1.1. Modelling granular sludge reactors Review
A systematic overview was created (https://ars.els-cdn.com/content/image/1-s2.0-S0043135418309473-mmc1.xlsx) of assumptions, goals, scales, software, calibration and validation of 167 granular sludge reactor models (Chapter II). This may help scientists and engineers to find a suitable starting point to tackle their specific question. It may also stimulate cross-pollination between the partly separate scientific communities studying anaerobic, aerobic and anammox systems. The review showed that models have been successfully applied to gain insight in the relationship between small scale phenomena (e.g. intragranule transport) and large scale operation (e.g. effluent quality), to assess the effect of alternative operational strategies or designs and to monitor unmeasured variables (e.g. biomass concentrations). This illustrates their potential to better understand, operate and design granular sludge reactors, analogous to the well-known models for flocculent sludge reactors.
It is a challenge for new modelling studies that there is not one generally accepted approach, nor is there one that takes into account all known phenomena (transformations, liquid and granule transport, intragranule transport, liquid-granule mass transfer, granule transformation and a size distribution, gas phase transport and liquid-gas mass transfer).
Additionally, there were some unclear assumptions for 19% of the models, which is especially problematic if calibrated parameter values are used for a model with other assumptions. Apart from the different reactor types that were described, the different goals of the studies were acknowledged as one of the main reasons for the observed variety of assumptions (Figure 8.1). Yet, no clear goal was defined in one third of the reviewed papers.
Another reason for the variety of assumptions is the lack of understanding of the principles and kinetics of some phenomena. For example, predicting the granule size (distribution) is challenging because the dependency of detachment, attachment and
breakage kinetics on operating conditions are not well characterized. For anaerobic reactors, it is challenging to find appropriate assumptions for the liquid phase transport without tracer tests or computational fluid dynamics for a specific reactor. Also transport and conversions of particulate organics are not well characterized. Finally, the effects of the vertical gas phase concentration gradients on liquid-gas transfer were not yet known (Chapter V further investigated these effects).
Some assumptions appeared to be at least partly habitual within fields of research.
For example, biofilm models with perfect granule retention were most popular for aerobic and anammox reactors, while apparent kinetics and wash-out of the conceived biomass suspension was more popular for anaerobic reactors, without explicitly mentioned reasons (Chapter IV further investigated the implications of both approaches). Also the popularity of pH predictions for anaerobic granular sludge and absence of such calculations for aerobic and partial-nitration anammox granular sludge could not be directly related to its importance for the reactor performance.
Even though more and more complex models become available, some goals still warrant simpler ones. Finding an appropriate degree of complexity for a certain goal and range of operational conditions is an important challenge for modelling granular sludge reactors, as for every complex system with interacting biological, physical and chemical phenomena. A top-down approach has been used by some, which means that a simple model is first used and more underlying phenomena are added until the macroscale dynamics of interest are predicted with the required accuracy. This approach was also used in this thesis to predict the ammonium removal in every next cycle of an aerobic granular sludge reactor (Chapter IV, section 4.3). Others have used a bottom-up approach, where models with more microscale phenomena are used to simulate macroscale performance and as such determine when and why certain phenomena can be neglected. Also this approach was used here, to see when and why apparent kinetics can be used (Chapter IV) or the vertical gradients of the gas phase composition and pressure can be neglected (Chapter V).
Figure 8.1. Graphical abstract of Chapter II, the review.
Numerical errors
The software that was found most popular for modelling aerobic and partial nitritation-anammox granular sludge reactors was Aquasim (Chapter II). However, unrealistic gaps in the nitrogen mass balance had been reported when considering a granule size distribution by linking several biofilm compartments with different biofilm thicknesses via an artificial advective flows to mimic the mixing in the reactor. In Chapter III, it was found that these unrealistic results originated from numerical errors which arose during the addition of the large, artificial mass flow rates, to the much smaller rates that were actually of interest (the reactions, input and output). The limited number of significant digits with which the numbers are stored by the software results in a loss of accuracy when fast artificial flows are applied. Similar numerical errors were seen when simulating a granular sludge sequencing batch reactor by linking a biofilm and mixed compartment with artificial advective flows. A new approach was proposed, which links the compartments with diffusive links instead. As such, numerical errors were avoided because a diffusive mass flow rate automatically decreases when the concentrations in the compartments converge. A step-by-step procedure was provided, which was also easier to implement and led to faster simulations (Figure 8.2). This increases the application potential of Aquasim.
Figure 8.2. Graphical abstract of Chapter III on numerical errors.
