1 Introduction

Probably the most common technical question since publication of the IWA Anaerobic Digestion Model No. 1 (Batstone et al. 2002) has been “When will the ADM2 be published?”. Indeed, it was asked during presentation of the ADM1 in Brussels in 2010 at AD IX. At that time, it was due to apprehension that the model would be replaced in 1–2 years, but since then (and in the 13 years since publication), there has been genuine interest as to what should replace, eventually, the ADM1.

So far, there has been no compelling reason to release an ADM2 as such. The ADM1 itself was based on a broad range of other, largely comparable models (Angelidaki et al. 1999; Costello et al. 1991b; Kalyuzhnyi and Fedorovich 1998a; Siegrist et al. 1993; Vavilin et al. 1997), which did not vary substantially in concept, only implementation. Its strengths were broad basis and concept compatibility with the IWA ASM series (Henze et al. 2000), a clear and complete presentation of all model elements, as well as reference implementations, and importantly (given the large numbers of parameters), a complete and consistent parameter set. However, given the amount of previous model development work, it is unlikely that model structure would change substantially, unless core alternative processes (e.g., acetate oxidation) were found to have (Wett et al. 2014) a far higher incidence than thought, or to be inadequately described by extensions, there is no current need for a re-release of the core model. Indeed, the main (structural) part of the ADM1 which was original, has caused some problems, and is input of complex particulates as Xc, which is undefined and generally causes continuity issues when coupled to other models (Nopens et al. 2009). This is discussed further in Sect. 4.

While there is limited need for changes in biochemical structure (and this need can be largely addressed by plugins), or the underlying COD-uptake-yield structure (note there has been some discussion of this (Kleerebezem and van Loosdrecht 2006), a number of limitations have emerged, particularly over the last 5 years, which the aggregate modelling literature is not addressing sufficiently, or in a sufficiently comprehensive way. This review focuses on identifying and discussing these fairly disparate issues, and proposes initial approaches to address them. Scope is limited to mechanistic and semi-mechanistic models, with stochastic models (e.g. García-Gen et al. 2015; Pullammanappallil et al. 1998) including multi-order empirical, regressive, and expert systems models forming another class of models, with generally a focus on system characterisation for control and soft sensors, and system optimisation, rather than understanding and fundamental characterisation as is used in mechanistic models.

2 New technologies

The last 10 years have seen substantial expansions in the range of technologies utilised in anaerobic digestion. This is further reviewed recently (Batstone and Rodriguez 2015; Batstone and Virdis 2014; Jensen et al. 2014b), but broaden the scope of anaerobic technologies to new applications. These utilise improved understanding of the underlying process, and its kinetic or metabolic limitations [e.g., plug-flow anaerobic digestion (Dvorak 2012)], or advances in associated wastewater treatment technologies such as aerobic membrane bioreactor processes to enable high-solids wastewater treatment through anaerobic membrane bioreactors (Liao et al. 2006). A summary is shown in Fig. 1. This shows historic processes such as mixed digesters and traditional high-rate processes (UASB reactors, internal circulation, EGSB), as well as anaerobic lagoons and waste stabilisation lagoons, which remain very common for tropical and subtropical (and even temperate) climates (Shilton and Harrison 2003).

Fig. 1
figure 1

Emerging processes in Anaerobic Digestion (shown in solids fill) against hatched existing processes). Key modelling goals and needs are also shown

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Modelling goals are also shown in Fig. 1, with those around historic processes being relatively mature, and focused on specific problems, and those around emerging processes focused on elementary process description.

2.1 Anaerobic lagoons/waste stabilisation ponds

Anaerobic lagoons are generally deeper and often used for primary wastewater treatment (Shilton and Harrison 2003) and industrial wastewater treatment (Jensen et al. 2014b). Key operational problems are hydraulic design (Shilton and Harrison 2003), including the response of hydraulics to changes in ambient temperature, and accumulation of solids, also including the effect of temperature (Papadopoulos et al. 2003).

Non-biological, hydraulic modelling only has been extensively used to address the issue of hydraulic design (see review in Shilton and Harrison 2003), but these have not generally been combined with biological models, mainly due to numerical complexity and model stability when coupling biological rate equations with CFD equations. Simplified hybrid models have been used (Alvarado et al. 2012), as a stirred-tank hydraulic combined with biological kinetics would be inappropriate given the complex hydraulics.

So far the problem of sludge accumulation has been addressed only through simple stirred tank or compartmentalised reaction (1st order) accumulation models (Saqqar and Pescod 1995).

The two problems of sludge accumulation and hydraulics are complex and linked. As lagoons are covered to capture methane, costs of desludging and methane loss will increase, which increases the motivation to model. At the same time, the ability to simultaneously model hydraulics, biological transformations, and distributed behaviour of sludge (as well as sludge-hydraulic coupling) will continue to improve by the use of reactive CFD. The difficulty has been noted above, but this is quite realisable given current techniques, and hence represents an opportunity. This is a primary example of a problem where multi-phase reactive distributed parameter modelling is core to the overall problem.

2.2 Liquid mixed digesters

Anaerobic sludge digestion was original focus of kinetic modelling of anaerobic processes (Gossett and Belser 1982; Pavlostathis and Gossett 1986) as well as a key focus for the ADM1 and similar models (Batstone et al. 2002; Siegrist et al. 2002). This is hence one of the most mature applications of anaerobic process modelling, and remains a key focus.

