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APPLICATION OF MODIFIED FMTLXLYLZ DIMENSIONAL EQUATION TO
SLUDGE FILTRATION USING SLUDGE DRYING BED
__________________________________
BY
NNOROM CHRISTIAN NDUBUEZE
PG/M.ENG/08/48216
_________________________
A THESIS SUBMITTED IN PARTIAL FULFIILLMENT OF THE REQUIRMENNT
FOR THE AWARD OF MASTER OF ENGINEERING (M.ENGR. IN WATER AND
ENVIRONMENTAL ENGINEERING)
TO
DEPARTMENT OF CIVIL ENGINEERING
FACULTY OF ENGINEERING
UNIVERSITY OF NIGERIA NSUKKA
JANUARY, 2011.
1
APPLICATION OF MODIFIED FMTLXLYLZ DIMENSIONAL EQUATION TO
SLUDGE FILTRATION USING SLUDGE DRYING BED
2
CERTIFICATION
NNOROM CHRISTIAN a post graduate student in department of Civil Engineering, with the
Registration Number PG/ M.ENG/08/48216, have successfully completed the requirements for
the research work for the of Degree of Master of Engineering, (Water and Environmental
Engineering) the work embodied to thesis. The thesis is original, and has not been submitted part
or full’s for they other diploma or degree of this or any other university.
___________________________________
SUPERVISOR
PROF. J.O. ADEMILUYI
WATER AND ENVIRONMENAL ENGINEERING
CIVIL ENGINEERING
__________________
DATE
__________________________________
HEAD OF DEPARTMENT
ENGR. J.C. EZEOKONKWO
CIVIL ENGINEERING
__________________
DATE
__________________________________
DEAN FACULTY OF ENGINEERING
ENGR. PROF. J.C. AGUNWAMBA
__________________
DATE
__________________________________
EXTERNAL EXAMINAR
__________________
DATE
3
DEDICATION
This work is dedicated to my Father Mr. Paulinus N Nnorom for providing me with the
opportunity to live the life of my dream.
4
ABSTRACT
A natural filtration on sludge drying bed has resulted to a modified equation incorporating the
compressibility coefficient. The equation was derived using the application of a modified
FMTLXLYLZ dimensional analysis technique. The equation was validated using experimental
data from a pilot scale sand drying bed and there was a close agreement between theory and
experiment with a correlation coefficient ranging from 0.94 to 0.98. The experimental slope and
intercept was found to be (1260913.48 s/m6 , 4872.53 s/m3) (5359604.57 s/m6, 844882.56 s/m3),
(112117050.4 s/m6, -2135816.16 s/m3), and (145562880 s/m6, -30497917.03 s/m3) while the
theoretical values of slopes and intercepts are (1257426.75 s/m6, 5270.26 s/m3),( 4579418.42
s/m6, 905658.24 s/m3), (112117075 s/m6, -21358166.74 s/m3),and (206699290.5 s/m6, 4589555.58 s/m3) respectively.
5
ACKNOWLEDGEMENT
I thank God almighty for making this work a success.
I am indebted to Prof. J.O Ademiluyi for supervising the work. His assistance and
guidance provided me with the energy to push forward in the mist of unforeseen challenges.
Thanks to Prof. J.C Agunwamba for his invaluable advice during the work. Thanks to Engr. P
Nnaji for assisting in correcting the work. Thanks to Mr. Darlington Onyekachukwu Onyishi for
his support in providing me with relevant journals used for the work. Thanks to Glory Uchechi
Nnorom, my elder sister for her moral and financial support throughout the entire periods of the
work. Thanks to my mother for her support and understanding during my trying times.
Other academic and non-academic staffs of the department are all acknowledged for their
constructive criticism. And thanks to the bone of my bone, my wife Lois Nwamalubia Nnorom
for her constant support and understanding even in the face of the most trying and challenging
periods of my career.
