Chapt9_DesignofPercolatingfilters[1]

cmutsvangwa: Wastewater Engineering, Dept. of Civil and Water Engineering, NUST 05/10/2006 9-1

Chapter 9

DESIGN OF PERCOLATING FILTERS (Selected models)

Design of percolating filters A Medium of rocks, stones or plastic with diameter of 25-100mm (optimum diameter=38mm) is common with a depth varying from 0.9 to 3m. Plastic media is light and has a high specific area and greater percentage of voids (94-98%). It ensures even distribution of flow. Also it can be of random or modular variety. The only disadvantage is the high costs compared to a stone media. Design parameters

hydraulic loading (m3/m2.day) volume of settled wastewater applied per m2 of available filter media per day

AQHL =

Volumetric BOD loading (kg BOD/m3.day) BOD applied per m3 available

filter media per day

fVdaykgBODVL /=

BOD surface loading (kg BOD/m2.day) BOD load applied per area of filter

per day

fAdaykgBODSL /=

Specific area of media (m2/m3) Surface area per unit volume and

increases as the media size decreases Depth of filter bed ranges from 1.5 to 3m. Larger depths should be selected

for effective nitrification. Design approaches There are several design formulae and most of them are empirical and the common ones given below: Based on volume per capita Volume of media 0.51m3/person

Chapter 9 Design of percolating filters

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= personmequivalentpopulation /51.0orpopulationfilter of Volume 3

Based on volumetric loading

( ) .day)/mloading(m Volumetric

/mdwfDesign media of Volume 333 day=

Volumetric loading in m3/m3.day (0.25-1.0 m3/m3.day) Based on dosing rate

( )

=

day3

3

mkgBODrate dosage1000

mgBOD/lstrength sewagedaymdwfDesign

media of Volume

Where: DWF in m3/day Sewage strength in mg BOD/l Dosage rate in kgBOD/m3.day (0.05-0.12 kg BOD/m3.day)

Lamb and Owen Model

( )1509.02.7 =T

ei

e eVSQ

BODBODBOE

Where: BODi =influent BOD of settled wastewater, mg/l BODe =effluent BOD mg/l Q =inflow wastewater, m3/day V =volume of filter medium, m3 S =specific surface of medium (m2/m3) T =temperature, oC Pike Model

( ) nTei

e

SQakBODBODBOE

+= 1511

Where; BODi =influent BOD, mg/l BODe =effluent BOD, mg/l

Q =hydraulic loading, m3/m2.day k =first order rate coefficient a =temperature coefficient m, n =coefficients relating to properties of medium


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National Research Council formula (NRC) For a single stage, the following relationship is used:

5.01

/

1

532.01

1

+==

VFQBODBOD

BODBODEi

ei

Where: V =volume of filter, m3 Q =flow, m3/min F =recirculation factor BODi = Influent BOD, mg/l BOD/e =Effluent BOD, mg/l

( )21.011

rrF +

+=

Where: r =recirculation ratio, Q Qr

For the second stage:

5.0

//

/

1

/1

/

/

2

1

532.01

1

+=

FVQBOD

BODBODBOD

BODBODBODE

ee

e

finalee

Where: V/ = volume for the second stage F/ =Recirculation factor for the second stage =Effluent BOD from the first stage filter, mg/l /eBOD =Final effluent BOD from the second stage filter finaleBOD Advantages of a two-stage filter are that the total volume of the two stages is always less than for a single-stage filter, achieving the same effluent quality. The NRC equation is mostly utilized by means of a design chart (Fig. 1). Example 1 Using the design chart (Fig. 1), suggest the diameter for 2 identical biological filters with the following design criteria:

Design flow =3500m3/day BOD of wastewater =310mg/l Required effluent BOD =60mg/l Recirculation flow =35% of the inflow


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Assume the filter beds operate in parallel (sharing the flow equally) Solution

% BOD reduction = =3 1 0 6 0

3 1 01 0 0 8 0 %

-=x

Recirculation flow = = 350010035 =1225m3/day

Recirculation ratio = =1225/3500 =0.35 Volume of filter from design chart = ( )( )( )Vf = 1 0 0 0 3 1 01 0 0 3 5 0 05 0 0 0 =2170m3 Assuming a depth of 2m for the filter, the diameter of filter:

D VnH= 4 =21704

231422x

x x. =26m

Fig. 1 Single stage biological filter design chart for NRC equations


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Example 2(Metcalf and Eddy, 1995) A municipality waste having BOD of 250mg/l is to be treated by a two stage trickling filter. The effluent quality is 25mg/l of BOD and the inflow is 2Mgal/d. The depth pf both filters is 6ft and the recirculation ratio is 2:1. Find the required filter diameters. Assume T=20oC.


