Malestar Social.

Key milestones in anaerobic digestion modelling are listed in a review by Donoso-Bravo et al. (2011). This section reviews some of the milestones in greater detail, as these models contributed to the development of the Anaerobic Digestion Model No. 1 (ADM1). A comprehensive list of all AD models is provided in review papers by Appels et al. (2008) and Lauwers et al. (2013).

2.2.1. Two-microbial-culture model

In 1977, Hill & Barth (1977) developed a mathematical model to simulate the digestion process of animal waste. The development was motivated by the benefits that a dynamic model would allow one to study the digester’s stability when it is subjected to different operating conditions.

The model considers only two microbial groups, namely acid-formers and methane-formers, to be responsible for the conversion of organics to VFAs and from VFAs to methane gas respectively. Other variables accounted in the model are commonly analysed parameters such as volatile matter/solids, VFAs, soluble organics, cations, carbon dioxide and ammonia. This model assumes the stoichiometry of soluble organics to be the same as glucose, and that VFAs is broadly representable as acetic acid.

Variables are represented by a set of multiple non-linear differential equations that ensure mass and charge balances are maintained continuously. All insoluble organics must be solubilised first before it is amenable to degradation. This conversion is simply based on a 1:1 stoichiometry and is not subjected to any kinetic rates. The only inhibitor taken into account by the model is the presence of unionised ammonia on the growth of methane-formers.

All kinetic and physicochemical constants applied for the model were sourced from previous investigation works related to similar waste substrate, and no parameter calibration was made. For model validation, the author selected four variables which were deemed most important for animal waste digestion, namely methane gas, volatile matter/solids, VFAs and alkalinity. For the steady-state period the model was found capable of fitting actual experiment data with reasonable accuracy but failed to predict well during transient periods.

2.2.2. Steady-state acid phase model

A study by Eastman & Ferguson (1981) pointed out the likelihood of the acid phase, which consists of the hydrolysis of particulates to soluble organics and the subsequent fermentation to VFAs, to be the rate-limiting step during anaerobic digestion. In retrospect, earlier models (Andres, 1969; Graef & Andrew, 1974) considered acetolastic methanogenesis as the rate-limiting step and thus did not include any acid phase mechanisms.

Hydrolysis, in particular, was reported to be a potential rate-limiting step in anaerobic digestion, especially when digesting particulate organic substances. The overall digestion rate could be constrained during periods

understanding the composition make-up between particulate and soluble organics is regarded as crucial for establishing the rate-limiting factor in context. This fact was well supported by other researchers (Gujer & Zehnder, 1983; Pavlostathis & Gossett, 1988).

The acid phase model includes a first-order function to describe the hydrolysis step and Monod’s equation to describe the growth of acid-formers (in association with the utilisation of soluble organics). Recognising that different particulates within a complex substrate could hydrolyse at dissimilar rates, a first-order function was proposed as the most appropriate method to describe the lumped/effective hydrolysis effect.

The research confirmed robustness of the acid phase across a wide range of pH and/or solids concentration. Following the “two-phase digestion” approach proposed by Pohland & Ghosh (1971) where two separate reactors are operated in series but under different conditions, Eastman & Ferguson (1981) proved that the digester’s stability can be greatly improved when each reactor is operated at conditions most optimally suited for the acid-forming bacteria and methanogenic archaea.

2.2.3. Dynamic single-stage high-rate anaerobic reactor model

A major advancement in anaerobic modelling was presented in the work by Costello et al. (1991). Using the model framework developed by Mosey (1983), this model introduced the effects of hydrogen inhibition, product inhibition, and most notably, a larger ecosystem of anaerobic bacteria which are fundamentally involved in the degradation process. Unlike prior models which only considered a single acidogenic step to form acetic acids, this model accounts for intermediate volatile acids such as propionic and butyric acids as well.

A unique development made by the author was to incorporate a comprehensive set of inhibition and regulation functions into the model structure. It is implemented by multiplying the relevant inhibition functions to a substrate’s utilisation rate formula as described by Monod’s equation. The inclusion of inhibition and regulation effects based on hydrogen gas concentration in the biogas is an important feature of this model.

Inhibition functions influence substrate uptake rates of acidogens and acetogens, whilst regulation functions modify the production rates of the acidifiers’ end-products (propionic acid, butyric acid, acetic acid and lactic acid). Other inhibitory phenomena built into the model were:

• Individualised pH inhibition function for each type of bacteria - glucose, lactic acid, propionic acid and butyric acid

• Product inhibition effect as a result of product accumulation and high product-to-substrate ratio: - A competitive inhibition function was proposed for propionic acid and butyric acid bacteria.

Only acetic acid is considered as the cause of inhibition. VFAs, including lactic acid, were deemed non-influential

- A non-competitive inhibition function was proposed for glucose and lactic acid bacteria. VFAs are the cause of inhibitory products.

2.2.4. Development of higher complexity models

Angelidaki et al. (1993) enhanced the model initially developed by Hill & Barth (1977), with the intention to simulate free ammonia inhibition on methanogens more accurately. This improvement is critical for digesters treating substrates containing high protein or ammonia in particular. As free ammonia concentration depends on pH and temperature the research focused on improving pH prediction and the temperature correction of dissociation constants. According to the authors, free ammonia inhibition could recover spontaneously and prevent system failure. It was reported that as VFAs accumulates, the reduction in pH would cause a shift in ammonia equilibrium, resulting in lower free ammonia concentration.

One of the first universal non-substrate specific models was created by Vavilin et al. (1994). The model is intentionally simplified to describe key anaerobic steps only, where carbohydrates, proteins and lipids are lumped as a single hydrolysed substrate term, while propionate served as the only fatty acid intermediate. Despite having a simplified structure the model included decay mechanisms for dead biomass to assimilate back to the ecosystem as degradable and non-degradable components. The inclusion of extra processes, such as sulphate reduction and syntrophic methanogenesis, further adds sophistication to this generic model. The sulphate reduction process involves the conversion of sulphates into sulphides, with acetate and propionate as substrates. Consequently, sulphate reducing bacteria are added to the model’s ecosystem.

2.3. Anaerobic Digestion Model No. 1 (ADM1)