Introduction and Background

Mechanistic models describing the full scope of underlying physical, chemical, and biological processes taking place during biological filtration of drinking water are critical to accurately and precisely predict the removal of toxic and noxious water quality

constituents, including algal biotoxins (Rittmann and McCarty 1980, Zhang and Huck 1996, Hozalski and Bouwer 2001a, Rittmann and Stilwell 2002, Qiongqiong et al. 2008).

Developing mechanistic models of these treatment systems can expand our current understanding of the governing theory describing these underlying processes, leading to improvements in full scale design and operation. Ultimately, models describing biological treatment processes may further both the operator’s and engineer’s comprehension of the performance of these systems under a variety of environmental, operational, and hydraulic conditions expected in practice (Rittmann et al. 2002).

Of all the advantages complex computer simulations can bring, often the most difficult question is how to efficiently structure the model based on scientific theory to produce accurate and repeatable representations of reality, within a certain level of

acceptable statistical confidence. Biological treatment systems are notoriously some of the most complex systems to model, as these processes are highly variable in space and time and depend on countless physical and metabolic interactions among existing microbial

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populations, many of which cannot be detected or monitored (i.e., in real time) using advanced bio-molecular techniques (Kirk et al. 2015, Azeloglu and Iyengar 2015, Rittmann et al. 2002). The environmental variables driving these microbiological treatment systems (such as pH, water temperature, nutrient concentrations) are also dynamic, wide-ranging, and difficult to monitor (Kirk et al. 2015, Azeloglu and Iyengar 2015, Rittmann et al. 2002). Moreover, the scientific theory governing the fate, distribution, and subsistence of these microorganisms and nutrients sustaining the growth of these microorganisms is a

combination of several disciplines, where uncertainty may arise from multiple assumptions or conventions tailored by each. Finally, there are issues with scale up of the numerical simulations of these systems, where the behavior of one system on the laboratory scale is often not in agreement with the behavior of the system on a larger scale (Hozalski and Bouwer 2001b).

Despite the challenges identified above, the advancement in computing power over the last decade has enabled the development of new mechanistic biological models (i.e., in systems biology) that can mathematically account for the high complexity of these systems (Faust and Raes 2012, Song et al. 2014). However, many of the mechanistic, systems

biology models that have been developed to describe microbial growth and community (i.e., metabolic) interactions may suffer from over-parameterization and inclusion of unnecessary complexity (Banga and Balsa-Canto 2008, Chis et al. 2011b, Villaverde and Banga 2014). Overparameterization refers to the fact that any mathematical model, no matter how far away from the true representation of reality, can fit the experimental data, given that the number of parameters in the model structure is sufficient to fit the data (Chis et al. 2011b, Villaverde and Banga 2014). But, are the parameters in the model realistic or

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even physically relevant? Can each parameter be measured independently of the system at hand? Is all the complexity included in the model structure absolutely necessary to

reproduce the experimental data? After considering these key questions, it is apparent that a model structure that minimizes the number of physically relevant parameters (all of which can be measured independently), avoids unnecessary complexity, and ensures computational efficiency is advantageous in the long run.

As of current, little research has been conducted regarding the development of numerical simulations to predict algal toxin removal in biological filters. However, a

significant amount of modelling work has been conducted regarding the removal of organic compounds (more specifically biodegradable dissolved organic carbon or assimilable organic carbon) in these filtration systems (Rittmann and McCarty 1980, Billen et al. 1992, Laurent et al. 1999, Zhang and Huck 1996, Hozalski and Bouwer 2001a, 2001b, Rittmann et al. 2002, Rittmann and Stilwell 2002, Qiongqiong et al. 2008). Rittmann and McCarty

(1980) was one of the pioneering studies to model biofilm processes and apply the same principles in drinking water treatment filtration applications. The model developed in their study assumed that a steady state biofilm could exist in porous media, where a thickness of biofilm could be predicted from a general bulk substrate concentration existing in the interstitial pore space. Standardization of this model for drinking water treatment

applications was presented in Rittmann (1990) that developed operational principles and guidelines for drinking water treatment biological filtration systems based on four model parameters and normalized loading curves. Details of the actual model parameters, theoretical approach, and loading curves developed were presented in the background section for reference.

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Billen et al. (1992) developed the CHARBROL model for simulation of biodegradable dissolved organic matter (BDOC) in the granular biological activated carbon process during drinking water treatment. The CHARBROL model took into consideration three different fractions of biodegradable organic carbon with different assimilation capacities (i.e., rapid/slow degradation) and showed that BDOC removal was directly proportional to the influent BDOC concentration at specific empty bed contact times (EBCTS) (Billen et al. 1992).

Zhang and Huck (1996) introduced another steady state biofilm model for analyzing the removal of assimilable organic carbon (AOC) in plug flow biological reactors, which was similar to that proposed by Rittmann and McCarty (1980). This study determined that the dimensionless empty bed contact time, which is a function of the actual empty bed contact time, specific surface area of the medium, and the ease of biodegradation/diffusion in the biofilm, is an effective predictor for effluent AOC concentrations, which appropriately described the linear experimental relationship observed between influent AOC

concentration and effluent AOC concentration.

