prediction of clean-bed head loss in crumb rubber filters

The Pennsylvania State University

The Graduate School

College of Engineering

PREDICTION OF CLEAN-BED HEAD LOSS

IN CRUMB RUBBER FILTERS

A Thesis in

Environmental Engineering

by

Hao Tang

copy 2008 Hao Tang

Submitted in Partial Fulfillment of the Requirements

for the Degree of

Master of Science

December 2008

The thesis of Hao Tang was reviewed and approved by the following

Yuefeng F Xie Professor of Environmental Engineering Thesis Co-Advisor

John M Regan Associate Professor of Environmental Engineering Thesis Co-Advisor

Shirley E Clark Assistant Professor of Environmental Engineering

Peggy A Johnson Professor of Civil Engineering Head of the Department of Civil amp Environmental Engineering

Signatures are on file in the Graduate School

iii

ABSTRACT

Pilot crumb rubber filters were tested to study their clean-bed head loss under the

influences of three design and operational parameters (media size media depth and filtration

rate) Filter media compressions were observed during the filtration test Statistic analysis of the

field data was used to investigate the applicability of the Kozeny and Ergun equations in

predicting the clean-bed head loss in crumb rubber filters A statistical model was also developed

to evaluate the effects of the three parameters and to better predict the clean-bed head loss Both

the Kozeny and Ergun equations were unacceptable for crumb rubber filters especially when the

compressed media depth and porosity from the filtration tests were not available The statistical

model developed based on the original media depth and porosity was statistically valid and was

able to provide best-fit to the actual head loss data without using the compressed media depth and

porosity obtained in filter tests The results from this study indicated that the statistical model

could be used in place of the Kozeny and Ergun equations for the prediction of clean-bed head

loss in crumb rubber filters

iv

TABLE OF CONTENTS

LIST OF FIGURES v

LIST OF TABLES vi

ACKNOWLEDGEMENTS vii

Chapter 1 INTRODUCTION 1

Statement of Problem 1 Objectives 2 Thesis Organization 3

Chapter 2 BACKGROUND 4

Manufacture of Crumb Rubber 4 Characterization of Filter Media 5 Theory of Crumb Rubber Filtration 7 Head Loss Theory 12

Chapter 3 MATERIALS AND METHODS 16

Filter Setup 16 Filter Media 16 Design and Operational Conditions 18 The Kozeny and Ergun Equations 18 Statistical Modeling 19 Regression Verification 20

Chapter 4 RESULTS AND DISCUSSION 24

Media Sphericity 24 Prediction by the Kozeny Equation 27 Prediction by the Ergun Equation 29 Development of a Statistical Model 33 Effects of Parameters 36

Effect of filtration rate 38 Effect of interaction between filtration rate and media depth 39 Effect of filter depth 40 Effect of media size 41 Effect of interaction between media size and filtration rate 42

Prediction by the Statistical Model 42

Chapter 5 CONCLUSIONS 45

Bibliography 46

v

LIST OF FIGURES

Figure 1-1 Overview of research objectives and scope for model development and verification 3

Figure 2-1 Sieve results of crumb rubber media 6

Figure 2-2 Schematic diagram of filter medium configurations 8

Figure 2-3 Comparison of performances between a crumb rubber filter and a sandanthracite filter treating secondary effluent at 6gpmft2 9

Figure 2-4 Crumb rubber filter performances under various media size conditions 12

Figure 3-1 Experimental setup of the crumb rubber filter 17

Figure 4-1 Prediction of clean-bed head loss by the Kozeny equation 28

Figure 4-2 Residual analysis of the Kozeny equation using compressed media depth and porosity 29

Figure 4-3 Prediction of clean-bed head loss by the Ergun equation 31

Figure 4-4 Residual analysis of the Ergun equation using compressed media depth and porosity 32

Figure 4-5 Actual head loss profiles at all filter configurations 36

Figure 4-6 Pareto chart of the standardized effects showing the results of medium and high level factorial calculation 38

Figure 4-7 Impact of filtration rate on filter depth for a crumb rubber filter that has media size of 120 mm and filter depth of 09 m 39

Figure 4-8 Impact of media compression for the filter configuration of 066 mm crumb rubber media and 06 m media depth 41

Figure 4-9 Prediction of clean-bed head loss by the statistical model 43

Figure 4-10 Residual analysis of the statistical model using initial media depth and porosity 44

vi

LIST OF TABLES

Table 2-1 Physical characteristics of crumb rubber media 7

Table 2-2 Typical properties of several filter media 10

Table 4-1 Sphericity estimates by the Kozeny and Ergun equations for crumb rubber media 26

Table 4-2 Parameters in the statistical model 35

vii

ACKNOWLEDGEMENTS

I would like to thank my advisors Dr Yuefeng Xie and Dr John Regan for many years

of mentoring and for helping me to become the person I was meant to be I would also like to

thank Dr Shirley Clark for being on my committee Mr Joe Swanderski and his staff at

University Park Wastewater Treatment Plant for providing research facilities and my colleagues

at Penn State for their friendship and encouragement Finally I wish to thank my parents my

wife Wen and my sons Shunyu and Jinyu Without them I could not have accomplished this

Chapter 1

INTRODUCTION

Statement of Problem

Scrap tire stockpiles cause health and environmental concerns by presenting a potential

fire hazard and providing breeding ground for vectors of disease The properties of scrap tires

such as volume flammability toughness durability etc make their storage and elimination

difficult (USEPA 1993) According to the data compiled by Rubber Manufacturers Association

275 million tires remained in stockpiles across the United States in 2003 and approximately 290

million new scrap tires are generated each year (USEPA 2006) Various recycling technologies

have been recommended for conservation of natural resources and minimization of environmental

impacts of these tires The use of crumb rubber a scrap-tire-derived material as a filter medium

is an innovative technology that has been investigated as a potential ldquogreen engineering solutionrdquo

for wastewater treatment and disposal of scrap tires As a compressible material crumb rubber

could form an ideal porosity gradient in filters because the top layer of the media was least

compressed while the bottom layer was most compressed Crumb rubber filters favored in-depth

filtration and could allow longer filtration time and higher filtration rate which could

substantially increase the filtration efficiency (Graf et al 2000 Xie et al 2001) Their light

weight compact size and capability to remove turbidity phytoplankton and zooplankton also

allowed them to be used in ballast water treatment (Tang et al 2006a)

Since crumb rubber filtration has beneficial engineering applications it is important to

understand the effects of design and operational parameters on the filter performance Clean-bed

head loss is such an important filter performance parameter because water head must be provided

