Anthony Godlove PG/M.ED/11/58795 Anthony's... · 2015. 8. 29. · Anthony Godlove LMT DIMENSIONAL EQUATION FOR SLUDGE DRYING BED Coe nt mag er’s 1 PG/M.ED/11/58795 Engineering Coe

Anthony Godlove

LMT DIMENSIONAL EQUATION FOR SLUDGE DRYING BED

Content manager’s

1

Anthony Godlove

PG/M.ED/11/58795


Engineering

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Digitally Signed by: Content manager’s

DN : CN = Webmaster’s name

O= University of Nigeria, Nsukka

OU = Innovation Centre

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LMT DIMENSIONAL EQUATION FOR SLUDGE DRYING BED LMT DIMENSIONAL EQUATION FOR SLUDGE DRYING BED LMT DIMENSIONAL EQUATION FOR SLUDGE DRYING BED LMT DIMENSIONAL EQUATION FOR SLUDGE DRYING BED

ANTHONY GODLOVEANTHONY GODLOVEANTHONY GODLOVEANTHONY GODLOVE

PG/M.PG/M.PG/M.PG/M.ENG/ENG/ENG/ENG/11/5942611/5942611/5942611/59426

DEPARTMENT OF CIVIL ENGINEERING, DEPARTMENT OF CIVIL ENGINEERING, DEPARTMENT OF CIVIL ENGINEERING, DEPARTMENT OF CIVIL ENGINEERING,

FACULTY OF ENGINEERING, FACULTY OF ENGINEERING, FACULTY OF ENGINEERING, FACULTY OF ENGINEERING,

UNIVERSITY OF NIGERIA, NSUKKAUNIVERSITY OF NIGERIA, NSUKKAUNIVERSITY OF NIGERIA, NSUKKAUNIVERSITY OF NIGERIA, NSUKKA

JUNEJUNEJUNEJUNE, 2013, 2013, 2013, 2013

i


A THESIS WRITTEN

BY

ANTHONY GODLOVE

PG/M.ENG/11/59426

IN PARTIAL FULFILLMENT FOR THE AWARD OF MASTER

OF ENGINEERING (M. Eng.)IN WATER RESOURCES AND

ENVIRONMENTAL ENGINEERING

SUPERVISED BY

PROF. J.O. ADEMILUYI

DEPARTMENT OF CIVIL ENGINEERING,

FACULTY OF ENGINEERING,

UNIVERSITY OF NIGERIA, NSUKKA

JUNE 2013

ii

APPROVAL

This research study has been approved by the supervisor,Prof. J.O. Ademiluyi

and the Department of Civil Engineering, for Anthony Godlove with

registration number PG/M.Engr./11/59426.

___________________ _____________

Prof. J.O. Ademiluyi Date

Supervisor

___________________ _____________

Engr. Prof. O.O. Ugwu Date

HOD, Department of Civil Engineering

___________________ _____________

Ven. Prof. T.C. Madueme Date

Dean, Faculty of Engineering

iii

CERTIFICATION

Anthony Godlove, of Department of Civil Engineering with registration

number: PG/M.Engr./11/59426 has satisfactorily completed this research work

in partial fulfillment of the requirement for the award of Master in Engineering

in Water Resources and Environmental Engineering. The work embodied in this

thesis is original, and has not been submitted in part or complete for any other

certificate of other universities or similar institutions.

___________________ _____________

Prof. J.O. Ademiluyi Date

Supervisor

___________________ _____________

Engr. Prof. O.O. Ugwu Date

HOD, Department of Civil Engineering

___________________ _____________

Ven. Prof. T.C. Madueme Date

Dean, Faculty of Engineering

iv

DEDICATION

This thesis is dedicated to the Almighty God which bestowed on us the

gifts of wisdom, knowledge and understanding and also to my beloved parents

Mr. and Mrs. Anthony Nchari.

v

ACKNOWLEDGMENTS

I am very much grateful to my supervisor, Professor J.O. Ademiluyi of

the Department of Civil Engineering, University of Nigeria Nsukka, for his

guidance, advice and encouragement throughout my study to ensure that this

research work was a success. I would like to specially thank Engr. Professor

J.C. Agunwamba for his helpful advice on my project. With much gratitude I

would like to express my sincere acknowledgement to Arimieari .L. Wilcox for

her assistance and encouragement that enabled me to carry out my work

smoothly and in good order. My sincere gratitude goes to Engr. C. Anyanwu

and the staff of the Civil Engineering laboratory, University of Nigeria Nsukka,

who have been assisting me all through the period of the laboratory work. I am

thankful to all my colleagues for their friendship and suggestions most

especially Enya. A. Awka, Michael Okah and Ijeoma Onuigbo. I would like to

extend my thanks to my Pastor Rev. Daniel Ugwuoke for his invaluable advice,

encouragement and support that enabled me to complete this research work.

Finally I would like to thank my family members for their love, patience and

support toward the success of my research work.Director God’s Love Computer

Services Sis. Charity Chidiebere (Adoration Sister) I appreciate all your

patience and love while type setting this work. God bless you.

vi

ABSTRACT

A sludge drying bed of 1.2m by 0.75m was designed and used in dewatering

sewage sludge collected from the University of Nigeria, Nsukka wastewater

treatment plant. This was used to determine a modified LMT dimensional

equation incorporating the Compressibility Coefficient. The Specific Resistance

parameter of modified equation based on natural means of filtration was used to

determine the filterability of sludge, while the Compressibility Coefficient of

the derived equation was used to determine the Compressibility of sludge. From

the results of experiment for unconditioned sludge the Specific Resistance (R)

was calculated to be 2.1718x107 m/kg using the modified equation while

4.3435x107 m/kg was obtained from Carman equation. Ferric Chloride was used

to check the effect of conditioner on Specific Resistance, which gave the

following results: the Specific Resistance of 11.5144x107 m/kg, 9.9893x10

7

m/kg, 6.3264x107 m/kg, 5.0735x10

7 m/kg and 3.0857x10

7 m/kg for a

conditioner concentration of 10g, 20g, 30g, 40g and 50g respectively. From the

results of experiment Specific Resistance decrease as the amount of Ferric

Chloride increases. Also Ferric Chloride conditioning has influence on

Compressibility Coefficient of sludge. The results gave Compressibility

Coefficient (S) of 88.6 m2/

KN, 84.00 m2/KN, 81.1 m

2/KN, 74.7m

2KN, and 70.7

m2/KN. The result of the experiment shows that Ferric chloride has effect on the

filterability of sludge and the compressibility coefficient of sludge.

vii

TABLE OF CONTENTS

Title page .................................................................................................... i

Approval ..................................................................................................... ii

Certification ................................................................................................. iii

Dedication .................................................................................................. iv

Acknowledgment ........................................................................................ v

Abstract ...................................................................................................... vi

Table of contents ......................................................................................... vii

List of tables ................................................................................................ xi

List of figures .............................................................................................. xii

List of symbols ........................................................................................... xiii

CHAPTER ONE: INTRODUCTION

1.1 Background of Study .............................................................................. 1

1.2 Research Problems ................................................................................. 2

1.3 Significance of Study ............................................................................. 2

1.4 Objective of Study ................................................................................. 2

1.5 Scope and Limitationof the Research ..................................................... 3

CHAPTER TWO: LITERATURE REVIEW

2.1 Sewage Sludge Dewatering .................................................................... 4

2.2 Sludge Treatment Process .................................................................. 5

2.2.1 Thickening ......................................................................................... 5

2.2.2 Stabilization ....................................................................................... 5

viii

2.2.3 Conditioning ...................................................................................... 6

2.2.4 Dewatering .......................................................................................... 6

2.3 Operation Equipment ........................................................................ 7

2.3.1 Filter Presses ..................................................................................... 7

2.3.2 Belt Filter Presses.............................................................................. 7

2.3.3 Vacuum Filtration ............................................................................. 8

2.3.4 Centrifugation ................................................................................... 8

2.3.5 Drying Beds ....................................................................................... 9

2.3.6 Lagoons .............................................................................................. 12

2.4 Specific Resistance ........................................................................... 13

2.5 Compressibility of Sludge .................................................................. 14

2.6 Sludge Filtration Theories .................................................................. 14

2.6.1 Almy and Lewis (1912) ..................................................................... 14

2.6.2 Sperry (1916) ...................................................................................... 15

2.6.3 Baker (1921) ....................................................................................... 15

2.6.4 Weber and Hershey (1926).................................................................. 16

2.6.5 Carman (1934, 1938) .......................................................................... 16

2.6.7 Tiller (1953) ........................................................................................ 17

2.6.8 Anazodo (1974) ................................................................................. 17

2.6.9 White and Gale (1995) ........................................................................ 18

2.6.10 Hemant (1981) .................................................................................. 19

2.6.11 Ademiluyi, Anazodo and Egbuniwe (1982)....................................... 19

ix

2.6.12 Ademiluyi (1984) .............................................................................. 20

2.6.13 Ademiluyi et al (1985) ...................................................................... 21

2.6.14 Ademiluyi et al (1987) ...................................................................... 22

2.6.15 Ademiluyi et.al (2012) ...................................................................... 23

CHAPTER THREE: RESEARCH METHODOLOGY

3.1Study Area .............................................................................................. 24

