Optimal sizing of Activated Sludge Process with ASM3

Transcription

1 International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 1 19 Optimal sizing of Activated Sludge Process with ASM3 Walid El-Shorbagy 1*, Abdulhameed Arwani 2, and Ronald L. Droste 3 1 Civil and Environmental Engineering Dept., UAE University, AlAin, UAE (Corresponding Author) 2 Parsons International Limited, PO Box 5498, Abu-Dhabi, UAE 3 Civil Engineering Dept., Ottawa University, Canada Abstract-- A mathematical framework is developed for use in optimal sizing of a wastewater treatment system that includes primary clarification and an activated sludge process. The International Water Association (IWA) model; ASM3, is used in the developed framework, as it is among the most comprehensive models that closely describe the biological reactions taking place in the activated sludge process. A nonlinear optimization problem is formulated with the objective to produce optimal sizes of different units with least cost while meeting the effluent requirements. The optimization model is applied to an illustrative activated sludge system treating domestic wastewater of typical strengths. The effect of a number of parameters and conditions on the optimal solution and the associated state variables is investigated. This includes the solids retention time, temperature, influent conditions, effluent requirements, in addition to a number of ASM3 parameters. The findings indicate that the temperature significantly affects the optimal size of aeration tank. Increase in the soluble components (biodegradable substrate and ammonia-ammonium nitrogen) of the influent results in increased volume of the aeration tank, air flow rate, and the total cost. The system is found to be most sensitive to variability of influent characteristics and maximum growth rate of autotrophic biomass. Index Term-- Activated Sludge; ASM3; mathematical modeling; optimization; model sensitivity. I. INTRODUCTION The most widely used biological treatment process for municipal and industrial wastewater is the activated sludge (AS) process. Recent developments in process modeling have resulted in the inauguration of advanced dynamic generalpurpose models. Among the most common and recent applied AS models is the International Water Association (IWA) model; ASM3. The main objective of a treatment plant design, in general, is to provide a cost effective treatment for a given wastewater. Mathematical models are usually employed in a trial-and-error fashion to achieve such an objective. Upon evaluating the performance, the design is iteratively modified until it becomes satisfactory. The composite nature of such problems generally makes it difficult to test all design possibilities. Moreover, the design process becomes more difficult when considering the complex biokinetics of treatment operations and the potential interaction between treatment processes that may all lead in some cases to counterintuitive performance. An alternative to this design paradigm is one in which the design process, essentially a search through design possibilities, is automated using optimization. In an optimization-driven design context, the designer supplies mathematical descriptions of design objectives and constraints, e.g., minimize total cost while meeting effluent targets and maintaining system-governing relations. An optimization algorithm is then used to identify one or more design alternatives that best meet these criteria. The optimum design is the one that satisfies certain constraints and is the best among several alternatives with respect to prescribed criteria; among which the cost. This approach has the advantage of being capable of considering design objectives, constraints, and performance comprehensively and simultaneously. In addition, it can be extended to provide system-wide optimization wherein all of the plant s processes are optimized together. The most common design parameters that the designer usually selects are the dimensions of the units that make up the plant (biological reactors and settlers) and its operational variables [1] such as hydraulic retention time (RT), sludge retention time (SRT), areas, volumes, and sludge recycle flow from the settlers. During the last decade, several studies have treated the problem of wastewater systems optimization following different approaches. Examples include studies from [1], [2], [3], [4], [5], [6], and [7]. Reference [1] presented a mathematical formulation based on ASM1 for the optimum design of a new AS treatment plant. The minimum volumes of the biological reactors and the minimum total cost (including construction and operation costs) have been considered as optimization criteria. Practical results are also included, as a case study, using the design of the second stage of the Galindo-Bilbao wastewater treatment plant. This study applies recent developments in modeling and understanding of AS process to develop a mathematical framework that can optimally size its various units. The model combines unit processes models and ASM3 for the biological reactor within an overall optimization framework as an analysis and design tool. An optimal solution for typical input conditions and effluent requirements is obtained based on prescribed constraints and assumptions. The study also investigates the effect of varying a number of conditions on the obtained optimal solution. This includes the effect of

2 International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 1 2 temperature, influent and effluent characteristics, in addition to a number of ASM3 model parameters. II. SYSTEM DESCRIPTION AS Systems constitute two main units, one for biological treatment and the other for physical treatment or sedimentation, namely, aeration tank and secondary (final) settling tank, respectively. In most AS treatment plants, especially conventional and complete-mix plants, a primary sedimentation unit is installed before the AS system [8]. The presence of primary sedimentation unit is necessary for removing inert organics that may adversely affect the biological reactions coming after. The proposed optimal sizing model considers the interaction among primary sedimentation, biological treatment, and final sedimentation in terms of process continuity and costs. Optimizing the AS system separately or incorporating it in a comprehensive treatment system that includes both liquid and sludge treatment streams is a controversial research issue. This study considers optimizing the AS system alone for two main reasons. First, the system can be optimized alone then incorporated into a comprehensive optimization model that includes the sludge-processing streams. Second, it has been proven that there is a negligible difference in t. The system layout is shown in Fig. 1. All the streams are numbered to facilitate the description of the model. Stream 1 represents the system