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Anthony Godlove
LMT DIMENSIONAL EQUATION FOR SLUDGE DRYING BED
Content manager’s
1
Anthony Godlove
PG/M.ED/11/58795
LMT DIMENSIONAL EQUATION FOR SLUDGE DRYING BED
Engineering
Content manager’s Name
Digitally Signed by: Content manager’s
DN : CN = Webmaster’s name
O= University of Nigeria, Nsukka
OU = Innovation Centre
: Content manager’s Name
Webmaster’s name
a, Nsukka
2
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
LMT DIMENSIONAL EQUATION FOR SLUDGE DRYING BED
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
Table B3: The Effect of Ferric Chloride on Specific Resistance
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
Table B5: The Effect of Ferric Chloride on Specific Resistance
using one bucket of Sludge with 40g of Ferric Chloride ................... 51
Table B6: The Effect of Ferric Chloride on Specific Resistance
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
between Modified Equation and Carman’s Equation. ......................... 42
Figure 4.9: Comparison of the Effect of Fecl3 on Solid Content
between Modified Equation and Carman’s Equation. ......................... 43
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.
Table B3: The Effect of Ferric Chloride on Specific Resistance using one
bucket of Sludge with 20g of Ferric Chloride
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
Area A (m2) = 0.9 Hydrostatic pressure P = ρgh (N/m
2) = 175.63 Dynamic
viscosity µ (N.S/m2) = 0.8386 solid content C mass/vol. (kg/m
3) = 96.8 b =
51
5.7001x107
s/m6 R = 9.9893x10
7 m/kg. Weight of dry solid Wd (kg) = 0.0547.
Percentage of solid expressed in decimal Ps = 0.12. Specific gravity of sludge
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
Height h(m) = 0.017, Temp (oC) = 28 density of water (kg/m
3) = 996.23
Area A (m2) = 0.9 Hydrostatic pressure P = ρgh (N/m
2) = 165.97 Dynamic
viscosity µ (N.S/m2) = 0.8916 solid content C mass/vol. (kg/m
3) = 96.8 b =
4.0615x107
s/m6 R = 6.3264x10
7 m/kg. Weight of dry solid Wd (kg) = 0.0553.
Percentage of solid expressed in decimal Ps = 0.13. Specific gravity of sludge
Ssl = 1.03, S = 81.1 m2/kN.
Table B5: The Effect of Ferric Chloride on Specific Resistance using one
bucket of Sludge with 40g of Ferric Chloride
Time t (s) Volume of filtrate V(m3) t/v V^2 V*t/v
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
Height h(m) = 0.016, Temp (oC) = 30 density of water (kg/m
3) = 995.65
Area A (m2) = 0.9 Hydrostatic pressure P = ρgh (N/m
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
7 m/kg. Weight of dry solid Wd (kg) = 0.0553.
Percentage of solid expressed in decimal Ps = 0.15. Specific gravity of sludge
Ssl = 1.03, S = 74.7 m2/kN.
Table B6: The Effect of Ferric Chloride on Specific Resistance using one
bucket of Sludge with 50g of Ferric Chloride
Time t (s) Volume of filtrate V(m3) t/v V^2 V*t/v
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
Height h(m) = 0.015, Temp (oC) = 30 density of water (kg/m
3) = 995.65
Area A (m2) = 0.9 Hydrostatic pressure P = ρgh (N/m
2) = 146.5 Dynamic
viscosity µ(N.S/m2) = 0.8386 solid content C mass/vol. (kg/m
3) = 96.8 b =
2.1101x107
s/m6 R=3.0857x10
7 m/kg. Weight of dry solid Wd (kg) = 0.00550.
Percentage of solid expressed in decimal Ps = 0.17. Specific gravity of sludge
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
Height h(m) = 0.016, Temp (oC) = 30 density of water (kg/m
3) = 995.65
Area A (m2) = 0.9 Hydrostatic pressure P = ρgh (N/m
2) = 156.28 Dynamic
viscosity µ(N.S/m2) = 0.8386 solid content C mass/vol. (kg/m
3) = 86 b =
10.0518x107
s/m6 R =17.6433x10
7 m/kg. Weight of dry solid Wd (kg) = 0.0540.
Percentage of solid expressed in decimal Ps = 0.04. Specific gravity of sludge
Ssl = 1.06, S = 305.5 m2/kN.
Table C8: One Bucket of conditioned Sludge with two liters of distilled Water
Time t
(s)
Volume of filtrate V(m3) t/v V^2 V*t/v
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
Height h(m) = 0.015, Temp (oC) = 29 density of water (kg/m
3) = 995.94
Area A (m2) = 0.9 Hydrostatic pressure P = ρgh(N/m
2) = 146.60 Dynamic
viscosity µ(N.S/m2) = 0.8642 solid content C mass/vol. (kg/m
3) = 82.8 b =
8.2442sx107
s/m6 R =13.6715x10
7 m/kg. Weight of dry solid Wd (kg) = 0.0553.
54
Percentage of solid expressed in decimal Ps = 0.04. Specific gravity of sludge
Ssl = 1.06, S = 328.3 m2/kN.
Table C9: One Bucket of conditioned Sludge with three liters of distilled Water
Time t
(s)
Volume of filtrate V(m3) t/v V^2 V*t/v
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
Height h(m) = 0.014, Temp (oC) = 30 density of water (kg/m
3) = 995.65
Area A (m2) = 0.9 Hydrostatic pressure P = ρgh (N/m
2) = 136.74 Dynamic
viscosity µ(N.S/m2) = 0.8386 solid content C mass/vol. (kg/m
3) = 81.2 b =
7.5630x107
s/m6 R =12.3017x10
7 m/kg. Weight of dry solid Wd (kg) = 0.0558.
Percentage of solid expressed in decimal Ps = 0.04. Specific gravity of sludge
Ssl = 1.06, S = 331.7 m2/kN.
Table C10: One Bucket of conditioned Sludge with four liters of distilled Water
Time t
(s)
Volume of filtrate V(m3) t/v V^2 V*t/v
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
Height h(m) = 0.013, Temp (oC) = 32 density of water (kg/m
3) = 995.09
Area A (m2) = 0.9 Hydrostatic pressure P = ρgh (N/m
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
7 m/kg. Weight of dry solid Wd (kg) = 0.0553.
Percentage of solid expressed in decimal Ps = 0.04. Specific gravity of sludge
Ssl = 1.06, S = 451.3 m2/kN.
Table C11: One Bucket of conditioned Sludge with five liters of distilled Water
Time t (s) Volume of filtrate V(m3) t/v V^2 V*t/v
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
Height h(m) = 0.012, Temp (oC) = 33 density of water (kg/m
3) = 994.76
Area A (m2) = 0.9 Hydrostatic pressure P = ρgh(N/m
2) = 117.1 Dynamic
viscosity µ(N.S/m2) = 0.77043 solid content C mass/vol. (kg/m
3) = 78 b =
6.9223x107
s/m6 R =10.9265x10
7 m/kg. Weight of dry solid Wd (kg) = 0.044.
Percentage of solid expressed in decimal Ps = 0.04. Specific gravity of sludge
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.