3.2 Sample Collection .................................................................................. 24

3.3 Method of determining parameters ......................................................... 26

3.3.1 Solid Content ...................................................................................... 26

3.3.2 Volume of filtrate ............................................................................... 26

3.3.3 Area of filtration ................................................................................ 26

3.3.4 Time of filtrate ................................................................................... 26

3.3.5 Height of sludge ................................................................................. 26

3.3.6 Pressure of filtration ........................................................................... 26

3.3.7 Dynamic viscosity .............................................................................. 27

3.3.8 Specific Resistance of Sludge ............................................................ 27

3.3.9 Weight of dry solid ............................................................................ 28

3.3.10 Specific gravity of sludge ................................................................. 28

3.2.11 Percentage of solid content expressed as a decimal .......................... 28

3.3.12 Compressibility Coefficient .............................................................. 28

3.4 Effect of Conditioning on Specific Resistance of Sludge ...................... 28

3.5 Effect of Dilution on Specific Resistance ……………………………....29

3.6 Derivation of sludge filtration equation using Anazodo’s method ……29

x

CHAPTER FOUR: EXPERIMENTAL RESULTS AND DISCUSSION

4.1 Validation of Modified Equation ........................................................... 37

4.2 Effect of Chemical Conditioner on the Specific Resistance ................... 38

4.3 Effect of Hydrostatic Pressure on Specific Resistance ............................ 39

4.4 Effect of Dilution on Specific Resistance ............................................... 40

4.5 Comparisons of calculated value of Specific Resistance of

Modified Equation and Carman’s Equation .................................................. 41

CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS

5.1 Conclusion .............................................................................................. 44

5.2 Recommendations ................................................................................... 44

REFERENCES .......................................................................................... 43

APPENDICES ............................................................................................ 48

xi

LIST OF TABLES

Table 3.1: LMT Dimensions ........................................................................ 29

Table A1: Showing filtration of unconditioned sludge obtained on a

20 minutes interval for 12 hours......................................................... 48

Table B2: The Effect of Ferric Chloride on Specific Resistance

using one bucket of Sludge with 10g of Ferric Chloride .................... 50


using one bucket of Sludge with 20g of Ferric Chloride .................... 50

Table B4: The Effect of Ferric Chloride on Specific Resistance using

one bucket of Sludge with 30g of Ferric Chloride ............................. 51


using one bucket of Sludge with 40g of Ferric Chloride ................... 51


using one bucket of Sludge with 50g of Ferric Chloride ................... 52

Table C7: One Bucket of conditioned Sludge with one liter of

distilled Water.................................................................................... 53

Table C8: One Bucket of conditioned Sludge with two liters of

distilled Water.................................................................................... 53

Table C9: One Bucket of conditioned Sludge with three liters of

distilled Water.................................................................................... 54

Table C10: One Bucket of conditioned Sludge with four liters of

distilled Water.................................................................................... 54

Table C11: One Bucket of conditioned Sludge with five liters of

distilled Water.................................................................................... 55

xii

LIST OF FIGURES

Figure 3.1: schematic diagram of sand drying bed ........................................ 25

Figure 3.2: Graph of t/v against solid content................................................ 33

Figure 4.1: Graph of t/v against volume of filtrate ....................................... 37

Figure 4.2: Graph of Specific Resistance (R) against concentration

of Ferric Chloride ............................................................................... 38

Figure 4.3: Graph of Compressibility Coefficient (S) against concentration

of Ferric Chloride .............................................................................. 39

Figure 4.4: Graph of Specific Resistance (R) against Hydrostatic

Pressure. ............................................................................................. 40

Figure 4.5: Graph of Specific Resistance against Solid Content .................... 40

Figure 4.6: Graph of Compressibility Coefficient against Solid content ........ 41

Figure 4.7: Comparison of the Effect of Fecl3 on Specific Resistance

between Modified Equation and Carman’s Equation. ......................... 42

Figure 4.8: Comparison of the Effect of Fecl3 on Hydrostatic Pressure


Figure 4.9: Comparison of the Effect of Fecl3 on Solid Content


xiii

LIST OF SYMBOLS

A = Cross sectional area (m2)

V = Volume of filtrate (m3)

T = Time of filtration (Hrs)

H = Driving Head of sludge (m)

∆H = Change in sludge

R = Specific resistance (m/kg)

g = Acceleration due to gravity (m/s2)

µ = Dynamic viscosity of filtrate (N.S/m2)

ρ = Density of filtrate (kg/m3)

S = Compressibility coefficient (m2/KN)

b = Slope of t/v versus v (s/m6)

∆e = Change in void ratio

∆P = Change in pressure

P1 = Initial pressure (N/M2)

Wd = Weight of dry sludge (kg)

Ps = Percent of solid content expressed in decimal

C = Solid content (kg/m3)

VsI = Volume of sludge (m3)

SsI = Specific gravity of sludge

Hs = Sludge height (m)

1

CHAPTER ONE

INTRODUCTION

1.1 Background of Study

Sewage sludge is generated as a result of treating municipal wastewater

to remove organic and inorganic impurities from dilute solutions. Thepresence

of organic and inorganic impurities in sewage sludge arising from municipal

wastewater discharges poses a major problem and may be a deciding factor in

determining the choice of utilization of dewatering option (Ademiluyi et al

2012). The impurities accumulated in the sludge can render the material unfit

for any beneficial use. Wastewater treatment processes result in the production

of large volume of sludge. These sludge’s generated in wastewater management

process are difficult to handle and dispose of, because of their high water

content about 97.5% (Ademiluyi et al 1984).

Sludge can be dewatered using the natural sand drying beds and mechanical

methods (Vacuum filtration, filter press, and centrifugation). The natural sand

drying bed method is one of the earliest natural processes and most common

option used for sludge dewatering, before the introduction of mechanical

processes.

Drying beds method are usually used for small industrial or community

wastewater treatment plants to dewater sludge which rely on drainage and

evaporation to effect moisture reduction and also requires a large amount of

land for its operation.

2

The mechanical methods have the advantage of high capacity per unit of

space and are often used in large wastewater treatment plant.LMT (length, mass

and time) dimensional analysis is a mathematical technique used to check

derived equations and computations,(Rajput, 1998). The handling of sewage

sludge is one of the most significant challenges in wastewater management. In

many countries sewage sludge is a serious problem due to its high treatment

costs and the risks to environment and human health.

1.2 Research Problems

Since the treatment of sewage sludge by natural drying bed depends upon

climatic conditions, there is significant increase in the amount of time needed to

attain temperatures needed for volume reduction in colder climate.

1.3 Significance of Study

The significant of this study is that it will form a base for further research

work, into the development of dimensional equation of sludge filtration.

1.4 Objective of Study

The objectives of this study are summarized based on the following:

i. To incorporate the Compressibility Coefficient using LMT dimensional

analysis to formulate a sludge filtration equation.

ii. To investigate the effect of chemical conditioning on the Specific

Resistance and Compressibility Coefficients of sewage sludge.

3

1.5 Scope and Limitationof the Research

The scope of this research is limited to the domestic sewage sludge from

University of Nigeria, Nsukka wastewater treatment plant, based on natural

drying bed.

4

CHAPTER TWO

LITERATURE REVIEW

2.1 Sewage Sludge Dewatering

Generally, the wastewater discharged from domestic premises like

residences, institutions, and commercial establishments is termed as

“Sewage/Community wastewater”. It comprises of 99.9% water and 0.1%

solids and is organic because it consists of carbon compounds like human

waste, paper, and vegetable matter etc. Wastewater treatment processes result in

the production of large quantities of sludge. The word “sludge” can be defined

as solid sediment that results from wastewater treatment plants. Dewatering is a

physical unit operation used to reduce the moisture content of sewage sludge so

that it can be handled and/or processed as a semi-solid instead of liquid

(Metcalf & Eddy, 2004). Dewatering process increases solid content or sludge

between 20 to 35% (Agunwamba, 2001).

Dewatering is only one component of the wastewater solids treatment

process and must be integrated into the overall wastewater system so that

performance of both the liquid and solid treatment is optimized. This is a major

economical factor in the operation of wastewater treatment plants (Mehradadi,

et al, 2006). Dewatering of sewage sludge prior to drying or disposal is an

important step because the lower the water content of the sludge, the less costly

it will be the transport, the less liable to degradation and odour production, and

the easier it will be to dry. Typical approaches involve addition of conditioning

5

chemicals to increase the dewatering rate and improve filtrate quality (Octavio,

2007). Therefore sludge generated by waste water treatment plant must undergo

treatment process such as dewatering, stabilization, conditioning and thickening

before disposal to the environment.

2.2 Sludge Treatment Process

2.2.1 Thickening

Raw sludge is usually watery and contains about 2% solid. This

percentage depends on the characteristic of the sludge. Thickening is a process

used in increasing the solids content of sludge by removing the water content,

thereby reducing the volume of the sludge. The reduction in volume is

important in that it enables the designer to predict the capacity of tank or

equipment required for other units. Gravity thickening is the simplest and least

expensive process for consolidating waste sludge.

2.2.2 Stabilization

Stabilization is a process of making the sludge less odorous and

putrescible, and to reduce the pathogenic organisms. Through stabilization

nuisance are removed by the addition of chemical to the sludge and also by

chemical oxidation of volatile matters. Primary processes of stabilization are

aerobic digestion, anaerobic digestion, Heat treatment and thermochemical

treatment. The most practical process for stabilization has been anaerobic

digestion. During anaerobic digestion, the sludge is stabilized through

biological degradation of complete organic substances in the absence of free

6

oxygen. Aerobic process is a method of sludge stabilization in which sludge

organics are decomposed by the micro-organism in the presence of oxygen.

2.2.3 Conditioning

A conditioning process is usually needed in order to obtain the sludge in

a suitable form for the dewatering process. This is achieved physically or

chemically. The physical process of conditioning includes freezing the sludge

or heating the sludge to a certain temperature. Freezing involves a slow freezing

process causing the formation of ice crystal which is easily separated from the

solids. The chemical processes involve coagulants which may be either

inorganic or organic chemicals. During chemical conditioning observed water is

released and the solids are coagulated and the moisture content can be reduced

to form about 95% to 70% chemical used include ferric chloride, organic

polymer lime and alum.

