Anaerobic digestion (AD) is an attractive treatment for this waste of difficult disposal. AD processes transform the organic matter contained in a certain waste in biogas as main product. This process is carried out for different kind of microorganisms which work in a coordinate and interdependent chain until biogas obtaining.

Anaerobic treatment of moderate and high strength wastes with high biodegradable content presents a number of advantages in comparison to the classical aerobic processes: a) quite a high degree of purification with high-organic load feeds can be achieved; b) low nutrient requirements are necessary; c) small quantities of excess sludge are usually produced and finally, d) a combustible biogas is generated. The production of biogas enables the process to generate or recover energy instead of just energy-saving; this can reduce operational costs as compared with other processes such as physical, physico-chemical or biological aerobic treatments (Borja et al., 2006).

Previous works carried out at pilot-scale have shown that most of agro-industrial residues, such as sugar beet pulp, potato pulp, potato thick stillage and brewer’s grains, can be treated anaerobically with an efficient solids stabilisation and energy recovery, if the applied process-type (one or two stages) is selected according to the C:N ratio of the residues. These works demonstrated that at hydraulic retention times (HRT) of between 10 and 20 days, normally, the 50-60% of the organic matter was degraded. The ultimate anaerobic biodegradability was higher and lied between 76% (brewer’s grain) and 88% (potato pulp), which demonstrated that more than 60% of the available energy potential could be used in the industrial processes. The gas production varied between 300 and 500 m3 biogas per ton of dry matter with a methane content of 60-70%. The undigested solids, which were separated from the effluent of the reactors could be completely stabilised after a short aerobic post-treatment to be used as a soil conditioner (Borja et al., 2006).

A number of kinetic models have been proposed for the process of anaerobic digestion. Early models were based on a single-culture system and used the Monod equation or variations. More recently, several dynamic simulation models have been developed based on a continuous multi-culture system; these correspond to the major bioconversion steps in anaerobic digestion but again make the assumption that culture growth obeys Monod type kinetics. Doubt has been expressed by several investigators on the validity of applying the Monod equation to waste treatment as the specific growth rate is expressed only as a function of the concentration of the limiting substrate in the reactor. The Monod equation contains no term relating to input substrate concentration; this implies that the effluent substrate concentration is independent of the input concentration. Experimental results do not always agree with this implication; for example the anaerobic digestion of dairy manure, beef cattle manure at mesophilic and thermophilic temperatures, rice straw or poultry litter (Borja et al., 2003).

Deviation from the Monod relationship in many digestion systems may be due to their complexity. This complexity has necessitated the use of generalized measures of feed and effluent strength, namely total Chemical Oxygen Demand (COD) and volatile solids (VS), which may not truly reflect the nature of the growth-limiting substrate. Utilizable carbon in the digester is derived from the hydrolysis of polymeric compounds, constituting the waste, by exo-enzymes in the extracellular medium or on the surface / vicinity of the microorganisms: only these hydrolysed, assimilable compounds can be considered as the growth-limiting substrate in terms of the Monod relationship. Extra-cellular hydrolysis is often considered the rate-limiting step in anaerobic digestion of organic wastes (Borja et al.,

2003) and for a model to be truly valid this must be taken into account.

Multi-culture system kinetics may be desirable in view of the heterogeneous nature of the microbial population performing the various bioconversion steps involved. However, the kinetic models based on this premise necessarily involve a number of kinetic equations and coefficients making them highly complex, as shown by the reported models (Borja et al., 2003). Complexity does not necessarily equate to accuracy and there is still a strong case in favour of a simpler kinetic treatment based on a single culture system. Methanogenesis is particularly suited to this approach as there is a strong holistic characteristic in the process. Various cultures and bioconversion steps in digestion are interdependent and the whole process has certain self-regulatory characteristics within the process limits.

Kincannon and Stover (1982) proposed a widely used mathematical model to determine the kinetic constants for immobilized systems and high-rate reactors. In this model the substrate utilization rate is expressed as a function of the organic loading rate by monomolecular kinetics for biofilm reactors such as rotating biological contactors and biological filters (Kapdan and Erten, 2007). A special feature of the modified Stover-Kincannon model is the utilization of the concept of organic loading rate as the major parameter to describe the kinetics of an anaerobic filter in terms of organic matter removal and methane production (Buyukkamaci and Filibeli, 2002; Kapdan and Erten, 2007).

The modified Stover-Kincannon model allows to calculate the maximum substrate utilization rate by the microorganisms (Rmax) and the saturation constant (Kb) in anaerobic digestion processes (Yu et al., 1998). Therefore, this model allows determining the effluent substrate concentration for a known volume of reactor and an initial concentration of the substrate. The modified Stover-Kincannon model has been used for different substrates and reactor configurations: anaerobic hybrid reactors treating petrochemical waste (Jafarzadeh et al., 2009), anaerobic treatment of synthetic saline wastewater by Halanaerobium lacusrosei (Kapdan and Erten, 2007), anaerobic digestion of soybean wastewaters (Yu et al., 1998) and molasses (Buyukkamaci and Filibeli, 2002) in a filter and in a hybrid reactor, respectively.

The aim of the present study was focused on the AD of two-phase OMSW at two different influent substrate concentrations and on the determination of kinetics constants of the system using the above-mentioned modified Stover-Kincannon model.