Hozalski and Bouwer (2001a, 2001b) presented the first transient biofilm model that was applied and validated to predict biodegradable organic matter (BOM) removal in drinking water treatment practice. The Hozalski and Bouwer model incorporated substrate (BOM) transport, aqueous cell transport/growth, as well as biofilm thickness growth/loss mechanisms. An innovative feature in the model developed by Hozalski and Bouwer (2001a, 2001b) was the introduction of an instantaneous biofilm loss term from the backwashing process.

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More recently, a comprehensive biofiltration model based on similar principles to Rittmann and McCarty (1980) was developed by Rittman et al. (2002) to predict the removal of multiple species of water quality constituents as mediated by several types of bacteria within a biofilm community (heterotrophs, autotrophs, etc.). This model, called the Transient State Multiple Species (TSMS) took into account the dynamics of biofilms during drinking water treatment by considering four different bacteria types (heterotrophs, ammonia oxidizers, nitrite oxidizers, inert biomass), seven chemical species

(biodegradable organic matter, ammonium nitrogen, nitrite/nitrate nitrogen, soluble microbial products, dissolved oxygen), eight distinct chemical reactions to describe the utilization of these species in the biofilm, substrate transport of species in the

biofilm/porous media, growth, decay, lysis of biomass, and biofilm detachment processes. Qiongqiong et al. (2008) developed a relatively simple steady state, analytically based simulation of biological filtration of natural organic matter (NOM) to Hozalski et al. (2001a,2001b) for drinking water treatment applications without considering diffusion of substrate within the biofilm or mass transfer limitations of substrate transport from the bulk liquid to the surface of the biofilm (which was fundamental to most previous models proposed by Rittmann et al.). The model introduced by Qiongqiong et al. (2008) considered the transport of natural organic matter (NOM), aqueous cells (attachment only), and

growth/detachment of solid biomass cells (and no effects such as backwashing).

The main drawback to these previously developed models is the fact that they attempt to integrate microscopic (pore scale) approaches into a macroscopic (continuum based) model structure. The microscopic approaches that are included are generally focused on substrate mass transport to the biofilm surface as well as diffusive transport of substrate

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throughout the biofilm. The parameters associated with the microscopic transport, including the molecular diffusion coefficient in liquid and in the biofilm for most water quality constituents, are generally difficult to constrain and measure independently. Moreover, the significance of these parameters, from an operational or design standpoint is rather limited outside the realm of research. Thus, it may be more beneficial to “back out” and consider only the macroscopic level of processes occurring within the porous media of a biological filter, to not only simplify the processes occurring, but to provide a realistic framework for design, operation, and monitoring.

Importantly, all of the currently published biological filtration models do not consider important feedback processes between the microorganism growth and the hydraulic conductivity or porosity of the media. This mechanism, also referred to as “bioclogging,” is a critical process affecting the development of the flow field throughout the course of the filter operation (Thullner et al. 2002a, 2002b). The study of bioclogging has been introduced in the groundwater field and is especially relevant for bioremediation processes, as it produces heterogeneity in the availability of electron donors (i.e., organic carbon) and acceptors (i.e., oxygen) over time. In effect, the formation of a biofilm on immobilized media from microorganisms within the influent water will block the pore space over time and result in a channeling or the development of preferential flow paths. This biological-physical feedback process affects the dynamic availability of substrate within a biological filter, which ultimately influences the stability of these biofilm communities. Including this bioclogging feedback process will also provide valuable information on the development of head loss across the filter over time for optimal hydraulic performance.

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A more pertinent aspect that has not yet been introduced in these previous simulations is the advent of modelling the change in community structure of the microorganisms over time that are actually present and performing the degradation. A critical assumption that each of these previous studies has made is that all microorganisms are capable of degrading any given substrate at any given time, which may be far from the case in the dynamic environment of a biofilter. Although Rittmann et al. (2002), Rittmann and Stilwell (2002) has considered the fluctuation in abundance and distribution of different communities (autotrophs, heterotrophs, inert biomass) these studies do not attempt to define what populations within these communities are actually performing the task at hand. This assumption may drastically overestimate the actual treatment efficiency of the system, given that the presence of certain bacteria to perform the degradation are transient in nature, and may change due to different environmental stimuli (nutrients) or hydraulic conditions (fluctuations in the HLR). Including this change in the bacterial community structure may also better reflect the removal of algal toxins in biological filtration systems, as the removal efficiencies of toxins greatly depends on the presence of microorganisms that are specific to the degrading process (Ho et al. 2012a).

Therefore, considering the previous limitations in mechanistic biofiltration models presented in the scientific literature, the focus of this chapter will be to develop and validate an efficient and reliable one- and two-dimensional numerical model that can simulate the biodegradation of microcystin within a biological filter. The numerical

simulations will be verified using developed analytical solutions and parameters calibrated using a sequence of experimental, laboratory-based investigations. Ultimately, the primary objective after developing this model will be to achieve an improved predictive

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understanding of the most important biological treatment mechanisms and to identify key operational and design parameters that improve the reliability and efficiency of algal biotoxin removal in biofiltration systems.

2. Experimental and Mechanistic Modelling Approach