2.2.4 Dewatering

Dewatering is a process that is used to reduce the water content of the

sludge for easier handling. It can be achieved naturally on sand drying bed,

thermally or mechanically. Natural drying process is achieved by the use of

drying beds in which the water content is usually lost by natural evaporation

and percolation. Thermal drying is used in sludge dewatering where there is a

cheap source of heart. The heat is used to evaporate water from sludge,

mechanical method of sludge dewatering is achieved by filtering sludge under

7

pressure. The dewatering equipment’s usually used are filter press, belt filter

press, centrifuges, vacuum filter, drying beds and lagoons.

2.3 Operation Equipment

2.3.1 Filter Presses

Plate and frame filter presses, recessed plate and membrane plate presses

are used to dewater sludge. In filter press wet conditioned sludge is forced into

the spaces between filter cloth sheets pressure is therefore applied which

drained the water resulting in the formation of sludge cake. The filter press has

a cheap maintenance cost due to low moving parts grouped with its ability to

operate under high pressure differentials with no constant super vision required.

2.3.2 Belt Filter Presses

Belt filter presses are continuous-feed dewatering devices that use the

principles of chemical conditioning, gravity drainage, and mechanically applied

pressure to dewater sludge. Belt filter presses need a polymer to process the

sludge. The process then works the same way as gravity belts but the method is

complemented with pressing the sludge between two belts. This process may

therefore be combined with gravity belt thickening. This technique increases the

dry solids (DS) level by 10 to 20 % depending on the sludge quality and the

equipment (Oscar T. 2008).The belt filter press has proved to be effective for

almost all types of municipal wastewater sludge and biosolids. Good chemical

conditioning is the key to successful and consistent performance of the belt

filter press, as it is for other dewatering processes.

8

2.3.3 Vacuum Filtration

Vacuum filtration is a technique of sludge dewatering through the

application of vacuum pressure, it is usually employed to separate solids from

liquid. This is affected by means of a porous medium allows the liquids to pass.

The media employed from this purpose include steel mesh, cotton wool, nylon,

and tightly wound coil springs. Among the vacuum filters, the revolving drum

is most widely used. It consists of a rotating drum covered with filter medium

when pressure of about 50cmHg to 650cmHg is applied the sludge can be

separated from the liquid and collected against the screen which is rinsed to

prevent clogging. The drum speed the depth of submergence, vacuum level the

degree of agitation of the sludge is the variables that control the filter yield.

2.3.4 Centrifugation

A centrifuge is a device in which the solid – liquid separation is enhanced

by the use of centrifugal force. This is accomplished by rotating the liquid at

high speeds to subject the sludge to increase gravitational forces. It consists of a

rotating screw conveyor which lies inside the bowl that rotates at different

speeds. The rotation separates the sludge solids to the other side of the bowl,

while the liquid is removed at the opposite end. It produces about 10.8 to 22%

of cake. The efficiency of centrifuge is dependent on the increase in length and

diameter of the bowl. A larger diameter bowl result in slower speed under the

same operating power.

9

2.3.5 Drying Beds

Drying beds are usually used for small industrial or community waste

treatment plants where land is readily available. Garg (2008) stated that, sludge

drying beds are open beds of land, 45 to 60cm deep, consisting of about 30 to

45cm thick graded layer of gravel varying in size from 15cm at bottom to

1.25cm at top, and overlain by 10 to 15cm thick coarse sand layer. Open jointed

under drain pipes (15cm in diameter), (a) 5 to 7m c/c spacing are laid below the

gravel 1 in 100. a surrounding wall is used to contain the liquid sludge when

applied to the bed rising about 1 meters above the sand surface.

The sewage sludge from the digestion tank is brought and spread over the

top of the drying beds to a depth of about 20 to 30cm.Dewatering action is

essentially gravity drainage aided by air drying. A portion of the moisture drains

through the bed, while most of it is evaporated to the atmosphere. It takes about

two weeks to two months, for drying the sludge, depending on the weather and

condition of the bed. After drying, the solids are removed and either disposed of

in all landfill or used as manure on farmland.

There are five types of drying beds:

1. Conventional sand drying beds

2. Paved

3. Artificial Media

4. Vacuum-assisted, and

5. Solar

10

1. Conventional Sand Drying Beds

Conventional sand drying beds are usually used for small medium sized

communities. Structural requirements of this type of bed are simple with

containment walls for the liquid, a soft, permeable media that allows for

drainage of filtrate, and a collection system of under drain pipes. Feed piping is

simple, with a single discharge inlet from digestion, thickening, or a holding

tank. The need for this media to remain porous prohibits cake removal by

machinery and raises concern over plugging and need for replacement. Sludge

removal is accomplished by manual shoveling into wheelbarrows or trucks, or

by a scraper, fronted loader, or special mechanical sludge removal equipment

after it has drained and direct sufficiently (Metcalf and Eddy, 2004).

2. Paved Drying Beds

There are a limited number of paved drying beds. The advantages of

paved drying beds include equipment access and reduced maintenance. Most

beds are rectangular in shape, 20 to 50ft wide by 70 to 15ft long. Concrete,

asphalt, or soil cement is used for drying bed liners. There are two types of

paved drying beds that have been used as an alternate to sand drying beds, a

drainage type and a decanting type.

The drainage type works similarly to a conventional bed in that under

drainage is collected, but sludge removal is improved by using a front-ed loader.

This type of paved drying bed requires more area than conventional sand beds.

The decanting type of paved drying bed is advantageous for worm, aid, and

11

semi-arid is climates. This type of drying bed uses low-cost impermeable

supernatant and mixing of the drying sludge for enhanced evaporation.

3. Artificial-Media Drying Beds

Artificial-media can be sued such as stainless steel wedge wire or high-

density polyurethane formed into panels. In a wedge wire drying bed, liquid

sludge is spread onto a horizontal, relatively open drainage medium. The bed

has a shallow, rectangular, water tight basin fitted with a false floor of wedge

wire panels with slotted openings of 0.01inchs. An outlet valve to control the

rate of drainage is located below the false floor. In the high-density

polyurethane media system, interlocking panels are formed for installation on a

sloped slab or in prefabricated steel self-dumping trays. Each panel has an eight

percent open area for dewatering and contains a built-in underlain system.

4. Vacuum-Assisted Drying Beds

This method is used to accelerate dewatering and drying. Vacuum-

assisted drying beds incorporate the use of a vacuum pump with sand drying

bed. Solids are applied to a depth of 12 to 30 inches. Polymer, used to enhance

performance, is injected to the sludge in the inlet line. Filtrate drains through the

multimedia filter into a sump. After the solids drain by gravity, a vacuum

system is started. When the cake cracks and vacuum is lost the vacuum is shut

off and solids removed.

12

5. Solar Drying Beds

A method used to enhance the dewatering and drying of liquid, thickened,

or dewatered bio solids is solar is solar drying in covered drying beds. The

system’s main source of drying energy is solar radiation. The solar drying

system, which is a sophisticated “greenhouse”, consists of a rectangular base

structure, translucent chamber, sensors to measure atmospheric drying

conditions, air louvers ventilation fans, a mobile electromechanical (called a

‘mole’) that agitates and moves the drying bio solids, and a microprocessor that

controls the drying environment.

2.3.6 Lagoons

Drying lagoons are used for dewatering of digested sludge, thickening,

and the temporary storage of waste sludge (Hammer, M; et al, 2000). This

method is not suitable for dewatering untreated sludge’s, limed sludge’s or

sludge’s with a high-strength supernatant because of their odour and nuisance

potential. Lagoons performance is also affected by climate, like that of drying

beds. Precipitation and low temperatures also inhibit dewatering. Lagoons are

constructed by excavation or enclosed area by dikes. Drainage may be improved

by blanketing the bottom with sand and installing under drains. Lagoons are

most applicable in areas with high evaporation rates. Dewatering by subsurface

drainage and percolation is limited by increasingly stringent environmental and

ground water regulations.

13

Unconditioned digested biosolids are discharged to the lagoon in a

manner suitable for an even distribution, and the liquid is recycled to the

treatment facility. Biosolids are removed mechanically, usually at a solids

content of 25 to 30 percent (Metcalf and Eddy, 2004).

2.4 Specific Resistance

The term specific resistance was first proposed by Carman (1934) and

was defined by him as the pressure that is required to procure a unit rate of flow

of liquid of unit viscosity through unit cube of cake. It is an important

parameter used to describe sludge filterability. During the process of filtration,

the liquid and solid particles of the sludge are separated by passing the sludge

on a filter medium which allows the filtrate to pass through while the solid

component is captured on the filter medium. The filtrate moving under gravity

encounters a resistance to flow through the filter medium and also through the

filter cake formed on the medium. As the filtration processes continues, the

resistance to flow of fluid through the medium becomes negligible while the

resistance to filtration exerted by the sludge cake steadily increases the cake

height. The driving force required to overcome the resistance offered by the

cake and the filter septum, is provided by the difference of pressure between the

deposited zone of the cake and the bottom of the filter septum. The resistance

offered to the filtrate can therefore determine the dewaterability or filterability

of the sludge.

14

2.5 Compressibility of Sludge

The compressibility of a sludge is a very important attribute of sludge,

hence there is the need to include it in sludge filtration equation, and is defined

as the decrease in unit volume per unit increase in pressure. It’s a measure of

the ease, with, which the solid particles collected on the filter medium are

deformed. The greater its value, the more compressible is the sludge cake and

the more the resistant is the cake to passage of filtration. When a compressive

load is applied to sludge, a decrease in its volume takes place, the decrease in

volume under pressure is known as compression and the property of the sludge

mass pertaining to its tendency to decrease in volume under pressure is known

as compressibility.

2.6 Sludge Filtration Theories

Sludge filtration theories and derived equations have been based on

experimental, assumptions and conditions, as given by researchers. Some

researchers modify already existing theory in order to introduce a new concept

for evaluating sludge filtration equation.