2

to accommodate the increase of head loss resulting from the accumulation of particulates in the

filter media (Cleasby and Logsdon 1999) There are numerous models for the prediction of

clean-bed head loss but the Kozeny and Ergun equations are most accepted models (Trussell et

al 1999a) These two equations however were developed for conventional rigid granular media

filters Their applicability in the crumb rubber filter was not clear because of the crumb rubber

media compression which changed the filter configurations during the filtration process and

much higher filtration rates

Objectives and Scope

The principle objective of this research was to evaluate the applicability of the Kozeny

and Ergun equations for clean-bed head loss prediction in crumb rubber filters Statistic analysis

was also conducted to investigate the impacts of three design and operational parameters and to

develop a statistical model for the prediction of head loss in crumb rubber filters

A general flow chart showing an overview of the research scope with regard to model

development and verification is shown in Figure 1-1 and summarized as follows

3

Figure 1-1 Overview of research objectives and scope for model development and verification

(1) Conduct filtration tests by varying media size media depth and filtration rates to

obtain actual clean-bed head loss data under various filtration conditions

(2) Estimate the crumb rubber media sphericity based on empirical fitting of filtration test

data

(3) The filtration test data and sphericity estimates are applied to the Kozeny and Ergun

equations respectively to determine whether the two equations can be used in crumb rubber

filtration

(4) Develop a statistical model based on three design and operational parameters

Thesis Organization

The thesis is composed of five chapters Chapter 1 describes the problem and objectives

of the study Chapter 2 reviews previous studies on crumb rubber filtration and head loss theories

Methodologies are described in Chapter 3 Chapter 4 elaborates on the results and discussion of

the study Conclusions are summarized in Chapter 5

Chapter 2

BACKGROUND

Manufacture of Crumb Rubber

Crumb rubber is made by a combination or application of several size reduction

technologies Typically the crumbing processes involve shredding the tire into progressively

smaller pieces removing the metals (belts and bead wire) using magnets blowing away the

fibers and then grinding to further reduce the material to a given size The manufacturing

technologies can be further divided into two major categories mechanical grinding and cryogenic

reduction

Mechanical grinding is the most commonly used process The method consists of

mechanically breaking down the rubber into small particles using a variety of grinding

techniques such as cracker mills and granulators The steel components are removed by a

magnetic separator (sieve shakers and conventional separators such as centrifugal air

classification and density are also used) The fiber components are separated by air classifiers or

other separation equipment These systems are well established and can produce crumb rubber

(varying particle size grades quality etc) at relatively low cost

The cryogenic process consists of freezing the shredded rubber at an extremely low

temperature (far below the glass transition temperature of the compound) The frozen rubber

compound is then easily shattered into small particles The fiber and steel are removed in the

same manner as in mechanical grinding The advantages of this system are cleaner and faster

operation resulting in the production of a fine mesh size The most significant disadvantage is the

slightly higher cost due to the added cost of cooling (eg liquid nitrogen)

5

The crumb rubber media used in this study was produced using the first process No

cooling was applied to make the rubber brittle The tires are first developed into chips of 50 mm

in size in a preliminary shredder The tire chips then entered into a granulator where the chips

were reduced to a size to less than 10 mm at ambient temperature and most of the steel and fiber

were liberated from the rubber granules The steel then was removed magnetically and fiber was

removed using shaking screens and wind sifters The fine grinding process generally was

conducted by cracker mills which was currently the most common and productive method of

producing tire rubber The end product was usually an irregularly shaped particle with a large

surface area varying in size from 475 mm to 045 mm (Hsiung 2003)

Characterization of Filter Media

Crumb rubber has been sieved for three media sizes according to the sieve analysis using

American Society for Testing and Materials (ASTM) Standard Test C136-01 Sieve analysis of

Fine and Coarse Aggregates (ASTM 2001) Sieve results were plotted in Figure 2-1 for

determination of media characteristics As summarized in Table 2-1 the effective size (for which

10 of the grains are smaller by weight) was 066 mm 120 mm and 190 mm for the size range

of 05 ndash 12 mm 12 ndash 20 mm and 20 ndash 40 mm crumb rubber media Their uniformity

coefficients (Ratios of sieve size that will permit passage of 60 of media by weight to the sieve

size that will permit passage of 10 of media by weight) were determined to be 139 153 and

128 respectively (Tang etal 2006a) Density of crumb rubber is not correlated with media size

and the value of 1130 kgm3 is uniform for all sizes crumb rubber media Porosity is defined as

the ratio of volume of the void space to the bulk volume of crumb rubber media (Trussell et al

1999) It is expressed in Eq 1 and was determined by measurements of the dry weight of the

media loaded into the filter column and the height of the media in the column

6

Where

= the dry weight of the media loaded into the filter column

Eq 1

= the porosity of crumb rubber media

= the density of crumb rubber

= the cross section area of the filter column

= the height of the dry media in the column

The packed porosity was 062 058 and 054 for the size range of 05 ndash 12 mm 12 ndash 20

mm and 20 ndash 40 mm crumb rubber media respectively

Figure 2-1 Sieve results of crumb rubber media (Regenerated from Hsiung 2003)

7

Table 2-1 Physical characteristics of crumb rubber media (Source Tang et al 2006a)

Theory of Crumb Rubber Filtration

The crumb rubber filter resembles an ideal filter bed configuration consisting of the

largest size media on the top medium size in the middle and the smallest size at the bottom as

shown in Figure 2-2a (Xie et al 2001) For conventional media filters however the fine grains

tend to settle on the top of the filter while the coarse grains accumulate at the bottom during

stratification after filter backwash (Figure 2-2b) Such media size distribution of conventional

media filters will easily clog the filter bed surface which causes a high head loss Compressibility

of the crumb rubber media results in a favorably porosity gradient (Figure 2-2c) Compression

increases with pressure throughout the filter columns Consequently the crumb rubber filter bed

has the smallest pore size at the bottom and the largest pore size on the top

As a result an ideal porosity profile can be formed in filter bed and the filtration

efficiency can be increased The crumb rubber media results in lower head loss and higher

filtration rate and water production According to a comparative study of a sandanthracite filter

and a crumb rubber filter in tertiary treatment (Hsiung 2003) at the filtration rate of 6 gpmft2

both filters performed similarly on turbidity removal However the crumb rubber filter could

continuously run for 50 hours while the sandanthracite filter could only run 3 hours before the

filter bed was clogged (Figure 2-3) For the crumb rubber filtration therefore backwash

8

frequency and head loss development can be reduced while filter run time and water production

rate can be increased

Figure 2-2 Schematic diagram of filter medium configurations (Source Xie et al 2001)

9

Figure 2-3 Comparison of performances between a crumb rubber filter and a sandanthracite filter treating secondary effluent at 6gpmft2 (a) Turbidity removal (b) Head loss development (Source Hsiung 2003)

