**Not: Figürlerin, Tabloların ve Formüllerin daha yüksek çözünürlüklü görüntüleri için görsele sağ tıklayıp “resmi yeni sekmede aç” seçeneğini seçiniz**

## KINETIC MODELS USED IN ACTIVATED SLUDGE TREATMENT

Ahmet Samsunlu

Associate Professor, Dr., Ege University Engineering Sciences Faculty Head of Department of Environmental Engineering, Ismir, Turkey

Fasun İldes

Chemical Engineering, M.Sc., Ege University Engineering Sciences Faculty. Assistant of Environmental Engineering Department, Ismir, Turkey

**1. Introduction**

Since the activated sludge waste treatment process was developed in England during the early 1900’s, many variations of the original process have been developed and used. In waste water treatment. In 1912, H.W. Clarke, studied wastopurification through its aeration in the presence of microorganisms. Edward Arden and William Lockett in Manchester Corporation carry out similar experiments (1).

High purification levels were achieved by Arden and Lockett through use of an aeration process. Arden and Lockett reported these results in April 1914; in a paper entitled “Experiments on the oxidation of Sewage without the Aid of Filters.”

Hielsemsreported in 1951 that the rate of activated sludge growth for three industrial wastes was observed to be proportional to the biochemical oxygen demand (BODE reduction as long as nutritional deficiencies did not exist.

In 1952, Hoover and Forges reported the development of an empirical formula for the composition of activated sludge microorganisms.

In 1954, Eckenfelder and O’Connor proposed a mathematical model for activated sludge wastewater treatment. This model was modified and expanded in publications by Eckenfelder during the period from 1960 to 1971.

In 1962, Mc Kinney constructed a mathematical model for com¬pletely mixed activated sludge (CHAS) treatment systems.

When Eckenfelder began to utilize and publish completely mixed equations extensively, using the nomenclature and basic approach previously so widely disseminated, a considerable amount of confusion developed.

Two apparently different CMAS mathematical models were severely retarding the application of this extremely desirable and widely applicable process variant. A detailed study of both mathematical models has shown them to be identical.

Biological model, includes use of both stoichiometry and kinetics for the study of a wide variety of biological processes.

Many models of biological treatment of wastewaters have been developed that use selected biological growth and substrate utilization equations for the particular process being modeled.

Although it may not be possible to regulate all of the intricate physical, chemical and biological reactions occuring in such a dynamic system, it is possible to achieve the control necessary to accomplish an acceptable degree of wastewater stabilization in activated sludge processes.

Factors that must be considered in the operation of activated sludge processes include.

A) Influent characteristics

B) Loading criteria

C) Selection of reactor type

D) Sludge production

E) Oxygen requirements and transfer rate.

In this paper, a kinetic model for design of completely-mixed activated sludge processes have been described.

Kinetic coefficients which were obtained from several treat¬ment models were given and the appropriateness of there to the real system were searched and discussed.

**2. Kinetic models for the activated sludge treatment processes **

**2.1 The variety of models**

Activated sludge treatment process is the most common known and used (2).

We know three types of mathematical models. These are expressed by following:

1. Completely mixed reactor without biological solids recycle;

2. Completely mixed reactor with biological solids recycle;

3. Plug flow reactor with biological solids recycle.

Figure 1: Treatment Models

**2.2 Frequently used system in model analyses**

Completely mixed models with recycling are the systems where the effluent sludge from the settling tank is fed back to the aeration tank (6).

The changes in the quality and the quantity of the wastewater play an important role in selecting the type of the reactor (9) •

It is essential to know before hand the type of the reaction that is going to happen in the reactor.

The advantages of the completely mixed system are as follows:

1. Instantaneous loads and toxic materials can be diluted better than they are in the other systems;

2. Using two series of reactors can be helpful in the treatment of hot industrial waste;

3. The aeration in a completely mixed biological system is distributed uniformly along the tank;

4. There is a uniform substrate and microorganism distribution within the reactor;

5. In a completely mixed activated sludge system 95 % of the BOD5 can be removed and the efficiency of the treatment is high.

Considering these advantages a completely mixed model can be chosen for active sludge treatment systems. In this study also completely mixed system is chosen.