The key challenge in this area is that of input characterisation (kinetics and stoichiometry), as principal issue in system and parameter identification, especially with particulate substrates where hydrolysis coefficient, energy density, and degradable fraction define performance under the majority of operating states (Donoso-Bravo et al. 2011; Jensen et al. 2011). Due to fundamental limitations, the complex particulate concept (Xc) in the ADM1, or analogous states in other models (Siegrist et al. 2002) has been generally discarded (see discussion in Sect. 4), and inputs defined as inerts (XI), and degradable, either aggregate, or separated into carbohydrates, lipids, and proteins (the latter approach enables energy density and nitrogen fraction to be defined).

Approaches to characterisation have either been biological, using a batch test or on-line data to enable estimation of parameters (Batstone et al. 2009; Girault et al. 2012; Jensen et al. 2011), direct chemical measurement, either inferential (e.g., COD, N, VS), or directly (Buffiere et al. 2008; Zaher et al. 2009), or by empirical techniques (e.g., spectroscopy and correlation analysis) (Jimenez et al. 2014). Another approach is upstream model based analysis (or continuity based on whole plant modelling (De Gracia et al. 2011; Nopens et al. 2009). This is a highly active area that is only now seeing some consolidation into a defined approach, and a key issue is translation and comparison between different approaches, as well as validation in full-scale systems, with, often kinetics being difficult to estimate (Jensen et al. 2011).

Another emerging focus in mixed-digester modelling has been the emergence of mixed feed digestion (Mata-Alvarez et al. 2011), and codigestion with sewage sludges, particularly of opportunistic feeds such as glycerol (Jensen et al. 2014a) and fats, oils, and greases (FOG) (Razaviarani and Buchanan 2015). The use of modelling to enable mechanistic analysis of mixed feed digestion is particularly important (Astals et al. 2014), potentially to identify the underlying basis for synergistic (Pagés-Díaz et al. 2015), or antagonistic (Long et al. 2012) responses. Many of the underlying mechanisms are well represented in structured models such as the ADM1, which particularly include the balance between pH depression caused by increased carbohydrate degradation, and elevation (and potential ammonia inhibition) caused by increased protein degradation. Mechanisms such as LCFA and glycerol inhibition may need to be added, and there is some evidence that threshold style rather than non-competitive is a more appropriate function, even for biostatic inhibitors such as ammonia, salts, and organic acids (Astals et al. 2015; Pratt et al. 2012). Physicochemical and hence pH modelling is undergoing revision, including complex chemistry, precipitation, and the linked phosphorous-sulfur cycles, and this is discussed further in Sects. 3 and 4.

Computational fluid dynamics has been widely used to evaluate digester mixing efficiency, but distributed parameter models are now being coupled to reactive models such as the ADM1 (Gaden 2014; Van Hulle et al. 2014), mainly to investigate the impact of non-ideal mixing on process performance.

Other emerging areas of anaerobic modelling mainly related to the increased use of pretreatment to enhance degradability speed and extent. To date, this has mainly focused on characterising the effect of enhancement [reviewed extensively in (Carrère et al. 2010)], but there is further work identifying how new pathways such as acetate oxidation (Rivera-Salvador et al. 2014; Wett et al. 2014) may influence response from pretreatment, or play a role in high-rate, high temperature anaerobic digestion (Ho et al. 2014).

2.3 Biofilm high-rate anaerobic digestion

This analysis focuses on biofilm high-rate anaerobic digestion, which includes biofilters and granular high-rate systems, including upflow anaerobic sludge blanket (UASB), attached film fixed and fluidized bed, expanded granular sludge bed (EGSB), and internal circulation reactors (IC). It should be noted that granular systems from a biofilm modelling perspective are simply self supporting biofilms, and approaches are generally common. These systems have an extensive history of modelling, mainly focused on process modelling, particularly process modelling of the balance between acid producing and acid consuming processes (Costello et al. 1991a), but also (for example), competition for electrons (Kalyuzhnyi and Fedorovich 1998a). A further review of classic anaerobic biofilm process modelling (granular and non-granular) is provided in (Saravanan and Sreekrishnan 2006). There has been more recent work in combined hydraulic-reactive modelling, for example, particularly novel reactor designs such as the spiral granular process (Chen et al. 2012), but also in conventional granular systems (Batstone et al. 2005), expanding from 1-D to multidimensional (Ren et al. 2009). Consideration of degradable substrate as media (a shrinking core combined with growing biofilm) expands application to solids substrates (see Sect. 2.6; da Rocha et al. 2013). Another historic focus has been modelling biofilm structure [reviewed in (Saravanan and Sreekrishnan 2006)], with this extending to multi-dimensional analysis to evaluate the microscopic effects of interspecies (Batstone et al. 2006). An emerging field has been on modelling new applications for this technology, with a key application being domestic wastewater treatment. This requires effective description of low-temperature operation (Donoso-Bravo et al. 2013), inclusion of sulfate as an electron acceptor, and inclusion of methane solubility (Batstone 2006). This has now translated particularly to application of emerging high-rate processes.

