Abstract
During biological wastewater treatment, substrates undergo simultaneous diffusion and reactions inside microbial aggregates, creating microscale spatial substrate gradients and limiting the macroscale reaction rates. For flocculent and anaerobic granular sludge, this rate-limiting effect of diffusion is often lumped in model parameters, like the half-saturation coefficients of Monod kinetics in activated sludge models (ASM). Yet, an explicit description of the reaction-diffusion process with biofilm models is more common for aerobic granular sludge (Chapter II). This chapter investigates how the simultaneous reaction and diffusion affect the apparent conversion kinetics of aerobic granular sludge and examines the implications of using apparent half-saturation coefficients in models. To this end, the macroscopic reaction rates predicted with a one-dimensional biofilm (1D) model (Chapter III) were fitted with Monod kinetics. The results showed that the macroscale rates could indeed be described using apparent kinetics, at the very least over a time scale where the microbial population distribution stays fixed. However, the coefficients were sensitive to changes in the microbial population distribution, which can be affected by long-term changes in operating conditions. Also the activity of organisms that compete for the same substrates affect the parameter value. Be that as it may, apparent kinetics also depend on the operating conditions for flocculent and anaerobic granular sludge, but they have still been used successfully for design and optimization. Therefore, the last section of this chapter illustrates that they may also have applications for aerobic granular sludge. A simple model for ammonium removal using apparent half-saturation coefficients for oxygen and ammonium was applied to a full-scale reactor, taking advantage of the sequential operation and on-line monitoring data for regular recalibration.
The contents of this chapter were published as:
Baeten, J.E., van Loosdrecht, M.C.M. and Volcke, E.I.P. (2018) Modelling aerobic granular sludge reactors through apparent half-saturation coefficients. Water Research 146, 134-145.
Introduction
Given the increasing interest in aerobic granular sludge technology, the need for reliable and user-friendly mathematical models is growing. So far, modelling efforts have mainly focussed on lab-scale systems. The most popular approach is to explicitly describe diffusion of substrates inside granules with 1D or 2D biofilm models (Chapter II). The reaction rate at every point in a granule is then typically calculated with Monod kinetics (Eq. 4.1).
µ = µMax Slim
K+Slim Eq. 4.1
Where µ is the specific growth rate (d-1), µMax the maximal specific growth rate (d-1), Slim the limiting substrate concentration (g.m-3), K the intrinsic half-saturation coefficient (g.m-3). Such biofilm models can predict spatial gradients of solutes and microbial populations inside granules and are thus useful to gain insight in the microscale behaviour. Yet, their complexity can hinder their adoption and effective use by the industry for reactor design and optimization.
One important barrier is the search for reliable parameter values. In literature, strongly different values for microscale parameters can be found, as illustrated in Figure 4.1 for the biomass density and oxygen diffusion coefficient inside biofilms. Sensitivity analyses have also shown that the latter can significantly influence simulation results (Boltz et al., 2011, Su and Yu, 2006b). A second option is to measure parameter value, but easily measurable parameters such as the number, density and size of granules depend on the operating conditions (de Kreuk et al., 2005a) and their changes are still challenging to predict (Chapter II). Finally, calibration can be performed, but a rational selection of a limited number of parameters to adjust is difficult with so many parameters to choose from. A guideline for calibration of biofilm models has only recently been published and thus the practical applicability is still to be confirmed (Rittmann et al., 2018), especially for granular sludge reactors with their own particularities.
Figure 4.1. Variation of measured oxygen diffusion coefficients inside biofilms relative to the value in water (data from Stewart (1998)) and assumed densities of heterotrophic biomass inside aerobic granules in different biofilm models (Beun et al., 2001, Kagawa et al., 2015, Ni et al., 2010, Xavier et al., 2007).
To develop practically applicable models, the guideline formulated by Wanner et al.
(2006) should be used: “A model should be as simple as possible, and only as complex as needed”. This paraphrase of Occam’s razor also lay at the basis of the widely applied activated sludge models (ASM). The primary goal of these models was to predict the macroscale
behaviour of wastewater treatment plants, more specifically the effluent quality, oxygen requirements and sludge production (Henze et al., 2000). These goals were deemed achievable without explicit consideration of microscale processes like diffusion, even though it was known that substrate gradients can exist and affect removal rates (Benefield and Molz, 1983, Hamdi, 1995, Matson and Characklis, 1976). In ASM, the rate-limiting effect of diffusion is simply accounted for by using apparent half-saturation coefficients (Kapp) in Monod kinetics.
