(i) hydrolysis (slow decomposition of polymeric substances to easy biodegradable substances, (ii) substrates assimilation by microorganisms correspondingly with Monod

equation and (iii) growth and decay of microorganisms, what can be written in form:

(5)

where: f(S) — substrate concentration related function, X — biomass concentration, gdm/m3,

Kd — biomass decay constant, 1/d.

Organic substrates in the wastewater are in the form of: suspended solids, colloids and soluble matter. In overall form it can be described as C18H19O9N. Due to their different forms (easy degradable, slowly degradable and not biodegradable fractions) they can be oxidized, assimilated or not biologically decomposed.

identified correspondingly to commonly used methodology [29-31]. Typical wastewater consists 10-27% of soluble easy biodegradable substances (Ss), 1-10% of not biodegradable soluble substances (Si), 37-60% of slowly biodegradable suspended solids (Xs) and 5-15% of very slowly biodegradable suspended solids (Xi) [31-34].

Easy biodegradable organic substances are an energy sources for denitrifying and phosphorus accumulating bacteria (PAB) and its concentrations have direct impact on the nitrogen and phosphorus removal.

Nitrogen in wastewater appear usually in form of soluble non-organic forms (mainly ammonium nitrogen, seldom nitrites and nitrates), organic soluble (degradable and not degradable) and as the suspended solids (slowly degradable, not degradable and as a biomass). Nitrogen compounds transformations are carried by autotrophic and heterotrophic bacteria and elementary processes need to preserve adequate technological conditions for these microorganisms.

The polymeric substances hydrolysis is catalysed by extracellular proteolytic enzymes to transform into simple monomers, which can be assimilated by microorganisms.

This process and ammonia nitrogen assimilation is related to fraction of nitrogen in biomass (5-12%). The nitrogen assimilation rate depends on the C/N ratio.

Another process of nitrogen transformation is nitrification — oxidation of ammonium nitrogen to nitrites and nitrates by chemolithotrophs: Nitrosomonas, Nitrosococcus and Nitrosospira in first phase (hydroxylamine is the intermediate product) and Nitrobacter, Nitrospira, Nitrococcus in the second phase, what can be described in form [35]:

NH+ + 1,5O2 ^ NO — + H2O + 2H+ — 278kJ / mol

NO — + 0,5O2 ^NO- — 73kJ / mol

Nitrifying bacteria, as autotrophs, take the energy from carbon dioxide and carbonates. The utilisation rate for Nitrosomonas is equal to 0.10 gdmo/gN-NH4, and for Nitrobacter — 0.06 gdmo/gN — no2 [1]. The important process parameters are: oxygen supply (4.6 g O2/1gN-NH4), temperature (5 — 300C), sludge/biomass age (more than 6 days is recommended), biomass organic compounds loading (over 0.2 g BZT5/gdm is recommended) and BOD/N ratio: when the value is more than five — organic compounds removal dominates, when is lower than three — the nitrification is a prevailing process. The decrease in alcanity is the result of nitrification (theoretically: 7.14 g CaCO3/1 g N-NH4) and it causes decrease in pH from 7.5 — 8.5 to 6.5.

Nitrates are transformed in the dissimilation reduction process (Pseudomonas, Achromobacter, Bacillus and others) to the nitrogen oxides and gaseous nitrogen correspondingly to the path:

2NO3 ~4e > 2NO3 ~2e+2 H > 2 NO ~2 e > N2O ~2 e > N2

In the terms of dissolved oxygen deficiency (anaerobic or anoxic conditions) those organisms use nitrates as H+ protons acceptors.

Denitrifying bacteria, as the heterotrophs, need organic carbon for their existence. The source of organic carbon can be: organic compounds in wastewater (internal source), easy assimilated external source of organic carbon, e. g. methanol/ethanol, or intracellular compounds as an energetic source. This ratio of organic carbon should be in range of 5 — 10 g COD/g N-NO3 [35].

In the figure 3 the elementary processes of nitrification and denitrification in nitrogen removal are shown [11]. It is easy to recognise that denitrification is partly the reverse process to the nitrification. Due to the fact that some nitrifying bacteria can live without oxygen and some denitrifying bacteria can survive in oxygen conditions there is the possibility to carry out the simultaneous nitrification and denitrification (SND) in one reactor. As the SND reactor both continuous and sequencing batch reactors can be used. In
the SBR-SND reactor high removal efficiency for organic and nitrogen compounds can be achieved — 79% and 96% respectively [36]. The biomass growth rate can be in range of 0.3 — 0.75 gSDM/gsub rem [37]. Similarly high nitrogen removal efficiency in SND process in continuous reactor (about 90%) can be achieved at certain pH and N-NH4 concentration [38]. The nitrite concentration rise indicates that the nitrification process has stopped after the first phase. The process can run at low C/N ratio.

The short version of SND process needs preservation of certain technological conditions. Important conditions are aerobic and anoxic conditions, what in one reactor system can be achieved by intermittent aeration and non aeration. It causes the characteristic variability of parameters such: pH, redox potential or nitrogen compounds concentration [39]. Examples of changes of some variables in bioreactor with intermittent aeration are presented in figure 4 [40].

The blockage or limitation of second phase of nitrification can be achieved by limitation of oxygen availability up to approximately 0.7 mg O2/dm3 [41] or by free ammonia inhibition, which concentration is impacted by the temperature and pH of wastewater. Anthonisen et al. [42] identified the limiting values of partial and full inhibition of second phase of nitrification: 0.1 g N-NH4/m3 and 1.0 g N-NH4/m3 respectively. They proposed the description of free ammonia concentration in the reactor in form [42]:

S _ 17 sn-nh4 *10P

NH3 14 exp (6344/T) + 10pH

where: Sn-nh4 — ammonium nitrogen concentration, mg/dm3,

T — temperature, K.

The free ammonia concentration has an impact on the ammonium nitrogen removal velocity, what is described by substrate inhibition model presented by Haldane [43]:

where: vnh — ammonia nitrogen and ammonium removal velocity, mgN/mgsmh,

rNHmax — ammonia nitrogen and ammonium removal maximum velocity, mgN/mgsm, KsNH3 — saturation constant, mgN-NH3/dm3,

KiNH3 — inhibition constant, mgN-NH3/dm3.

For the mathematical description of organic and nitrogen compounds removal many existing models are used with certain modifications, e. g.: substrate inhibition in Brigs — Haldane model [44] or ASM1 model [45], intermittent aeration or oxygen limitation inhibition in ASM1 [46-48], or two stages process of nitrification and denitrification in ASM3 model [49].