2.4 Emerging non-biofilm High-Rate (ABR, AnMBR)

Anaerobic baffled reactors (ABR) have been extensively used as an alternative to biofilm systems, particularly for low strength wastewater (Barber and Stuckey 1999), and this analysis has extended to model based analysis, both of hydrodynamics, and kinetics [see recent review (Zhu et al. 2015)]. ABRs are particularly interesting where each stage is measured, as kinetics are exposed by the relatively short hydraulics in the first stage, which enables effective parameter identification.

However, the major development in high-rate systems over the last 5 years has been widespread application of anaerobic membrane bioreactor (AnMBR) systems, particularly for domestic wastewaters. This is now a very large field, and full coverage is beyond the scope of this review, a number of reviews have been done, all of which highlight low-strength wastewater treatment, including applications (Liao et al. 2006), issues (particularly technical extensions) (Stuckey 2012) as well as a review specifically on domestic wastewaters (Ozgun et al. 2013). These together provide an excellent review of the scope, applications, and issues in anaerobic MBR systems, which commonly are flux management, dissolved methane control, optimal design and configuration, and generation of byproducts and behaviour of recalcitrant components. They also highlight the advantages of AnMBR systems, which are inherent decoupling of hydraulic and solids retention times, production of high-quality effluent, ever-decreasing energy consumption (Shin et al. 2014), and the ability to apply to a broad range of novel processes (Batstone and Virdis 2014). Evolution of AnMBR designs have been evident, towards the now dominant design of hollow fibre submerged AnMBR systems.

The reviews have not extensively assessed modelling of AnMBRs, but it is an active area, with a current focus that aligns with the outcomes of the reviews above. The strongest focus of modelling has been on fouling prediction and control, with particularly the work of Robles addressing this problem in developing a mechanistic cake accumulation model (Robles et al. 2013b) and applying both mechanistic and empirical models for cake accumulation control (Robles et al. 2013a, 2014). Cake accumulation models have also been combined with CFD in a multi-dimensional domain (Boyle-Gotla et al. 2014). However, these have not generally considered biological reactions. Reactive models have been applied to general AnMBR issues, considering accumulation of soluble inerts (Benyahia et al. 2013), general performance modelling (Spagni et al. 2015). However, what has not been done is reactive modelling to link accumulation and presence of particular constituents such as colloidal organics, fats, and SMP, as well particulate and reactive membrane cakes to fouling (Dereli et al. 2015).

There is clearly strong scope for increased coupling of reactive process modelling and reactor design, with a particular focus on coupling hydraulics, membrane physical interactions, and multiphase reactions to further optimise this promising process.

2.5 Plug flow reactors (PFR)

Plug glow reactors are increasingly being used, particularly in North America for high-solids manure digestion system. Plug flow anaerobic digestion feeds sludge at a high concentration (8–12 %) with the solids moving progressively along a rectangular or circular cross-section trench and reducing to 3–6 % at the outlet. Hydraulic retention time is normally >20 days, but space use is effective due to high solids concentration and the enhanced kinetics of plug flow digesters. The very high ammonia concentrations (3–5 gN L−1) enabled by high feeds solids provide inherent protection against low pH failure, such that the key consequence is an elevated organic acid level (>1000 mg COD L−1). There is very limited formal literature on plug flow reactors, with some found on microbial community (Li et al. 2014). Designs can be relatively simple, or more complex and engineered e.g., the DVO design has a sophisticated U-shaped digester design, with gas induced corkscrew mixing, ammonia recovery by pH and temperature elevation (to 70 °C), and use of high-pH effluent to scrub gas of CO2 and H2S (with the gas being used to reduce effluent pH due to supply of CO2 as an acid) (Frear and Dvorak 2013). Ammonia stripping is enabled by high temperature and high pH applied during ammonia stripping by DVO.

Plug flow reactors are subject to an interesting set of process constraints. The hydraulics allow better utilisation of the volume, but increases risk of overloads, where less effective buffering is provided by the digester volume. Put simply, if the digester fails near the start, that failure can progressively spread to the remainder of the digester. However, the very high ammonia concentrations (3–5 gN L−1) enabled by high feeds solids provide inherent protection against low pH failure, such that the key consequence is an elevated organic acid level (>1000 mg COD L−1). This is a problem that can be addressed readily through anaerobic process modelling and dominant mechanisms of convection-reaction. Designs also utilise potentially gas lift radial mixing, which could benefit from CFD (or coupled CFD-kinetics).

2.6 Leach bed reactors (LBR)

Leach bed reactors (LBRs) apply a reactive percolation liquid to digest a solid phase at high concentrations. The liquid can be simply recirculated, or further treated through a high-rate anaerobic process (e.g., biofilter (Linke et al. 2015)), or chemical process such as ammonia removal. The leach bed is most commonly operated in batch or semi-batch mode (Gehring et al. 2015), but continuous mode operation is also possible (Linke et al. 2015). LBRs have been widely applied to grass, straw, and maize silage (Gehring et al. 2015; Linke et al. 2015), municipal solid bioreactors (la Cour Jansen 2011), animal manures (Saritpongteeraka et al. 2014), and is generally applicable to any structured solid substrate. They are also applicable to generation of alternative products such as hydrogen and organic acids (Lei et al. 2015).

Leach bed systems are complex to operate, with the feeds being largely carbohydrates (i.e., poorly buffered), often having high ammonia levels from the outset, and existing in multi-stage configuration with mixed batch-continuous processes. They generally do not achieve the full methane potential of the underlying substrates (Lei et al. 2015).