**3. The assumption for completely mixed model and formulation**

**3.1 Completely mixed activated sludge model assumptions and concepts.**

Some of the more basic assumptions incorporated within model are as follows:

1. Suspended growth completely mixed reactor;

2. operation with 6.6.settling;

3. Operation at steady state;

4. The removal mechanisms approximate first order kinetics in most cases, or two order kinetics;

5. Monod kinetics is used for rate of substrate utilization;

6. No active microorganisms are contained in the influent waste stream;

7. All waste utilization occurs in the biological reactor;

8. The total biological mass in the system is equal to the biological mass in the reactor;

9. Operation with recycle;

10. Solids retention time (0c) is major controling design and operational parameter;

11. Organism growth and decay considered;

12. Overall mass balance based on stoichiometric equation.

**3.2. Formulation of the model**

Biological wastewater treatment systems that use the growth and synthesis of a microbial community as a means of waste¬water stabilization involve very complex reactions.

**3.2.1 Lawrence Formulation**

The first describes the relationship between the net rate of growth of active organisms and rate of substrate utilization. (2) (3). Completely mixed recycling model assumed.

net of change

(of microbial mass) = (Growth rate) – (Washout rate)

in which

dX/dt = net growth rate of microorganisms in the reactor. (mass/volume-time)

Y = growth yield coefficient. (mass of microorganisms / mass of substrate utilized)

dF/dt = rate of substrat utilization by microorganisms (mass / volume-time)

K_{d} = microorganisms decay coefficient (time^{-1})

X = concentration of microorganisms (mass / volume)

The rate of substrate utilization may be approximated by the

following expression;

net substrate utilization

(net substrat utlization rate) – (The flow substrate into the reactor)

(The flow substrate out the reactor) – (Substrate decay rate in the reactor)

A steady-state condition will eventually result in which the

microbial mass in the reactor will reach a constant value

dX/dt = 0

dS/dt = 0

When this occurs,

in which,

(dF/dt)/X = q = maximum rate of substrate utilization per unit weight of micororganisms (time^{-1})

Θ_{C} = biological solids retention time and is defined as

=X_{T}/(∆x/∆t)_{T}

X_{T} = Total active microbial mass in treatment system.

(∆x/∆t)_{T} = Total quantity of microbial mass withdrawn daily.

S = concentration of substrate surrounding the microorganisms. (mass/volume)

K_{S} = substrate concentration at which rate of waste utilization per unit weight of microorganisms is one-half the maximum rate.

(mass/volume).

V = activation basin volume (reactor volume)

Q = wastewater flow rate.

k_{d} = microorganisms decay coefficient. (time^{–}^{1})

effluent substrate concentration (S_{1}) obtained from Θ_{C}^{-1 }equations

In steady-state, total microorganisms concentration in the reactor,

Θ_{C}^{m} = the lower value at which process failure occurs.

As Θ_{C }is reduced, S_{1} increases until it equals.

So an the process fails. Thus Θ_{C}^{m}, found by setting S_{1} = S_{0}

In the limiting case when S_{0} >> K_{S}

Two particular values, (θ_{c}^{m}, θ_{c}^{d} ) will be defined here and will be related later to the basic parameters and to particular treatment systems,

θ_{c}^{m} = the lower value or minimum 9c at which a complete failure of the biological process will occur.

θ_{c}^{d} = the 9c value to be used for design

The ratio (θ_{c}^{m}/ θ_{c}^{d}) gives the safety factor for the system and generally varies from 2 up to 20.

**3.2.2 Eckenfelder Formulation**

Figure 2: Ec kenfelder Completely mixed model

It has been shown by Eckenfelder that batch removal of a mixture of organics by activated sludge can usually be approximated by the relationship (5).

Grau further showed that when the initial substrate concen-tration of the mixture is varied (but the microorganism remains constant, equation becomes:

When the kinetic concept is applied to a completely mixed system (St = Se), the removal relationship becomes

and equation (2) becomes

Equation (4) logically states that the overall removal rate, (So-Se)X_{V}t^{-1}, decreases as the fraction of BOD remaining, S_{e}/S_{0}, too decreases.

