mathematical models for domestic biological

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activated sludge models from the ASM1 to ASM3 and ASM2/ASM2d and, a brief description of the biochemical processes involved in them. In the. “Gheorghe ...

Environmental Engineering and Management Journal

May 2010, Vol.9, No. 5, 629-636

“Gheorghe Asachi” Technical University of Iasi, Romania


MATHEMATICAL MODELS FOR DOMESTIC BIOLOGICAL WASTEWATER TREATMENT PROCESS Szabolcs Szilveszter1, Botond Ráduly2, Beáta Ábrahám2, Szabolcs Lányi2, Dan Robescu Niculae1 1

Politehnica University, Faculty of Energetic, 060042 Bucharest, Romania Sapientia University, Department on Technical and Natural Sciences, 530104 Miercurea Ciuc, Romania


Abstract The paper analyses conceptually the activated sludge models used in the modeling of biological processes which occur under domestic wastewater treatment. Modeling and simulation can significantly contribute to the understanding and design of activated sludge wastewater treatment plants (WWTPs). A mathematical model of a WWTP is able to predict how the WWTP will react under various operating conditions. A wastewater treatment plant model describes the biochemical and physical processes involved in the technical purification of wastewater. Through the biochemical processes the organic matter and nutrient content of the wastewater is eventually converted into carbon-dioxide, nitrogen and a particulate fraction (cell material).

Key words: activated sludge, biochemical process, biomass characterization, mathematical model, wastewater treatment Received: January, 2010; Revised: May 2010; Accepted: May, 2010

1. Introduction The activated sludge treatment is today’s most popular type of biological wastewater treatment. In its over 100 years of history the initial aerobic oxidation process, developed for organic carbon removal, it has been completed with other biological nutrient removal processes to meet the more and more severe emission limits and to deal with the increasing magnitude and complexity of wastewater loads. The modern activated sludge processes are very reliable, produce high quality effluent and are considered to be the most cost-effective way to remove organic materials from wastewater (Hulsbeek et al., 2002; Podaru et al., 2008). Modeling and simulation can significantly contribute to the understanding and design of activated sludge wastewater treatment plants (WWTPs) (Banihashemi et al., 2008; Maurer and Gujer 1998). A mathematical model of a WWTP, which is able to predict how the WWTP will react under various operating conditions, is an excellent tool for the design, analysis, control, forecasting and 

optimization of WWTPs, helping to assure high effluent quality. A wastewater treatment plant model describes the biochemical and physical processes involved in the technical purification of wastewater. Through the biochemical processes the organic matter and nutrient content of the wastewater is eventually converted into carbon-dioxide, nitrogen and a particulate fraction (cell material) (Chirila et al., 2009). This latter can be removed from water by means of physical separation processes. Hence the activated sludge WWTP models usually consist of two interconnected sub-models: the activated sludge model and the settler model (Antohe and Stanciu, 2009; Tunçsiper, 2009; van Veldhuizen et al., 1999; Weijers and Vanrolleghem, 1997). This article intends to present conceptually the mathematical models which are used for the modeling of the biological processes occurring under domestic wastewater treatment. Mechanistic WWTP modeling part of the article will present the evolution of activated sludge models from the ASM1 to ASM3 and ASM2/ASM2d and, a brief description of the biochemical processes involved in them. In the

Author to whom all correspondence should be addressed: e-mail: [email protected]

Szilveszter et al./Environmental Engineering and Management Journal 9 (2010), 5, 629-636