Fundamentally, LBRs are also one of the most complex systems to simulate effectively, containing gas, liquid and reactive solid phases, as well as complex interactions between biologically active solids and liquid and gas flows (qL, qG in Fig. 2). Particularly as a batch process, the hydraulics and effective volume of the solid bed can change, which then has an integrated impact on concentration in the liquid phase. An outline of the interacting processes is shown in Fig. 2. Modelling is limited, and approaches can be divided into those that apply a lumped parameter approach to identify process characteristics (Nopharatana et al. 2003), and those that attempt to represent the full mechanistic process. The latter are impressive, and generally develop strong insight into how these fundamentals interact. ADM1-style models have been applied, including simulation of the high-rate leachate treatment process (e.g., (Thamsiriroj et al. 2012), CFD and changes in bed porosity have been considered (Shewani et al. 2015). Municipal landfills represent a large scale leachbed, with modelling largely focused on the water balance (Berger et al. 1996), since this predicts leachate generation, but also with some process modelling (Kim et al. 2007). However, with the emergence of engineered landfills and in-vessel municipal digestion (Chugh et al. 1999), this will be an increased target for mechanistic modelling.

Fig. 2
figure 2

Mechanisms for modelling in a leach bed system, including mass transport, and multi-phase reaction between particulate phase (X) and the soluble phase (S) [modified from (Batstone and Rodriguez 2015)]

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One of the reasons that mechanistic modelling is useful is that leach bed reactors fully expose potential imbalances between acid producing processes and acid consuming, as these are generally separated between the bed and the high-rate reactor, and this requires a mechanistic modelling approach. The balance of factors can vary substantially between crop residues (which are carbohydrate dominated, and represent souring behaviour), and manures and municipal solids waste, which have higher ammonia levels, and hence can be dominated by ammonia inhibition. Particularly coupling dynamic long-term changes in bed physical characteristics with mass transport, reaction, and the relatively short term changes that occur in the high-rate anaerobic reactor is a challenging problem that offers the potential for insight into how to optimise these processes towards the performance of mixed digesters.

2.7 Conclusions: technologies

Anaerobic modelling has now evolved to the point where evaluation of existing processes, as well as the requirements of new reactors is exposing the limits of treating the digester as a completely mixed process. This is most evident in emerging processes such as leach bed reactors and plug-flow reactors. However, it is also becoming more important in systems such as sludge digesters, high-rate anaerobic systems, and anaerobic MBRs, where aggregate performance can be adequately simulated by a mixed tank, but challenging situations such as high-solids, co-feeds, or membrane-fluid coupling require consideration of spatial variance. This is increasing the importance of including spatial variance (including potentially coupling CFD and reactive models), and techniques are either developing, or on the cusp of being available to properly consider and apply modelling to achieve fundamental insight into- and improvements that would not otherwise be enabled. We also note that anaerobic processes are not limited to engineered systems, and in fact, the principles of anaerobic modelling can be applied to the natural environment (with soil and marine methane cycles being critical—see Sect. 3 discussing environmental anaerobic cycles). Another fascinating (and advanced application) is simulation of gut processes, from a basic analytical perspective (Muñoz-Tamayo et al. 2010), but also from an advanced perspective, using mechanistic modelling to determination variation in both processes and physical configuration (Godon et al. 2013), which can provide clues as to how to potentially build a better anaerobic digester.

3 Emerging anaerobic processes

Anaerobic digestion modelling has been extensively applied to investigate the core processes themselves (nominally those that appear in the ADM1), but also a variety of alternative organic substrates such as lactate (Hinken et al. 2014) and ethanol (Peiris et al. 2006). Alternative electron acceptors are another key topic (see below). However, modelling problems associated with novel processes are now emerging that need a rethink as to what constitutes an “anaerobic” process.

The classical scheme of the anaerobic digestion pathway should be particularly transformed into another concept where the major electron flows from inorganic sources would be depicted. Figure 3 shows a mechanistic scheme of the anaerobic transformations occurring in a digester where the emerging anaerobic processes are included. A summary of key aspects of these emerging processes is reviewed in Table 1.

Fig. 3
figure 3

Emerging metabolic processes in anaerobic digestion, including photo-anaerobic processes, sulfur-cycle (which interacts with the phosphorous cycle), metal oxidation–reduction cycles, alternative nitrogen cycles, and the action of methane and hydrogen as electron donor. The ADM1 representation of composites is shown as contested (?) due to issues raised in Sect. 4

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Table 1 Key catabolic mechanisms of emerging anaerobic processes
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3.1 Electrons without organics: chemo and lithotrophic processes (nitrogen, sulfur, metals, and hydrogen)

3.1.1 Anaerobic nitrogen conversions

Anaerobic digestion is characterised by a lack of electron acceptors, such that the substrate itself becomes the terminal electron acceptor. In practice, this occurs by the major intermediates carbon-dioxide (CO2) and hydrogen (H2), such that excess electrons are used (via H2) to reduce carbon-dioxide to methane. This has been extensively discussed in the ADM1 report (Batstone et al. 2002) and elsewhere, and hydrogen transfer to methanogens is energetically and diffusively limited, and one of the governing mechanisms in anaerobic processes. Anaerobic processes are inherently electron-rich, and hence alternative, more favourable electron acceptor molecules are readily utilised. The key alternative electron acceptors are sulfate and nitrate/nitrite.