Besides compressibility the crumb rubber has several other physical properties that offer

advantages over conventional media Typical properties of conventional filter media and crumb

rubber media are shown in Table 2-2 The porosity of crumb rubber is higher than other media

which will capture more solids and increase the filter run time The mechanisms of crumb rubber

filtration are interception adsorption coagulation and sedimentation inside the filter bed In

addition small hairs that protrude from sides of crumb rubber particle further help capture solids

in voids (Xie et al 2000)

10

Table 2-2 Typical properties of several filter media

Property Garnet Illmenite Sand Anthracite GAC Crumb rubber

Effective size (mm) 02-04 02-04 04-08 08-20 08-20 06-19

Uniformity coefficient 13-17 13-17 13-17 13-17 13-24 12-16 Density (gml) 36-42 45-50 265 14-18 13-17 11-12 Porosity () 45-58 NA 40-43 47-52 NA 54-62

Hardness (Moh) 65-75 50-60 7 20-30 Low Very low

Sphericity was a shape factor of filter media According to the literature related with

filtration theories the grain shape was usually described by either shape factor (ξ ) or sphericity (

ψ ) The relationship between them was shown in Eq 2

grainofareasurfaceactualspherevolumeequivalentofareasurface

=ψ Eq 2

ψξ 6= Eq 3

where

=ψ sphericity dimentionless

=ξ shape factor dimentionless

The literature values for sphericity of common filter materials were calculated from head

loss experiments and therefore many of the sphericity values are empirical fitting parameters for

head loss rather than true independent measurements of shape (Crittenden et al 2005) In this

study the sphericity estimates of crumb rubber media were obtained from empirical fitting of

head loss data based on conventional equations

The Density of crumb rubber is 1130 kgm3 (Tang etal 2006a) which is much lower

than that of conventional media (eg 2650 kgm3 for sand) This can substantially reduce the

11

backwash water flow rates required for filter backwash Previous research (Hsiung 2003) has

demonstrated that a backwash flow rate of 214 gpmft2 was required to achieve 30 bed

expansion for a 3-feet-deep sandanthracite filter while a same-depth crumb rubber filter only

required a backwash flow rate of 105 gpmft2 to achieve the same degree of bed expansion

In addition to its use in tertiary wastewater treatment research on crumb rubber filtration

for ballast water treatment indicated that crumb rubber filters could remove up to 70 of

phytoplankton and 45 of zooplankton in addition to the removal of particles (Figure 2-4)

Compared with conventional granular media filters and screen filters crumb rubber filters

required less backwash and developed lower head loss (Tang 2006a) When statistical

approaches were applied to develop empirical models including a head loss model that partially

resembles the Kozeny equation to evaluate the influences of design and operational factors the

results indicated that the behaviors of the crumb rubber filtration for ballast water treatment could

not be described by the theories and models for conventional granular media filtration without

modification (Tang 2006b) Considering the much lighter weight of a crumb rubber filter

compared with conventional filters it was suggested as a competitive solution in ballast water

treatment

12

Figure 2-4 Crumb rubber filter performances under various media size conditions (a)Phytoplankton removal (b) Zooplankton removal (Source Tang et al 2006)

Head Loss Theory

Several disciplines have made important contributions to the development of models

characterizing flow through porous media The current theory of creeping flow through filter

media is largely based on experimental work and theoretical analysis published by Henry Darcy

13

Darcy observed that the flow through a bed of filter sand was directly proportional to the

hydraulic head acting on the sand bed and inversely proportional to its depth (Darcy 1856) The

following is the equation Darcy proposed

[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where

Q = flow rate through the sand bed

K = a coefficient dependent on the nature of the sand (units of velocity)

A = the area of the sand bed (in plain)

H = the height of surface of the influent water above the top of the sand bed

0H = the height of the surface of the effluent water above the bottom of the sand bed

LΔ = depth of the sand bed

The head loss through the sand could be defined

0HLHH minusΔ+=Δ Eq 5

Darcyrsquos equation could then be expressed in a more commonly used form

⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6

Following Darcy developments in the prediction of head loss through porous media were

advanced by civil and chemical engineers Kozeny (1927a b) Fair and Hatch (1933) and

Carman (1937) developed a model for predicting Darcy resistance from the characteristics of the

porous media And Ergun (Ergun and Orning 1949 Ergun 1952) combined the linear and

nonlinear models to produce one comprehensive model of porous media flow appropriate for a

wide range of Reynolds numbers

14

In the laminar range of flow the Kozeny equation (Fair et al 1968) is used to depict the

head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where

h = head loss in depth of bed

L = depth of filter bed

g = acceleration of gravity

ε = porosity

va

= grain surface area per unit of grain volume = specific surface (Sv) = for spheres

and

d6

eqdψ6

for irregular grains

eqd = grain diameter of sphere of equal volume

V = superficial velocity above the bed = flow ratebed area (ie the filtration rate)

μ = absolute viscosity of fluid

ρ = mass density of fluid

k = the dimensionless Kozeny constant commonly found close to 5 under most filtration

conditions (Fair et al 1968)

The Kozeny equation is generally acceptable for most filtration calculations because the

Reynolds number Re based on superficial velocity is usually less than 3 under these conditions

and Camp (1964) has reported strictly laminar flow up to Re of about 6 (Cleasby and Logsdon

1999)

μρ Re Vdeq= Eq 8

15

It was found that the actual head loss was often greater than that predicted from the

Kozeny equation particularly when higher velocities are used in some applications or when

velocities approached fluidization (as in backwashing considerations) In this case the flow may

be in the transitional flow regime where the Kozeny equation is no longer adequate Ergun and

Orning (1949) employed the hydraulic radius approach which Carman and Kozeny used to

characterize linear losses to develop a term for kinetic losses The results were nearly the same as

Eq 7 To create an equation for losses though porous media over a wide range of flow conditions

Ergun and Orning added the Kozeny term for linear losses The Ergun equation is adequate for

the full range of laminar transitional and inertial flow through packed beds (Re from 1 to 2000)

Compared with the Kozeny equation the Ergun equation includes a second term for inertial head

loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9

Note that the first term of the Ergun equation is the viscous energy loss that is

proportional to V The second term is the kinetic energy loss that is proportional to V2

Comparing the Ergun and Kozeny equations the first term of the Ergun equation (viscous energy

loss) is identical with the Kozeny equation except for the numerical constant The value of the

constant in the second term k2 was originally reported to be 029 for solids of known specific

surface (Ergun 1952a) In a later paper however Ergun reported a k2 value of 048 for crushed

porous solids (Ergun 1952b) a value supported by later unpublished studies at Iowa State