influent while stream 4 is the effluent. Streams 2 and 3 connect primary clarifier to the aeration tank and aeration tank to secondary settler, respectively. Stream 5 is the underflow from the secondary settler which is divided into stream 6 (recirculation of sludge from final settler to aeration tank) and stream 7 which represents along with stream 8 the wastage sludge streams that might be subjected to further treatment or disposal according to the applied legislations. III. UNIT PROCESSES PERFORMANCE MODELS Several models have been developed to describe the performance of unit processes that make up the AS system. The incorporation of a particular model into the overall system model highly influences the system design and the insights gained from the system analysis as well. The mathematical formulations describing the system components utilized in this study are presented below. Primary Clarification Modeling the performance of primary clarifiers involves modeling the two main functions they fulfill, namely, clarification and thickening. The overflow rate (q) and influent suspended solids concentration (X SS1 ) (the subscript number denotes the stream in Fig. 2) have been identified as two important parameters that affect the performance of primary clarifiers. For the clarification function, several theoretical and empirical models have been proposed over the last two decades. Theoretical mathematical models, though helpful in understanding the sedimentation process, are still far from being reliable and effective design tools [9]. Empirical models are more suitable for the design of primary clarifiers in the absence of more valid theoretical models. The reference suggests the following expression: X X SS2 SS1 b 1[ a exp( X SS1 cq)] where a, b (mg/l), and c (d/m) are positive parameters. q is the overflow rate (in m/d) and defined as: Q q 2 A p where Q 2 is the primary effluent flow rate and A p is the primary clarifier surface area. Thickening function of primary clarifiers is mainly modeled using the deferential thickening technique, which is based on the limiting flux theory [1]. This technique proposes that the primary sludge concentration (X SS8 ) equals: X SS8 ( g / L) [ k( n 1)] 1/ n n A n 1 Q p 8 1/ n where k (m/d) and n are settling constants of primary sludge and their ranges are (65 46 m/d) and (1 5), respectively [11]. A p and Q 8 (underflow rate) are in m 2 and m 3 /d, respectively. In this study, no certain model is considered to predict the removal of organic matter. Instead, the species distribution of the suspended solids in the primary effluent is assumed to be the same as in the primary influent. i.e. X i2 = X i1 (X SS2 /X SS1 ). Using Equations 1 to 3 and the flow and mass balance equations, primary clarifier can be designed. q is usually chosen as the decision variable, i.e., its specification leads to complete design of the primary clarifier. Activated Sludge Standard biokinetic models are widely accepted in practice for the design of AS process [1]. owever, such models comprise too many approximations and their prediction of systems behavior is poor. In contrast, advanced multicomponent models that encompass evolving understanding of phenomena in biotreatment, like ASM models, are the most application in the design and research of AS systems [12]. In this study, ASM3 model [13] has been chosen as the basis for the design of AS process. ASM3 was developed to correct for some defects noticed in ASM1 and to incorporate latest advances in the modeling of AS systems. In ASM3, all the conversion and the decay processes of the two groups of organisms are clearly separated. The new addition in ASM3 is the assumption that all substrate passes storage before being metabolized in the heterotrophic microorganisms. Moreover, the ammonification known with its difficult quantification, was eliminated in ASM3 as it is fast and minimally affects other processes. In the literature ASM3 is rarely utilized in its full version and a reduced version is usually adopted [14]. A reduced ASM3 based model is utilized here by considering two reduction

3 International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 1 21 assumptions that are common in literature and utilized by several studies. Such assumptions are: (1) A completely aerobic bioreactor is assumed where oxygen is controlled all the time to be 2 mg/l. Therefore, all anoxic reactions are neglected and the oxygen dynamics are not taken into account [12], [15], [16]. (2) Alkalinity dynamics are neglected. ence, the state variable describing the total alkalinity is excluded [3], [17]. This assumption is logical since the effect of alkalinity on other reactions is minor given the small values of its stoichiometric coefficients in the original model [13], [18]. More simplifying assumptions beside the aforementioned ones are considered in other studies [12], [15]. The resulting reduced ASM3 model consists of 1 components and 7 biochemical processes compared to 13 components and 12 processes in the original model. Typical values for the stoichiometric and composition parameters as suggested by Reference [19] at 2 o C were utilized to produce the stoichiometric matrix of the reduced ASM3 (Table I). The stoichiometric matrix was used to write the conversion rate of each component as explained in Reference [19]. To design the aeration tank, the stream constituents around the AS system AIR are calculated using steady state mass balances: follows [8]: (dx i /dt)v = Q 2. x i2 [Q 4. x i4 + Q 7. x i7 ] + r xi V = (4) where x i is a vector of the state variables [S I, S S, S N4, S NOX, X I, X S, X, X STO, X A, X SS ]. r xi is the component conversion rate of.1 [ x i, V is the aeration tank volume, and Q denotes the flow rate. Solids Retention Time (SRT) is among the most important Secondary Sedimentation design parameters in AS systems and defined as follows: SRT = V. X 3 /[Q 7. X 7 + Q 4. X 4 ] (5) Other important design parameters include the ydraulic Residence Time (RT) defined as V/Q 2, the Recycle Ratio (r) defined as Q 6 /Q 2, and the Waste Ratio (w) defined as Q 7 /Q 2. The total oxygen requirement is the sum of the oxygen required for the removal of organic matter (RO ) plus the oxygen requirement associated with nitrification (RO A ) and defined as follows (Grady et al, 1999): RO RO A (1 f XI b Q ( S X S ) 2 S 2 S 2 S3 1 1 b SRT ) Y SRT (1 f XI ba SRT ) Y Q ( S S S ) 2 N NOX N basrt where f XI is the production of X I in endogenous respiration, Y is the aerobic yield of heterotrophic biomass, and Y A is the yield of autotrophic biomass per NO 3 -N, and b and b A are identical to b,o2 and b A,O2. For diffused air systems, the air requirement can be calculated from the following dimensional expression (Grady et al, 1999): 6.