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ECKENFELDER AND SCHULTZ-GERMAIN MODELS Eckenfelder Model (1963) The model was developed by relating depth, hydraulic loading and media characteristics. Eckenfelder Model (1963) assumed that BOD removal in trickling filters was proportional to the contact time of the wastewater with the biological slime layer and also to the total active microbial mass in the slime layer (Horan, ). Assuming first-order removal kinetics, this assumption can be expressed as:

)exp( kXtLL

o

e = Where: k =removal rate constant X =mass of organisms in slime layer, mg/l


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t =contact time of wastewater with the slime layer Li =influent BOD, mg/l Le =effluent BOD, mg/l

Retention time, QADt =

Flow in the filter us tortuous and is a function of the media geometry and packing characteristics. Therefore the actual contact time t is expressed as:

n

m

QDCAt =

Where: D =depth of filter, m Q =surface hydraulic loading, m3/day A =surface area of filter medium, m2C, m, n =media constants (C ranges from 0.4-0.8, Vienstra, 1997) It is assumed that the mass of the organisms in the slime layer is proportional to the surface area of the media:

AX AkX 1= Substituting t and X in previous equation:

= n

m

o

e

QDCAkk

LL

1exp

Taking , and is the treatability factor. The treatability factor incooperates the surface area of active slime layer per unit volume at 20

Akkko 1=oC. Therefore equation

becomes:

= n

m

oo

e

QDCAk

LL exp

With a uniform attachment of slime layer throughout the filter depth and a surface which is constant over time, equation becomes:

= no

o

e

QDk

LL exp ( )no

i

e DQkBODBOD = exp


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The general form of Eckenfelder model is also given as

=

n

maie Q

AkDSSS exp

Where: m, n =constants characteristic of medium Sa =specific surface of the medium, (m2/m3) Se =BOD effluent from the filter Si =BOD influent to the filter Q =flow rate, m3/day A =cross sectional area of filter, m2

Computation of constants ko and n are from pilot studies. Samples are taken from various depths and the BOD remaining is calculated. Taking logarithms of Eckenfelder equation we get;

no

i

e DQkBODBOD =ln

A best fit plot of i

e

BODBODln versus filter depth, D on for different loading rates gives

a series of straight lines (Fig. 1), or plotting i

e

BODBOD vs D on a semi log paper.

BODiBODeln

gradient m1 at different loading rates

m2m3

depth

Fig. 1


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noi Qkm

=

Qnkm oi logloglog += There a best fit plot of these gradients against the loading rates on a log-log paper gives a straight line and the gradient is equal to the constant n and an intercept of -ko .

log-log paper

mi

loading rate, Q

Also ko at any temperature is related to the Arrhenius equation:

( ) ( ) 2020 = TOTO kk varies from 0.015 to 1.045 for carbonaceous BOD removal and 1.035 is normally assumed for a conservative design (Droste, 1997; Metcalf, 1995). When a treatability constant measured at one depth is used to design a filter of a different depth, the treatability constant must be corrected for the new depth using the following relationship (Horan, ):

x

DDkk

=

2

112

Where: k2 =for D2 k1 =forD1 x =0.5 for vertical and rock filters x =0.3 for cross-flow plastic medium filters


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cmutsvangwa: Wastewater Engineering, Dept. of Civil and Water Engineering, NUST05/10/2006 9-10

Schultz-Germain equation (1966) The rate of change of the organic matter is proportional to the organic matter remaining:-

SkdtdS /= (1)

As stated earlier, the actual retention time in a filter is given as:

n

AQCDt

= (2)

Integrating equation (1)and substituting equation (2) for the time limit:

= nieAQCDkSS

/

exp (3)

Where: Si =influent organic loading Se =effluent organic loading When , the above equation becomes: Ckk /=

= nieAQDkSS exp

= ni

e

AQDk

SS

exp (4)

Where: Q =hydraulic loading, m3/day A =cross-sectional area of filter, m2 n =media constant k =rate constant Determining constant, n and the rate constant (k) Again pilot tests have to be conducted at different depths and various hydraulic loading rates and the BOD remaining is measured.


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Taking logarithms of above equation:

n

i

e

QADk

SS

=

ln

A plot of i

e

SS versus D on a semi log paper (for various loading rates and depths)

yield straight lines. The slopes of the lines: n

i QAksslope

==

semi-log paper

BODiBODe

gradient s1 at different loading rates

s2s3

depth

Taking the logarithms of the above equation:

( )

=AQnks logloglog

The slopes of each curve, s versus AQ are plotted on a log-log paper and yields a

straight line.


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log-log paper

si

loading rate, AQ

, m/day

The slope of the line is equal to the constant n and k from the intercept. The

constant k can also be found from equation, n

i

e

QADk

SS

=

ln , since n is now

known, and its numerical value is substituted in the equation. The values of i

e

SS

versus n

QAD

are plotted on a semi log paper and the slope is equal to k. This

approach yields a better result.

Semi-log paper

i

e

SS

loading rate, ?=

nQAD , m/day


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Examples (Droste, 1997) n trickling filter in the following table obtained at 20oC,

From the laboratory data ofind the constants in the Schultz-Germain formula.


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14



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Other examples (Metcalf and Eddy)

References

1. Droste R., (1997), Theory and Practice of Water and Wastewater Treatment, John Wiley, UK

2. Metcalf and Eddy, (1995), Wastewater engineering, treatment, disposal and reuse, McGraw Hill, New York, USA

3. Horan 4. Venstra S., and Polprasert C., (1997), Wastewater treatment Part I, IHE,

DELFT.


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Chapt9_DesignofPercolatingfilters[1]

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