second part of the mechanistic modeling the state variables of the activated sludge models are introduced based on biodegradability, solubility and model type considerations. The last two part of the article renders in brief the settler model because without a settler model the mass balance of an activated sludge WWTP using biomass recirculation cannot be closed and the selection of values for the kinetic and stoichiometric coefficients of a mathematical model known as model calibration also is presented briefly. 2. Mechanistic WWTP modeling 2.1. Activated sludge models Mechanistic (theoretical) models are based on the underlying physics and bio-chemistry governing the behavior of the processes involved in activated sludge wastewater treatment. Emphasis is put on the modeling of conversion processes in the biological reactor and on the hydrodynamic modeling of the settler tanks, and less on the hydraulic modeling of the whole treatment plant. WWTP models usually do not explicitly describe flow propagation through the reactors, as in most of the cases treatment plant hydraulics are not sufficiently well known and can only be approximated. A commonly applied simplification is that the plant is considered as a few constant-volume-continuously-stirred-tank-reactors (CSTR) in series, this way the mixing phenomena are modeled. The modeling of the biochemical processes is based on several basic kinetic equations, describing bacterial growth, substrate utilization and the endogenous metabolism (decay) of bacteria, as well as the hydrolysis of entrapped organics. In the last 40 years several activated sludge models have been developed, describing the biochemical processes in a various manner (Eckenfelder., 1966; Marais et al., 1976; van Haandel et al., 1981). The “state-of-the-art models” for activated sludge processes are considered to be the ASM1 – ASM3 models developed by the IWA Task Group (Henze et al., 2000). These models incorporate carbon oxidation, nitrification, denitrification, and ASM2d also describes the biological and chemical phosphorus removal. The ASM models have been “updated” several times since the first coming out of the ASM1 and most of the problems identified in the earlier versions have been corrected. The models are based on COD units (use chemical oxygen demand to define carbonaceous material); ASM3 has a total organic carbon (TOC) based version as well. The Activated Sludge Model No. 1 can be considered as the reference model, since this model triggered the general acceptance of WWTP modeling, first in the research community and later on also in industry. Many of the basic concepts of ASM1 were adapted from the activated sludge model defined by Dold et al. (1980). A summary of the research developments, that resulted in ASM1 was given by


Jeppsson (1996). Many basic concepts were adapted from an earlier model called the University of Cape Town (UCT) model. Important concepts adapted were the bisubstrate hypothesis and the death-regeneration hypothesis. In accordance with practical experiments, it was proposed that the biodegradable COD in the influent wastewater consisted of two fractions: readily (Ss) and slowly biodegradable COD (Xs). This was the bisubstrate hypothesis presented around 1980. The readily biodegradable COD was assumed to consist of simple molecules able to pass through the cell membrane and immediately used in biosynthetic processes by the organisms. Moreover, the active biomass was divided into two types of organisms: heterotrophic biomass (XH) and autotrophic biomass (XA) in accordance that which kind of substrate types they need for metabolism and process, autotrophic biomass produce nitrate (SNO) from ammonium ions (SNH) by nitrification process and heterotrophic biomass use oxygen (SO) for the hydrolysis of substrate (SS, XS). The slowly biodegradable COD (XS), which consists of larger complex molecules, was found to be enmeshed by the sludge mass, adsorbed and then required extracellular enzymatic breakdown before being transferred through the cell wall and used for metabolism. The death-regeneration hypothesis was introduced in an attempt to single out the different reactions that take place when organisms die. In the death-regeneration model, the decayed cell material was thought to be released through lysis. One fraction was considered non-biodegradable and to remain as an inert residue (XI), while the remaining fraction was considered to be slowly biodegradable (XS). This part could thus return to the process and be used by the remaining organisms as substrate through hydrolysis (SS), consequently providing an explanation to the observation described above: the buildup of biodegradable material during the anaerobic period (Jeppson, 1996). There are a total of 8 biochemical processes modeled in ASM1. Fig. 1 presents in a schematic way how the different compounds participate in the conversion processes, here only a list of them is provided the kinetics and stoichiometric parameters used in equations can be found more briefly in Henze et al. (2000): - aerobic growth of autotrophic and heterotrophic biomass; - decay of autotrophic and heterotrophic organisms; - ammonification of soluble organic nitrogen; - anoxic growth of heterotrophic biomass (denitrification); - hydrolysis of entrapped organics and organic nitrogen. Activated Sludge Model 3 (ASM3) was developed to correct some of the deficiencies of the earlier ASM1 and to include the advances in activated sludge modeling achieved in the decade following the publication of ASM1 (Gujer et al., 1999). It includes 12 biochemical processes and 13 components. Neither biological nor chemical phosphorus removal processes are included in ASM3. However, these can

Mathematical models for domestic biological wastewater treatment process

easily be added to it. Siegrist et al. (2002) developed a relatively simple Bio-P module for ASM3, which was able to deliver accurate prediction both for a Swiss municipal WWTP and a pilot plant. The main difference between ASM1 and ASM3 is the recognition of the importance of storage polymers in the heterotrophic conversions in the activated sludge processes in ASM3 (Gujer et al., 1999).