6
LIST OF TABLES
Table 3.1: Filtration Variables and FMTLxLYLZ units
35
Table 3.2: Experimental result of the natural filtration observation
57
Table 3.3: Data used to calculate experimental slope and intercept
58
59
61
62
Table 3.7: Data used to calculate theoretical slope and intercept
63
64
65
66
Table 3.11: Data for filtration experiment using 10g of Ferric Chloride
67
68
69
70
Table 3.15: Data for filtration experiment using 50g Ferric Chloride
71
Table 3.16: Variation of ferric chloride Dosage on Specific Resistance
72
Table 3.17: variation between specific resistance and Initial solid content
73
Table 3.18: Relationship between Specific Resistance and Time
73
Table 3.19: Determination of Void ratio using sludge conditioned with 10g ferric chloride
74
Table 3.20: Compressibility coefficient from sludge conditioned with 10g ferric chloride
75
76
77
7
78
79
Table 3.25: Determination of Void ratio using 40g ferric chloride conditioner
80
81
Table 3.27: Determination of Void ratio using 50g ferric chloride conditioner
82
83
8
LIST OF FIGURES
Fig 3.1: Diagram of the sludge filtration set up
33
Fig 3.2: variation of t/v versus initial solid content of sludge ( M)
37
Fig 4.1: correlation between theoretical and experimental plot of t/v versus v
42
42
43
43
Fig 4.5: variation of t/v versus v for 10g of Ferric Chloride Conditioner.
44
45
45
Fig 4.8: variation of t/v versus v for 40g of Ferric Chloride Conditioner
46
Fig 4.9: variation of t/v versus v for 50g of Ferric Chloride Conditioner
46
Fig 4.10: Variation of specific resistance versus Initial solid content (M).
47
Fig 4.11: Variation of Specific Resistance versus pressure
48
Fig 4.12: Variation of pressure with void ratio for conditioned sludge.
48
Fig 4.13: variation of Compressibility Coefficient with pressure for conditioned sludge
49
9
LIST OF SYMBOLS
A
=
Cross sectional area (cm2)
V
=
Volume of filtrate cm3
T
=
Time of filtration (Hrs)
H
=
Driving Head of sludge (cm)
∆H
=
Change in sludge height
R
=
Specific resistance (m/kg)
g
=
Acceleration due to gravity (m/s2)
µ
=
Dynamic viscosity of filtrate (poise)
ρ
=
Density of filtrate (Kg/m3)
S
=
Compressibility coefficient (m2/KN)
C
=
Intercept on the t/v axis (s/m3)
b
=
Experimental Slope of t/v versus v (s/m6)
b.1
=
Theoretical slope of t/v versus v
C1
=
Theoretical intercept of t/v versus v
∆e
=
Change in void ratio
.e
=
Void ratio
P1
=
Initial pressure (KN/M2)
Wd
=
Weight of dry sludge ( g)
PS
=
Percent of solid content expressed in decimal
M
=
Initial solid content (/
Vsl
=
Volume of sludge (M3)
Ssl
=
Specific gravity of sludge
Hs
=
Initial sludge height (m)
10
TABLE OF CONTENT
Title page
i
Certification
ii
Dedication
iii
Abstract
iv
Acknowledgment
v
List of Tables
vi
List of figures
vii
List of symbols
viii
Table of content
ix
CHAPTER ONE: INTRODUCTION
1
1.1
Sludge and sand drying bed
1.2
Research Problem
2
1.3
Objective of project
2
1.4
Justification of project
2
1.5
Scope of study
3
CHAPTER
TWO: LITERATURE REVIEW
2.1
Sludge treatment process
4
2.1.1
Thickening
4
2.1.2
Stabilization
4
2.1.3
Conditioning
5
2.1.4
Disinfection
6
11
2.1.5
Dewatering
7
2.1.5.1
Vacuum filtration
7
2.1.5.2
Centrifuge
7
2.1.5.3
Belt filter press
8
2.1.5.4
Filter Press
8
2.1.5.5
Conventional sand drying bed
8
2.1.5.6
Paved drying bed
9
2.1.5.7
Artificial media drying beds
10
2.1.5.8
Vacuum-assisted drying bed
11
2.2
Drying
11
2.3
Definition of Terms
11
2.31
Specific Resistance
11
2.3.2
Compressibility coefficient
14
2.4
Limitation of Carman’s Equation
16
2.4.1
Variability of (R) during filtration process
17
2.4.2
The problem of variable hydrostatic head
17
2.4.3
Relationship between volume and time.