( RO RO AFR n e A ) A where AFR is the air flow rate in m 3 /min, (RO + RO A ) is the total oxygen requirement in kg/h, and n e is the field oxygen transfer efficiency expressed as the percent of the oxygen in the air actually transferred to the liquid. The value of n e depends on the nature of the diffuser and the depth at which the air is released. It typically lies in the range of 6 to 15% with 1% as an average value. In AS systems, for economic reasons, the equipment used to transfer oxygen also provides the turbulence necessary to maintain solids in suspension. This results in constraints on process design and operation. The upper and lower feasible bioreactor volume (in m 3 ) can be related to the AFR and to the minimum air input rate (AIR) as follows [8]: 1AFR AFR V 1 U AIR L where AIR L and AIR U values depend on the type of diffusers used. Values of 2 and 9 m 3 /(min1 m 3 ) are generally applied, respectively. For the types of oxygen transfer systems typically used nowadays, the maximum volumetric oxygen transfer rate that can be achieved economically on a sustainable basis is around.1 kg O 2 /(m 3.h). This imposes another constraint on V. The lower limit based on oxygen transfer can be expressed as V ( RO RO 3 kgo2 /( m h)] Like the primary clarifier, the secondary sedimentation tank performs two functions, clarification and thickening. Clarification, in this study, is modeled according to [2] where the effluent suspended solids concentration (X SS4 ) is given as follows: IV. OPTIMIZATION PROBLEM FORMULATION An optimum sizing of the system units is obtained using the processes models described above along with an optimization technique. The objective function (total cost function) is minimized subject to constraints (8) given by design equations A 6.21 ln( MLSS SVI ) ( mg / L).67 ln( ) ln( SR) X SS 4 ) where MLSS is equal to X SS3 (g/l), SVI (Sludge Volume Index) is in (ml/g), is the side water depth in the settling tank (m), and SR is the (6) surface overflow rate (m/h) which is equal to Q 4 /A f (A f is the surface area of final settler). The thickening function is modeled according to the solids flux theory as given by [11] and presented earlier (Eq. 3). The settling constants appear in the equation represent thickening (7) properties of the wastage sludge. The ranges for n and k considered earlier are applicable also for the final settler [11]. X SS5, A f and Q 5 replace X SS8, A p, and Q 8, respectively. One can choose the SRT, RT, and r as decision variables to design the AS system (aeration tank and secondary settler).

4 International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 1 22 and variable constraints where the constraints defining a feasible design space. The set of constraints described earlier is used to provide a steady-state solution for the AS system shown in Fig. 1. Any equation-solving program can be used for this purpose. A Microsoft Excel program was developed and utilized in solving the system by selecting feasible values for q, SRT, RT, and r (decision variables). The obtained solution represents a starting point for the optimization model that proceeds in establishing a search direction and step size toward new solution points of improved objective function value. Cost Functions (objective function) The total cost of the wastewater treatment system is the sum of the capital costs of all unit processes and the costs associated with pumping flow between these units. The cost functions compiled and developed by [1] were considered in this study and presented in Table II. The total annual cost in 23 dollars is used to express the total system cost. Since the capital cost is expressed as a lump sum, a design life of 2 years and a discount rate of 7% are assumed to amortize the capital costs. The Engineering News Record construction cost index of 23 is used to update the capital costs and the costs for material and supply from the base year they were developed (1971) into the year of study (23). Annual operation and maintenance costs are calculated by multiplying the person-hour requirement by the hourly wage rates. The cost for pumping is the product of the power requirement and the unit power cost. The objective function f(x) is the summation of capital, operation, maintenance, material and supply and power costs for all the units and processes in the system considered. V. APPLICATION PROBLEM The model described above is applied to the system shown in Fig. 1. The influent wastewater characteristics are assumed as medium strength wastewater as given by [21] and listed in Table III. Parameters appear in the model are either ASM3 stoichiometric and kinetic parameters or other parameters associated with settling models or cost calculation equations. Stoichiometric and kinetic parameters are assumed to have the same typical values suggested in the original model as explained in [19] (Table IV). A number of parameters varying with the temperature are summarized in Table V. The values shown in the table were deriven from models original studies as explained before. The CRF is calculated assuming a design life of 2 years and a 7% discount rate. All capital costs ate multiplied by CRF to be annual costs. Since the cost functions are developed in the year 1971, they are updated to the year of the study. Using Engineering News Record construction cost index, the cost of 1971 (BCI = 1581) is updated to the cost of 23 (CI = 6581) as follows, cost on 23 = cost on 1971 CI (BCI) 1. OMW and EC are to be defined according to local practices. In this study, they are assumed to be 8.3 and.5 dollars, respectively. P and PE are used to calculate the pumping power cost. Effluent quality is of great importance in the design process. Three main species are of interest in the effluent, organic content, TSS, and ammonia/ammonium nitrogen. Effluent characteristics are to be set according to local regulations. In this study, they are chosen as usually recommended in literature. According to [21] in a well-operating AS plant that is treating domestic wastewater, the soluble carbonaceous BOD 5 in the effluent will usually vary from 2 to 1 mg/l. Suspended organic material will range from 5 to 15 mg/l, and non-biodegradable organics will range from 2 to 5 mg/l. According to the same reference, the AS process can achieve as low as 1 mg/l of TSS in the effluent. Regarding the ammonia/ammonium nitrogen, the system is assumed to achieve complete nitrification. Bounds on variables are very important to derive the solution to a feasible region. Bounds are set based on literature findings [21]. The abovementioned constraints are applied to the optimization problem. Using the General Algebraic Modeling System (GAMS) program, the optimization problem is solved. The solution (presented in Fig. 2) is found to be robust to different starting points, which indicates the possibility of being a global optimum. The TSS and SS (indicating BOD) are reduced from 23 and 162 in the influent to 1 and.568 in the effluent, respectively. The total annual cost associated