Fig. 1. Substrate flows for autotrophic and heterotrophic biomass in the ASM1 and ASM3 models (modified from Gujer et al., 1999)

The aerobic storage process in ASM3 describes the storage of the readily biodegradable substrate (SS) into a cell internal component (XSTO). This approach requires that the biomass is modeled with cell internal structure, similar to ASM2 which will be described later in this work. The energy required for this process is obtained via aerobic respiration. This internal component is then subsequently used for growth. In ASM3 it is assumed that all SS is first taken up and stored prior to growth. A division of the storage and growth process, allowing growth to take place on external substrate directly, is not considered. The death regeneration concept is replaced by endogenous respiration, which is closer to the phenomena observed in reality. Also, ASM3 allows differentiating between aerobic and anoxic decay. Fig. 1 illustrates the difference in COD flows between ASM1 and ASM3. The first thing to notice is that the conversion processes of both groups of organisms (autotrophs and heterotrophs) are clearly separated in ASM3, whereas the decay - regeneration cycles of the autotrophs and heterotrophs are strongly interrelated in ASM1. This change of decay concept (and introduction of the storage step) means that there exist more “entry” points for oxygen utilization resulting in, at some points, easier separation and characterization of the processes. Second, there is a shift of emphasis from hydrolysis to storage of organic matters. This gives a change in how wastewater characterization should be defined since

the separation between SS and XS now should be based on the storage process rather than on the growth process. Still, the separation remains somewhat based on biodegradation rates. In ASM3 hydrolysis represents a less dominating importance on the rates of oxygen consumption since only hydrolysis of XS in the influent is considered. The compounds present in the wastewater are divided in 13 categories; these constitute the state variables of ASM3: SALK - alkalinity of the wastewater [mole HCO3/m3] SI - inert soluble organic material [g COD/m3] SS - readily biodegradable organic substrates [g COD/m3] SN2 - nitrogen [g N/m3] SNH4 - ammonium plus ammonia nitrogen [g N/ m3] SNOX - nitrate plus nitrite nitrogen [g N/m3] SO2 - dissolved oxygen [g COD/m3] XA - nitrifying organisms [g COD/m3] XH - heterotrophic organisms [g COD/m3] XI - inert particulate organic material [g COD/m3] XS - slowly biodegradable substrates [g COD/m3] XSS - suspended solids [g/m3] XSTO - organics stored by heterotrophic organisms [g COD/m3] There are a total of 12 biochemical processes modeled in ASM3. Fig. 1 presents in a schematic way how the different compounds participate in the conversion processes. The kinetic expressions of the conversion processes are presented in detail in Henze et al. (2000), here only a list of them is provided: - hydrolysis of organic matter in readily available soluble substrate - anoxic and aerobic storage of soluble substrate - growth of heterotrophic organisms under aerobic and anoxic conditions - endogenous respiration of the heterotrophic organisms under aerobic and anoxic conditions - aerobic growth of autotrophic organisms - aerobic and anaerobic endogenous respiration of the autotrophic organisms - aerobic and anaerobic respiration of the storage products. The Activated Sludge Model 2 (ASM2) model is an extension of the ASM1 model, but more complex and includes more components which are required to characterize the system. Additional biological processes are included, primarily in order to deal with biological phosphorus removal. The most significant difference between ASM1 and ASM2 is the fact that the biomass has a cell internal structure, and therefore its concentration cannot simply be described with the XH (heterotrophic organisms) parameter. In addition, the model also contains two chemical processes which may be used to model chemical precipitation of phosphorus. The ASM1 model was based entirely on COD for all particulate organic matter, as well as the total