2.6.1 Almy and Lewis (1912)

The theory of filtration was pioneered by Almy and Lewis in 1912,who

filtered chromium hydroxide in a small plate and frame press at a series of

constant pressures. Their equation is given below:

m

n

m

kp

dt

dv=

2.1

15

Where n and m are indefinite powers of the relationships, p is the

pressure, (N/m2) and v is the volume (m

3) and k is a constant of proportionality

which varies with type of material to be filtered and the conditions of operation.

2.6.2 Sperry (1916)

Sperry in 1916 used the analogy between the filtration process and

groundwater flow to derive his filtration equation. Sperry’s theory was based on

theoretical rather than experimental considerations. He assumed that since

poiseuille’s law holds for ground water flow, then it should also represent the

basic law of filtration.

Upon this theoretical base, he derives a general equation which stated

that, the rate of flow was considered to be strictly proportional to the first power

of p and v. This is his modified poiseuille’s law equation.

R

P

dt

dv=

2.2

Where R is the resistance to flow of filtrate through the filter cake and the fitter

medium.

2.6.3 Baker (1921)

Baker agreed with Sperry’s analogy, but was in disagreement with Almy

and Lewis as regards to the relationship that the rate of flow was proportional to

indefinite powers (n and m) of pressure and volume on this basis he obtained an

integrated equation of the form given below:

V(m+1)

= (m+1) KA2 p

nt3 2.3

16

Where V is volume (m3) k is a constant of proportionality, A is the area (m

2), P

is the pressure (N/m2) and t is the time (sec).

2.6.4 Weber and Hershey (1926)

The original equation of Almy and Lewis was modified by Weber and

Hershey into the integrated form below

( ))1(

2

)1(

1

1

12

t

S

Vr

P

A

V

θ

θ

θ

θθ

+

+

+=

+−+

2.4

Underwood (1926) criticized the above equation on the ground that it contains

an error and propose an equation with the introduction of a concept of specific

resistance, which is given below as:

θθ

dt

dyCprr

S )(11= 2.5

Where 11r is the resistance of unit cube cake when under unit pressure, with unit

rate of filtrate flow passing through it.r is average resistance per unit cube of

cake.

2.6.5 Carman (1934, 1938)

Carman with the concept of specific resistance proposed a sludge

filtration equation for dewatering of sludge at constant pressure, given as;

PA

RV

pA

Vrct

µµ +=

2

2

2 2.6

Where R is the Specific Ressitance (m/kg), P is the pressure (N/m2), V is the

volume (m3), A is the Area (m

2) µ is the dynamic viscosity (N.S/m

2).

17

The above equation gives a straight line when t/v is plotted against v. Carman

assumed that his equation should be used for compressible cake, although

derived from rigid cake consideration.

Due to an invalid method of derivation and the disparity between theoretical

and experimental data, the equation above was described to be in error.

2.6.6 Ruth (1935, 1938)

The idea of specific resistance was given more light by Ruth who

demonstrated experimentally that the plot of filtrate volume V versus time t

followed a parabolic relation in line with theoretical predictions based on

Carman’s equations. Investigation of local cake conditions as, controlling the

overall filtration resistance began with the introduction of permeability –

compression cell by Ruth, who suggested a means for relating the average

specific resistance with the local values.

2.6.7 Tiller (1953)

Tiller held that in ordinary filtration processes the solids closest to the

filter medium is packed more densely than the others and that the filtration

resistance depends on the porosity. His point of view is that, at the point of

contact between filter medium and cake, porosity is minimal and it is a

maximum at the top along the cake height. He showed theoretically that the

plots of v versus t curves for constant pressure filtration were not perfect

parabolas, if there exist a pressure drop across the medium, it will result to a

fraction of the pressure, loss across the cake, therefore the average filtration

18

resistance was not constant and that the t/v versus t curve was not straight, so in

essence the assumptions that the flow rate and average porosity were constant

and independent of distance through the filter bed was found to be invalid.

2.6.8 Anazodo (1974)

Anazodo objected to Carman’s equation on its formulation point of view.

He argued that the approximation of compressible filter cakes to a rigid bundle

of capillary tubes or to non-compressible sand-beds did not make sense. He

used a dimensional approach to derive an equation for sludge filtration at

constant pressure. This method does not involve the utilization of Poiseuille’s

and Darcy’s law. He stated that the effective factors that could influence the

volume of filtrate are P,A,µ,C, r and t. Finally, he combined force and mass

creating, FMTLx,Ly,Lz dimensional analysis for the compressible sludge, to

arrive the equation below.

f

trPCA

Cr

AV

=

µ21

21

212

2.7

In his equation Anazodo assumed f = ½ because the relationship between

V and t was established to be parabolic. He finally arrived at:

21

21

24

5

rC

trAV

µ=

2.8

19

2.6.9 White and Gale (1975)

White and Gale rejected Anazodo’s deviation using dimensional question

on the ground that, Anazodo failed to justify the prediction that the volume of

filtrate obtained after a fixed time is proportional to the filtration area to the

power of 45 and also that Anazodo need not assume f = 1/2 .

They pointed out that Carman’s equation which only predicts volume of filtrate

to be just proportional to the area was preferable Gale and White then suggested

that Anazodo’s partial equation should be written as

32212 )( −−= bb CrtAPV µ 2.9

It was concluded that the relationship between V and A should be

experimentally determined, so that if b=1, Carman’s equation should be

accepted, and if b = 5/4, Anazodo’s equation is preferable. Both parties finally

agreed that the determination of the correct value of b based on theoretical and

experimental consideration will guide the choice of the filtration equation.

2.6.10 Hemant (1981)

Hemant modified Ruth’scake filtration theory and argued that it was

inadequate to explain most of the constant pressure filtration data, and therefore

stressing about particle migration within a cake, he asserts that Ruth’s theory

that at constant pressures filtrates volume various time plot on a log-log scale

would yield a shape of 0.5 was too definite (it has been found to be between

0.25 and 0.5). His equation is given below:

20

Log cava

PaLog

aLogt

aV

αµ+

+

++

+=

2

)2(

2

1

2

1

2.10

Where V is the volume (m3), P is the pressure, µ is the dynamic viscosity

(N.S/m2).

Commenting on the variability of specific resistance, Hermant claimed that, the

assumption that average specific resistance is constant, is not valid for analysis

of data collected only about 20 minutes, and also that in constant filtration tests,

flow rate decreases continually with time and so do pressure Pm across the

medium. As the total pressure drop P is constant, the pressure drop (P – P2)

across the cake continuously decreases and approaches P. Hermant has hinted

that the hydrostatic head should be accounted for in the basic equation for

industrial vacuum sludge filtration. He argued that there is variable pressure

until the constant pressure of the vacuum is reached.

2.6.11 Ademiluyi, Anazodo and Egbuniwe (1982)

In 1982, Ademiluyi et al carried out an investigation to determine

experimentally the true value of the exponent ‘b’ which relates to the volume of

filtration to the area of filtration. The average value of ‘b’ was found to be 0.19

± 0.02 when using effective area of filtration. At the end of the experiment, they

suggested that the total area of filtration should be used in Carman’s equation,

while the effective area of filtration should be sued in Anazodo’s dimensional

equation for sludge filtration at constant vacuum pressure.

21

The equations formulated by Ademiluyi, Anazodo, and Egbuniwe after the

substitutions of ‘b’ in the partial dimensional equation are:

12.2)(

.11.2)(

24.0

76.2

2

12.1

82.12

Cr

tPAV

and

Cr

tPAV

eff

µ

µ

=

=

Where A and Aeff are the total Area and the effectiveArea of the Buchner

funnel respectively.

2.6.12 Ademiluyi (1984)

Ademiluyi accounting for compressibility coefficient developed an

equation for compressible sludge to be used in routine laboratory investigation.

The equation has been suggested to replace the traditional Carman’s equation in

view of its limitations. In the new equation, compressibility attribute has been

accounted for and specific resistance parameter has been treated as a local

variable rather than the traditional average value in the Carman’s equation.

The equation is given below:

13.21

1)((

1

0

0

112

ψ

ψγβψψ

βγαβ

+

+++

−

+= =+−− InH

st ssss

The equation assumed the concept of terzaghi compressibility coefficient

which was found to be less than one. The limitation of the above equation lies

in the difficulty of evaluating some of its variables dimensional homogeneity

and also because of the presence of which is not a dimensionless pure number.

22

2.6.13 Ademiluyi et al (1985)

Ademiluyi et al proposed new equations based on LMT dimensional

analysis for use in laboratory sludge filtration investigation. Also, the derived

equations were done based on theoretical and experimental considerations.

They arrived at the following equations:

V = P At0.91µ-1.5

C0.59

r-1.19

t1/2

2.14

Or V = P Aeff1.38µ-15

C-0.12

r-0.62

t1/2

2.15

2.6.14 Ademiluyi et al (1987)

Ademiluyi et al proposed a concept of sludge filterability referred to as

sludge dewaterability number (SDN) that was found to be dependent on not

only the equipment design but also on the sludge treatment prior to dewatering.

They stated that filter medium has significant effects on SDN and it has been

experimentally demonstrated that sludge shearing affects SDN. A dimension

less number was suggested as a measure of sludge dewaterability. This number

is referred to as sludge dewaterability number (SDN). SDN equation as

proposed by Ademiluyi et al (1987) can be stated as:

SDN �∆��

��

��

�� 2.16

Where,

SDN = Sludge Dewaterability Number

C0 = Initial Concentration of Sludge

H0 = Initial Manometric Height

23

t = Time of Filter Run

∆H = Change in Manometric Height after Time t

Cf = Concentration of Filtrate

Vi = Instantaneous Velocity

Cc = Concentration of Cake

2.6.15 Ademiluyi et.al (2012)

Ademiluyi and others, proposed an equation for sludge filtration based on

the concept of specific resistance using LMT dimensional analysis, which is

given as

17.22

bC

PghAR

=

µ

It is noteworthy that the traditional Carman’s equation – Anazodo and

Ademiluyi and his co-worker did not account for the compressibility coefficient

in the formulation of their equations.