A materials balance with respect to substrate removal at equilibrium was expressed by Eckenfelder as:

because

then

Dividing by Q

and rearranging:

Substituting the food to microorganism ratio (F=S_{0}X_{V}^{-1}t^{-1}) in this model and solving for the effluent concentration, S_{e}, yields:

Figure 3: BOO removal rate

Assuming kF^{-1} S_{0}^{-1}

becomes

in which:

Q = influent flow rate, volume per unit time

S =substrate, BOD5

S_{e} =effluent soluble substrate concentration, BOOS mg/1

S_{0 }=influent substrate concentration (8005 basis, 11401)

V =volume, 1

T =aeration period, hour or day basis

F =food (substrate) concentration

k =BOD bottle reaction rate, KBOD, common log basis

X_{v }=VSS concentration (mg/1)

The accumulation of volatile suspended solids mass in an activated sludge system can be computed as,

At steady state

Dividing by Q

Rearranging

Figure 4: Graphical solution for constants (a) and (b)

Figure 5: BOD removal of wastes

**3.2,3 GAUDY and CHIU formulation;**

Figure 6: Continuous flow reactor

Q = flow rate (1/s)

V = volume of reactor

S_{0} = influent substrate concentration (mg COD/l)

X_{0} = concentration of microorganisms (mg/l)

S_{1} = concentration of substrate reactor and effluent (mgVSS/l)

a) Biomass egulilibriunrate variation of microorganism concentration in the reactor,

At steady state

b) Substrate utilization formula

At steady state,

The substrate concentration is,

And the microorganism concentration is

Where, S_{1} and S_{0}= substrate concentrations,

X_{1} = microorganism concentration in the basin

μ_{m} = maximum specific growth rate

K_{S }= growth increasing coefficent

k_{d} = decay coefficent

Θ_{C} = t = mean cell residence time

Are assumed.

**4. Experimental studies for completely mixed activated sludge mathematical models**

**4.1. Experimental studies by W, Zokenfelder and Adams**

Tischler and leckenfelder have developed several mathematical models, to define the kinetics of DOD removal, leckenfelder showed that the removal of specific compounds in the activated sludge process was zero order, in very low substration and in mixtures of organics (5).

The removal mechanism approximates first order kinetics in most cases. The experimental program was oriented towards evaluating the effectiviness of equation (5),

in predicting activated sludge performance at various organic loadings and varying strength influent organic concentrations. Pepton was employed as the substrate and was supplemented with adequate nutrients. Two series of experiments were conducted. The first set of tests was designed to examine equation (A); at a constant detention time and varying the F/M by changing the influent substrate concentration.

In the second of tests, it was desired to examine the effects of influent substrate concentration on effluent quality under constant organic loading conditions. F/M is approximately 0,20 lb TOC/Day lb MLVSS. (90.6g TOC/day, 453 g MLVSS).

The activated sludge systems were operated until stabilized conditions were achieved in two weeks of model study. Influent and effluent BOD, TOC and suspended solids values were moni¬tored daily in system.

The results of Test I indicated that the soluble effluent TOC concentrations increased with increasing F/M. The results of Test II infer that the soluble effluent BOD increased with increased influent concentrations.

The results of Test I and II are correlated in Fig:7

Figure 7: Correlation of equation 3 with peptone substrate

Figure 8: Correlation of influent and effluent peptone waste

At a constant organic loading (Test II).

The observation the soluble effluent TOC concentrations in. ferreithat TOC varied from 12 to 44 mg/1

The correlation of influent and effluent organic concentration on at a constant organic loading is presented in fig. 8. Since TOC is used instead of HOD, the correlation does not pass through zero and equations (A) and (8), were modified for the X-intercept.

The data in fig. 9 indicate very good agreement with eq.A.

Figure 9: Correlation of equation(3) with organic chemical waste

Table 1: Operating Data (5)

Application to design:

In designing industrial treatment plants, a detention time

or aeration volume is calculated based on an average influent BOD concentration. An effluent BOD concentration can be established by regulatory criteria and a design organic loading, determined from treability investigations.

In the operation of a plant, generally it is assumed that increased influent organic concentrations can be assimilated by increasing the recycle flow.

Design parameters are S_{0} S_{e}, F, Θ, MLVSS and K. Adequate dissolved oxygen levels and the effluent. BOD can be determined by assuming practical MLVSS concentration is maximum.

