Online identification of activated sludge settling properties

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Wat. Res. VoL 29, No. I 1, pp. 2587-2590, 1995

Pergamon

0043-1354(95)00109-3

Copyright © 1995 ElsevierScienceLtd Printed in Great Britain. All rights reserved 0043-1354/95 $9.50 + 0.00

RESEARCH NOTE O N L I N E I D E N T I F I C A T I O N OF ACTIVATED S L U D G E SETTLING PROPERTIES R. T E N N O , * E. K. R E N K O and M. P E L K O N E N Laboratory of Sanitary and Environmental Engineering, Helsinki University of Technology, Kemistintie 1, SF-02150 Espoo, Finland

(First received December 1994; accepted in revised form March 1995) Abstract--Activated sludge settling properties can be characterised with two time-varying parameters. A simple method is presented for online identification of these parameters. The method is obtained as an exact solution of the filtration problem; it is obtained on the basis of the settling process description and the parameters variation process description. The method is suitable for practical application. It is a more exact solution of the identification problem than the alternative regression analysis method. An easily implementable system is proposed for automatic characterisation of the sludge settling properties.

Key words--activated sludge, settling, identification

INTRODUCTION The sludge settling properties have a crucial impact on treated water quality. High quality can hardly be achieved with sludge with poor settling properties. The sludge settling properties are affected by many factors but can be characterised by two main parameters: the specific settling velocity and resistance velocity (Renko et al., 1992). These parameters are time-varying in general and constant in diminished time scale (1-5 h). The purpose of this paper is to show how the time-varying settling process parameters can be estimated online using an easily implementable system. MODEL

Settling process A typical settling curve (e.g. Ramalho, 1983; Gray, 1990) as a function of time and concentration can be described with the following model (Renko et al., 1992) dh

dt = c - ~ f ( X ) h t '

X

ho=H,

fiX)=x2+fl,

(1)

where h = sludge blanket interface height, H = initial height, X = a c t i v a t e d sludge concentration, c~ = specific settling velocity, c =resistance velocity, caused by non-absolute (lim hi:/:0) thickening, /~ = small parameter for description of the special *Author to whom all correspondence should be addressed.

situation in low concentration case when the settling velocity cannot be improved by reduction of the sludge concentration, only. Typical values of these parameters are ~ = 2-10 kgSS/m3h, c = 0.2-1 m/h, = 0.02-0.1 kgSS2/m 6. The sludge zone interface height for infinite settling period lim h t = c/~f(X) and the zone settling velocity ZSV = ~ f ( X ) h o - c can be used as well known characteristics for interpretation of these parameters and the model (1).

Time-varying Parameter A long-term (daily) variation of the settling process parameters can hardly be predicted but the shortterm (sampling interval) can be predicted correctly, since the change in parameters is slow enough. In the simplest case variation of the parameters can be approximated by the linear model (for basic ideas of stochastic differential equations, see ]kstrom, 1970) 0t=Ot+#,

dOt=q~Otdt+adWt,

(2)

where 0t = vector of time-varying parameters, 0 t = [ c t , ~ t ] T, # = m e a n , # = [ P l , / h ] r, q ~ = a u t o regression of the fluctuation process, (W~) = Wiener process for modelling of the uncertainties, cr = standard deviation of the errors caused by model inadequacy.

Measurements The sludge blanket interface height and the concentration cannot be observed strictly, but with errors. In the simple case the errors can be characterised as

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2588

Research Note

additive "white noises" using Wiener processes. The observation model in this case has the form d~ =F(~,X)V0, d t + r I d V l,

( t = X ~ + r 2V 2,

(3)

where ~ , ( = o b s e r v e d values of the height and concentration, respectively, q , Q = standard deviations of the observation errors, F(~, X ) = vector with the following coordinates

J

meter

Valv

Pump

&

| Aeration tank |

F(~, X) = [1, - f ( X ) ~ ] v. The model (3) has a more practical form when the dependence on unobservable concentration is eliminated d~ = F(~, ~')T0t dt + r Ld V~ + r2/~lf(~')' ~ d V 2.

~

(4)

This model can be obtained using linear approximation of the function

I/o[

•

Suspended solids meter

Fig. 1. Automatic testing system.

~f( X ) ~-- af(¢ ) + t~lf(~ )'r2 V2 in ~ =/~l and X = ~ neighbourhood. Heref(~')" is the derivative of the function f ( ~ ) . IDENTIFICATION

It is simple to show that the settling process parameters can be estimated online using the following relationship m r + T = a o Jr- a i m t +

al TtA B 2 + ATTt A x (~t+, -- ~,-- Arm,),

7t+~ = al'ha[ + bb x - al TtAA TTta~ B2 + ATytA ,

(5) (6)

where m, = conditional mean of the time-varying parameters, m s = M{0,[¢0 . . . . . ~ }, 7~ = covariance of the estimation errors, r = sampling internal, a0 = vector, a0 = - q,pT, a~, b = matrices, aj = I + Oz, b = a~/~, I = identity matrix, B = observation dependent scalar and A = vector B 2 = {r~ + [rz/~lf(f)'#12}T,

A T = [1,f(¢)~]t.