with the optimized sizes is about $598,138; this is 23.3% less than the total cost associated with the initial solution ($78,258). The primary clarifier overflow rate is found at its upper limit indicating a less efficient clarification. This also indicates that more saving can be attained by eliminating this unit (5.6% saving is achieved by eliminating the primary clarifier). owever, such a finding does not mean a feasible option from a practical engineering point of view. Similarly, since the sludge pumping represents a major capital cost, the optimal sizes are found associated with minimum recycle ratio (r =.25) indicating that further saving can be achieved by reducing r as well as RT. This is obvious since the obtained effluent quality in terms of S S and S N4 are far less than their lower applied limits (.568 < 2. g/m 3 for S S and.778 < 1. g/m 3 for S N4 ). Thus an acceptable effluent can be produced with less cost by reducing RT and/or r. According to [8], practically, selection of SRT for domestic wastewaters is usually controlled by factors other than soluble substrate removal. This is apparent in the solution where both effluent soluble COD (S S ) and effluent ammonium (S N4 ) are relaxed while the effluent suspended solids (X SS ) is at its lower limit 1 g/m 3 and therefore limiting the optimal solution. Values of the total effluent COD (soluble COD plus particulate COD) and the total nitrogen (ammonium plus the nitrate/nitrite) in the obtained solution are 45.2 g/m 3 and 3.4 g/m 3, respectively. Such values fall within acceptable practical ranges even though they are not constrained in the original formulation. This proves again the valid argument made earlier stating that constraining the TSS is adequate and should implicitly constrain the total COD. This is due to the

5 International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 1 23 fact that a major portion of total COD is in particulate form that is constrained by the TSS. Similarly, the low levels of total nitrogen are attributed to low level of ammonia in the influent. The major portion of the MLSS is heterotrophic biomass (43.37%) while the inert particulate organics comprises 37%. The rest is slowly biodegradable substrate (7.69%), autotrophic biomass (2.54%), and organics stored by heterotrophs (9.48%). This is compatible with the practical expectation that the two main portions contributing to the MLSS are inert organics and active biomass. VI. EFFECT OF SOLIDS RETENTION TIME As was mentioned earlier, SRT plays a major role in determining the performance of AS system. Earlier studies showed that SRT is usually controlled by flocculation requirement of suspended solids for proper sedimentation in the final clarifier and not the removal of soluble substrate. Reference [8] has stated clearly that once the SRT was sufficient for effective flocculation and treatment to occur, further increases had only minor effects on the soluble substrate removal. This indicates that increasing SRT above the required value would not affect the effluent quality significantly. This is investigated here by finding the optimal solutions at different values of SRT (starting from 3.5 days; the value considered in the base design). Fig. 3 shows the effect of SRT on the effluent biodegradable substrate (S S3 ) and ammonium/ammonia nitrogen (S N3 ). For SRT larger than 8 days, the decrease in effluent soluble substrate is very small. The same trend is noticed for the ammonium/ammonia nitrogen. On the other hand, the total COD in the effluent shows a completely different effect. The COD decreased rapidly with increased SRT reaching a minimum value at 8days then increased again. Although such decrease and increase happened only within a range less than.5 mg/l, it is still worthwhile to be noticed. Mathematically, this is attributed to the low drop in soluble COD after 8 days while the production of biomass and inert particulates contributing to the total COD continues to occur. The total cost system increased with SRT at the same rate even after 8 days. Increase in the cost is mainly due to increase in the aeration tank volume and oxygen requirement. VII. EFFECT OF TEMPERATURE Wastewater treatment systems can operate in a wide range of ambient temperatures varying from less than 1 o C to about 4 o C. The temperature is known to significantly affect different treatment processes with different levels and its effect on biological treatment is obvious. In AS processes, such effect is associated with biological growth of different species of biomass to remove pollutants from the wastewater. The temperature affects the biological reactions in two ways; by influencing the rates of reactions and by affecting the rate of diffusion of substrate to the cells. Quantifying the temperature effect is usually considered by varying the kinetic and stoichiometric parameters governing the biological rates. For ASM Models, a number of kinetic parameters significantly vary with temperature as shown in Table V at four temperature values; 1 o C, 2 o C, 3 o C, and 4 o C (values at 1 o C and 2 o C are given by [19] and estimated at other temperatures from Arhenius Equation). Table VI lists typical values of other kinetic parameters not affected by temperature [19]. The model performance under different temperatures is examined by finding the optimal solution for each set of kinetic parameters at a certain temperature. The results are summarized in Table VII. Obviously the temperature change did not affect the optimal design of the primary clarifier or the secondary clarifier. Design of both unit operations remains unchanged for the various temperatures examined. Moreover, the primary clarifier overflow rate still at its practical upper bound which indicates that this unit is not effectively participating in the treatment process and economically a reduction in the total cost can be achieved by considering a system without such a unit. Total system cost increased at low temperatures and at high temperatures with minimum cost found when operating at 2 o C. At low temperatures, the rate of reaction for all processes is slow especially for the autotrophic biomass which is known to have lower reaction rate than heterotrophic biomass. Such low reaction rates of autotrophic biomass affects the treatment process significantly. This type of biomass is responsible for the removal of ammonium/ammonia nitrogen (S N4 ); that is at its effluent requirement limit. This indicates that this component has dictated the system to operate at higher sludge age and higher RT to allow some time for the autotrophic biomass to remove S N4. RT is directly related to volume of aeration tank, which in turn caused the system cost to increase. This becomes clear if we compare the design at 1 and 4 o C where the design SRT is almost the same while the RT at 1 o C is higher and effluent S N4 is at its limit. ence the