A plant can be designed an average effluent BOD based on an average influent concentration. The maximum allowable effluent concentration can be established from regulatory discharge criteria. The design detention time can be used in equation A; to calculate the maximum allowable influent concentration to the system.

Design Example:

An industrial plant discharges a wastewater with a flow of 1.3 mg day and an average BOD of 785 mg/l. Regulatory dis¬charge criteria have established an average effluent BOD of 30 mg/1 and a maximum BOD of 60 mg/l. Design and activated sludge treatment plant to meet average effluent quality and

specifiy equalization requirements to maintain the effluent BOD below the maximum allowable level.

Given criteria:

S_{0 }(avg) = 785 mg/1

Q = 1,3 mgd. (4920.5 to/d)

S_{e} (avg) = 30 mg/1 total

S_{e }(max) = 60 mg/1 total

Eff. SS (avg) = 30 mg/1 (a % 85 volatile)

Eff. SS (max) = 50 mg/1 (a % 85 volatile)

BOD content of SS = 0,4 mg BOD/mg VSS

K = 13 day^{-1}

Determine:

Detention time under average conditions.

Maximum allowable So to maintain Se << S_{e(max)} at design detention time.

Calculations:

Maximum influent:

Soluble Se (max) = 60 – 0,4 (50 x 0.85)= 43 mg/1 maximum allowable soluble effluent BOD.

Consequently, equalization requirements must be designed to maintain the influent BOD to the activated sludge basin less then 1164 mg/l. The equalization requirements can be reduced by effectively utilizing sludge recycle.

If the MLVSS could be increased to 4000 mg/1 fairly rapidly to correspond to transient influent BOD concentrations:

Hence, by increasing the MLVSS from 2500 to 4000 mg/1, the equalization requirements can be designed for a maximum effluent of 1470 mg/1 instead of 1164 mg/l.

**4.2 Experimental studies by Thomas W. Keyes and Takashi Asano:**

The Bozeman Wastewater Treatment Plant was constructed in 1970. The plant is located approximately 3 miles (5 km) north west of the city of Bozeman (3).

During August 16 th and December 13 th 1973 (the mean average daily flow rate) was 4.01 mgd. (15178 to/d). The treatment plant is a completely mixed activated sludge system.

Mean values of the influent wastewater to the treatment plant were (3)

biochemical demand (BOD5) = 176 mg/l.

Total suspended solids (TSS) = 94 mg/l.

pH = 7.4 Temperature = 13.2°4

Sampling locations which composite samples were collected by the plant operators are also shown in figure 1.

The equations of Lawrence and McCarthy used for a specified system and environmental conditions; the kinetic coefficients Y, K, Ks and k may be determined experimentally.

S_{e} is a direct function of either ec or U. The mean cell residence time, ec, is a treatment control parameter.

The substrate removal efficiency in a activated sludge process is defined.

The objectives of the study were,

a) to determine the average wastewater loadings and the activated sludge plant performance for the period August 20, December 13, 1973;

b) to determine whether it is feasible to increase the wastewater flow rate to the activated sludge system.

A summary of the qulitative and quantitative parameters

for the period of the analysis is shown in Table II.

Table II: Summary of qualitative and quantitative parameters, August 16, to December 13, 1973.

Parameters | Value |

Influent flow rate to plant | 4.01 mgd (15178 to/d) |

Influent flow receiving only primary treatment | 56.5 % |

Hydraulic detention time of primary clarifiers | 2.48 h |

Flow rate to aeration tank | 1.74 mgd (6583,9 to/d) |

TSS loading to aeration tank MLTSS | 49 mg/l |

Secondary clarifier effluent BOD5 | 3360 mg/l |

Secondary clarifier effluent TSS | 25 mg/l |

Reduction of GODS (activated sludge process only) | 16 mg/l |

Reduction of TSS (activated) | 73.8 % |

Return sludge TSS | 67.2 % |

Influent flow rate to plant | 9395 mg/l |

In the analysis of the Bozeman activated sludge process; was computed on the basis of the aeration tank volume. In the period No. 1, August 21 – 31, 1973:

Θ_{C} = 6.20 – 9.54 days, is found;

in the period No. 2, September 19 – 26, 1973:

Θ_{C} =11.14 – 16.58 days, is found;

in the period No. 3, December 1 – 6, 1973:

Θ_{C} =5,59 – 6,46 days, is found.