18
2.4.4
Relationship between volume and area of filtration
18
2.4.5
The concentration Term
18
2.4.6
Relationship between R and P
19
2.4.7
Area of filtration
19
2.5
Apparatus used in filtration experiment
19
2.6
Filtration Theories
21
12
2.6.1
Almy and Lewis (1912)
21
2.6.2
Sperry (1916)
21
2.6.3
Baker (1921)
22
2.6.4
Weber and Hershey (1926)
22
2.6.5
Carman (1934, 1938)
22
2.6.6
Ruth (1933, 1935)
23
2.6.7
Tiller (1953)
24
2.6.8
Grace (1953)
24
2.6.9
Rushton et al (1973)
25
2.6.10
Anazodo (1974)
25
2.6.11
Gale and White (1975)
26
2.6.12
Hemant (1981)
26
2.6.13
Ademiluyi jo , Anazodo and Egbuniwe (1982)
27
2.6.14
Ademiluyi (1984)
28
2.6.15
Ademiluyi et al (1982, 1987)
28
2.6.16
Agunwamba et al (1988)
29
2.6.17
Ademiluyi (1991)
30
CHAPTER THREE: RESEARCH METHODOLOGY
3.1
Study Area
31
3.2
Materials and Method
31
3.3
Dimensional analysis
33
3.4
Theory of Experiment
34
13
3.5
Method of evaluating filtration parameters
39
3.5.1
Initial solid content
39
3.5.2
The Area of filtration
39
3.5.3
The compressibility coefficient
39
3.5.4
Density of filtrate
39
3.5.5
Dynamic Viscosity
39
3.5.6
Weight of dry solid
40
3.5.7
Specific Resistance of sludge
40
3.5.8
Thickness of Dry sludge
40
3.5.9
Time of Filtration
40
3.5.10
Volume of Filtrate
40
3.5.11
Percentage of solid content expressed in decimal
40
CHAPTER
FOUR: RESULTS AND DISCUSSIONS
4.1
Experimental validation of equation
41
4.2
The Effect of chemical conditioning on the specific resistance
44
4.3
Variation of Initial solid content with specific resistance
47
4.4
Variation of Hydrostatic pressure with specific resistance
47
CHAPTER
FIVE: CONCLUSION AND RECOMMENDATION
48
REFERENCES
52
APPENDIX I
57
APPENDIX II
58
APPENDIX III
67
APPENDIX IV
74
14
CHAPTER ONE
INTRODUCTION
1.1
SLUDGE AND SAND DRYING BED DEWATERING
Domestic wastewater result from the use of water in dwellings of all types and includes
water after use and the various waste materials added: body waste, kitchen waste, household
cleaning agents and laundry soap and detergents. In contrast to the general uniformity of
substances found in domestic waste water, industrial waste water show increasing variation as
the complexity of industrial processes rises. The character of these waste materials is such that
they cause significant degradation of receiving waters and hence results to environmental health
hazard and pollution. One of the steps in the control of pollution is the treatment of waste water
before disposal. In the process of treating waste water, sludge is generated and constitutes the
most challenging problem facing the environmental engineer. This sludge has high water content
and is usually subjected to dewatering to reduce the moisture.
Sludge drying bed is one of the earliest processes used in the dewatering of sludge before
the introduction of mechanical processes. The waste can be dewatered in an open or covered
sand bed which also requires a large amount of land for its operation. Sand drying bed is affected
by such uncontrollable factors as Rainfall, Humidity and Temperature. The process is cost
effective and easy to operate than the mechanical system and usually produces sludge cake of
about 25-40% solid.
15
1.2
RESEARCH PROBLEM
The dewatering of sludge using vacuum filtration theory has been adopted in full scale in
the 1920s. Since then, various contributors for example Carman, 1934; Ruth, 1935; Coackley,
1958; Heertjes, 1964; Gale R.S, 1967; Anazodo, 1974; Ademiluyi j o, 1981etc) have been
presenting equations aimed at improving the performance of the vacuum filtration process.
However, their research was limited to experimental work which could not provide an insight
into the interactive nature of sludge filterability since filterability is an interactive property
expressing the relationship between the suspension to be filtered and the filtering medium.
1.3
OBJECTIVE OF PROJECT
The objective of the project is to present sand drying bed equation that will account for
compressibility coefficient through the application of a modified FMTLXLYLZ dimensional
approach.
1.4
JUSTIFICATION OF PROJECT
The general lack of agreement between experiment and theory in sludge filtration under
constant vacuum filtration approach discovered by the body of researchers has led to great
controversies which have resulted to the modifications of filtration equations as is contained in
literature. Therefore, this research opens new direction into the nature of sludge filtration
phenomenon and will enable new research into the natural filtration method which may result to
an end to the present controversies.