volume of aeration tank is higher and so is the cost. At low temperature, the rate is low so the RT increased to the time required. In contrast, although RT at high temperature is much less, the high rate produced better effluent quality of S S and S N4. On the other hand, contrary to the expectation that the rate of reaction increases dictate a shorter sludge age as the temperature increases, the increase in reaction rates resulted in very high concentration of X I and low concentrations of X and X A in the aeration tank. Due to the high rate of death at high temperatures, most of the biomass was converted to X I. This required higher SRT and RT to maintain the level of treatment required. This eventually increased the volume of aeration tank and the AFR required. Both contributed to the increase in cost. Comparing the situation at low and high temperatures, the particulate substrate apparently controls the biological process and requires longer sludge age at high temperatures. In contrast, at low temperatures soluble substrate controls and this clearly appears if one compares the soluble effluent characteristics at the both situations. At low temperatures, soluble components are at their effluent limits

6 International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 1 24 while these components at high temperatures are at very low levels. In summary, temperature affects the AS process design significantly. According to this study the best operating temperatures are around 2 o C. This is consistent with what is reported in literature about optimum operating temperature for the AS process [21]. owever, the above discussion is based on the assumption that the kinetic parameters follow in nature the Arhenius equation considered in calculating such parameters at different temperatures VIII. EFFECT OF INFLUENT CARACTERISTICS In this section, the model performance is examined for various scenarios of influent characteristics. Influent flow rate In the base solution the influent flow rate was 4, m 3 /d (15 m 3 /h), which is considered an average for a domestic wastewater treatment plant. The performance was examined for other flow rates keeping the concentrations of species the same. Results are summarized in Table VIII. Clearly, a change in the flow rate affects the system cost because the sizes of the units are changed to accommodate the increased flows. owever, biological treatment remains unchanged since the concentrations of influent organics were not changed. Such performance is expected. Strength of wastewater This section explores the effect of influent strengths different from the base medium-strength wastewater upon the optimal cost and design. The influent characteristics were varied one at a time to observe the effect of each condition on the system design Table IX reports the optimized solutions for various influent conditions along with the influent conditions. In case 1, only the readily biodegradable substrate (S S ) was changed to 324 mg/l as COD while other characteristics were unchanged. This resulted in a more expensive system (7.8% increase in cost) which is attributed mainly to the increase in aeration tank volume and air flow rate. The volume increase is due to the higher RT required for the metabolism of the increased mass of S S and to eventually higher needed AFR. owever it is noted that the SRT is lower than the base design associated with higher concentration of heterotrophic biomass maintained in the aeration tank. In case 2, only ammonium plus ammonia nitrogen (S N4 ) concentration was changed to 5 mg/l as N. Again other characteristics were kept at the base design. This resulted in significant increase in the optimized system cost (1.6% increase). This is attributed again to the significant increase in the aeration tank volume and the AFR. In contrast to case 1, the AFR increase here is due to the increase in the oxygen requirement of autotrophic biomass while in case 1 it was due to the increase in the oxygen requirement of heterotrophic biomass. In this case, the SRT suffers a significant increase. This is due to the low concentration of X maintained in the aeration tank and the low wastage ratio. owever, better quality is noticed in the effluent. In case 3, both soluble components in case 1 and 2 (S S and S N4 ) were changed together to examine their combined effect. The increase in optimal cost is found to be major (18.1%) again due to the increase in V and AFR which is now reach high value due to the increase in the oxygen requirement for both heterotrophic and autotrophic biomass. Further increases in RT, SRT, and are noticed due to the combined increase. Comparing the above three cases indicates that S N4 exerts more influence on the system than S S. This is expected since the reaction rate of autotrophic biomass is much lower than that for heterotrophic biomass, i.e, the treatment of S N4 is more expensive than the treatment of S S. In case 4, only the inert particulate organic matter concentration (X I ) was changed to 184 mg/l as COD. This component does not undergo any treatment during the process and some production of X I takes place through the aerobic endogenous respiration processes of heterotrophic and autotrophic organisms. So, the amount of X I increases during the biological treatment and then settles in the final sedimentation tank. The cost of the system after increasing X I in the influent is not much different from the base model cost. owever, this increase has altered the effluent quality (S N4 at its effluent limit) explained as follows. An increase in X I in the aeration tank caused a decrease in X and X A to keep the MLSS at its level and hence the volume of the tank stays at its minimum since it affects the cost significantly. In addition, extra wastage is required to remove the extra amount of X I. These actions result in lowering the SRT significantly and hence alter the effluent quality. Increasing the X I further in the influent has shown an increase in the system cost due the increased cost associated with waste sludge pumping. The biological treatment remains unaltered. This trend remains valid until the system starts to reach its capacity of removing solids in the primary and secondary clarifiers. Before reaching the clarifier limit, the extra amount of X I added is wasted with the wastage sludge out the system. The situation is completely different in case 5 when the slowly biodegradable substrate (X S ) is increased to 428 mg/l as COD. X S is consumed in the hydrolysis process to produce S S and a small amount of S N4. X S does not participate in other reactions. Thus the influence of increasing X S is very similar to the influence of increasing S S (case 1) as e evidenced by examining the system design produced for the two situations. The only difference comes from the small amount of S N4 produced during the hydrolysis. This small amount has required a small increase in the SRT and the RT. owever, some amount of X S has been removed in the primary clarifier and hence not converted to S S or S N4. Therefore, the total amount of S S and X S is less than the total in case 1 and this explains the reduction in AFR required in this case. In case 6, combining cases 4 and 5 is explored. The result is a combination of the results for the two cases. The most notable point here is the contribution of the primary clarifier. The huge increase in influent total suspended solids due to the increase in X I and X S forced the system to rely on the primary