The testing process is a periodic batch-type process. Similarly, initialisation of the calculations in algorithm (5)-(6) has to be periodic for height observations, i.e. condition ~t : H has to be used in the beginning of every test period. Identification of the parameters can be ineffective if the testing period is short. A long enough period can be chosen from the relationship T = 3H/ZSV.

properties. The system consists of a test cylinder, sludge blanket depth and suspended solids meters, and a computer. In order to avoid the wall effect the test-cyliner cannot be too small. In our application its diameter was chosen to be 13cm and its height 155 cm. The sludge concentration was measured by "Cerlic C S P - A / I T 500" suspended solids meter and the sludge blanket interface height by " M a r k l a n d 600" depth meter which reads the height by 3 cm interval. The system operates in a four-hour cycle, the entire cycle consisting the following operations:

I. Sample collection. By a computer command the sampling valve in the inlet hose is opened and the cylinder is filled gravitationally from the bottom with sludge drained from the aeration basin. The sampling valve remains open until the sludge interface reaches the level of the over-flow indication and the computer closes the valve. 2. Measurement. The computer reads the sludge blanket depth and suspended solids concentration data every six minutes. 3, Data analysing. Estimation of the settling process parameters according to algorithm (5)-(6). A special program ("Settling Test for Windows") was developed and used for performance of these calculations. 4. Emptying. The sludge in the cylinder is pumped back into the aeration basin.

Proof For p r o o f of the estimation algorithm, apply the solution of the linear filtration problem (Liptser and Shiryayev, 1978) on the processes (2), (4). IMPLEMENTATION The simple test system is shown in Fig. 1. It can be used for automatic identification of the sludge settling

APPLICATION

The estimation method has been tested on the pilot-plant process at the Suomenoia research station in Espoo and on the city treatment plant in Savonlinna. An example of the identification results obtained on the pilot-plant process is demonstrated in Figs 2-7.

Research Note

2589 7'

1.6 1.4-

¢o 6-

rn Regression

~0

Filtrated

o

c3

o

"[c~u,=edj

1.2

J~

o

5-

\

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0.¢ 0.4

CO

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IIIII

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1- ~ B ~ ! ~ | ~ u ~ u ~ | ~ ~ 2 4 6 8 10 12 14 0

IIIIIIIIllllllll]l

2

o

3

16

18

Time (days)

Time (hours)

Fig. 2. Settling curve: measured and calculated by the model (1) height.

Fig, 5. Dynamics of the settling velocity: estimated by regression analysis and using the filtration method (5)-(6).

6.

~"

r

o

t3

I--1 Regression

Filtrated 0.8-

Forecast

i

mm

o m

o

~

--J

r-

.c

rn

2. 0

2

4

6

8 10 12 Time Hays)

14

16

18

Fig. 3. Dynamics of the settling velocity: filtrated (current) and predicted (4 h forecast) velocity.

0

tl i: ,,,,.,,~.,....... ,

0

2

4

6

I I I I l l l l l l l l l l l l l l l l l l l l | l l l l l III IIIII IIIIIIIIIIIII III IIII I IIII

10 12 Time (days) 6

14

16

i

is

Fig. 6. Dynamics of the resistance velocity: estimated by regression analysis and using the filtration method.

0.8.

0.7-

-0.475

--)K-. Filtrated i

D

I

-0.45

Forecast i v

0.6-

-0.425 -~

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0.4-

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-0.375

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••••••••••••••••••••••••i•••••••••••••••••••••••m••••••••••••••|••••I••uI••••I••••I•••••••••

2

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18

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1

2

3

Time (hours)

Fig. 4. Dynamics of the resistance velocity: current and predicted (4 h forecast) velocity,

Fig. 7. Variation of the settling process parameters during a single test-settling period.

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Research Note

Settling curve verification

A typical curve is shown in Fig. 2 for data measured on the process and calculated by the model (1). This is typical accuracy which can be achieved in the case of online identification of the sludge settling properties using algorithm (5)-(6). Model identification

The following fluctuation process model has been verified on the basis of standard regression and time series analysis A0t =

-0.32 0.09

0.04 0 -0.91

lT

0.43 T 10.05 0.06 .AW,. - 3.44 + 0.06 0.30 Here the model is presented in the difference form, its quality is demonstrated in Figs 3 and 4. The 4 h forecast of settling process parameters calculated by the model is shown. The model has been obtained in two steps. In the first step the settling process was estimated from the observed height and concentration data using the following regression analyses model

The proposed method is a more effective way to reduce the estimation errors; it takes into account the fluctuation process model (2) which makes it possible to account for the previous test-settling process beside the current observations and in this way to reduce the estimation errors. Variation of the parameters is relatively small during a single test-settling period (Fig. 7). In practice, it can be ignored.

CONCLUSIONS The identification method proposed in this paper allows the estimation of the sludge settling parameters automatically using a very simple testsystem. The method is more precision than the alternative regression analysis method. The forecast of the sludge settling parameters is accurate enough for control application in 1 5 h period. The online identification method can be used in advanced control systems for prediction of the activated sludge concentration dynamics in the aeration tank and the stock dynamics in the settler (Tenno and Pelkonen, 1994).

A~, = F(~, ~)0z + Et, where E, = model error, 0 = constant parameter for every test-settling process. These parameters were considered as time-varying parameters in the second step. The fluctuation process parameters p, q, and were estimated then using the time series analyses of the estimated data (0,). Online identification

The estimation results obtained in automatic characterisation of the sludge settling properties are shown in Figs 5 and 6. Both results obtained with the proposed and regression analysis method are shown.

REFERENCES

/kstrom K. J. (1970) Introduction to Stochastic Control Theory. Academic Press., New York. Gray N. F. (1990) Activated Sludge. Theory and Practice. Oxford Univ. Press. Liptser P. S. and Shiryayev A. N. (1978) Statistics of Random Processes. Springer, Berlin. Ramalho R. S. (1983) Introduction to WasteWater Treatment Processes. Academic Press, New York. Renko E. K., Tenno R. and Pelkonen M. (1992) A model for sludge blanket interface settling curve. Proc. Conf. Sewage into 2000, Amsterdam, pp. 323 328. Tenno R. and Pelkonen M. (1994) Activated sludge concentration dynamics. Wat. Res. 28, 491-493.