The incorporation of compressibility coefficient ‘S’ into filtration expression

using the LMT system of dimensional analysis in deriving a modified equation

cannot be over emphasized.

24

CHAPTER THREE

RESEARCH METHODOLOGY

3.1 Study Area

The sewage treatment plant is situated at the University of Nigeria Nsukka

about 800m from the junior staff quarters. The treatment plant consists of a

screen (6mm bar racks set at 12mm Centre) followed by two Imhoff tanks, each

measuring about 6.667m� 4.667m�10m, designed for a population of 3,000-

4,000. The sedimentation compartment was designed for a surface setting rate

of 29.3m3/m

2 day and detention time of 11/2hr. The digestion compartment

storage volume is 0.057 m3/capital, while the period of digestion is 30 day at an

average temperature of 27�. Sludge is discharged from the Imhoff tank once

every 10 days onto one of the 4 drying beds, so that the beds are loaded at 40

days interval. The beds have a total area of 417m2. The effluent from the Imhoff

tank enters the two facultative waste stabilization ponds. The plant treats mainly

domestic wastewater.

3.2 Sample Collection

The sludge that was used for this study was collected from the Imhoff

tank situated at the sewage treatment plant of the University of Nigeria Nsukka,

with a bucket into the drying bed. The length of the drying is estimated as 1.2m,

the depth is 0.80m while the width is 0.75m. The lower course of gravel around

the under drains 0.20m extending above the top of the under drains. The top

course consists of 0.20m of clean coarse sand. The sludge depth is 0.30m. The

25

drying bed was designed with a metal wall with under drains pipe laid with

open joints. Sludge that remains on top of the sand bed is solidified by the

percolation of water down ward into the sand and also from the evaporation

from the surface of the sludge. Therefore, the area of the drying bed is estimated

to be 0.9m2. The schematic layout of a sand drying bed is shown in figure 3.1.

Figure 3.1: Schematic Diagram of Sand Drying Bed

0.1m

0.3m

0.2m

0.2m

1.2m

SLUDGE

SAND

GRAVEL

Perforated base

Under drainage

Measuring Cylinder

26

3.3 Method of Determining Parameters

3.3.1 Solid Content(C)

The solid content of the sludge is defined as the weight of dry mass of the

solid divided by the volume of the sludge. Parts of the conditioned sludge were

taken to the laboratory and oven dried at 1050c.These sludge were weighed

before and after oven drying to enable the determination of the solid content.

3.3.2 Volume of filtrate (v)

The volume of filtrate was taken by reading the meniscus of the

measuring cylinder for the level of filtrate. The filtrate volumes reading were

taken at reasonable time interval.

3.3.3 Area of filtration (A)

The total area is taken as the cross sectional area of the rectangular model

measured to be 1.2m by 0.75m respectively giving a value of 0.9m2

3.3.4 Time of filtrate (t)

This is the time it takes to collect a known volume of filtrate at the

interval of 20 minutes using a stop watch, observing the fall in sludge surface.

3.3.5 Height of sludge (Hs)

The height of sludge was taken by reading the meniscus of the measuring

tape calibrated at the side of drying bed.

3.3.6 Pressure of filtration (P)

The pressure was assumed to be the hydrostatic pressure, since is what is

exerted by a liquid when it is at rest. The height of a liquid column of uniform

27

density is directly proportional to the hydrostatic pressure.Hence the formula for

calculating the hydrostatic pressure of a column of liquid in SI units is:

Pressure of Filtration (P) = ��

Where,

P = hydrostatic pressure (Pa), (N/m2)

� = density of water (kg/m3)

� = gravity (m/s2)

� = height (m)

3.3.7 Dynamic viscosity (µ)

The dynamic viscosity of the filtrate was assumed to be the viscosity of

water since the filtrate was clear. An equation to calculate the viscosity of water

is:

µ =0.0168 x ρ x T-0.88

Where: µ = dynamic viscosity (N.S/m2)

T = Temperature (0c)

ρ= density (kg/m3) -0.88 and 0.0168 are constant

3.3.8 Specific Resistance of Sludge (R)

Is defined as a pressure required to procure unit rate of flow of liquid of

unit viscosity through unit cube of the cake. This parameter cannot be measured

in the laboratory, it can only be evaluated from the values of others parameters.

28

3.3.9 Weight of dry solid (Wd)

The weight of dry solid is the weight of the sludge after oven drying a

temperature of 1050c for twenty four hours

3.3.10 Specific gravity of sludge (Ssl)

This is measured in the laboratory using the density bottle method.

3.2.11 Percentage of solid content expressed as a decimal (Ps)

This parameter is determined at the end of the filtration run when the

cumulative volume of water is arrived at. It is calculated by subtracting the

volume of sludge to determine the percentage of the result.

3.3.12 Compressibility Coefficient (S)

The compressibility coefficient parameter can be measured in the

laboratory using the oedometer test. It was defined as the ratio ∆Ρ

∆eusing the soil

mechanic concept of soil deformation as presented by Terzaghi (1966).

3.4 Effect of Conditioning on Specific Resistance of Sludge

Ferric chloride (Fecl3) at concentrations of l0g, 20g 30g, 40g and 50g

were added each to one bucket of digested sludge of 10liters capacity and mixed

before filtration. For each filtration circle, the stop watch was started and the

volume of filtrate and height of sludge in the bed was recorded at 20 minutes

interval. The temperature of sludge for each filtration circle was also noted.

29

3.5 The Effect of Dilution on Specific Resistance

Also one bucket of sludge each of 10 liters was diluted with distilled

water of 1liter, 2liters, 3liters, 4liters and 5liters volumes and then conditioned

with 20g each to produce a filterable sludge of different solid contents.

3.6 Derivation of Sludge Filtration Equation Using Anazodo’s Method

As used by Anazodo (1974), he described length into Lx, Ly, and Lz (x, y,

z being three mutually perpendicular axes in space), and as well as making

distinction between inertial mass, ��which is the mass determined by

measurements of its momentum rather than measurements of its behavior in a

gravitational field and, the amount of matter, Mi. The dimensions of the

variables are summarized in the table below:

Table 3.1: LMT DIMENSIONS

Variables Symbol Dimensions

Volume of filtrate V L x LyLz

Filtration area A yLxL

Time of filtration T T

Mass of cake dry solids per unit volume of

filtrate

C 111 −−−

zyx LLLMµ

Pressure P 2111 −−−TLLLM yxzi

Dynamic viscosity µ 11 −−TLM zi

30

Specific resistance R Lz Mµ-1

The dimensional equation can be written as:

V = PaA

b C

c µ

d eR tf 3.1

Where a, b, c, d, e and f are exponents which can be positive or negative.

Using Mµ MiLxLyLz T for LMT dimensional formula to substitute for the terms

in equation 3.1, equation 3.1 becomes,

( ) ( ) ( )( ) ( ) ( ) fe

z

d

zi

c

zyx

b

yx

a

yxzi

TMLTLM

LLLMLLTLLLM

111

1112111 = LzLy Lx

−−−

−−−−−−

µ

µ

3.2

Before dimensional homogeneity can be satisfied, the exponent of each

dimension must be identical on both sides of equation (3.2)

Therefore,

For condition LxLy: 1 = -a + b – c 3.2a

For condition Lz : 1 = a – c- d + e 3.2b

For condition Mi : 0 = a + d 3.2c

For condition Mµ : 0 = c – e 3.2d

For condition T : 0 = -2a – d + f 3.2e

Five equations in six unknowns may be solved in terms of one unknown,

say

From equation (3.2c)

– a = d

From equation (3.2d)

c = e

31

Substituting c in equation (3.2b)

1 = a – c – d + e

1 = a – e - d +e

1 = a – d 3.2f

From equation (3.2f)

1 = a -d

1 = a – (-a)

1 = 2a

a = ½

If a = ½

Hence, d = - ½

From equation (3.2a)

1 = - a + b – c

1 = - ½ + b – c

b – c = 1 + ½ = 23

b – c = 23

b = 23 + c

From equation (3.2e)

0 = - 2 a – d + f

0 = - 2 (½) – (- ½) + f

0 = -1 + ½ + f

f = ½

32

∴ a = ½, b = 23 + c, c = e, d = - ½, f = ½

Hence

21

21

21 )

23(

tRCAPV cec −+= µ 3.3

Also e = c

( )

( )

( )

( )

( )

( )

( )

( ) 12.3

11.3

10.3

9.3

8.3

7.3

6.3)

5.3

4.3

2

13

2

2

13

2

3

21

32

1

3

21

3

3

21

21

21

21

21

21

23

21

23

21

C

C

c

c

c

c

c

c

ccc

ACRPA

V

t

ACRPA

Vt

ACRPA

Vt

ACRPA

V

t

ACRPA

t

V

ACRPA

tV

ACRPtA

V

ACRApt

V

RCAApt

V

−

−

−

−

−

−

−

−

=

=

=

=

=

=

=

=

=∴

µ

µ

µ

µ

µ

µ

µ

µ

µ

33

( )

( ) 14.3

13.3

2

3

2

3

C

C

ACRPA

V

V

t

ACRPA

VV

t

−

−

=

=

µ

µ

A plot of t/v against c gave a linear relationship

Figure 3.2: Graph of t/v against solid content

Hence, volume of filtrate (V) is proportional to solid content (C)

Therefore -2c = 1

∴c = - ½

( )

( )

17.3

16.3

15.3

2

3

2

3

21

PA

CRV

V

t

Hence

ACRPA

V

V

t

ACRPA

V

v

t x

µ

µ

µ

=

=

=−−

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

0 10 20 30 40 50 60 70 80 90 100

t/v

(S/m3)

solid content (Kg/m3)

34

Taking the slope of the line as (b), and equating the coefficient of (V), (R)

was calculated from the formula:

18.32

bC

PAR

=∴

µ

Equation (3.18) is the modified equation of Specific Resistance (R).