Both inhibition and utilisation of nitrate in general anaerobic digester conditions has been comprehensively assessed (Tugtas et al. 2010), and oxidised forms of nitrogen are short-lived in the aggregate digester. However, more complex problems are now emerging. Methane has generally been regarded as inert under anaerobic conditions, but is known to be (slowly) reactive under aerobic condition (Lieberman and Rosenzweig 2004). The focus for this has been biomanufacturing of polymers using methane as substrate. However, oxidised nitrogen has also been found to act as electron acceptors for the anoxic oxidation of methane (denitrifying anaerobic methane oxidation, DAMO process) (Raghoebarsing et al. 2006). This is further complicated by the fact that two domains respectively reduce nitrate to nitrite (archaea) and nitrite to nitrogen gas (bacteria) (Chen et al. 2014). The process is obviously of interest in wastewater treatment due to the ability to use methane to denitrify, and nitrate/nitrite to remove methane from mainline anaerobic treatment (McCarty et al. 2011). A simple model has been proposed that encompasses the two DAMO processes as a sole mechanisms and also includes substrate inhibition by nitrite (He et al. 2013). Another model encompases archeal DAMO only but also incorporates alternative electron acceptors such as Fe3+, Mn4+ or SO4 2−. The model is geochemically-oriented but the mechanisms are similar to those appearing in DAMO reactors. It does not include inhibition processes (Lopes et al. 2011), which are very important for the nitrite producing archaeal DAMO. A challenge in investigating this are that the organisms are extremely slow growing, and in fact, the bacteria can be outcompeted for nitrite by anammox organisms (Chen et al. 2014), a mechanism which has been considered in the Chen model (Chen et al. 2014). Modelling the complex interaction between DAMO and anammox organisms is important, since denitrifying archaea can coexist with either DAMO bacteria or anammox, but the latter two compete for nitrite.

Another key anaerobic N process is the anaerobic ammonium oxidation (Anammox). Modelling of Anammox in general is undergoing challenge and revision. A suitable model for Anammox conversions was published early (Koch et al. 2000), and has been widely applied. However, the catabolism is complex due to physical and inorganic interactions and the complex internal organization of the anammox cell. Additional inhibitory factors include the effect of pH, especially in underload situations(Carvajal-Arroyo et al. 2014a), and inhibition due to both unionized acids (free nitrous acid –FNA– and free ammonia –FA–) as well as ionized nitrite, which has an acute inhibitory effect on anammox activity (Puyol et al. 2014). Added to this is the ability of the organisms to store polymers (van Niftrik et al. 2008a), and maintenance requirements in challenging conditions (Carvajal-Arroyo et al. 2014a, b). Metallic interactions have also been found, with Fe(III) deposits accumulating in the anammoxosome complex (van Niftrik et al. 2008b), which may be a product of reduction reactions, or possibly related to FNA oxidation to form free radicals that help explain the role of FNA.

Overall, the anaerobic nitrogen cycle is complex, involving multiple competing organisms mediating multiple processes, and important, in both anaerobic and anoxic environments. This area requires more work, particularly in consolidation and analysis of mixed population systems.

3.1.2 Anaerobic sulfur conversions

Anaerobic sulfur cycling includes both sulfate reduction to sulfide, as well as potentially sulfide oxidation to both elemental sulfur and sulfate due to nitrate and fugitive (or intentionally) added oxygen or air. It is metabolically diverse, and connected to carbon, phosphorous, and even Fe and As cycles (Rodriguez-Freire et al. 2014) in anaerobic, and general wastewater treatment (see Sect. 4).

The classical key process in the sulfur cycle is the biological sulfate reduction performed by sulfate reducing bacteria (SRB) (Hao et al. 2014). These chemotrophic bacteria are able to anaerobically reduce the sulfate both autolithotrophically (using H2 as e-donor and CO2 as C source) and heterorganotrophically (using organic compounds as e-donor and C source). Sulfate reduction was not incorporated in the original ADM1 but it is relatively easy to implement as a side or main process (Fedorovich et al. 2003). SRB generally outcompete acetogens for organic substrate and with hydrogenotrophic methanogens for hydrogen (Kalyuzhnyi and Fedorovich 1998b). The produced sulfide is inhibitory (Utgikar et al. 2002). Strategies for inclusion are either to only include competition for hydrogen (Batstone 2006), or to include also competition with acetogens (Kalyuzhnyi and Fedorovich 1998b). The latter substantially increases model complexity efforts. Where the influent sulfate:COD ratio is relatively low, a reduced model (Batstone 2006) offers a fair representation of the S transformation processes. At high sulfate levels, it is possible that hydrogen is depleted and SRB use organic acids as source of electrons, and the sulfate reduction model should be upgraded with these additional biochemical routes (Barrera et al. 2015) (see also Barrera et al. 2013). Sulfate reduction is being increasingly assessed in metal sulfide interactions, and as a potential platform for metals recovery (Weijma et al. 2002). Relevant metals are Fe2+,3+, Zn2+, Cu2+, Pb2+, Cr2+, Ni2+ or Cd2+ with particular application to mining wastewater flows (Tang et al. 2009). Apart from metal partitioning, there are also biological effects in reduction of metals toxicity (Gonzalez-Estrella et al. 2015), and metabolic interactions (Bridge et al. 1999).

