves; the complete fitted Monod curve is shown only for the case without competition for substrates. An excess of all limiting substrates for the competing reactions was provided, so these are worst-case scenarios. B: The corresponding intragranule oxygen profile when the bulk liquid concentration is 2 g O2.m-3. The intrinsic half-saturation coefficient KO2,AOO and location with 90% of the AOO biomass are indicated. Simulation results are for the steady-state microbial population distribution at the reference case.
The effect of competition on apparent half-saturation coefficients is often overlooked (Arnaldos et al., 2015). Experiments to determine apparent half-saturation coefficients of flocculent sludge typically minimize competition, e.g. by withholding essential substrates for competing microorganisms or adding specific inhibitors (Manser et al., 2005). Also reaction-diffusion models that consider different reactions one by one, as applied by Shaw et al. (2015), cannot predict this effect. However, using a 3D biofilm model of a floc including simultaneous OHO, AOO and NOO activity, Picioreanu et al. (2016) demonstrated the effect of OHO growth on the apparent half-saturation coefficient of nitrifying organisms. In this chapter, a similar effect was observed of OHO, PAO and NOO on the AOO kinetics in aerobic granules. In an aerobic granular sludge reactor, the concentration of most organic (intracellular) substrates will decrease during the aeration phase of a cycle. Therefore the degree of competition from PAO and OHO and thus the apparent half-saturation coefficient of AOO will decrease over time, even within one cycle. Over a longer time scale, the influent composition can change and thus the average apparent kinetics can also vary between different cycles due to competition.
In contrast to ASM, there are no organisms that compete for the same substrates in the anaerobic digestion model 1 (Batstone et al., 2002). This could lead to more stable apparent kinetics in anaerobic granular sludge systems and might justify that they are more often used for such systems, but this still requires further study.
Influence of long-term changes in operating conditions
The response of the AOO growth rate to the bulk oxygen concentration becomes less steep for a decreasing influent ammonium concentration, which corresponds with an increasing apparent half-saturation coefficient (Figure 4.9A). This is caused by the AOO population shift to the inside of the granules when the influent ammonium concentration decreases (Figure 4.9B). This shift can be rationalized by the decreased AOO growth when less ammonium is present, leading to less AOO biomass at steady-state and thus less oxygen consumption. The increased oxygen penetration depth allows the population to survive deeper inside the granule. The increased diffusion distance of oxygen towards the AOO is the driver for the increased apparent half-saturation coefficient. Overall, the modification of the population distribution (microscale; Figure 4.9B) is visually more distinct than the effect on the total specific growth rate (macroscale; Figure 4.9A), which illustrates that microscale processes are not always that important for the macroscale reactor performance.
Figure 4.9. A: The total specific growth rate of AOO inside aerobic granules as a function of the bulk oxygen concentration, after reaching different steady-state microbial population distributions for different influent ammonium concentrations. The calibrated apparent half-saturation coefficients KO2,AOO,app are shown at the corresponding curves. B: Corresponding AOO population distributions at steady-state.
Besides the effect of long-term changes in microbial population distributions caused by changes in the influent NHx concentration (Figure 4.10A), the effects resulting from changes of the granule radius (B), reactor temperature (C), O2 set-point (D), influent VFA (E) and influent PO4 (F) were investigated as well (Figure 9.4 in the appendices shows the complete dependency of the total specific growth rate on the bulk oxygen concentration and the corresponding microbial population distributions at steady-state). When the granule radius increased (Figure 4.10B), the apparent half-saturation coefficient increased. This trend had already been demonstrated with static biofilm models, which assume a predefined microbial population distribution (Manser et al., 2005, Pérez et al., 2005, Picioreanu et al., 2016), but this chapter confirms the relationship when microbial dynamics are included. A higher
long-term reactor temperature caused a lower apparent half-saturation coefficient (Figure 4.10C).
This effect was solely due to the changing AOO population distribution as a result of changing temperature, because the coefficient itself was always determined at 20°C (during step 2 in Figure 4.2). When the coefficient was determined at the same temperature at which the new steady-state was achieved, the decrease as a function of temperature was less steep (grey line). This is because the term and long-term effect of temperature are opposite. A short-term temperature increase (during which the AOO population does not change) increases the oxygen consumption rate, leading to lower intragranule oxygen concentrations and thus a higher apparent half-saturation coefficient (Figure 9.5 in the appendices), in accordance with Picioreanu et al. (2016). Moreover, an increasing oxygen set-point (Figure 4.10D) initially decreases the apparent half-saturation coefficient and then increases the value. An increasing influent VFA concentration (Figure 4.10E) causes a small initial decrease, followed by a steep increase, while an increasing influent phosphate concentration (Figure 4.10F) decreases the coefficient first and then has a negligible effect. No prior research was found to compare these trends to, since no dynamic biofilm model has been used to study half-saturation coefficients before.
Figure 4.10. The apparent half-saturation coefficient of AOO for oxygen as a function of different long-term operating conditions under which a steady-state microbial population was obtained. The influent NHx (A), granule radius (B), reactor temperature (C), O2 set-point (D), influent VFA (E) and influent PO4 (F) were varied individually, between -30% and +30%
compared to their reference value.
As the retention time of most microbial aggregates in aerobic granular sludge reactors is much shorter than the 750 days simulated to ensure a stable microbial population, the influence of long-term changes in operating conditions predicted in this chapter (Figure 4.10) may be different in reality. One study found solid retention times of 6.2, 7.7 and 142.6 days for flocculent biomass, small granules and large granules respectively (Ali et al., 2019), which suggests that most aggregates are not in steady state. The numerical results of these simulations should thus be interpreted with care, but the principle that changing operating conditions affect microbial population distributions and therefore also apparent kinetics is still true.