The pressure (P) is the hydrostatic by the relation P = ρ g H

Where:

ρ = Density of water

g = Acceleration due gravity

H = Hydrostatic head of the sludge

The Hydrostatic head of the sludge at the end of a filtration can also be written

as H = H1 + ∆H

Where:

H1 = the initial sludge height

∆H = the change in sludge height

Substituting for P and H into equation (3.17)

We have

35

23.3

,

,

22.3

21.3

20.3

19.3)(

2

1

2

11

2

1

2

2

1

2

2

1

2

1

2

RWV

PVA

RWV

VPA

t

V

havewepHg

andPgHV

WCngSubstituti

CRV

HgA

CRV

gHA

t

V

CRV

HgAgHA

t

V

HgAgHA

CRV

V

t

HHgA

CRV

V

t

d

SI

d

SI

SI

d

µµ

ρ

ρ

µ

ρ

µ

ρ

µ

ρρ

ρρ

µ

ρ

µ

∆+=

∆=∆

==

∆+=

∆+=

∆+=

∆+=

VSI = Volume of sludge

Wd= Weight of dry sludge

Dividing equation 3.23 through by A

PwSPs

WVAlso

RWAV

VPA

RWAV

VPA

At

V

SI

d

SI

d

SI

d

SI

=

∆+= 24.3

2

1

2

µµ

Where:

Ps = percentage of solid content expressed in decimal

SSI = specific gravity of sludge

36

Pw = density of filtrate

28.3

27.3

:

26.3

25.3

1

2

1

2

1

2

2

1

2

e

P

PsRW

A

RPsWV

HPA

At

V

RPsW

PHA

V

A

RWPs

HAP

V

A

At

V

PwSA

WHsWhere

PsRWV

HPA

RPsWV

HPA

At

V

RPWSAVPw

PWA

RWPsSPwAV

WPA

At

V

dd

s

d

s

d

s

SI

d

d

s

d

s

sdSI

d

dSI

d

∆

∆+=

∆+=

=

∆+=

∆+=

µµ

µµ

µµ

µµ

Where: eHXV

As ∆=

31.3

:

30.3

29.3

2

1

3

2

1

3

1

2

A

PsRSW

HsPA

RPsWV

V

t

SP

eWhere

A

SPsRW

HPA

RPsWV

V

t

P

e

A

PsRW

HPA

RWPsV

V

At

dd

d

s

d

d

s

d

µµ

µµ

µµ

+=∴

=∆

∆

+=

∆

∆+=

Equation (3.31) is the modified dimensional equation of Compressibility

Coefficient (S).

Simplifying equation 3.31 further, (S) was calculated from the formula

32.32

WdPsR

bAS

µ=

37

CHAPTER FOUR

EXPERIMENTAL RESULTS AND DISCUSSION

4.1 Validation of Modified Equation

The modified equation (3.31) predicts that, the plot of t/v versus V should

yield a straight line of slope b, which is the only way the modified equation can

be shown to describe sludge filtration process. The high correlation coefficient

of the graph is 0.97 which indicates that there is a linear relationship between

t/v and v as is predicted by the equation.

The result obtained in the experiment of primary unconditional sludge

filtration which was used to validate the equation is presented in Table A1 as

seen in Appendix A.

Figure 4.1: Graph of t/v against volume of filtrate

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 200000 400000 600000 800000 1000000 1200000

t/v

(S/m3)

volume V (m3)

38

4.2 Effect of Chemical Conditioner on the Specific Resistance

The results of experiment obtained are to determine the effect of chemical

conditioner on the Specific Resistance and the Compressibility Coefficient of

the sludge as shown in table B2 to B6 in Appendix B.

The graph in figure 4.2 show that the Specific Resistance decreases with

increase in the concentration of Ferric Chloride which agrees with Carman’s

equation based on vacuum filtration. Also there is a decrease in Compressibility

Coefficient with increase in concentration of Ferric Chloride as shown in figure

4.3.

Figure 4.2: Graph of Specific Resistance (R) against concentration of Ferric

Chloride

0

20000000

40000000

60000000

80000000

10000000

12000000

14000000

0 0.01 0.02 0.03 0.04 0.05 0.06

SP

EC

IFIC

RE

SIS

TA

NC

E,

R (

M/K

G)

CONCENTRATION OF FERRIC CHLORIDE (FeCl3), Kg

Series1

39

Figure 4.3: Graph of Compressibility Coefficient (S) against concentration

of Ferric Chloride

4.3 Effect of Hydrostatic Pressure on Specific Resistance

The graph in figure 4.4 shows the effect of hydrostatic pressure on

Specific Resistance, the Specific Resistance increases as the Hydrostatic

Pressure increases, which is in agreement with Ademiluyi’s findings presented

in his work on constant vacuum filtration equation of filtration equation of

Compressible Sludge. As filtration continues, more and more solid settles

reducing the porosity of particles so that the pressure of water increases and also

the Specific Resistance.

0

10

20

30

40

50

60

70

80

90

100

0 0.01 0.02 0.03 0.04 0.05 0.06

CO

MP

RE

SS

IBIL

ITY

CO

EF

FIC

IEN

T,

M2

/KN

CONCENTRATION OF FERRIC CHLORIDE (FeCl3) Kg

Series1

40

Figure 4.4: Graph of Specific Resistance (R) against hydrostatic pressure.

4.4 Effect of Dilution on Specific Resistance

The results of experiment obtained are to produce a filterable sludge of

different solid contents as shown in table C7 to C 11 (see appendix C). The

graphs of figure 4.5 and 4.6 show that Specific Resistance increase with

increase in Solid Contents,while Compressibility Coefficient decreases with

increase in Solid Contents.

Figure 4.5: Graph of Specific Resistance against Solid Content

0

20000000

40000000

60000000

80000000

10000000

12000000

14000000

0 50 100 150 200

SP

EC

IFIC

RE

SIS

TA

NC

E,

R (

M/K

G)

HYDROSTATIC PRESSURE (N/m2)

Series1

0

2

4

6

8

10

12

14

16

18

20

77 78 79 80 81 82 83 84 85 86 87

SP

EC

IFIC

RE

SIS

TA

NC

E,

R (

M/K

g)

*1

0^

7

SOLID CONTENT (Kg/m3 )

Series1

41

Figure 4.6: Graph of Compressibility Coefficient against Solid Content

4.5 Comparisons of Calculated Value of Specific Resistance of Modified

Equation and Carman’s Equation (see appendix D for the calculation)

The graphs in figure 4.7 to 4.9 shows the comparisons of Specific

Resistance of modified equation and Carman’s equations with concentration of

Ferric Chloride, Hydrostatic Pressure, and Solid Contents, it explained that the

modified equation is in consonance with Carman’s equation, which can be

adopted in sludge dewatering investigation using sludge drying bed.

0

100

200

300

400

500

600

77 78 79 80 81 82 83 84 85 86 87

CO

MP

RE

SS

IBIL

TY

CO

EF

FIC

IEN

T,

M2

/KN

SOLID CONTENT (Kg/m3 )

Series1

42

Figure 4.7: Comparison of the Effect of Fecl3 on Specific Resistance

between Modified Equation and Carman’s Equation.

Figure 4.8: Comparison of the Effect of Fecl3 on Hydrostatic Pressure

between Modified Equation and Carman’s Equation.

0

50000000

10000000

15000000

20000000

25000000

0 0.01 0.02 0.03 0.04 0.05 0.06

SP

EC

IFIC

RE

SIS

TA

NC

E,

R (

M/K

g)

CONCENTRATION OF FERRIC CHLORIDE, Kg

Derive Equation

Carman Equation

0

50000000

10000000

15000000

20000000

25000000

0 50 100 150 200

SP

EC

IFIC

RE

SIS

TA

NC

E,

R (

M/K

g)

HYDROSTATIC PRESSURE (N/m3)

Derive Equation

Carman Equation

43

Figure 4.9: Comparison of the Effect of Fecl3 on Solid Content between

Modified Equation and Carman’s Equation.

0

5

10

15

20

25

30

35

76 78 80 82 84 86 88

SP

EC

IFIC

RE

SIS

TA

NC

E,

R (

M/K

g)

*1

0^

7

SOLID CONTENT, C (Kg/M3)

Derive Equation

Carman's Equation

44

CHAPTER FIVE

CONCLUSION AND RECOMMENDATIONS

5.1 Conclusion

From the results of the experimental data, the Specific Resistance values

obtained from the modified equation of unconditioned sludge is 2.1718x107m/kg,

this shows that modified equation is valid as, the lower the Specific Resistance the

more filterable the sludge. Carman equation was used to test the data obtained and

also gave Specific Resistance values of 4.3435x107m/kg. Ferric Chloride was used

to check the effect of conditioner on Specific Resistance. The results gave Specific

Resistance of 11.5144x107 m/kg, 9.9893x107 m/kg, 6.3264x107, 5.0735x107 m/kg,

and 3.0857x107 m/kg for a conditioner concentration of 10g, 20g, 30g, 40g and

50g respectively.This shows that the resistance to filtration decreases with increase

in the concentration of ferric chloride showing that the modified equation is in line

with Carman’s equation and it can be used for sludge drying bed.

Ferric Chloride also has influence on the Compressibility Coefficient from

the modified equation there is a decrease in Compressibility with increasing Ferric

Chloride, which gave the following results: Compressibility Coefficient of 88.6

m2/kN, 84.00 m2/kN, 81.1m2/kN, 74.7m2/kN, 70.7 m2/kN.

5.2 Recommendations

Based on the above results, it can be concluded that cake formed during

filtration process is compressible and not rigid and considering the satisfactory

performance of the natural filtration process using sludge drying beds, we are

recommending that the equation be tested further to determine its validity for use

in solving filtration problems. Finally the use of the natural method should be

developed further as a step in improving the sludge filtration theory.