University The second term in the equation becomes dominant at higher flow velocities because

it is a square function of V (Cleasby and Logsdon 1999) As is evident from Eq 7 and 9 the

head loss for a clean bed depends on the flow rate media size porosity sphericity and water

viscosity

Chapter 3

MATERIALS AND METHODS

Filter Setup

The filter study was carried out in the Kappe Environmental Engineering Laboratory at

the University Wastewater Treatment Plant University Park Pennsylvania USA A pilot filter

(Figure 3-1) was constructed with 152-cm-diameter transparent PVC columns A water pump

was used to supply the influent and backwash flow from a water storage tank An air pump was

connected to the bottom of the filter for air scour before water backwashing Filtration rate was

controlled by a flow meter installed in the filter outlet pipe Influent water was kept constant by

an overflow at 329 meters The head loss through the filter media was measured using the

difference between the water level in the filter and the water level in the glass tube connected to

the bottom of the filter

Filter Media

The crumb rubber media size was determined by sieve analysis using American Society

for Testing and Materials (ASTM) Standard Test C136-01 Sieve analysis of Fine and Coarse

Aggregates (ASTM 2001) As summarized in Table 2-1 the effective size (for which 10 of the

grains are smaller by weight) was 066 mm 120 mm and 190 mm for the size range of 05-12

mm 12-20 mm and 20-40 mm crumb rubber media Their uniformity coefficients were

determined to be 139 153 and 128 respectively and the packed porosity was 062 058 and

17

054 for 066 mm 120 mm and 190 mm crumb rubber media respectively The density of all

crumb rubber media was 1130 kgm3

Figure 3-1 Experimental setup of the crumb rubber filter

18

Design and Operational Conditions

Factorial design was used in this study The approach reduced the experimental burden

while was effective in seeking high quality results to analyze the effects of factors and

interactions Three levels of crumb rubber media sizes and media depths and 19 filtration rates

were investigated The filter was loaded with 066 mm 120 mm and 190 mm crumb rubber

media at each time For each crumb rubber medium the filter was loaded to a depth of 06 m 09

m and 12 m Before each filter run the filter was backwashed by air scour and then water flow

at the rate of 293 m3m2h For each filter configuration the filter was operated at 19 filtration

rates from 0 to 733 m3m2h Head loss was measured after the media depth was stable Porosity

was determined by the measurement of the dry weight of the media initially loaded to the filter

columns and the media depth (Eq 1)

The Kozeny and Ergun Equations

In the laminar range of flow the Kozeny equation (Fair et al 1968) can be used to depict

the head loss (Eq 7) which is proportional to filtration rate (V) media depth (L) porosity term (

( )3

21εεminus

) and media size term ( 2)6(eqdψ

) The equation is generally acceptable for the flow that

has the Reynolds number (Re) less than 6 (Cleasby and Logsdon 1999)

The Ergun equation (Eq 9) has an additional term which is proportional to V2 in

addition to the Kozeny equation to depict the inert head loss The equation is adequate for the full

range of laminar transitional and inertial flow The first term of the Ergun equation is identical

to the Kozeny equation except for the numerical constant (Cleasby and Logsdon 1999) The

constant of the second term (k2) was reported to be 048 for crushed porous solids (Ergun 1952)

19

The sphericity for crumb rubber media is the only unknown parameter in the two equations Their

values were determined by empirical fitting of data from the filtration tests

Statistical Modeling

A total of 171 filtration data sets were collected (3 media sizes times 3 media depths times 19

runs) Based on statistical requirements 70 of data sets were chosen to initiate the regression

and the remaining 30 were used to validate the corresponding regression results Regressions

were performed using a least squares criterion and assuming that the residuals were normally

distributed and independent and had constant variance These assumptions were checked after

the model had been fitted Sigma Plot 100 (SPSS Inc Chicago IL) was used to initiate the

fitting process for media sphericity and to conduct the statistical multiple nonlinear regression for

developing a statistical model

For the regression process for media sphericity each data set consisted of values of an

actual head loss its corresponding filtration rate compressed media depth at this filtration rate

porosity at the compressed media depth and media size Data except actual head loss were used to

calculate head losses based on the Kozeny or Ergun equation Regressions were then performed

by varying the sphericity values in the two equations to obtain the best fit of the estimated head

loss data to the actual head loss data

For the regression process for a statistical model each data set consisted of values of an

actual head loss its corresponding filtration rate media size and initial media depth Data except

actual head loss were used to calculate estimated head losses based on a multiplicative power-law

relationship Then regressions were performed by varying the model coefficients to obtain the

best fit between the calculated head loss data and the actual head loss data

20

Regression Verification

For each attempted fit of sphericity to actual head loss data the hypotheses tested were

that the derived sphericity of the equation was significantly different from zero Expressed

mathematically the hypothesis was as follow s

0

0

Similarly the hypotheses tested for each coefficient of the statistical model were as

follows

For numerical constant K

0

0

For exponent of filtration rate a

0

0

For exponent of media depth b

0

0

For exponent of media size c

0

0

By examining the p-value of each coefficient the null hypothesis can be rejected and the

alternative one can be concluded if the p-value was very small (lt005 in this study)

Analysis of Means (ANOM) was performed using two-sample t-test for some cases

where comparison of model coefficients was necessary For example when comparing the

21

sphericity estimates from the Kozeny and Ergun equations the hypothesis tested was that the

derived sphericity estimates from the Kozeny equation was significantly different from the one

from the Ergun equation Expressed mat m ical e hypothesis was as follows he at ly th

If the variances were not quite different pooled variance t-test was applied by using the

following equations to compute the t-statistic (Ott and Longnecker 2000)

1 1

With degrees of freedom equal to 2

2 Eq 10

1 1 Eq 11

If the variances were quite different separate variance t-test was applied by using the


With degrees of freedom equal to where frasl

Eq 12

By comparing the computed t-statistic with the corresponding one in the t-table the null

hypothesis can be rejected and the alternative one can be concluded if or

where α=005 in this study

Coefficient of determination (R2) is another criterion to verify these regressions It

represents the proportion of the total variability in the dependent variables that the regression

equation accounts for (Burton and Pitt 2001) as expressed in the following equation

22

Where SSerr is the sum of squared errors and SStot is the total sum of squares

R 1ssSS

Eq 13

An R2 of 10 indicates that the equation accounts for all the variability of dependent

variables and it is generally good and indicates a strong relation if R2 is large But it does not

guarantee a useful equation since high R2 can occur with insignificant equation coefficient if

only a few data observations are available Regressions in this study were validated based on the

following steps (1) examining the regression R2 and verification R2 (2) examining the residuals

of the resultant regressions statistically and graphically In addition the standard error of each

estimate which was computed from the variance of the predicted values was given as a measure

of the model variability

Graphical analyses of regressions were performed by examining the following

requirements according to Draper and Smith 1981 (1) residuals are independent (2) residuals

have zero mean (3) residuals have constant variance and (4) residuals follow a normal

distribution The purpose was to determine if the assumption of the regression error being

independent and normally distributed was valid Verification of the assumption of independent

residuals was performed by graphically plotting the residuals against its variables (filtration rate

media depth and media size) and observed values For this assumption to be valid the residuals

should be randomly distributed in these four plots around a zero line Verification of the

assumption of normal distribution of residuals was performed using a normal probability plot