Figure 10: Net growth rate versus substrate removal rate for determination of Y ant kd.

For Bozeman Wastewater Treatment Plant; S_{2}, θ, X_{2} and θ_{c} were calculated.

Equation 1 was used to calculate the relationship between 9c and (Si – S2) while maintaining a constant MLVSS concen¬tration in the aerator,

The results are shown in figure 11.

Figure 11: Substrate utilization (S_{1} – S_{2}), mg/l versus mean cell residence time, θ_{C} (days).

The settling characteristics of the sludge deteriorate as θ_{C} increases from 8 to 16 day. If a secondary clarifier effluent BOD5 concentration of 20 mg/1 is desired, the required BOD5 removal in the aerator would be 76 mg/1 (influent BOD5 96 mg/1).

From figure 11; at a hydraulic detention time of 3,0 h the required θ_{C} would be approximately 7 days in order to achieve a BOD5 removal of 76 mg/l.

The conclusions derived from the study are as follows (3): The importance of the use of mean cell, residence time for the control of activated sludge process performance was demonstrated.

It is necessary to know the value of θ_{C}; to expand the capa¬city of the activated sludge system.

To accomplish a higher BOD5 removal in the aeration tank it was necessary to lower the cell residence time and there by produce a younger more active biomass in the aerator.

The effect of the increased loadings to the activated sludge system and thus the lowering of hydraulic detention time in the secondary clarifier, produced a beneficial effect on the effluent TSS concentrations.

Figure12: Flow diagram of City of Bozeman Mont Wastewater Treatment Plant

**4.3 Experimental model studies by Samsunlu**

Experimental kinetic parameters have been obtained by Samsunlu as a result of the model studies in Eskisehir Textile Factory. Experiments were carried out for two different aeration periods, 2 h and 3 h; the effluent concentration of BOD5 have been de¬duced as 45 mg/1 and the treatment efficiency as 60 % (7). It is important to know, that during the experiments Xavg = 700 – 1200 mg/1 and average 9c = 2.8 days.

According to the Michaelis-Menten formula, we are able to determine parameter:

Figure 13: Relationship between 1/q and 1/S_{1}

From the graph it follows that,

q_{max }= 1,24 day^{-1}

The value of K_{S} has been deduced out as 52 mg/l

For the model studied in Eskişehir:

Figure 14: Relation between rate of substrate removal and rate of increase of microorganisms

From the graph, it follows that,

slope = Y = 0.72 and intercept = Kd = 0.10 day-1

As a result of the model experiments carried in Eskiphir Cotton Textile Industry the following kinetic parameters were obtained. For an effluent substrate concentration of S1 = 25 mg/1, 9c must be equal 5 days.

In this case treatment efficiency is **η**= 79 %.

For 9c= 8 days treatment efficiency.

**η**, becomes 86 % and the effluent Sl = 18 mg/l.

If the daily wastewater discharge is 6000 m3 and Θ_{C} = 8 days, microorganism mass in activation basin is:

with

S_{0} = 125 mg/1

K_{s} = 52 mg/1

Y = 0,72

k_{d} = 0,10 day^{-1}

q_{max} =1,24 day^{-1}

Θ_{C} = 8 days.

If wie substitute these values, (X) (V) is found to be 1974,106 mg/l.

If X is equal to 3000 mg/1, V will be 658 m^{3}. In this system

9c = 5 days = 79 %

9c = 12 days = 90 %

In these kinetic parameters, K, Y, qmax, Kd influent So effect greadily treatment efficiency and effluent BOD_{5}.

In these experiments, it has been found that the kinetic parameters Ks, Y, q_{max}, Kd and the effluent So effect significantly the treatment efficiency and the effluent BOD_{5}.

Due to the fact that the biological mass is variable in nature. The kinetic parameters found are not precise; yet they can be used in the design of a particular system.

In the evaluation of experimental results, Samsunlu determined the effects of dux, aeration time, volumetric load, sludge load, and BOD5 concentration and temperature in the basin, upon the treatment efficiency.

The relation between these parameters and the treatment effi-ciency are found to be:

**5. The data given in various completely mixed models Two models are assumed for completely mixed systems (6)**

1. CMAS model developed by Lawrence and McCarthy.

CMAS model is completely mixed solids recycle activated sludge system;

2. CHEMOSTAT model.

CHEMOSTAT model is completely mixed no solids recycle activated sludge system.