To better understand the changes in the half-saturation coefficient for different long-term operating conditions (Figure 4.10), the microbial population distribution was characterized for every steady-state by two simple measures: the average AOO population depth (Eq. 4.5) and total AOO biomass per granule (Eq. 4.2). A plot of the average population depth versus the value of the coefficient showed a clear positive correlation (Figure 4.11;
R2=0.74). This confirms the intuitive idea that an apparent half-saturation coefficient is a measure for the diffusion resistance. However, there was also a positive correlation between the total amount of biomass per granule and the half-saturation coefficient (Figure 4.11;
R2=0.85). This can be explained by the faster oxygen consumption and thus lower intragranule oxygen concentrations when more biomass is present. In other words, there is not only competition for substrates between different microbial groups, but also within the same group.
This correlation was already found with a static biofilm model assuming a homogeneous microbial population distribution (Pérez et al., 2005). During the simulations for this chapter, the average depth and size of the population changed simultaneously, but Figure 4.12 shows that a multiplication of both measures suffices to explain most of the variation and that it can be fitted well with a quadratic trendline with an intercept equal to the assumed intrinsic value KAOO,app = 0.3 (R2 = 1.00).
Figure 4.11. The apparent half-saturation coefficient of AOO for oxygen obtained for different long-term operating conditions as a function of the average population depth of AOO (A) and the population size of AOO per granule (B fitted with a linear trend line.
A B
Figure 4.12. The apparent half-saturation coefficient of AOO for oxygen obtained for different long-term operating conditions as a function of the average population depth times the population size of AOO per granule fitted with a quadratic trend line with intercept KO2,AOO = 0.3 g O2.m-3. The distribution of all values is projected as red lines on the y-axis.
Implications for modelling with constant apparent half-saturation coefficients Among all steady-state simulations, KO2,AOO,app varied between 0.42 and 3.04 g O2.m-3 (Figure 4.12). Consequently, apparent kinetics are expected to differ between plants and even for the same plant, simulations of long-term changes in operating conditions made with constant values should be interpreted with care. And even on a shorter term, the results indicate that apparent kinetics are not constant, because the degree of competition can fluctuate over time, e.g. when there is a sudden increase in influent organics, the competition for AOO by PAO and OHO will increase or when the influent ammonium drops, the competition for PAO and OHO by AOO will decrease. However, this does not mean that apparent kinetics are never useful. First of all, the 1D biofilm model always predicted a smooth saturation curve with increasing substrate concentrations, whatever the microbial population distribution or degree of competition. Therefore, the qualitative behaviour could still be simulated, if an appropriate new set of default apparent ASM2d parameters (or similar bioconversion model) is found based on the average behaviour of several full-scale plants. Apparent kinetics have also been successfully used for flocculent sludge, even though they depend on the operating conditions as well, as discussed in the introduction. Furthermore, also current 1D or 2D biofilm models for aerobic granular sludge reactors have a lot of uncertainties for long-term changing conditions. For example, it is still challenging to accurately predict changes in granule size distribution or microscale parameters like the effective diffusion coefficient (Chapter II).
Therefore, it is also not guaranteed that these biofilm models provide reliable quantitative predictions on long-term. Finally, the sequential operation of aerobic granular sludge reactors
allows on-line extraction of apparent kinetics from typical monitoring data, which might enable quantitative predictions after all, as illustrated in the last section of this chapter.
4.3. Are apparent-half saturation coefficients practically applicable?
The ammonium removal during the aeration phases of 100 consecutive full-scale reactor cycles (24 days) was simulated using a model with apparent half-saturation coefficients (Eq. 4.6), fed every cycle with parameter values that were estimated based on the ten preceding cycles (Figure 4.13). Within this timeframe, the initial ammonium concentration varied between 3.42 and 22.38 g N.m-3, while the oxygen concentration fluctuated between 0.1 and 4.25 g O2.m-3. The mean absolute error indicates that the predictive accuracy of the model stays quite low and stable. The average parameter values were rmax = 549 g N.m-3.d-1, KNHx,app = 1.1 g N.m-3 and KO2,app = 4.0 g O2.m-3, but they showed some fluctuations, especially from cycle 80 onwards. These fluctuations are partly due the limited identifiability when half-saturation coefficients and maximal rates are calibrated simultaneously (Chouakri et al., 1994), but also actual changes in apparent kinetics could have occurred. Apparent kinetics could have changed due previously discussed reasons, such as changes in the microbial population distribution or average influent organics concentration, which can alter the degree of competition. Also changes of the intrinsic ammonium half-saturation could have occurred, e.g.
due to a decrease in the reactor pH (Wiesmann, 1994). Carstensen et al. (1995) calibrated exactly the same model for a flocculent sludge plant and found apparent half-saturation coefficients that were lower than the ones found in this chapter, especially for KO2,app (KNHx,app
= 0.76 g N.m-3 and KO2,app = 0.71 g O2.m-3). This is in line with the expected higher diffusion resistance in granular sludge systems, including the bigger impact on the oxygen-related parameter (Figure 4.6).
Even though this model with apparent kinetics neglects many phenomena, it can be useful. First of all, the fact that the ammonium removal could be quite accurately predicted with the model provides an important insight: the ammonium removal rate at any given time is mostly determined by the oxygen and ammonium concentration. This fundamental insight
Even though this model with apparent kinetics neglects many phenomena, it can be useful. First of all, the fact that the ammonium removal could be quite accurately predicted with the model provides an important insight: the ammonium removal rate at any given time is mostly determined by the oxygen and ammonium concentration. This fundamental insight