Residuals that fall along a straight line in the plot and fall into the 95 confidence interval are

considered to be normally distributed If residuals fail to pass any one of these tests then the

regression is not valid for the data

Analysis of Variances (ANOVA) was performed to check constant variances for some

instances of the models if they passed the independence and normality tests The hypothesis

23

tested was that the variances were significantly different from each other The mathematical

expression was as follows

0

0

The Levenersquos test was performed with the assistance of MINITAB 15 (The Minitab Inc)

If the p-value was small (lt01 in this case) the null hypothesis can be rejected and the alternative

one can be concluded that the variances were not equal

Chapter 4

RESULTS AND DISCUSSION

Media Sphericity

Sphericity a physical parameter that defines the roundness of the media shape has to be

provided if the Kozeny and Ergun equations are used For crumb rubber media their values were

estimated by empirical fitting of the actual head loss data to the predicted head loss data

computed by the two equations using the compressed media depth and porosity Two initial

assumptions were made before the regressions (1) Sphericity values for different media sizes

were the same and (2) Sphericity values at different operating conditions were the same Based

on that regressions were first performed using 70 of all data sets without differentiating media

sizes However the residuals of both equations could not pass the normality test and therefore

made the regressions invalid indicating that the assumptions could be partially wrong The first

assumption was then modified as Sphericity values for different media sizes were different With

the modified assumptions regressions were individually performed using 70 of data sets of

each media size and the results were summarized in Table 4-1 The Kozeny equation gave a

sphericity of 067 064 and 062 while the Ergun equation gave a sphericity of 071 075 and

079 for the 066 mm 120 mm and 190 mm crumb rubber media respectively All the p-values

were less than 00001 showing these coefficients were significant Two-sample t-test indicated

that a decreasing trend did not exist for the estimates from the Kozeny equation while there was

an increasing trend for the estimates from the Ergun equation In addition it was statistically

proved that the Ergun equations gave a higher sphericity estimate than the Kozeny equation The

95 confidence intervals gave a range of variability for those estimates It has to be pointed out

25

that the regressions for 066 mm and 190 mm media failed the normality test showing that the

second assumption could be wrong for the two sizes That is for the 120 mm crumb rubber

media it was acceptable to assume sphericity did not change due to compression but for the

other two sizes this assumption might be invalid But these estimates still could be applied in the

evaluation process of two equations since they were able to provide the highest regression R2 and

verification R2 which addressed the most variability of dependent variables

Table 4-1 Sphericity estimates by the Kozeny and Ergun equations for crumb rubber media

Prediction by the Kozeny Equation

Figure 4-1 compared the actual head loss with the predicted head loss by the Kozeny

equation using the original and compressed media depth and porosity respectively to evaluate

the applicability of the equation in crumb rubber filters The 45-degree-line in the figure depicted

the hypothetic head loss estimates that were precisely equal to the actual values It was found in

Figure 4-1a that the R2 value was only 087 and the Kozeny equation under-estimated head loss

especially at high filtration rates at each filter medium configuration This implied that the

Kozeny equation has limitation for crumb rubber filters if no compressed media depth and

porosity were available to compensate the media compression The under-estimation was likely

due to the decreased porosity resulted from the decreased media depth

When the Kozeny equation was examined by using the compressed media depth and

packed porosity it was found in Figure 4-1b that the Kozeny equation could give better predicted

values using the appropriate sphericity estimates Regression of predicted and actual head loss

data by the 45-degree-line gave a R2 of 097 which indicated that predicted data by the Kozeny

equation was close to the actual head loss data and the equation could be used for crumb rubber

filters However it was also noticed in the figure that some predicted data at high actual head loss

values were under-estimated which indicate that the equation had limitation when the filtration

rate was high at each filter medium configuration

28

Figure 4-1 Prediction of clean-bed head loss by the Kozeny equation (a) Prediction using theoriginal media depth and porosity (b) Prediction using the compressed media depth and porosity

Figure 4-2 shows the residuals of the Kozeny equation against three variables and actual

head loss It was found that the residuals were independent against filter depth and media size

29

because they were almost centered at the zero line (Figure 4-2 b and c) but they were dependent

on filtration rate and actual head loss because as filtration rate or actual head loss increased

residuals went from positive to negative values (Figure 4-2 a and d) In addition to relatively

lower R2 shown in Figure 4-1 analysis of residuals is against the criterion of independent

residuals as a good model Therefore the Kozeny equation had limitations and the derived

sphericity estimates could not describe the real shape of grains

Figure 4-2 Residual analysis of the Kozeny equation using compressed media depth and porosity

Prediction by the Ergun Equation

To examine the performance of the Ergun equation in the changing environment of

configurations in crumb rubber filters the original media depth and packed porosity were used to

30

calculate the head loss which were then compared with actual head loss as was shown in

Figure 4-3a It was found that the Ergun equation gave a R2 of 095 as well as under-estimation of

head loss when the actual head losses were higher than 100 cm at high filtration rates However

the under-estimation was not as great as that of the Kozeny equation using the same data sets of

original media depth and porosity and the R2 value was also higher than that of the Kozeny

equation This suggested that although the inert head loss included by the Ergun equation could

adjust the predicted data at high filtration rates it was still not sufficient to address the head loss

increase caused by the decrease of porosity due to media compression

Same with the testing procedures for the Kozeny equation the data sets of compressed

media depth and porosity from field study were applied to reflect the effect of media

compression The predicted head loss data were calculated by the Ergun equation and were

compared with the actual head loss data As shown in Figure 4-3b it was found that the R2 value

was 099 which indicated that the Ergun equation might be suitable for crumb rubber filters

Comparing the R2 value with that of the Kozeny equation the Ergun equation had higher R2 and

showed better fit to the actual head loss In addition the Ergun equation did not under-estimate

data at high filtration rates in the way the Kozeny equation did This was because the inert head

loss shown as the second term in the Ergun equation was able to adjust the prediction of head loss

development at high filtration rates by portraying a linear relationship not between h and V but

between h and V2

31

Figure 4-3 Prediction of clean-bed head loss by the Ergun equation (a) Prediction using the original media depth and porosity (b) Prediction using the compressed media depth and porosity