According to a number of literature, kinetic parameters were found.

These are given in the following (6).

Table III: The values of kinetic parameters given in various

**6. The validity of model and system parameters**

A wastewater treatment system consists of various elements such as screen, primary sedimentation tank, activation basin, secondary sedimentation tank.

A mathematical model is actually an idealization of the real system. Thus we may state that:

mathamatical model = real system

Figure 16: The differences of the System and mathematical model is shown in.

The mathematical model acts upon the input by means of a transfer function and as a result, produces the output. The output of such a model is the function of two variables, namely time and system parameters (p.) System parameters

are actually variables that can be considered constant within a certain range of time and location. The data obtained from numerous experiments are used to define these parameters for a model.

As it may be expected while calculating the system parameters, deviations will between the output of the mathematical model and the real system. The capability of the model to represent the real system depends upon the extent up to which we can minimize these deviations.

The system has to be optimized and optimal parameters must be defined for the model.

In view of the above considerations, let us now investigate the validity of a model and its parameters developed for a completely mixed activated sludge treatment system.

Our mathematical model reflects the following characteristics:

1. it is developed by means of empirical methods;

2. it is a linear model;

3. it is a static model.

The kinetic equations used throughout the model have been considered to be linear by the first order and kinetic para¬meters have been thus investigated. At the same time, the model is assumed to be static; that is the parameters do not vary with time. The calculation of these parameters depends upon experimental data. The physical and biological operation of the system in addition to the governing rules within the system are not precisely known. Therefore, the mathematical model developed is empirical and local. In other words, the kinetic parameters that are characteristic of a certain country, region or treatment system can be calculated.

Actually, the so defined kinetic parameters are not accurate due to the fact that the system in dynamic by nature and that the physical laws governing the system are not precisely known.

As a result of the assumptions made in the development of a system, the parameters found are mean values. On the other hand, despite the fact that these parameters deviate from the real values characteristic of the real system, they are

valid and can be used in the design of a wastewater treatment system.

In Table III the values of kinetic parameters, given in various literature can be seen. The parameters defined for the same system (completely mixed activated sludge) assume values that are different from each other.

Input elements that vary with time cause the efficiency of the system in the steadystate condition to differ from the expected efficiency.

In the treatment system, the most significant design para-meter is considered to be Ac. The value of Ac in activated sludge systems according to Eckenfelders’s

Ac = 0.16 – 0.33 days

The efficiency of treatment being **η** = 85 % – 95 % According to Lawrence and McCarthy

9c = 4 – 14 days

The efficiency of treatment being **η** = 55 %

The reason for the difference between the two values of efficiency can be explained by the fact that the 9c must be at least 3 days so as to have floes developing in the secondary clarifier.

Tenney, Johnson and Symons investigated the following values for completely mixed processes (2):

1. Extented aeration of solids, θ_{C} = 30 days

2. Moderate aeration of solids, θ_{C} = 3 – 30 days

3. Minimum aeration of solids, θ_{C} = 3 days.

As a result of his studies, Pearson arrived at the conclusion that kinetic parameters can not be precisely calculated. He especially questions the values of qmax and Ks (7).

Gaudy expresses that, as a result of the variable character of biological masses, the coefficients which define the nature of the system are not accurate and that the equations derived on the basis of the assumption of a equilibrium state are questionable.

There is a tendency to accept the idea that the increase in MLVSS concentration in activated sludge tanks will produce a positive effect upon the treatment efficiency.

Yet, the extent up to which increase will be continued is not defined as a precis limiting value.

The kinetic parameters defined vary with each treatment system and with each investigation carried out on the sub-ject.

It is extremely difficult to represent the total system with only one parameter, say 9c.

Furthermore, it is doubtful whether the value of this para-meter is accurately defined or not.

As a result of Eckenfelder’s studies on pure pepton and mixed substrates, values for 9c have been calculated. These are completely different from the values formulated by Lawrence, Thomas, Keyes and Samsunlu:

θ_{C} = 0.18 -1.26 days (Eckenfelder)

θ_{C} = 7 days (Thomas and Keyes)

θ_{C} = 4 – 14 days (Lawrence)

θ_{C} = 8 – 10 days (Samsunlu)

Since mathematical models have been developed on the basis of assumptions regarding the qualities of the waste material and also on the basis of the characteristics of the investigator, the parameters calculated for each system will be different from each other.