7 International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 1 25 clarifier to achieve the required treatment. The overflow rate of primary clarifier is no longer at its upper practical limit in this case indicating the actual and effective need of this unit. In order to show the economic importance of primary clarifiers in situations like case 6, the same influent characteristics have been considered in a system without a primary clarifier. There is more load on the secondary clarifier and more total system cost (.63% increase in cost). In other situations, the treatment plant might fail to operate without a primary clarifier. Case 7 combines all the aforementioned cases representing a high-strength wastewater instead of the medium-strength wastewater considered in the base design. As expected, the solved system involves an increase in V, AFR, SRT, RT, and total system cost. owever, it is noticed that the design of primary clarifier and secondary clarifier have been unaffected by this change in the strength of influent wastewater indicating that the biological treatment alone was able to absorb the increase more economically than the two sedimentation processes. The last case shown in Table IX (case 8) examines the presence of heterotrophic biomass in influent. Results are design a very close to the base scenario. The presence of biomass in the influent helps the system achieve better quality of S S at lower SRT which at the same time altered the effluent of S N4 at an acceptable limit. The lower SRT has lowered the AFR which in turns cause a decrease in the total system cost. Otherwise the system design is similar to the base system designthe presence of autotrophic biomass in the influent was not tested because it is unlikely to happen. Effect of Effluent Limits The effluent requirements applied on the base design are derived from the practical limits recommended in the literature. Tightening the limits will govern the system capacity. The system reaches its full capacity when the effluent suspended solids are set to 6 mg/l. Slightly lower than this limit, the primary clarifier reaches its full capacity, so does the secondary clarifier and the biological treatment system. This indicates that for the conditions applied on the base design, the system cannot achieve lower concentration than this in the effluent. IX. SENSITIVITY TO MODEL PARAMETERS Uncertainty exists in the kinetic parameters due to their random nature and their temperature-dependence. In this section, the sensitivity of model results to kinetic parameters variations at low and high temperatures is explored. At low and high temperatures; 2 o C and 4 o C respectively, the kinetic parameters were assigned values suggested by [19] and shown in Table X. For every parameter, three runs were conducted at each temperature, one at the suggested parameter value, another at 5% of this suggested value, and the third at 15% of it. At each run, other parameters were kept at their original values Table X shows the percentage change in objective function (total cost) due to 5% change in parameter value (a minus sign indicates a reduction in cost). The table indicates that variability of kinetic parameters has different effects on the optimum solution. A general or specific trend for most effects cannot be drawn from the table. Moreover, all the changes are negligible except those imposed by the variability of b, A, and K A. The most apparent change is due to a reduction in A assumed value by 5% at 2 o C. The assumed value at this temperature is 1., which means if A becomes.5 for one reason or another then a system with 11.3% higher cost is required to achieve the same treatment requirements. Such indicates that the system is very sensitive to this parameter and poor estimation of it would lead to system malfunctioning. The sensitivity of model to A is explained here. The developed model has been assumed to perform complete nitrification which requires the concentration of ammonium/ammonia nitrogen in the effluent to be less than or equal to one. It is well known that the growth rate of autotrophic biomass is naturally very slow. Any alteration in this growth rate (variability of A ) would significantly affect the nitrification process which is limiting the solution most of the time. In the shown case, the decrease in the growth rate required the system to increase the SRT to allow more time for nitrification. ence the system cost increased significantly. X. CONCLUSIONS Significant cost savings can be achieved by utilizing the concept of optimization in the design of wastewater treatment facilities. This work presented the formulation and use of an optimal sizing model for the widely used AS process considering the ASM3 model to simulate the kinetic relations of relevant biochemical processes. The developed model was extended to examine the influence of various parameters and inputs upon the system performance and relevant results. SRT increase was found to produce a slight drop in effluent biodegradable substrate (S S3 ) and ammonium/ammonia nitrogen (S N3 ) while a minimum COD is achieved at 8 days after which COD increases. Temperature was found to have no effect on the optimal size of primary or secondary clarifiers but it does significantly affect the aeration tank performance. The system minimum cost was obtained at 2 o C associated with minimum aeration volume, RT, and SRT. The study portrayed the importance of considering kinetic parameters precisely in the design of AS process due to their major effect on the optimal system size. Increased flow rates result in increased cost because of increased sizes but the biological performance stays unchanged. Various influent conditions result in different responses of the optimized system depending on the influent characteristics. Soluble pollutants exert different influence than particulate ones reflecting the important need of careful characterization of the influent wastewater. Uncertainties and shock changes in such characteristics should be taken into consideration when a reliable and robust design is sought. Increase in the soluble components (S S and S N4 ) of the influent results in increased volume of the aeration tank, air flow rate, and the total cost with more pronounced effect found from the increased S N4.