45

REFERENCES

Ademiluyi J.O, Anazodo U.G.N, Egbuniwe (1982), Filterability and

compressibility of sludge part 1, effluent and water treatment journal vol.

22, no 11 pp 25 – 30.

Ademiluyi, J.O. (1984). Filtration Equation for Compressible Sludge at

Constant Vacuum Pressure”. Ph.D. Thesis in Civil Engineering at

University of Nigeria: Nsukka, Nigeria.

Ademiluyi J.O.,.N. Egbuniwe and .J.C. Agunwamba (1987) A Dimensionless

number as an index of sludge dewaterability, journal of engineering for

development vol. 1.

Ademiluyi, J.O. and Arimieari, L.W. (2012). “Evaluating, the Specific

Resistance of conditioned Sludge filtration as Natural drying bed.

International Journal of Current Research .

Ademiluyi, J.O., Egbuniwe, N. (1985). “LMT Dimensional Equations for

Compressible Sludge Filtration”.Nigerian Journal of Science Vol. 18, Nos

1

Agunwamba J.C. (2001) “Waste Engineering and Management Tools”.

Immaculate Publication Ltd; p. 186.

Agunwamba J.C. (2001) Waste engineering and management tools.Engr. Smith

Eight edition environmental science.

Almy, C. and Lewis, W.K. (1912). “Experiments loading to empirical

thickness”. I. Ind. Eng. Chem. Vol. 4, p. 528.

Anazodo, U.G.N. (1974) “Dimensional Equation for Sludge Filtration”. Effluent

and Water Treatment Journal, Sept. 1974 p 517.; pp. 422 – 423.

“Application of Solar Energy for Drying of Sludge from Pharmaceutical

Industrial Waste Water and Probable Reuse”.Int. J. Environ. Res. 1 (1):

42-48, Winter 2007

Baker F.R. (1921). “Theoretical derivation of filtration equation and

experimental tests on large sweetland filter in sugar refinery” Ind. Eng.

Chem. Vol. 13 Pp. 610 – 612.

"Belt Filter Press Dewatering of Wastewater Sludge", Journal of Environmental

Engineering, Vol. 114, No. 5, October 1988.

46

Carman P.C. (1934). A study of the mechanism of filtration pat 111. Journal of

the society of chemical industry.Transaction and communication. Vol. 53

No 9 PP30IT – 309T

Carman, P.C. (1938). Fundamental principle of industrial filtration; Transaction

– Institution of chemical engineers, Vol. 16 pp 168 – 188.

Garg, S.K. (2008) “Sewage Disposal and Air Pollution Engineering”. Hanna

Publishers; 2-B, Nath Market, NaiSarak, Delhi-110006.Pp.401- 404.

Hammer M.J; Hammer, M.J; Jr. (2000) “Water and Wastewater Technology”

.Prentice-Hall of India Private Limited; New Delhi-110001. Pp. 275-

276,421-430.

Hemant, R.M. (1981), Cake filtration empirically incorporating particle

migration: Filtration and separation, vol. 18 No. 1 pp 20 – 24.

ISSN: 1735-6865 Graduate Faculty of Environment University of Tehran.

Mehrdadi, N., Joshi, S. G., Nasrabadi, T. and Hoveidi, H. (2006). Application of

Solar Energy for Drying of Sludge fro pharmaceutical Industry Waste

Water and probable Reuse. Int. J. Environ. Res. 1(1): 42 – 48, Winter

2007 ISSN: 1735-6865 Graduate Faculty of environment, University of

Tehran.

Metcalf & Eddy (2004) “Wastewater Engineering: Treatment and reuse, 4th

Ed.

McGraw-Hill Book co; New York, N.Y.10020.Pp. 1558-1565, 1570-

1578.

Metcalf & Eddy Third edition wastewater engineering treatment, disposal and

reuse.

Octavio, P.S. (2007). Impact of Sludge Pre-Digestion: Disintegration of

Dewatering and Polymer Dose. M.Sc. Thesis, Centre for Water Science,

Cranfield University, pp. 1 – 2.

Oscar T. (2008) “Evaluation of Sludge Management in Wuhan,

China.Department of Microbiology, Swedish University of Agricultural

Sciences.

Rajput, R.K. (1998). “Fluid Mechanics and Hydraulic Machines”.S. Chand &

Company Ltd: (An Iso 9001:2000 Company). Ram Nagar, New Delhi.

Ruth, B.E. (1935)studies in filtration derivation of general filtration equation,

Industrial and engineering chemistry.p.708.

47

"Sludge Dewatering", Manual of Practice 20, Water Pollution Control

Federation, 1969 and 1983.

Sperry D.R.F. (1916), Deduction of filtration equation including term for cloth

resistance and experiments to verify same. Chem.And Meth. Engineering,

vol. 15 pp 198 – 203.

Terzaghi, K. (1966) Theoretical soil mechanics, John Wiley and sonsinc. N.Y

14th Printing.

Tiller, F.M. (1953).The role of porosity in filtration. Numerical method for

constant ate and constant pressure filtration based on Kozeny’s law,

chemical engineering progress vol. 49 no. 9 pp. 467 – 479.

Underwood, A.J.U. (1926), Derivation of filtration equation: Trans-inst

Chemical engineering (London) vol. 4 pp 19.

Weber, H.C. and Hershey, R.L. (1926), Some practical application of Lewis

filtration equation. J. Ind. Eng. Chem. Vol. 18 pp 341 – 344.

White, K.J. and Gale, R.S Comment on dimensional equation; A reply to

anazodos reply. E.W.T. Journal vol. 15 No. 8 pp 422 – 423.

White, K.J. and Gale, R.S. (1975), Comment on dimensional equation: E.W.T

Journal vol. 15 No. 2 pp 103.

48

APPENDIX A

Table A1: Showing filtration of unconditioned sludge obtained on a 20 minutes

interval for 12 hours

S/

N

o

Time t

(s)

Volume

V(m3)

t/V V2 V*t/V Height

of sludge

on

Drying

Bed

(h)m

Density

of water

(kg/m3)

at

different

temp.

Hydrost

atic

pressure

P = ρρρρgh

N/m2

Dynamic

Viscosity

µ N.s/m2

Solid

content

Mass/v

ol.

Kg/m3

1. 1200 0.01740 68965.52 0.00030276 1200 0.29 996.51 2832.08 0.92085 56.33

2. 2400 0.01900 126315.79 0.00036100 2400 0.26 996.23 2538.39 0.89159 42.33

3. 3600 0.01950 184615.38 0.00038025 3600 0.25 995.94 2440.05 0.8642 21.83

4. 4800 0.01989 241327.30 0.00039561 4800 0.24 995.65 2341.77 0.8386 68.17

5. 6000 0.02257 265839.61 0.00050940 6000 0.23 995.65 2244.19 0.8386 53

6. 7200 0.02432 296052.63 0.00059146 7200 0.22 995.09 2145.41 0.7918 74.33

7. 8400 0.02498 336269.02 0.00062400 8400 0.21 995.41 2048.55 0.8145 73

8. 9600 0.02587 371086.20 0.00066926 9600 0.20 994.43 1949.08 0.7502 102.33

9. 10800 0.02685 402234.64 0.00072092 10800 0.19 994.76 1852.24 0.7704 90.5

10. 12000 0.02776 432276.70 0.00077062 12000 0.18 995.65 1756.33 0.8386 115.5

11. 13200 0.02816 468750.00 0.00079232 13200 0.17 995.09 1657.82 0.7918 114.3

12. 14400 0.02898 496894.41 0.00083984 14400 0.16 995.65 1561.18 0.8386 115

13. 15600 0.02952 528455.29 0.00087143 15600 0.15 994.43 1461.81 0.7502 131

14. 16800 0.02997 560560.56 0.00089820 16800 0.14 995.65 1366.03 0.8386 151.67

15. 18000 0.03034 593276.20 0.00092052 18000 0.13 995.09 1267.75 0.7918 168.17

16. 19200 0.03058 627861.35 0.00093514 19200 0.12 994.43 1169.45 0.7502 182.5

17. 20400 0.03089 660407.90 0.00095419 20400 0.10 993.73 973.86 0.7129 160.5

18. 21600 0.03112 694587.40 0.00096845 21600 0.09 994.08 876.78 0.7311 138.9

19. 22800 0.03116 731707.52 0.00097095 22800 0.08 995.65 780.59 0.83.86 112.7

20. 24000 0.03119 769477.40 0.00097282 24000 0.07 995.65 683.02 0.8386 110

21. 25200 0.03223 781880.23 0.0010388 25200 0.06 955.09 585.11 0.7918 108

22. 26400 0.03278 805369.13 0.0010745 26400 0.05 995.09 487.59 0.7918 106

23. 27600 0.03334 826347.31 0.0011115 27600 0.04 995.65 390.30 0.8386 104.5

24. 28800 0.03398 847557.39 0.0011546 28800 0.03 995.65 292.72 0.8386 102.25

25. 30000 0.03450 869565.22 0.0011902 30000 0.02 995.94 195.20 0.8642 100.6

26. 31200 0.0.3487 894751.94 0.0012159 31200 0.02 995.65 195.15 0.8386 100.2

27. 32400 0.03545 913996.33 0.0012567 32400 0.02 996.23 195.26 0.89159 100

28. 33600 0.03599 933592.67 0.0012953 33600 0. 02 995.65 195.15 0.8386 99.23

29. 34800 0.03686 944112.86 0.0013586 34800 0. 02 995.94 195.20 0.8642 98.5

30. 36000 0.03724 966702.47 0.0013868 36000 0. 02 996.23 195.26 0.89159 96.45

31. 37200 0.03789 981789.39 0.001436 37200 0. 02 996.23 195.26 0.89159 90.5

32. 38400 0.03823 1004467.70 0.0014615 38400 0. 02 995.65 195.15 0.8386 88.7

33. 39600 0.03886 1019042.72 0.0015101 39600 0.01 995.94 97.60 0.8642 82.9

34. 40800 0.03945 1034220.53 0.0015563 40800 0. 01 995.65 97.57 0.8386 81.8

35. 42000 0.03989 1052895.46 0.0015912 42000 0. 01 996.23 97.63 0.89159 80.6

36. 43200 0.04032 1071428.57 0.0016257 43200 0. 01 996.23 97.63 0.89159 76

799200 1.07913 23804180.54 0.04354 799200 3.86 35837.82 37654.16 29.86749 3598.29

By regression analysis the slope b is given as

( ) ( )( ) ( )∑ ∑

∑ ∑ ∑−

−=

22vvn

vtv

vtvn

b

49

b = 7.6526x107

Height (H) = 0.3m,ρgh = 37654.16 N/m2, Area = 0.9m

2Dynamic Viscosity =

29.86749 N.s/m2, Solid Content (C) =3598.29 Kg/m

3, Wd = 0.553, Ps = 0.04.