Figure 4-4 shows the residuals of the Ergun equation against three variables and actual


32

because they were centered at the zero line (Figure 4-4 b and c) For the filtration rate however

the equation only displayed good residuals distribution when the filtration rate was high

indicating that the residuals were conditionally independent on filtration rate (Figure 4-4 a) And

they were dependent on actual head loss because when actual head loss was high residuals went

negatively higher (Figure 4-4 d) Although the R2 of the Ergun equation was relatively higher as

shown in Figure 4-3 analysis of residuals is against the criterion of independent residuals as a

good model Therefore the Ergun equation also had limitations although not as severe as the

Kozeny equation

Figure 4-4 Residual analysis of the Ergun equation using compressed media depth and porosity

33

Development of a Statistical Model

Both the Kozeny and Ergun equations had deficiencies for the prediction of clean-bed

head loss in crumb rubber filters and they may provided better fit when the data of compressed

media depth and porosity were used to reflect the media compression Their predictions using the

data of original media depth and porosity however could not provide the same degree of

comparison at all to the actual head loss data

The benefits of developing a statistical model for crumb rubber media are obvious (1)

No filtration tests need to be conducted to obtain the compression situations on media depth and

porosity (2) No hassle to derive a sphericity estimate since this value varies to the filtration

conditions and (3) the conventional equations are not good models for crumb rubber filtration

The statistical model development used a multiplicative power-law relationship which

resembled the Kozeny equation The model expressed in Eq 14 consisted of the three factors

examined in this study as independent variables filtration rate media depth and media size

ceq

ba dLVKh )()()(= Eq 14

Where

K = dimensionless constant for the statistic model

a = exponent of filtration rate

b = exponent of media depth

c = exponent of media size

Exponents of each factor and the numerical constant were obtained via regression using

70 of data sets The regression results were summarized in Table 4-2 The initial assumption of

the regression was that the model coefficients were the same for all media sizes However the

resultant group of coefficients failed the normality test indicating a probably wrong assumption

34

The assumption was then modified as the model coefficients were different among media sizes

The model then had a form as follows

ba LVKh )()(= Eq 15

Regressions were then performed individually using 70 of data sets for each media

size and all the three groups of coefficients passed the normality tests The p-values were less

than 00001 indicating that the coefficients were significant Standard errors and 95 confidence

intervals gave the ranges of the variability Regression R2 and verification R2 of the model were

higher than 0996 which demonstrated a potential to be a good model

Table 4-2 Parameters in the statistical model

Effect of Parameters

Three design and operational parameters (Media size media depth and filtration rate)

were investigated for their effects Figure 4-5 shows the actual head loss profile at all filter

configurations Factorial calculations were conducted by using these data to explore the effects of

factors and possible interactions

Figure 4-5 Actual head loss profiles at all filter configurations

37

Although three-level factorial design was conducted in this experiment only the

results of medium and high level factorial calculation were shown in Figure 4-6 because the

results would be more meaningful since crumb rubber filters were usually designed to operate

at medium and high levels of filtration rates Four of seven effects were judged significant by

Lenthrsquos method (Lenth 1989) with the significance level of 005 The threshold value was

denoted by the vertical line and factors filtration rate media depth media size interaction

between filtration rate and media depth and interaction between filtration rate and media size

were determined to have significant effects The interaction between filtration rate and media

depth could be explained by the compression as the filtration rate increases which

correspondingly decreases media depth and therefore confounds head loss The interaction

between filtration rate and media size although very small was likely due to the change of

sphericity during compression because the assumption of equal sphericity at different

filtration conditions were proved to be wrong for some media sizes It is obvious that the

Kozeny and Ergun equations could not be able to address these distinctive effects of crumb

rubber media The statistical model developed by the multiplicative power-law relationship

could be used to analyze these effects on clean-bed head loss in crumb rubber filters

Interaction between filter depth and media size and interaction between all three factors were

statistically insignificant therefore they were not included in the following discussion

38

Figure 4-6 Pareto chart of the standardized effects showing the results of medium and high level factorial calculation (Response is observed head loss in centimeters Significance level = 005)

Effect of filtration rate

The exponents of filtration rate shown as 155 151 and 175 for 066 mm 120 mm

and 190 mm crumb rubber media in the statistical model were all higher than 1 found in the

Kozeny equation This could explain the under-estimation of the Kozeny equation because the

filtration rate in crumb rubber filters had a larger impact than that in other conventional granular

media filters This caused the actual head loss to increase faster when the filtration rate was high

The faster increase was due to the rapid development of inert head loss that could not be

addressed by a linear relationship between head loss and filtration rate

39

Effect of interaction between filtration rate and media depth

The larger exponent of filtration rate was also believed to be caused by the interaction

between filtration rate and media depth due to compression of the filter media which was shown

in Figure 4-7 The filter depth was decreased as the filtration rate increased It was found that the

crumb rubber filter that had media size of 12 mm and filter depth of 09 m was compressed by

9 as the filtration rate increased from 0 to 73 m3m2h However for conventional granular

filters the filter depth and filtration rate were independent parameters In crumb rubber filters the

phenomenon could not be addressed by the conventional head loss models

Filtration rate (m3hourm2)

0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116

Figure 4-7 Impact of filtration rate on filter depth for a crumb rubber filter that has media size of120 mm and filter depth of 09 m

40

Effect of media depth

The exponents of media depth shown as 135 097 and 121 for 066 mm 120 mm and

190 mm crumb rubber media in the statistical model showed the influence of media compression

on clean-bed head loss because the exponent was found to be 1 in both the Kozeny and Ergun

equations The effect of media compression in crumb rubber filters was complicated according to

the head loss theories The compression decreased the media depth which could decrease head

loss but it also decreased the porosity at the same time which could increase head loss Figure 4-

8 showed the media depth and porosity terms change at one filter configuration It was found that

for a crumb rubber filter loaded with 066 mm crumb rubber media to a depth of 06 m as the

filtration rate gradually increased from 0 to 733 m3m2h the media depth was steadily decreased

by 136 However the decrease in media depth did not cause a corresponding decrease in its

exponent which was used to be 1 as shown in the Kozeny and Ergun equations In fact the

exponent of media depth was increased to 135 because the porosity term 3

2)1(εεminus

was increased

by 695 due to the compression The porosity term 3

)1(εεminus

in the second part of the Ergun

equation did not increase as much as the term 3

2)1(εεminus

in Kozeny equation which only

increased by 464 But it still played an important role when the filtration rate was high and the

inert head loss was dominant Therefore the exponent of media depth implied the overall

influence of media depth decrease and porosity terms increase in crumb rubber filters

41

Figure 4-8 Impact of media compression for the filter configuration of 066 mm crumb rubber media and 06 m media depth