8 International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 1 26 Increase in the inert particulate organic matter concentration (X I ) in the influent results in slight increase in the total cost as well as slight increase in the soluble organics and nitrogenous content in the effluent. The system is most sensitive to variability of influent characteristics and maximum growth rate of autotrophic biomass ( A ). Variability of these parameters should be considered in the design of AS plants. Ignoring their variability would involve major risks and possibility of failure. XI. REFERENCES [1] A. Rivas, E. Ayesa, A. Galarza, and A. Salterain, Application of Mathematical Tools to Improve the Design and Operation of Activated Sludge Plants. Case Study: The New WWTP of Galindo-Bilbao Part I: Optimum Design, Water Sci. Technol., 43, 7, pp , 21. [2] E. Ayesa, B. Goya, A. Larrea, L. Larrea, and A. Rivas, Selection of Operational Strategies in Activated Sludge Processes Based on Optimization Algorithms, Water Sci. Technol., 37, 12, pp , [3] B. Chachuat, N. Roche, and M.A. Latifi, Dynamic Optimization of Small Size Wastewater Treatment Plants Including Nitrification and Denitrification Processes Computers and Chemical Engineering, 25, pp , [4] S.E Scuras, A. Jobbagy, and C.P. Leslie Grady, Optimization of Activated Sludge Reactor Configuration: Kinetic Considerations Water Res., 35, 18, pp , 21. [5] T.A. Doby, D.. Loughlin, J.J. Ducoste, and F.L. de Los Reyes III, Optimization of Activated Sludge Designs Using Genetic Algorithms, Water Sci. Technol, 45, 6, pp , 22. [6] Walid El Shorbagy, Nawras Nabil, and Ronald L. Droste. (211). Optimization of A2O BNR Processes Using ASM and EAWAG Models: Model Formulation. Water Quality Research Journal of Canada, in press. [7] Walid El Shorbagy, Nawras Nabil, and Ronald L. Droste. (21). Optimization of A2O BNR Processes Using ASM and EAWAG Models: Model Performance. Elsevier Journal of Water Research, in Review. [8] C.P. L Grady, G. Daigger, and. Lim, Biological Wastewater Treatment, 2 nd ed. Marcel Dekker Inc., New York, [9] D. G. Christoulas, P.. Yannakopoulos, and A.D. Andreadakis, An Empirical Model for Primary Sedimentation of Sewage, Environment International, 24, 8, pp , [1] C. Tang, E. D. Brill Jr., and J. Pfeffer, Mathematical Models and Optimization Techniques for Use in Analysis and Design of Wastewater Treatment Systems, Research Report No. 194, Water Resources Center, University of Illinois, [11] S. Cho,. Chang, and C. Prost, Steady State Analysis of the Coupling Aerator and Secondary Settling Tank in Activated Sludge Process, Water Res., 3, 11, pp , [12]. Shahriar, C. Eskicioglu and R.L. Droste, Simulating Activated Sludge System by Simple-to-Advanced Models, Journal of Environmental Engineering, ASCE, 132, 1, pp. 42-5, 26. [13] W. Gujer, M. enze, T. Mino, and M. van Loosdrecht (1999), Activated Sludge Model No. 3, Water Sci. Technol, 39, 1, pp [14] T.T Lee, F.Y. Wang, and R.B. Newell, Robust Model-Order Reduction of Complex Biological Processes, Journal of Process Control, 12, 7, pp , 22. [15] G. Koch, M. Kühni, and. Siegrist, Calibration and Validation of an ASM3-Based Steady-State Model for Activated Sludge Systems-Part I: Prediction of Nitrogen Removal and Sludge Production Water Res., 35, 9, pp , 21. [16] M.A. Steffens, P. A. Lant, and R. B. Newell, A systematic approach for reducing complex biological wastewater treatment models Water Res., 31, 3, pp , [17] U. Jeppsson, Modeling Aspects of Wastewater Treatment Processes, PhD Thesis, Lund Institute of Technology, Lund, Sweden, [18] M. enze, C. P. Leslie Grady Jr., W. Gujer, G. Marais, and T. Matsuo, A General Model for Single-Sludge Wastewater Treatment Systems, Water Res., 21, 5, pp , [19] M. enze, W. Gujer, T. Mino, and M. van Loosdrecht, Activated Sludge Models ASM1, ASM2, ASM2d, and ASM3. (IWA Scientific and Technical Report No. 3.) London: IWA, 2. [2] N. Voutchkov, Relationship for Clarification Efficiency of Circular Secondary Clarifiers, Wat. Sci. Tech., 26, 9, pp , [21] Metcalf and Eddy, Wastewater Engineering: Treatment, Disposal, and Reuse, 3 rd ed., G. Tchobanoglous and F. L. Burton, eds., Tata McGraw- ill, New Delhi, India, [22] D. Tyteca, D., Mathematical Models for Cost-Effective Biological Wastewater Treatment, in Mathematical Models in Biological Wastewater Treatment, S.E. Jorgensen and M.J. Gromiec, eds., Elsevier Science Publishers, Amsterdam, [23] C. Tang, E. D. Brill Jr., and J. Pfeffer, Mathematical Models and Optimization Techniques for Use in Analysis and Design of Wastewater Treatment Systems, Research Report No. 194, Water Resources Center, University of Illinois, 1984.