Furthermore, there are also values deviations to a certain extent from the parameters in the real system.

One must be very careful when trying to use parameters for a different system in defining calculated another system. Values of parameters that are not suitable will greatly reduce the efficiency and the validity of the model. Extrem values must be used for those parameters that can not be accurately derived. It is not a logical procedure to develop design a model by considering the values of parameters given in literature,

In the development of mathematical models environmental factors such as temperature, pH, oxygen and mixing are not fully taken into consideration. Only one of these factors, temperature is given credit for in the design of a model. Yet, environmental factors, effect the efficiency of treat¬ment and the operation rules of a system.

Furthermore, there are other factors which effect the system design and the treatment efficiency, namely the recycle acti¬vated sludge, volumetric load, volumetric flux, mixing and aeration time.

In addition to these facts, the accurate calculation of a parameter requires long term analyses and experiments concerning the system,

However, since the mathematical model is empirical, linear and static by nature, and since the governing laws of a system connot be preciously defined, the model will be unique for that system and thus cannot be generalized so as to be applied to all systems.

**7. Conclusions**

Completely mixed activated sludge model is taken as the mathematical model for the biological treatment and its kinetic was discussed for the model application. The system was assumed to be static.

Since the system is basically danymic, the kinetic parameters obtained are approximate values (9). Because of the input parameters change with time; the efficiency of the steady state model to be different than which is expected.

In designing these models only one parameter θ_{C} and its variation is considered.

Uncertainity in θ_{C} because of biological restrictions avoids the explanation of system in detail. The basic parameters used in design of treatment plant are K_{S}, Y, k_{d} and θ

In designing a new treatment plant the values of the above parameters abtained for similar system not be used. But the biological model of the now system should be constructred and the kinetic parameters should be obtained from that model for the design purposes.

In these experiments, it has been found that the kinetic para-meters K_{S}, Y, q_{max}, k_{d} and the influent So affect signifi¬cantly the treatment efficiency and the effluent BOD_{5}.

Due to the fact that the biological mass is variable in nature, the kinetic parameters found are not precise yet, they can be used in the design of a particular system.

**References**

(1) Goodman, L. Brian, Englande, J. Andrew, A unified model of the activated sludge process, Journal WPCF, Vol. 46, No. 2,312 – 332, Febr. 1974

(2) Lawrence W. Alonzo, MacCarthy, L.Perry, A unified basis for biological treatment design and operations, Journal of the Sanitary Engineering Division, American Society of Civil Enginerr, on July 9, 1969

(3) Keyes, W. Thomas, Asano, Takashi, Application of kinetic models to the control of activated sludge pro¬cesses, Journal WPCF, Vol. 47, No. 11, 2574 – 2584 Nov, 1975

(4) Christiansen, R. Douglas, MacCarthy, L. Perry, Multi process biological treatment model, Journal WPCF, Vol. 47, No. 11, 2652 – 2662, Nov. 1975

(5) Eckenfelder, WeWe, Adams, EeC., A kinetic model for de¬sign of completely mixed activated sludge treting variable-strength Industrial Waste¬waters, Water Research, Vol. 9, 37 – 42, Perga_ mon Press 1975, Printed in Great Britain

(6) Wilk, Alexander, Kinetische Modelle des Belebtschlamm-verfahrens, Kommissionsverlag R. Oldenbourg, Munchen 1976

(7) Samsunlu, A., Pamuklu Tekstil Fabrikalari Artiklarinin Biyolojik Tasfiyesi ve Kinetigi, Docentlik Tezi, 1974, Kinetik and biologische Behandlung der Abwdsser aus Baumwoll-Textilbetrieben, Habilitationsschrift, 1974, IZMIR

(8) Orhan, Uslu, System Analysis Courses; Izmir, 1976

(9) Busby, B. Joseph, Andrews, F. John, Dynamic modeling and control strategies for the activated sludge process, Journal WPCF, Vol. 47, No. 5, 1055 -1068, May 1975