Effect of media size

The exponents of media size shown as -154 in the statistical model which did not

differentiate media sizes was between -2 in the Kozeny equation and -1 in the second term of

Ergun equation indicating that the Ergun equation might be able to address the effect of this

factor while the Kozeny equation could not

42

Effect of interaction between media size and filtration rate

Filtration rate affected crumb rubber media by changing their sphericity The assumption

of equal sphericity at one filter configuration was unacceptable for some media sizes when their

sphericity estimates were verified None of conventional equations could address this problem

yet since they both assumed that sphericity did not change However it was not necessarily the

case for crumb rubber media Compression could change the shape of the media especially when

the filters were operated at higher filtration rates which correspondingly exerted higher pressure

to change the media shape

Prediction by the Statistical Model

Because the statistical model was developed using actual head loss initial media depth

filtration rate and media size it had included the effect of media compression that changes the

filter configurations Also it addressed the problem encountered by the Kozeny and Ergun

equations that is test must be conducted at all filtration rates to obtain the data of compressed

media depth and porosity Figure 4-9 showed the comparison of actual head loss and predicted

head loss data by the statistical model at all filter configurations The statistical model did not

under-estimate head loss at high filtration rates in the way the Kozeny and Ergun equation did

The R2 value was as high as 0998

43

Figure 4-9 Prediction of clean-bed head loss by the statistical model

Figure 4-10 shows the residuals of the statistical model against three variables and actual

head loss It was found that the residuals were independent against all variables since they were

all centered at the zero line In addition when the hypothesis of equal variances of residuals

against actual head loss was tested the p-value for Levenersquos test was 0122 Comparing to

01 the default choice for rejecting the hypothesis of equal variances the p-value was

higher and therefore no conclusion could be made that they were not equal Because normality

independence and constant variances all applied the statistical model was valid for head loss

prediction of crumb rubber filters

44

Figure 4-10 Residual analysis of the statistical model using initial media depth and porosity

Chapter 5

CONCLUSIONS

(1) Both the Kozeny and Ergun equations were unacceptable for clean-bed head loss

prediction in crumb rubber filters especially when the test data of compressed media depth and

porosity were unavailable to compensate the media compression

(2) The effects of filtration rate media depth media size and their interactions in crumb

rubber filters were different from conventional granular media filters due to the media

compression

(3) A statistical model developed by the multiplicative power-law relationship is able to

predict clean-bed head loss in crumb rubber filters using the data of original media depth

filtration rate and media size The model is statistically valid and can be applied for crumb rubber

filtration

BIBLIOGRAPHY

Abdul-Wahab SA Bakheit CS and Al-Alawi SM (2005) Principle component and multiple

regression analysis in modeling of ground-level ozone and factors affecting its

concentrations Environmental Modeling and Software 20 1263

American Society for Testing and Materials (1993) Concrete and Aggregates 1993 Annual Book

of ASTM Standards Vol 0402 Philadelphia Pennsylvania ASTM

Bear J (1972) Dynamics of fluids in porous media Dover New York

Chen P (2004) Ballast water treatment by crumb rubber filtration ndash a preliminary study

Graduate Thesis Environmental Pollution Control Program at Penn State Harrisburg

Pennsylvania USA

Cleasby J L and Logsdon G S (1999) Granular Bed and Precoat Filtration Chap 8 in R D

Letterman (ed) Water Quality and Treatment A Hankbook of Community Water

Supplies McGraw-Hill New York

Ergun S and Orning A (1949) Fluid flow through randomly packed columns and fluidized

beds Inds and Engrg Chem 41(6) 1179-1184

Carman P (1937) Fluid flow through granular beds Trans Inst Of Chemical Engrg 15 150

47

Drapner NS Smith H (1981) Applied regression analysis 2nd ed John Wiley and Sons Inc

New York

Ergun S (1952) Fluid flow through packed columns Chem Eng Prog 48 2 89-94

Fair G Geyer J and Okun D (1968) Water and wastewater engineering Vol2 Water

purification and wastewater treatment and disposal Wiley New York

Fair G M and Hatch L P (1933) Fundamental Factors Governing the Streamline Flow of

Water through Sand J AWWA 25 11 1551-1565

Graf C and Xie Y F (2000) Gravity downflow filtration using crumb rubber media for tertiary

wastewater filtration Keystone Water Quality Manager 33 12-15

Crittenden JC et al (2005) Granular filtration Chap 11 in 2nd ed Water treatment principles

and design John Wiley amp Sons Inc Hoboken New Jersey

Hsiung S ndashY (2003) Filtration using a crumb rubber filter medium preliminary studies using

secondary wastewater effluent as feed MS thesis the Pennsylvania State University

University Park PA USA

Kozeny J (1927a) Ueger Kapillare Leutung des Wassers im Boden (On Cappillary Conduction

of Water in Soil) Sitzungsbericht Akad Wiss 136 271-306 Wein Austria

48

Kozeny J (1927b) Ueger Kapillare Leutung des Wassers im Boden (On Cappillary Conduction

of Water in Soil) Wasserkraft Wasserwirtschaft 22 67-78

Lang J S Giron J J Hansen A T Trussell R R and Hodges W E J (1993) Investigating

Filter Performance as a Function of the Ratio of Filter Size to Media Size J AWWA 85

10 122-130

Lenth RV (1989) Quick and easy analysis of unreplicated factorials Technometrics 31 469-

473

Ott RL Longnecker MT (2000) An introduction to statistics and data analysis 5th ed

Duxbury Press Florence Kentucky USA

Rubber Manufacturer Association (2002) US Scrap tire market 2001 Washington DC

Sunthonpagasit N amp Hickman HL Jr (2003) Manufacturing and utilizing crumb rubber from

scrap tires MSW Management 13

Tang Z Butkus M A and Xie Y F (2006a) Crumb rubber filtration A potential technology

for ballast water treatment Marine Environmental Research 61(4) 410-423

Tang Z Butkus M A and Xie Y F (2006b) The Effects of Various Factors on Ballast Water

Treatment Using Crumb Rubber Filtration Statistic Analysis Environmental

Engineering Science 23(3) 561-569

49

Trusell R Chang M (1999) Review of flow through porous media as applied to head loss in water

filters J Environ Eng 125 11 998-1006

Trussell R R Chang M M Lang J S Guzman V and Hodges W E Jr (1999) Estimating

the Porosity of a Full-Scale Anthracite Filter Bed J AWWA 91 12 54-63

Trussell R R Trussell A Lang J S and Tate C (1980) Recent Developments in Filtration

System Design J AWWA 72 12 705-710

United States Environmental Protection Agency (USEPA) (1993) Scrap tire handbook EPA905-