These have higher values than the intrinsic coefficients (K), which are the substrate concentrations at which half of the maximal growth rate is achieved in well-mixed reactors with perfectly suspended cells (Arnaldos et al., 2015).
Apparent half-saturation coefficients increase with the floc size (Pérez et al., 2005).
Because the floc size depends on the degree of mixing in a reactor, the parameter values can change up to a factor 3 or more when the aeration intensity changes (Chu et al., 2003). The size of micro-colonies inside flocs also influences apparent half-saturation coefficients (Picioreanu et al., 2016). The micro-colony size depends on the solid retention time, among others, so this is another reason to recognize apparent half-saturation coefficients as system specific and variable over time. For example, values between 0.074 to 3 g O2.m-3 have been found for the apparent half-saturation coefficient for oxygen of ammonium oxidizing organisms in flocculent sludge (Vannecke and Volcke, 2015). Nevertheless, all commercial modelling software such as Biowin, SUMO and WEST apply them for modelling flocculent sludge processes. The successful application of activated sludge models (Brdjanovic et al., 2015) demonstrates that models for design and optimization do not need a full description of all microscale processes.
Models with apparent half-saturation coefficients instead of reaction-diffusion kinetics have not only been used for flocculent sludge, but also for aerobic, anammox and particularly often for anaerobic granular sludge reactors. It is not immediately clear why apparent kinetics are less popular for aerobic granular sludge than for flocculent and anaerobic granular sludge, which indicates that the implications of this approach are not yet completely understood (Chapter II). Therefore, this chapter investigates how the simultaneous reaction and diffusion affect the apparent conversion kinetics of aerobic granular sludge through the following three research questions.
Can apparent half-saturation coefficients lump the reaction-diffusion process inside granules? It is important to verify whether Monod kinetics are able to capture the effect of short-term (minutes to hours) changes in limiting substrate concentrations on macroscale removal rates, as they can for flocs. Simulation results of a 1D biofilm model were used as a reference.
Which factors influence apparent half-saturation coefficients? Reactions that compete for the same substrates, e.g. ammonium and nitrite oxidation compete for oxygen, could alter intragranule substrate gradients and thus influence apparent half-saturation coefficients
(Picioreanu et al., 2016). Long-term (days to weeks) changes in operating conditions could induce changing microbial population distributions, on its turn also affecting the coefficients. A 1D biofilm model was used as a reference for this question as well.
Could apparent half-saturation coefficients be applicable in practice? Possible applications are illustrated by confronting a simple model for ammonium removal based on apparent half-saturation constants with on-line measurements from a full-scale aerobic granular sludge reactor.
Methodology
3.1. Can apparent half-saturation coefficients lump reaction and diffusion inside granules?
Reference operating conditions and 1D biofilm model
The same reference conditions as in Chapter III (section 3.2) were used, which were based on the experimental sequencing batch reactor described by de Kreuk et al. (2007b). A model of this reactor was set up in Aquasim (Reichert, 1994). This software comprises a dynamic 1D biofilm model, which calculates the microbial population distribution over the granule depth resulting from competition for space and substrates (Wanner and Reichert, 1996). The biological reactions were described with ASM2d (Henze et al., 2000) as corrected by Hauduc et al. (2010) and extended with two-step nitrification and temperature corrections.
As such, a basic representation of the metabolism of ordinary heterotrophic organisms (OHO), phosphate accumulating organisms (PAO), ammonium oxidizing organisms (AOO) and nitrite oxidizing organisms (NOO) was obtained to describe the COD, N and P removal. Mass transfer resistance from the bulk liquid to the granule surface was neglected. To model the intragranule transport, a compound-specific and temperature-dependent estimation of the effective diffusion coefficient inside a biofilm matrix was used (Stewart, 2003). Note that typical half-saturation coefficients for flocculent sludge were used as intrinsic values in the biofilm model, while they already lump the typical diffusion resistance of flocs. This may lead to an underestimation of conversion rates, but it is not expected to influence the conclusions of this study, as the results are interpreted qualitatively. Moreover, the use of true intrinsic parameters could overestimate the rates, since a 1D biofilm model cannot account for the effect of oxygen depletion in microcolonies (Picioreanu et al., 2016).