Sulfide oxidation through microaerobic treatment is a low cost method to remove sulfides through addition of small amounts of air or oxygen into gas or liquid phases (Diaz and Fdz-Polanco 2012; Jenicek et al. 2008). When sulfide is oxidised in a digester at limited oxygen levels, it reacts to elemental sulfur (requiring only 0.5 mol O2 per mole S2−). Availability is then limited for further biological reduction, which means air injection is effective for sulfide control. A new recent process has been discovered relating the sulfur cycle with the phosphorous cycle which is particularly interesting in enhanced biological phosphorus removal (EBPR) processes (Wu et al. 2013). This process leads to recover S as S0 globules production in a syntrophic association between EBPR and S-cycle bacteria, theoretically allowing to recovery also P as Poly-P and C as PHA and to eliminate N in a nitrification/autotrophic denitrification step (Wu et al. 2014). This process has been recently proposed and still needs more confirmation about the complete biological mechanisms, so there is a clear opportunity associated to the development of a model to describe accurately this complex bacterial association.

3.1.3 Other metallotrophic and lithotrophic processes

While many metallotrophic processes involve the sulfur cycle [that of arsenic being particularly fascinating (Rodriguez-Freire et al. 2014)], there are many examples of direct metal reduction, including of naturally iron (Lovley et al. 1987) but also exotics such as uranium (Lovley et al. 1991) and chromium (Focardi et al. 2013) as covered in the biogeochemical literature. This is also important to processes such as anaerobic biocorrosion, with sulfate reducers known to directly accept electrons from metallic iron surfaces (Chen et al. 2015), and the produced hydrogen sulfide acting as electrochemical catalyst (Enning and Garrelfs 2014). Paradoxically, the mechanism of iron sulfide precipitation attenuates, rather than accelerates corrosion due to the loss of the catalyst. Modelling metal-microbe interactions, particulary in the wastewater sector is limited, given its importance on the phosphorous and sulfur cycles.

The other important non-carbon emerging substrate is hydrogen. Hydrogen as an alternative product to methane (via particularly fermentation) has historically been a research target, including detailed modelling (Penumathsa et al. 2008). In particular, variable stoichiometry fermentation models have been a strongly researched field (González-Cabaleiro et al. 2015), with broader applicability to biotechnology and understanding of microbial metabolism and electron management (Hoelzle et al. 2014). However, a new focus for hydrogen is emerging with the increasing need to store peak electricity from renewables, and the ease of generating hydrogen electrochemically, and need to upgrade methane for vehicle and grid use, hydrogen to methane is now of interest. This has been shown to be relatively simple, with digesters generally having excess capacity and fast response to hydrogen addition (Díaz et al. 2015; Zhang et al. 2013). The key issues are availability of bicarbonate and managing pH. While references to modelling this have not been found, the ADM1 in stock form is capable of modelling the bulk processes and controlling mechanisms. Electrogenic methane production in the reactor on carbon cathodes is also of interest (Cheng et al. 2009) (though configuration is a challenge), and there is still debate as to whether this occurs via cathodic hydrogen production (enhanced by biological catalysts), or by direct electron transfer. The basic principles of electron addition (via hydrogen or other) can of course be extended to VFA synthesis (Zhang et al. 2013), which requires exclusion of archaea but is an important area for the emerging biorefinery field.

3.2 Energy without electrons: anoxygenic phototrophic bacteria (purple phototrophic bacteria)

The use of biological light-consuming processes for wastewater treatment is not new (Munoz and Guieysse 2006) with a focus on algae and photosynthetic bacteria (which reduce CO2 to organics producing oxygen as electron sink). However, non-photosynthetic treatment has been promoted in recent years driven by the extraordinary and complex metabolism of phototrophic bacteria, which are among the most metabolically diverse organisms existing (Hunter 2008). They also mediate biogeochemical cycles of C, N, P, S, H and Fe (Hunter 2008). Recently, purple phototrophic bacteria (PPB) have been proposed as an alternative to aerobic waste activate sludge (WAS) processes in mainline domestic wastewater treatment via assimilative, rather than reactive carbon and nitrogen removal (Batstone et al. 2015), with complete, single step domestic wastewater treatment demonstrated in principle (Hülsen et al. 2014). This adds to research on the use of PPB for treating industrial wastewater in pure (Kim et al. 2004) and mixed culture (Chitapornpan et al. 2013) systems. One of the important aspects of PPB is the ability to operate without sterile systems due to use of infrared light, which enables PPB to outcompete other heterotrophic and methanogenic organisms (Hülsen et al. 2014).