9 International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 1 27 T ABLE I STOICIOMETRIC MATRIX OF TE REDUCED ASM3 BASED MODEL Component I j Process S I S S S N4 S NOX X I X S X X STO X A X SS Expressed as COD COD N N COD COD COD COD COD SS Process rate equation j, all j. X S X 1 ydrolysis k.. X KX X S X Aerobic storage of S S k S STO.. X S K S S S Aerobic growth of X K. K STO S N4 N4 S X STO X X Aerobic endog b, O. X Respiration of X 2 Aerobic respiration b STO, O. X STO of X 2 STO Aerobic growth of X A, nitrific. STO N4 S N A.. X A K S A, N 4 Aerobic endog b Respiration of X A, O. X A A 2 S I : soluble inert organics, S S : readily biodegradable substrates, S N4 : ammonium, S NOX : nitrite plus nitrate, X I : inert particulate organics, X S : slowly biodegradable substrates, X : heterotrophic biomass, X A : autotrophic (nitrifying) biomass, X STO : organics stored by heterotrophs, X SS : total suspended solids, k : hydrolysis rate constant, K X : hydrolysis saturation constant, k STO : storage rate constant, K S : saturation constant for substrate S S, : heterotrophic max. growth rate of X, K N4 : saturation constant for ammonium, K STO : saturation constant for X STO, b,o2 : aerobic endogenous respiration rate of X, b STO,O2 : aerobic respiration rate for X STO, A : autotrophic max. growth rate of X A, K A,N4 : ammonium substrate saturation for X A, b A,O2 : aerobic endogenous respiration rate of X A. T ABLE II SUMMARY OF COST FUNCTIONS UTILIZED IN TE STUDY Process Unit Primary Clarifier [22] Primary Sludge Pumping [22] Aeration Tank [23] Diffused Aeration [23] Secondary Clarifier [22] Return & Waste Sludge Pumping [22] Capital (1971$) A Q Operation Maintenance (personhours/yr) (personours/yr) 17.1A Q 9.23A Q Material and Supply (1971$/yr).76 X N4 Power (k Wh/yr) 8.62A. X Q 23.85Q / p V Q a A Q Q a 17.1A Q 74.4 a 9.23A.55 Q Q A Q 23.85Q / p A is the surface area in m 2, Q is the flow in m 3 /hr, V is the volume in m 3, Q a is the air flow rate in m 3 /min, is the pumping head in meters, and p is the pumping efficiency.

10 International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 1 28 T ABLE III T YPICAL COMPOSITION OF UNTREATED MEDIUM DOMESTIC WASTEWATER [21] Contaminants Concentration (mg/l) Solids, Total (TS) 72 Total Dissolved (TDS) 5 Fixed 3 Volatile 2 Suspended Solids (SS) 22 Fixed 55 Volatile 165 BOD, 5-day, 2 o C (BOD 5 ) 22 Total Organic Carbon (TOC) 16 Chemical Oxygen Demand (COD) 5 Nitrogen (total as N) 4 Organic 15 Free ammonia 25 Nitrites Nitrates T ABLE IV SUMMARY OF MODEL PARAMETERS Symbol Characterization Value/range Units A B c Constant in Christoulas model for primary clarification Constant in Christoulas model for primary clarification Constant in Christoulas model for primary clarification T T mg/l.35 d/m k Settling constant of primary sludge m/d n Settling constant of primary sludge kw Settling constant of wasting sludge m/d nw Settling constant of wasting sludge SVI Sludge Volume Index of sludge <2 ml/g Side water depth of final clarifier >3.1 M ne Efficiency depends on diffuser and depth at which air pumped 6-15% AIR U Maximum air input rate 9 m 3 /(min.1m 3 ) AIR L Minimum air input rate 2 m 3 /(min.1m 3 ) CRF Capital Recovery factor.944 BCI Base (1971) Cost Index 1581 $ CI Cost Index for $ OMW Operating maintenance wages 8.3 $ per hour EC Electricity cost.5 $ per kwh P Pumping head 1. m PE Pumping efficiency.6