In Aquasim, the granule depth was divided into 20 grid points. The total reactor volume was split up into a biofilm and a mixed compartment, coupled with a diffusive link (exchange coefficient 10000 m3.d-1) to let the liquid phases behave as one perfectly mixed, fluctuating water volume without numerical errors (Chapter III). Transformation processes in the mixed compartment were inactivated and the biofilm compartment was chosen small (0.45 L) so that it contained only 0.03 L of bulk liquid (1% of the total reactor volume). This makes the contribution of suspended biomass to macroscale reaction rates negligible, facilitating the
interpretation of the results. More details on the model are provided in the Appendices: the stoichiometric matrix (Table 9.1), composition matrix (Table 9.2), process rate equations (Table 9.3), parameter values (Table 9.4, Table 9.5, Table 9.6 and Table 9.7) and model validation results.
Calculation of apparent half-saturation coefficients
Apparent half-saturation coefficients of the growth reactions of all microbial groups in the 1D biofilm were determined for all their limiting soluble substrates (Table 4.1) using the method schematized in Figure 4.2. In summary, the method comprises an initial prediction of the microbial population distribution and then a fixation of this distribution to study the response of these granules to changing substrate concentrations, analogous to the method of Picioreanu et al. (2016). The model in Aquasim was first run with the reference operating conditions for 750 days to ensure a steady-state microbial population distribution (step 1).
Next, the stoichiometric coefficients of all biomass variables were set to zero to obtain a fixed population distribution during the determination of the apparent half-saturation coefficient, independent from the duration of the simulations. This was done because changes in the distribution are also not expected during short-term changes of substrate concentrations, as occur during one reactor cycle. All reactions except for one growth reaction from Table 4.1 were subsequently deactivated to avoid competition for the limiting substrate. This is analogous to experimental assessments of half-saturation coefficients, where the activity of competing organisms is minimized by depriving them of substrates or adding deactivating agents (Manser et al., 2005). After these preparations, the granules were subjected to a step-wise decreasing concentration of one substrate, while all other substrates for the active growth reaction were kept available in excess (1000 g.m-3) (step 2).
1D biofilm model
Step 1 - predict the microbial population distribution for the specific
Step 3 – calculate the apparent half-saturation coefficient of that limiting substrate for that microbial group Calculate the total biomass of
the microbial group (Eq. 4.2) Fit Monod kinetics (Eq. 4.4)
AquasimExcel
Total specific growth rate in a granule µtot
Limiting substrate concentration Slim
1D biofilm model Monod fit
Figure 4.2. Method to estimate the apparent half-saturation coefficient Kapp of one microbial group for one substrate using the 1D biofilm model. Only step 2-3 were repeated to estimate this parameter for other microbial groups and substrates. *For research question three, the operating conditions were different from the reference case to evaluate the effect of long-term changes in operation on the microbial population distribution and associated apparent half-saturation coefficients. **For research question two, more than one growth reaction was kept active to assess the effect of competition.
Table 4.1. Overview of determined apparent half-saturation coefficients for the respectively seven, five and two limiting substrates (VFA represents Volatile Fatty Acids and F
Fermentable organic matter) for OHO, PAO and AOO and NOO growth. The coefficients were determined individually, by keeping only one reaction active at a time (the number in between brackets refers to the reaction under concern, as specified in supplementary information).
The simulation results were exported to Excel to calculate the amount of biomass of the microbial group of interest by integration of the local concentration over the granule depth (Eq. 4.2).
MXtot,i =∫ XidV where MXtot,i represents the total biomass of the microbial group of interest in a granule (g COD), Xi the local biomass concentration (g COD.m-3) at a distance z (m) from the granule core, δ the granule radius (m) and Vgranule the volume of the granule (m3). Then, the total (macroscale) specific growth rate in a granule via growth reaction j of this group, µtot,j (d-1), was calculated for every applied limiting substrate concentration by numerical integration of the local rates over the granule depth (microscale) and successive division by the total amount of biomass (Eq. 4.3).
where ṙj represents the local volumetric rate of the growth reaction of interest j (g COD.m-3.d-1) at a distance z from the granule core. This rate ṙj was calculated by Aquasim as the local specific growth rate times the local biomass concentration.
After every step change of the substrate concentration, a new steady-state total growth rate was reached as soon as the substrate gradients stabilized. Monod kinetics (Eq.