Because PPB grow anoxygenically there is an excess of electrons to dispose, but they only can sink electrons via biosynthesys or, alternatively, by hydrogen production via the nitrogenase complex (Fang et al. 2005), and hence the COD (electron) balance between catabolism and anabolism is almost 1 (McKinlay and Harwood 2010). Since they are phototrophic but also chemotrophic, fermentative and anaerobic oxidation mechanisms can be applied to model their metabolism. But the most important mechanism of PPB is photoheterotrophy (Gordon and McKinlay 2014; McKinlay and Harwood 2010), which involves the coupling of the TCA and Calvin-Benson cycles with an ETC fuelled by light energy in a cyclic electron re-use (anoxygenic cyclic phosphorylation). PPB cannot source electrons from water (photosynthetic organisms) but can oxidise reduced compounds such as Fe2+, HS−/S2−, S2O3 − or H2 (Overmann and Garcia-Pichel 1998). Further complicating this, PPB bacteria can storage poly-P as well as carbon PHA and polysaccharides (Brandl et al. 1991; Klein et al. 1991; Liang et al. 2010; Melnicki et al. 2009). However, unlike other polymer and poly-P organisms, energy for accumulation is derived from light, which means they can store under anaerobic conditions. This means that the ASM2d (Henze et al. 2000) is not applicable to PPB.

Metabolic models have been developed for PPB oriented to explain the complex metabolism of these bacteria (Golomysova et al. 2010; Klamt et al. 2002) but these are unsuitable for wastewater applications. Such a model needs inclusion of photoheterotrophy on different substrates, photoautotrophy by using hydrogen, chemotrophy of simple organics with concomitant hydrogen production, and also incorporate hydrolysis of particulates and biomass decay. Other potential mechanisms include, especially for polyphosphate accumulation, potentially nitrogen fixation where this is limiting, and engagement in the sulfur cycle. This is clearly a challenge for which existing modelling paradigms are unsuitable.

3.3 Conclusions: processes

We now need to expand substantially our understanding of what constitutes an “anaerobic” process, with new processes not focused on the core carbon metabolism, and emergence of anaerobic processes (such as phototrophic growth), where energy, translated directly to ATP is cheap, but electron transfer is expensive. While most of these processes are not catered for by the existing structure of anaerobic digestion models, the core principles of biochemical and physicochemical processes, metabolic conservation, and mechanistic understanding are applicable, and the same approach used to analyse these exciting new processes.

4 Whole wastewater treatment plant modelling

Plant-wide modelling of wastewater treatment has been a key focus particularly in development of commercial software (for example, Biowin is inherently a plant-wide model, while other packages enable plant-wide modelling), and this includes modelling of the sludge digester, as not only does generation of methane and digestion of solids influence operating costs, but performance also influences the rest of the plant through release of nitrogen and phosphorous in the reject water. The goal of integrating the ADM1 within plant wide modelling was done very early by the benchmarking taskgroup (Rosen et al. 2006), and this development (and further development) have highlighted a number of compatibility issues between the ASM series (Henze et al. 2000) and the ADM1, and some core limitations of the IWA models in general. The Benchmark Simulation Model No. 2 has recently been released (Gernaey et al. 2014), and contains plant wide nitrogen and carbon cycle simulation, but not phosphorous. This section reviews needs for plant wide modelling (one of the key focuses for anaerobic process modelling), in conjunction with other needs identified above.

4.1 Input translation: the problem with Xc

When different models with different states are linked, a translator is needed that preserves state continuity between the different models. That is, translates ASM states such as XS, SS etc. to ADM1 states such as Xch, Ssu, Sac. This translator should also ensure elemental continuity (CHONSP) and maintain a consistent physicochemical state, even though acids and bases may be removed or transformed through the interface (i.e., pH). The alternative is plant wide state continuity through a common model such as used in the ASDM in Biowin (see also Grau et al. 2009).

Development of the interface within the BSM2 identified that the complex organics state (Xc) was unsuitable as a primary input (which was its intended purpose), due to a number of reasons, including:

  1. (a)

    Fixing of nitrogen content, and carbon oxidation state, and degradability (to the underlying value of Xc), without the ability to readily and separably vary for primary and activated sludge. This also has the potential to violate continuity in a plant wide model.

  2. (b)

    Implementation of the two step process of disintegration followed by hydrolysis means that the overall solubilisation process becomes two-step, in opposition to evidence (Batstone et al. 2009; Vavilin et al. 1996). This can be artificially addressed by artificially raising the hydrolysis rate (or disintegration rate), but is an otherwise unnecessary circumvention and un-mechanistic. It also results in artefacts around anaerobic decay.

It is therefore ironic that the Xc state is somewhat unsuitable for use in its primary purpose to characterise wastewater sludges. For the reasons above, the BSM2 interface model used carbohydrates, proteins, and lipids as primary input (Nopens et al. 2009), and we also recommend this approach in general (i.e., substrates in general should be characterised on this basis using the methodologies outlined in Sect. 2.2.

4.2 Phosphorous modelling

Plant wide phosphorous modelling has been a challenge in general, and particularly where different models are used for activated sludge and anaerobic digestion processes. Only the group at University of Cape Town (Ekama et al. 2006) has addressed the problem in a plant wide context. Phosphorous modelling is however, an essential requirement of future models, particularly considering the focus on phosphorous load in many catchments, need to recovery phosphorous, and its new transformations in emerging processes (Batstone et al. 2015). It is noted that this is not just a problem relating to activated sludge BNR processes, but also all emerging processes identified in Sect. 2, particularly high-strength, domestic, or manure, and links into many of the new processes identified in Sect. 3.