1.5 SCOPE OF STUDY
The sludge used for this study is limited to domestic sludge from the University of
Nigeria Nsukka waste treatment site. No chemical analysis of the filtrate and the sludge were
carried out.
16
CHAPTER TWO
LITERATURE REVIEW
2.1
SLUDGE TREATMENT PROCESS
The sludge generated in the course of waste water treatment also needs to undergo
treatment to enhance its handling and final disposal. Sludge treatment process includes:
Thickening, Stabilization, Conditioning, Disinfection, Dewatering and Drying.
2.1.1 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 solid 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. We have the gravity thickening, floatation thickening, centrifugation,
gravity belt thickening and rotary drum thickening.
2.1.2 STABILIZATION:
Living organisms consumes the organics in the sludge. Sludge are stabilized to reduce
pathogens; eliminate offensive odors. Through stabilization nuisance are removed by the
addition of chemical to the sludge and also by chemical oxidation of volatile matters. We have
several ways of achieving sludge stabilization and they include; Lime stabilization, Heat
treatment, anaerobic digestion, Aerobic digestion and Composting. In lime stabilization the P H
of the sludge is raised above 12 to create an unfavourable condition for the micro-organisms.
Heat treatment is also used to stabilize the sludge by heating the sludge in a continuously in
a pressure vessel to a temperature of about 2600C. Heat treatment renders affects the solids in
such a way that the sludge is amenable to dewatering without conditioning with chemicals.
17
In aerobic sludge digestion, the sludge is aerated for an extended period of time in an open
unheated tank using conventional air diffusers or surface aeration equipment. It is similar to the
activated sludge process. Anaerobic digestion of sludge involves the decomposition of organic
and inorganic matter in the absence of molecular oxygen.
2.1.3
CONDITIONING:
Sludge conditioning improves the filtration of sludge. Chemicals are used and also heat
treatment. The use of chemical to condition sludge makes for economical benefit because of its
increased yield and flexibility. During chemical conditioning absorbed water is released and the
solids are coagulated and the moisture content can be reduced to from about 95% to 70%.
Chemicals used include ferric chloride, organic polymer, Lime and alum. The type of dewatering
device used and sludge property affects the selection of chemical and dosage of the sludge. Solid
concentration will also affect the dosage of the conditioning agent. The PH and alkalinity may
also affect the performance of conditioner. Also the method used to dewater the sludge may
affect the selection of chemical conditioner because of the difference in the mixing equipment
employed.
The sludge structure is broken by the application of the heat treatment on the primary
sludge. It is also used to reduce the water affinity of sludge solids to enable the sludge to dewater
easily. The partially oxidized sludge from the heat treatment unit may be dewatered by vacuum
filtration, centrifugation, belt press or a drying bed.
18
2.1.4 DISINFECTION
When sludge is applied to land, protection of public health requires that contact with
pathogenic organism be controlled.
Disinfection of liquid aerobic and anaerobic digested sludges is best accomplished by
pasteurization or long term storage. Liquid digested sludge is normally stored in earthen lagoons.
Storage requires that sufficient land be available. Storage is often necessary in land application
systems to retain sludge during periods when it cannot be applied because of weather or crop
condition. In this case the storage facility can be used as a means of providing disinfection.
Typical detention time s for disinfection is 60 days and 120 days.
There are many ways of destroying bacteria using disinfectants namely:
1. Pasteurization
2. High PH treatment
3. Addition of chlorine to stabilize
4. Disinfection with other chemicals
5. Disinfectant by high energy irradiation.
Pasteurization involves two methods: The direct injection of steam and the indirect heat
exchange. Because heat exchangers tend to scale or become fouled with organic matters, it
appears that the direct steam injection is the most feasible method.
The thermophilic aerobic digestion coupled with anaerobic digestion may also be used
for the pasteurization of sludge.
19
2.1.5
DEWATERING
This process is used to reduce the water content and increase solid content to between
20 – 30%. Sludge can be dewatered mechanically or naturally on sand bed with a good result.
The available dewatering equipments are Vacuum filters, centrifuges, belt filter press drying
beds and lagoons. Amongst these equipments Sand drying bed is one of the earliest processes
used in the dewatering of sludge before the introduction of mechanical processes. The waste can
be dewatered in an open or covered sand bed which also requires a large amount of land for its
operation. Sand drying bed is affected by such uncontrollable factors as Rainfall, Humidity and
Temperature. The process is cost effective and easy to operate than the mechanical system and
usually produces sludge cake of about 25-40% solid.