4.4) were finally fitted to this steady-state total specific growth rate µtot,j as a function of the limiting substrate concentration Slim (g.m-3) with the solver in Excel by adjusting Kapp (g.m-3) to minimize the sum of squared errors (step 3).
µtot,j ≈ µMax,j Slim
Kapp+Slim Eq. 4.4
The maximal specific growth rate µMax,i was not calibrated, but kept the same as in the biofilm model. To find the other apparent half-saturation coefficients (Table 4.1), only step 2 and 3 were repeated for the other reactions and limiting substrates.
To determine the apparent half-saturation coefficients of PAO, an excess of the storage compound PHA had to be introduced to minimize limitations by this intracellular limiting substrate during step 2. To this end, the precursor VFA was fed with a high concentration (10,000 g COD.m-3) to the granules for more than 2 hours before changing the concentration of the limiting soluble substrate of interest. As such, there was time for PHA to accumulate.
3.2. Which factors influence half-saturation coefficients?
The factors that influence half-saturation coefficients were studied by means of an example, more specifically the effect of oxygen on the growth of ammonium oxidizing organisms (AOO), characterised by KO2,AOO,app.
Influence of competition
The effect of oxygen on the macroscale AOO growth rate was again determined according to Figure 4.2, but this time the aerobic growth reactions of other microbial groups were kept active one by one during step 2 (reactions number 5, 16 and 24 in Table 9.1 in the Appendix of Chapter IV). The required substrates for the other growth reactions were provided in excess to get an idea of the maximum possible interference. For example, the effect of simultaneous aerobic OHO growth was assessed by keeping the reaction active in the model and providing VFA, NHx and PO4 at a concentration of 1000 g.m-3.
Influence of long-term changes in operating conditions
Again, KO2,AOO,app was determined with the method shown in Figure 4.2, but this time after reaching the steady-state microbial population distribution for other operating conditions in step 1. The influent VFA, NHx and PO4 concentrations, temperature, O2 set-point and the granule radius were varied individually, to -30%, -20%, -10% and +10%, +20% and +30% of their reference value. For every new steady-state thus obtained, KO2,AOO,app was determined.
The observed changes of KO2,AOO,app were related to two measures that characterize the microbial population distribution. The first one is the total AOO biomass present in the granule MXtot,AOO, calculated with Eq. 4.2. The second indicator was the average depth of the AOO population, calculated by numerical integration in excel (Eq. 4.5).
Average population depth = δ-∫ zXAOOd (4
3.3. Are apparent-half saturation coefficients practically applicable?
On-line monitoring data from a 9600 m3 aerobic granular sludge reactor treating 14,300 m3.d-1 of sewage in Garmerwolde, The Netherlands, were used. Every reactor cycle starts with a feeding phase of 1-1.5 hours, during which influent is fed from the bottom to create a plug-flow, which enables simultaneous effluent discharge from the top. Afterwards, aeration is provided during a reaction phase of 1-5 hours. Finally, a short settling phase allows the granules to stay in the reactor, before the cycle is repeated. Details on the plant operation and performance can be found in Pronk et al. (2015). Dissolved oxygen was measured in-situ and ammonium ex-situ (5-10 min interval; Hach Lange; Filtrax, AMTAX). Data from August 2017 were extracted from the database as average values per minute. Signals from the ammonium sensor during automatic cleaning and calibration of the device were filtered out.
A model for ammonium removal with Monod kinetics was applied to the data from the aeration phases. The model described the removal rate as a function of the ammonium concentration SNHx (g N.m-3) and dissolved oxygen concentration SO2 (g O2.m-3) (Eq. 4.6), using a maximal ammonium removal rate ṙmax (g N.m-3.d-1) and apparent half-saturation coefficients KNHx,app (g N.m-3) and KO2,app (g O2.m-3).
dSNHx By fitting several cycles at once, a wide variety of combinations of NHx and O2 concentrations was taken into account, which benefits parameter identifiability. The mean absolute error (MAE, Eq. 4.8) was used to quantify the goodness-of-fit for every cycle, which compensates for the different number of measurements per cycle (n)
MAE=∑ |Cni NHx,i-SNHx,i|
n Eq. 4.8
Calculations were performed in Matlab: ‘ode45’ was used to solve the differential equation and for calibration ‘lsqnonlin’ was used in combination with ‘multistart’ to find the global minimum of the SSE.
Figure 4.3. Moving window used for calibration and prediction of the ammonium removal in the full-scale reactor.