Solving for the Specific Resistance and the Compressibility Coefficient

of Sludge we have

bC

PAR

=

µ

2

R = 2.1718x107m/kg,

WdPsR

bAS

µ

2

=

S = 4.34m2/KN

50

APPENDIX B

Table B2: The Effect of Ferric Chloride on Specific Resistance using one

bucket of Sludge with 10g of Ferric Chloride

Time t (s) Volume of filtrate V(m3) t/v V^2 V*t/v

1200 0.00148 827586.21 2.1025E-06 1200

2400 0.002585 928433.27 6.68822E-06 2400

3600 0.003745 961281.71 1.40250E-06 3600

4800 0.004765 100734523 2.2705E-05 4800

6000 0.005328 112676056 2.8356E-05 6000

0.01787 4851406.98 0.000073871 18000

Height h (m) = 0.019, Temp (oC) = 29 density of water (kg/m

3) = 995.94

Area A (m2) = 0.9 Hydrostatic pressure P = ρgh (N/m

2) = 185.63 Dynamic

viscosity µ (N.S/m2) = 0.8917 solid content C mass/vol. (kg/m

3) = 96.8 b =

6.6100x107

s/m6 R = 11.5144x10

7 m/kg. Weight of dry solid Wd (kg) = 0.0588.

Percentage of solid expressed in decimal Ps = 0.10. Specific gravity of sludge

Ssl = 1.04, S = 88.6 m2/kN.



Time t (s) Volume of filtrate

V(m3)

t/v V^2 V*t/v

1200 0.00175 685714.29 3.0625-E-06 1200

2400 0.003285 730593.61 1.07912E-05 2400

3600 0.004625 77837.39 2.13906E-05 3600

4800 0.005462 878798.97 2.9833E-05 4800

6000 0.006332 947567.91 40094E-05 6000

0.02145 4021053.17 0.0001051713 18000

Height h(m) = 0.018, Temp (oC) = 30 density of water (kg/m

3) = 995.65


2) = 175.63 Dynamic


3) = 96.8 b =

51

5.7001x107

s/m6 R = 9.9893x10



Ssl = 1.03, S = 84.00 m2/kN.

Table B4: The effect of Ferric Chloride on Specific Resistance using one bucket

of Sludge with 30g of ferric Chloride

Time t

(s)

Volume of filtrate V(m3) t/v V^2 V*t/v

1200 0.006635 180859.081 4.4023E-05 1200

2400 0.009672 248138.958 9.3548E-05 2400

3600 0.0011256 319829.424 1.26698E-04

3600

4800 0.0012366 388161.087 1.52918E-04 4800

6000 0.0013179 455269.7473 1.73686E-04

6000

0.053108 1592258.3 5.9686E-04 18000


3) = 996.23


2) = 165.97 Dynamic


3) = 96.8 b =

4.0615x107

s/m6 R = 6.3264x10



Ssl = 1.03, S = 81.1 m2/kN.




1200 0.008353 143661 6.9773E-05

1200

2400 0.010926 2196595 1.1938E-04

2400

3600 0.012766 281999.1 1.5267E-04 3600

4800 0.013935 344456.4 1.8050E-04 4800

6000 0.014945 401472.1 2.2037E-04 6000

0.060925 1391248.1 7.42693E-04 18000

52


3) = 995.65


2) = 156.28 Dynamic

viscosity µ(N.S/m2) = 0.8386 solid content C mass/vol. (kg/m

3) = 96.8 b =

3.2535x107

s/m6 R = 5.0735x10



Ssl = 1.03, S = 74.7 m2/kN.




1200 0.009635 124545.9 9.2833E-05 1200

2400 0.014265 168243.9 2.0349E-04 2400

3600 0.016412 219351.7 2.6942E-04 3600

4800 0.017562 273317.4 3.0846E-04 4800

6000 0.018455 325115.11 3.4059E-04 6000

0.076329 1110574 1.21479E-03 18000


3) = 995.65


2) = 146.5 Dynamic


3) = 96.8 b =

2.1101x107

s/m6 R=3.0857x10



Ssl = 1.02, S = 70.7 m2/kN.

53

APPENDIX C

Table C7: One Bucket of conditioned Sludge with one liter of distilled Water

Time t (s) Volume of filtrate

V(m3)

t/v V^2 V*t/v

1200 0.00344 348837.219 1.18.336x10-5

1200

2400 0.00540 444444.444 2.916x10-5 2400

3600 0.006463 557016.868 4.17704x10-5 3600

4800 0.00721 668742.025 8.19841x10-5 4800

6000 0.007659 783392.088 5.86603x10-05 6000

0.030172 2799432.631 0.000193084 18000


3) = 995.65


2) = 156.28 Dynamic


3) = 86 b =

10.0518x107

s/m6 R =17.6433x10



Ssl = 1.06, S = 305.5 m2/kN.

Table C8: One Bucket of conditioned Sludge with two liters of distilled Water

Time t

(s)


1200 0.005683 211156.060 3.22965x10-5 1200

2400 0.007699 311728.796 5.92746x10-5 2400

3600 0.008815 408394.782 7.77042x10-5 3600

4800 0.009577 501200.794 9.17189x10-5 4800

6000 0.060167 590.144.585 0.000103368 6000

0.641941 2022625 0.000364362 18000


3) = 995.94

Area A (m2) = 0.9 Hydrostatic pressure P = ρgh(N/m

2) = 146.60 Dynamic


3) = 82.8 b =

8.2442sx107

s/m6 R =13.6715x10


54


Ssl = 1.06, S = 328.3 m2/kN.

Table C9: One Bucket of conditioned Sludge with three liters of distilled Water

Time t

(s)


1200 0.0076 187.894.757 5.776x10-5 1200

2400 0.0095.53 281229.980 9.1260 x10-5 2400

3600 0.010613 339206.633 0.000112641x10-5 3600

4800 0.011328 423728.814 0.00012832 x10-5 4800

6000 0.012058 497801.377 0.00145395 x10-5 6000

0.051152 1669861.54 0.00053538 18000


3) = 995.65


2) = 136.74 Dynamic


3) = 81.2 b =

7.5630x107

s/m6 R =12.3017x10



Ssl = 1.06, S = 331.7 m2/kN.

Table C10: One Bucket of conditioned Sludge with four liters of distilled Water

Time t

(s)


1200 0.008014 149737.959 6.4224x10-5 1200

2400 0.01014 236686.391 0.00010282x10-5 2400

3600 0.011081 324880.426 0.012279x10-5 3600

4800 0.011727 409311.845 0.00013752x10-5 4800

6000 0.012514 479463.00 0.00015660x10-5 6000

0.053476 1600079.62 0.00058395 18000


3) = 995.09


2) = 126.90, Dynamic

viscosity µ(N.S/m2) = 0.7918, solid content C mass/vol. (kg/m

3) = 80.26 b =

55

7.3779x107

s/m6 R =11.9334x10



Ssl = 1.06, S = 451.3 m2/kN.

Table C11: One Bucket of conditioned Sludge with five liters of distilled Water


1200 0.08415 142602.5 7.08122x10-5 1200

2400 0.010521 228115.2 0.00011069 2400

3600 0.11661 308721.4 0.00013598 3600

4800 0.12362 388286.7 0.00015282 4800

6000 0.12882 465766.2 0.0016596 6000

0.05584 1533492 0.00063626 18000


3) = 994.76

Area A (m2) = 0.9 Hydrostatic pressure P = ρgh(N/m

2) = 117.1 Dynamic


3) = 78 b =

6.9223x107

s/m6 R =10.9265x10



Ssl = 1.06, S = 505.6 m2/kN.

56

APPENDIX D

CALCULATED VALUE OF MODIFIED EQUATION OF SPECIFIC

RESISTANCE AND CARMAN’S EQUATION

Using Carman’s filtration equation, the Specific Resistance can be

evaluated from the calculated values.

Hence, bc

pAR

=

µ

22

From the result collected from the unconditioned sludge, we obtain

R = 4.3435x107m/kg

The Effect of Ferric Chloride (Fecl3) on Specific Resistance

R1 = 23.0288x107m/kg, R2 = 19.8938 x10

7m/kg, R3 = 11.8560 x10

7m/kg, R4 =

10.5704 x107m/kg, R5= 6.1713 x10

7m/kg

The Effect of Fecl3 on Solid Content.

R1 = 32.2161x107m/kg, R2 = 26.5214x10

7m/kg, R3 = 24.6033 x10

7m/kg, R4 =

23.8668 x107m/kg, R5 = 21.8522 x10

7m/kg.

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Anthony Godlove PG/M.ED/11/58795 Anthony's... · 2015. 8. 29. · Anthony Godlove LMT DIMENSIONAL EQUATION FOR SLUDGE DRYING BED Coe nt mag er’s 1 PG/M.ED/11/58795 Engineering Coe