K-001 USEPA Region 5 USA October

United States Environmental Protection Agency (USEPA) (2006) Scrap tire cleanup guidebook

EPA-905-B-06-001 USEPA Region 5 and Illinois EPA Bureau of Land USA January

Xie Y Bryon K Gaul A (2001) Using crumb rubber as a filter media for wastewater filtration

2001 Technical Meeting of American Chemical Society Rubber Division Cleveland

OH USA

MS_Thesispdf

Chapter 1INTRODUCTION



Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory

Chapter 3MATERIALS AND METHODS

Filter Setup

Filter Media





Chapter 4RESULTS AND DISCUSSION

Media Sphericity





Although three-level factorial design was conducted in this experiment only the results of medium and high level factorial calculation were shown in Figure 4-6 because the results would be more meaningful since crumb rubber filters were usually designed to operate at medium and high levels of filtration rates Four of seven effects were judged significant by Lenthrsquos method (Lenth 1989) with the significance level of 005 The threshold value was denoted by the vertical line and factors filtration rate media depth media size interaction between filtration rate and media depth and interaction between filtration rate and media size were determined to have significant effects The interaction between filtration rate and media depth could be explained by the compression as the filtration rate increases which correspondingly decreases media depth and therefore confounds head loss The interaction between filtration rate and media size although very small was likely due to the change of sphericity during compression because the assumption of equal sphericity at different filtration conditions were proved to be wrong for some media sizes It is obvious that the Kozeny and Ergun equations could not be able to address these distinctive effects of crumb rubber media The statistical model developed by the multiplicative power-law relationship could be used to analyze these effects on clean-bed head loss in crumb rubber filters Interaction between filter depth and media size and interaction between all three factors were statistically insignificant therefore they were not included in the following discussion







Chapter 5CONCLUSIONS

BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

The thesis of Hao Tang was reviewed and approved by the following

Yuefeng F Xie Professor of Environmental Engineering Thesis Co-Advisor

John M Regan Associate Professor of Environmental Engineering Thesis Co-Advisor

Shirley E Clark Assistant Professor of Environmental Engineering

Peggy A Johnson Professor of Civil Engineering Head of the Department of Civil amp Environmental Engineering

Signatures are on file in the Graduate School

iii

ABSTRACT














iv

TABLE OF CONTENTS

LIST OF FIGURES v

LIST OF TABLES vi













Bibliography 46

v

LIST OF FIGURES

















vi

LIST OF TABLES





vii

ACKNOWLEDGEMENTS







Chapter 1

INTRODUCTION





















2















3





data



filtration


Thesis Organization





Chapter 2

BACKGROUND







reduction














5
























6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

iii

ABSTRACT














iv

TABLE OF CONTENTS

LIST OF FIGURES v

LIST OF TABLES vi













Bibliography 46

v

LIST OF FIGURES

















vi

LIST OF TABLES





vii

ACKNOWLEDGEMENTS







Chapter 1

INTRODUCTION





















2















3





data



filtration


Thesis Organization





Chapter 2

BACKGROUND







reduction














5
























6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

iv

TABLE OF CONTENTS

LIST OF FIGURES v

LIST OF TABLES vi













Bibliography 46

v

LIST OF FIGURES

















vi

LIST OF TABLES





vii

ACKNOWLEDGEMENTS







Chapter 1

INTRODUCTION





















2















3





data



filtration


Thesis Organization





Chapter 2

BACKGROUND







reduction














5
























6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

v

LIST OF FIGURES

















vi

LIST OF TABLES





vii

ACKNOWLEDGEMENTS







Chapter 1

INTRODUCTION





















2















3





data



filtration


Thesis Organization





Chapter 2

BACKGROUND







reduction














5
























6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

vi

LIST OF TABLES





vii

ACKNOWLEDGEMENTS







Chapter 1

INTRODUCTION





















2















3





data



filtration


Thesis Organization





Chapter 2

BACKGROUND







reduction














5
























6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

vii

ACKNOWLEDGEMENTS







Chapter 1

INTRODUCTION





















2















3





data



filtration


Thesis Organization





Chapter 2

BACKGROUND







reduction














5
























6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

Chapter 1

INTRODUCTION





















2















3





data



filtration


Thesis Organization





Chapter 2

BACKGROUND







reduction














5
























6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

2















3





data



filtration


Thesis Organization





Chapter 2

BACKGROUND







reduction














5
























6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

3





data



filtration


Thesis Organization





Chapter 2

BACKGROUND







reduction














5
























6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

Chapter 2

BACKGROUND







reduction














5
























6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

5
























6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

6

Where


Eq 1








7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

7



















8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

8




9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

9









10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

10










=ψ Eq 2

ψξ 6= Eq 3

where










11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

11
















treatment

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

12


Head Loss Theory




13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

13




[ ]0HLHL

KAQ minusΔ+Δ

= Eq 4

Where










⎥⎦⎤

⎢⎣⎡ΔΔ

=LHK

AQ

Eq 6







14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

14


head loss

( ) Vva

gk

Lh 2

3

21⎟⎠⎞

⎜⎝⎛minus

=εε

ρμ Eq 7

where




ε = porosity

va


and

d6

eqdψ6











1999)

μρ Re Vdeq= Eq 8

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

15











loss

( ) ( )g

VvakV

va

gLh 2

32

2

3

2 11174εε

εε

ρμ minus

+⎟⎠⎞

⎜⎝⎛minus

= Eq 9











viscosity

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

Chapter 3


Filter Setup










Filter Media







17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

17




18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

18















( )3

21εεminus









19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

19























20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

20





0

0


follows


0

0


0

0


0

0


0

0





21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

21






1 1


2 Eq 10

1 1 Eq 11




Eq 12







22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

22


R 1ssSS

Eq 13























23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

23



0

0




Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

Chapter 4


Media Sphericity




















25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

25


























28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY




















28




29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

29











30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

30



















between h and V2

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

31




32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

32








Kozeny equation


33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

33














ceq


Where









34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

34



ba LVKh )()(= Eq 15













37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY








37



















38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

38










39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

39










0 20 40 60 80

Filte

r dep

th (c

m)

102

104

106

108

110

112

114

116


40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

40














2)1(εεminus

was increased


)1(εεminus



2)1(εεminus





41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

41







42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

42


















43










44


Chapter 5

CONCLUSIONS






compression




filtration

BIBLIOGRAPHY









Pennsylvania USA







47


New York















48





10 122-130


473











49













OH USA

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

MS_Thesispdf




Thesis Organization

Chapter 2BACKGROUND




Head Loss Theory


Filter Setup

Filter Media






Media Sphericity













BIBLIOGRAPHY

prediction of clean-bed head loss in crumb rubber filters

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