Mixed
Apparent conversion kinetics
In scientific literature, biofilm models were most popular for aerobic granular sludge (Chapter II), but they are complex, lead to slow simulations and it is difficult to find appropriate values for micro-scale parameters like effective diffusion coefficients, biomass densities, porosities, detachment and attachment rates. Therefore, Chapter IV evaluated how the simultaneous reaction and diffusion affect the apparent conversion kinetics of aerobic granular sludge. The applicability of these apparent kinetics was assessed for direct use in models, which is a popular approach for anaerobic granular sludge (Chapter II) and flocculent sludge.
By using the corrected biofilm modelling approach in Aquasim (Chapter III), the effect of different substrate concentrations in the bulk liquid was investigated. A smooth saturation curve was observed with an increasing substrate concentration for the growth reactions of all microbial groups, which could be approximated via Monod equations with apparent half-saturation coefficients. This parameter lumps the effect of diffusion inside the granules instead of describing it separately via Fick’s law. Different microbial groups had different apparent half-saturation kinetics for the same substrates due to their different intrinsic kinetic parameters and distribution inside the granules. Different substrates had different apparent half-saturation coefficients for the same microbial group due to differences in diffusion coefficients and intrinsic kinetic parameters. The time it takes for the intragranule substrate gradients to form was found negligible when the macroscale reactor behaviour is of interest.
Apparent kinetics of microbial groups in aerobic granules were found to be time and system dependent. First of all, the effect of an increasing substrate concentration changed when other reactions consuming a shared substrate were occurring simultaneously. For example, an increasing oxygen concentration increased the ammonium oxidation rate less when heterotrophs inside the granule competed for oxygen, leading to a higher apparent half-saturation coefficient of ammonium oxidizers for oxygen (Figure 8.3). So, even during a single cycle, the apparent kinetics change due to changing rates of competing reactions. Secondly, apparent half-saturation coefficients were influenced by the microbial population distribution, which changes due to fluctuations in the influent composition, granule size, temperature, operational strategy etc. The influence of the microbial population distribution on its apparent half-saturation coefficients could be described by two simple statistics: the average depth and total mass of the population in a granule.
Even though apparent kinetic parameters can thus not be seen as constants, the sequential operation of aerobic granular sludge reactors allowed regular recalibration of apparent kinetics from typical monitoring data of a full-scale reactor, which may be used for model predictive control or to identify the most limiting substrate in a specific reactor. Moreover, qualitative questions may still be answered with constant apparent kinetics, as the effect of the substrate concentration on the conversion rate was always characterised by a smooth
saturation curve. This was further illustrated in Chapter VII, where the fate of influent methane was investigated for different operational conditions and designs using apparent kinetics.
Figure 8.3. Graphical abstract of Chapter IV on apparent conversion kinetics.
1.2. Liquid-gas transfer
Tall reactors, like full-scale aerobic granular sludge reactors (typically 6-9 m), show a more pronounced difference of the composition and pressure of the gas bubbles between the bottom and top than lab-scale reactors. The composition gradient is due to the longer vertical distance over which liquid-gas transfer occurs while the bubbles rise and the pressure gradient is due to the hydraulic pressure created by the taller water column. The composition and/or pressure gradients are often neglected or simplified in liquid-gas transfer models, both in granular sludge (Chapter II) and other (waste)water treatment reactors (Chapter V). Yet, several authors had already noticed that these gradients affect the total absorption or stripping rate under specific conditions. For example, a former PhD student in our research group derived a 2-5 times higher liquid-phase concentration of nitrous oxide from gas measurements on a small stripping flask than on a full-scale reactor and partly attributed this to the stronger vertical gradients on full-scale that were neglected (Mampaey et al., 2015). To better understand these phenomena, Chapter V evaluated the effects of the vertical gas phase composition and pressure gradients on the total liquid-gas transfer rate.
An equation for the total liquid-gas transfer rate was analytically derived from a gas phase mass balance including the effects of the composition and pressure gradient (comprehensive model; Eq. 5.7). A sensitivity analysis showed that the total liquid-gas transfer rate is proportional to the overall volumetric liquid-gas transfer coefficient of oxygen KLaO2 and reactor surface area A. It is linearly dependent on the mole fraction in the inlet gas xGin,i, liquid phase concentration CLi and molar mass Mi of the volatile substance that is moving between the two phases. The reactor height H, diffusion coefficient Di and Henry coefficient hi have
more complex, non-linear effects. Moreover, the effect of every parameter depends on the other parameter’s values. This behaviour is thus more complex than most popular liquid-gas transfer models capture.