Szilveszter et al./Environmental Engineering and Management Journal 9 (2010), 5, 629-636

concentration of the activated sludge, whereas ASM2 includes poly-phosphates (XPP), a fraction of the activated sludge which is of primary importance for the performance of the activated sludge system, but which does not exert any COD. For this reason, the possibility of including total suspended solids (TSS) in the model was introduced. TSS allows for inclusion of mineral particulate solids in the influent to treatment plants, as well as generation of solids in the context of precipitation of phosphorus. It is assumed that phosphorus-accumulating organism (PAO) may release phosphate (SPO4), from poly-phosphate (XPP) and utilize the energy which becomes available from the hydrolysis of XPP, in order to store cell external fermentation products (SA) in the form of cell internal organic storage material XPHA (Fig. 2). The storage of ortho-phosphate, SPO4, in the form of cell internal poly-phosphates, XPP, requires the PAO to obtain energy, which is gained from the respiration of XPHA. These organisms grow only at the expense of cell internal organic storage products XPHA. As phosphorus is continuously released by the lysis of XPP, the organisms consume ortho-phosphate, SPO4, for the production of biomass. Growth of PAO is modeled as an obligate aerobe process.

Fig. 2. Substrate flows for storage and growth of PAOs in the ASM2 model (Henze et al., 1995)

The Activated Sludge Model 2d (ASM2d) model is a minor extension of ASM2, including two additional processes to account the fact that phosphorus accumulating organism (PAOs) can use cell internal organic storage products for denitrification, whereas ASM2 assumes PAOs to grow under aerobic conditions, ASM2d includes also denitrifying PAOs in the model. Processes in ASM2d are almost the same as in the ASM2 model, the hydrolysis, nitrification and chemical precipitation of phosphates are the same. There are minor differences in the processes related to phosphorus-accumulating organisms, the growth of phosphorus-accumulating organisms, and the poly-phosphate storage is also modeled in anoxic environment not only in aerobic environment, as in the case of the ASM2 model. There are a total of 21 processes taken into account in ASM 2d where 19 are biological and 2 chemical type process (Jeppson, 1996; Henze et. al., 2000; Petersen, 2000): - aerobic, anoxic and anaerobic hydrolysis of slowly biodegradable substrate;


- aerobic growth of heterotrophic organisms on fermentable substrate (SF) and fermentation product (SA); - anoxic growth of heterotrophic organisms on SF and SA, denitrification; - fermentation of SF and SA (acetate); - lysis of heterotrophic organisms, phosphate accumulating organisms (PAO) and also lysis under different storage products poly-phosphate (XPP) and organic storage material (XPHA); - aerobic and anoxic of poly-phosphate, storage of ortho-phosphate (SPO4) in the form of XPP; - aerobic and anoxic growth of PAO’s; - growth and lysis of nitrifying organisms; - chemical precipitation of phosphorus, precipitation and redissolution of phosphate (SPO4). 2.2. Restrictions of activated sludge models ASM3 (and ASM1) was developed for the simulation of the aerobic and anoxic treatment of domestic wastewater in activated sludge systems. It is not advised to apply it to situations where industrial contributions dominate the characteristics of the wastewater. ASM3 (and ASM1) has been developed based on experience in the temperature range of 8–23 °C. Outside of this range model application may lead to very significant errors and even model structure may become unsatisfactory. ASM3 (and ASM1) does not include any processes that describe biomass behaviour in an anaerobic environment. Simulation of systems with large fractions of anaerobic reactor volume may therefore lead to gross errors (Henze et al., 2000). Development of ASM3 is based on experience in the range of pH values from 6.5 to 7.5. The concentration of bicarbonate alkalinity (SALK) is supplied to give early warnings when pH values below this range are to be expected. Alkalinity must be dominated by bicarbonate. ASM3 cannot deal with elevated concentrations of nitrite. ASM3 (and ASM1) is not designed to deal with activated sludge systems with very high load or small SRT (