Considering plant wide modelling, both ASM (specifically the ASM2d for phosphorous) and ADM1 models are inadequate to consider plant wide modelling. Part of this is because the physicochemistry models in both do not consider more complex effects such as ion activity and ion pairing, which strongly influence phosphate availability, and hence its partitioning in precipitates (Batstone et al. 2012). Indeed, plant-wide P description requires continuous ionic strength tracking; extensive consideration of non-ideality (including ion activities instead of molar concentrations) and consideration of complexation processes (Flores-Alsina et al. 2015). The other issue is additional biological transformation of phosphorous (see Sect. 4.2.2 for details). Finally, as outlined in S3.1.1 and S4.2.3 there is a strong interaction with the sulphur and iron cycle. Hence both physicochemical and biological process extensions are needed in a plant wide context. A summary of the processes is included in Fig. 4.

Fig. 4
figure 4

Plant wide P transformations, including flow of phosphorous in the system

Full size image

4.2.1 ASM/ADM interface

The first interface between ASM and ADM is based on the methodology described in Nopens et al. (2009). When including P and a plant wide physicochemical approach (see Sect. 4.2.2), this approach should further expanded with the Continuity-Based Model Interfacing principle (CBIM) (Volcke et al. 2006) ensuring elemental conservation principles. It is important to highlight that depending how P is modelled in the AD, Phosphorus Accumulating Organisms (PAOs), poly-hydroxy-alkanoates (PHA) and poly-phosphates (PP) will be treated differently. Methods may include instantaneous decay and translation in the interface, or dynamically (via uptake/decay processes) within the AD model. In any case, the total COD, C, N, P, S, K, Mg, Fe… load would at both sides of the interface will be the same, but the distribution amongst the different state variables will be different.

4.2.2 Physicochemical

The physicochemical problem is readily addressed by implementation of a plant-wide common physicochemical model, which also addresses the interface problem. This is justified on the basis that acid–base active components (particularly elemental ions) are generally present throughout the process, and that reasonable and consistent plant-wide pH prediction is a core requirement. The case for a generalized plant-wide pH model has been extensively made previously (Batstone et al. 2012), and resulted in formation of the IWA Taskgroup for a Generalized Physicochemical Model (PCM). Taskgroup activities have resulted in proposals for implementation of pH (including activity and ion speciation/pairing) in the ASM/ADM series (Flores-Alsina et al. 2015; Solon et al. 2015), generalized precipitation using this model (Kazadi Mbamba et al. 2015a, b), and application of a generalized physicochemical approach including precipitation (Lizarralde et al. 2015) in the plant wide biological model of Grau et al. (2007).

4.2.3 Biological

The ASM2d effectively considers the role PAOs in the line (Henze et al. 2000). Similar processes should be included in the sludge line (Ikumi et al. 2011) describing the effect that PAOs, PHA, PP might have on the anaerobic digestion products (biogas, phosphorus precipitates). However, these models do not consider the interaction with sulfur and iron under aerobic or anaerobic conditions. This metal-phosphorous-sulfur interaction is complex, and affects the whole water cycle (Pikaar et al. 2014). In brief, sulfate is reduced to sulfide in the sewer and primaries, with the sulfide binding with Fe2/3+, which causes phosphorous to release. The sulfide is biologically reoxidised to sulfur and sulfate in the activated sludge process, and iron oxidised to Fe3+. This releases iron to bind with phosphorous (iron phosphate), at the same time as biological assimilation and poly-P (PP) accumulation occurs. In the anaerobic digester, sulfate is again reduced to sulfide. Both precipitated (iron phosphate) and biological phosphorous (PP, biomass) might be chemically and biologically released through both re-dissolution of iron phosphate and hydrolysis of PP (Ge et al. 2013). Because of a pH increase, calcium and magnesium phosphates are formed/precipitated. At the same time, Fe3+ is reduced to Fe2+ (using hydrogen or sulphide as electron donors). The latter can precipitate in form of FeS reducing the overall sulfide inhibition of the AD bacteria and potential corrosion/odour problems. Some of these processes have been discussed in Sect. 3, and require a considerable extension to the base models, depending on (for example) the complexity of the phosphorus/sulphur/iron model used.

4.3 Conclusion on whole wastewater treatment plant models

Plant wide P modelling has a profound impact, particularly at physico-chemical level. As a key wastewater treatment objective, it will require a major, but unavoidable, additional degree of complexity when representing cationic/anionic behaviour in activated sludge (AS)/anaerobic digestion (AD) models. An important factor to consider is the close interaction between the S and the Fe system. Therefore, reliable P plant wide model predictions should also consider including these elements (Se, Fe) when describing the fate of the different pollutant at plant wide level.

5 Conclusions

The consistent themes throughout this review are increased demands on modelling, in terms of complexity, particularly in anabolic processes, need to consider complex behaviour (including distributed parameter and non-linear characteristics in space), and the need to better characterise inputs and their primary conversion processes, as well as supporting models such as the chemistry models. There are commonalities between the challenges in all three areas examined, particularly the emerging importance of non-carbon metabolisms (especially sulfur), and its interactions with other cycles, including that of the iron and phosphorous cycles. While the problems have increased in complexity, the approaches used so far are highly compatible with these new challenges, and application of the existing methodologies will enable a consistent and transparent approach. As to the original question: Is an ADM2 required? It is evident that modelling is currently being used in a productive way to support science and engineering, but the models being used are still in a state of flux. While there are readily justifiable and uniform modifications (such as removal of the Xc state), to move forward with a common basis for an ADM2, a uniform approach to the many challenges and mechanisms is needed, which may require still further development of the underlying research.