The gradients of the gas phase composition and pressure were found to affect the total liquid-gas transfer rate, but the degree of these effects strongly depended on the solubility and driving force for stripping or absorption (Figure 8.4). The mole fraction gradient became more important for substances that are more soluble. The pressure gradient became especially important for very poorly soluble substances when the driving force for absorption increased (i.e. when the inlet gas has a higher content) and also for soluble substances when the driving force for stripping increased (i.e. when the inlet gas has a lower content). For aerobic wastewater treatment specifically, the hydraulic pressure significantly affected the absorption of oxygen and stripping of nitrogen, due to their low solubility and high atmospheric concentration. The mole fraction gradient became important for stripping of carbon dioxide or nitrous oxide, both soluble gases with low atmospheric concentrations. Neither gradient was very influential for methane stripping, given its low solubility and low atmospheric concentration. Some of the models used in literature, which assume uniform values for the gas phase composition and/or pressure (Eq. 5.9-Eq. 5.10 and Eq. 5.13-Eq. 5.14), gave strong deviations from the comprehensive model in some cases. For all these substances, an arithmetic mean mole fraction and pressure (Eq. 5.11) gave a reasonable approximation of the effects of the vertical gradients.
The analytical derivation of the liquid-gas transfer rate provides three benefits over a numerical derivation. First, a qualitative sensitivity analysis could be performed more easily, since a visual inspection of the equation already shows the influence of some parameters and partial derivatives could be derived (Eq. 10.47-Eq. 10.49). Secondly, the analytical solutions can be incorporated into any modelling software with limited extra effort and computational demand. For example, the Matlab codes of the Benchmark Simulation Models (BSM) can be adapted via copy-paste of one equation, without adding differential equations or Simulink blocks or links. Finally, the equations could be implemented in a spreadsheet, which resulted in a user-friendly tool for the selection of appropriate assumptions for a specific volatile substance in a specific reactor (https://ars.els-cdn.com/content/image/1-s2.0-S004313542030381X-mmc2.xlsx).
Figure 8.4. Graphical abstract of Chapter V on liquid-gas transfer.
1.3. Off-gas analyses
The idea that the composition of the gas leaving wastewater treatment processes can be used for monitoring and control is not new, but so far, practical applications have been mainly limited to monitoring the aeration efficiency and sometimes greenhouse gas emissions.
Chapter VI showed that there is more potential for off-gas analyses on sequentially fed and aerated systems, such as aerobic granular sludge reactors. This originates from the absence of feeding and discharge during aeration phases, which enables the derivation of reaction rates and reacted amounts from simpler mass balances and creates a well-mixed reactor, simplifying representative sampling. It was demonstrated, through application on full-scale data, how a single set-up can be used to simultaneously monitor aeration characteristics, liquid phase concentrations, oxygen consumption rates, greenhouse gas emissions, wastewater characteristics and the sludge production (Figure 8.5). The wastewater characteristics that were examined are the influent methane concentration (via off-gas methane measurements), the presence of high TOC/COD (via off-gas carbon dioxide and oxygen measurements combined with liquid phase mass balances) and the COD/N ratio (via oxygen measurements combined with liquid-phase mass balances). The aeration characteristics and liquid phase concentrations were derived from the relationship derived in Chapter V between the measured total liquid-gas transfer rate, liquid phase concentration and overall volumetric liquid-gas transfer coefficient (Eq. 5.11).
Novel insights in the full-scale aerobic granular sludge reactors were also obtained from the off-gas data. The oxygen liquid-gas mass-transfer coefficient KLaO2 increased during periods of constant aeration. This suggested a slow degradation of surfactants, which hinder the mass-transfer at the beginning of aeration. Secondly, the carbon dioxide emission rate showed a comparable cyclic trend as the oxygen absorption rate, due to the coupling of their respective production and consumption via heterotrophic conversions and acid production
during nitrification. Thirdly, methane showed a stripping profile at the beginning of aeration, which indicated that most of it originated from the sewage entering during the preceding feeding phase. Finally, nitrous oxide showed two peaks, one at the beginning of the aeration phase, which was attributed to heterotrophic and nitrifier denitrification during the anaerobic feeding phase, and a second one during aeration, which was attributed to nitrification activity, via the hydroxylamine or nitrifier nitrification pathway.
One major challenge was identified for off-gas analysis. The fast dynamics of the aeration rate and liquid phase concentrations in a sequentially operated reactor lead to significant errors in the derived variables when the aeration rate is low, since this increases the residence time in the floating hood. The design of a floating hood for sequencing batch reactors is thus more crucial compared to most continuously operated reactors.
Figure 8.5. Graphical abstract of Chapter VI on off-gas analyses.
1.4. Fate of influent methane
Chapter VII combined the findings of two other chapters to study the fate of methane