2.1.5.1 VACUUM FILTRATION
In vacuum filtration atmospheric pressure, due to a vacuum applied downstream of the
filter media, is the driving force on the liquid phase that causes it to move through the media.
The vacuum filter consist of a horizontal cylindrical drum that rotates partially submerged in a
vat of conditioned sludge. The surface of the drum is covered with a porous medium, the
selection of which is based on the sludge characteristics. Type of filter commonly used are cloth
belts or coiled springs.
2.1.5.2
CENTRIFUGE
The centrifuge is widely used in the industry for separating liquids of different
densities, thickening slurries, or removing solids.
20
2.1.5.3
BELT FILTER PRESS
Belt filter press are continuous feed sludge-dewatering device that involves the
application of chemical conditioning, gravity drainage, and mechanically applied pressure to
dewater sludge.
2.1.5.4
FILTER PRESSES
Dewatering is achieved in this device by forcing water from the sludge under high
pressure. Chemically conditioned sludge is pumped into the space between the plates, and
pressure of 690 to 1550 kN/M2 is applied and maintained for 1 to 3 Hrs forcing the liquid
through the filter cloth and plate outlet ports.
2.1.5.5 CONVENTIONAL SAND DRYING BEDS.
The conventional sand drying bed is used for small and medium size communities but
for population of over 20000 people alternative method may be considered. In a typical sand
drying bed, sludge is placed on the bed in 200 -300mm layer and allowed to dry. Sludge
dewaters by drainage through the sludge mass and supporting sand and by evaporation from the
surface exposed to the air. Most of the water leaves the sludge by drainage, thus the provision of
an adequate under-drainage system is essential. Drying beds are equipped with lateral drainage
line sloped at a minimum of 1% and spaced 2.5-6m apart. The drainage line should be
adequately supported and covered with coarse gravel or crushed stone. The sand layer should be
from 230-300mm deep with an allowance for loss from cleaning operations. Deeper sand layer
generally retard the draining process. Sand should have a uniform coefficient of not over 4 and
an effective size of 0.3 – 0.75mm. The drying area is partitioned into individual beds, 6m wide
by 6 to 30m long or a convenient size so that one or two beds will be filled in a normal loading
circle. The interior partitions commonly consist of two or three creosoted planks, one on top of
21
the other, to a height of 380-460mm, stretching between slots in precast concrete posts. The outer
boundary may be of similar construction or may be made of earthen embankments for open
drying beds. Concrete foundation walls are required if the beds are to be covered.
Piping to the sludge beds should drain to the bed and should be designed for a velocity of
0.75m/s cast iron or plastic pipe is commonly used. Distribution boxes are required to divert the
sludge flow into the bed selected. Splash plates are placed in front of the sludge outlet to spread
the sludge over the bed and to prevent erosion of the sand.
Sludge can be removed from the drying bed after it has been drained and dried
sufficiently. Dried Sludge has a coarse, cracked surface and is black or dark brown in color.
The moisture content is approximately 60% after days under favorable conditions. Open
beds are used were adequate area is available and is sufficiently isolated to avoid complaints
caused by occasional odors. Open sludge bed should be located at least 100m from dwellings to
avoid odors nuisance. Covered bed with the greenhouse types of enclosures are used were it is
necessary to dewater sludge continuously throughout the year regardless of the weather and
were sufficient isolation does not exist for the installation of open beds.
22
2.1.5.6 PAVED DRYING BED
There are two types of the above drying bed: a drainage type and a decanting type. The
drainage type functions similarly to a conventional sand drying bed in that underdrainage is
collected, but sludge removal is improved by using a front-end loader. Sludge drying may also
be facilitated by frequent agitation with mobile equipment. With design, the bed are normally
rectangular in shape and are6 – 15m wide by 21 – 46m long with vertical side walls. For a given
amount of sludge, this type of paved drying bed requires more area than the conventional sand
beds.
The decanting type of drying bed is relatively a new design and it is used in a warm,
arid and semi arid climate. This type of drying bed uses a low cost impermeable paved bed that
depends on the decanting of supernatant and mixing of drying sludge for enhanced evaporation.
Decanting may remove about 20-30% of the water with good settling sludge. Solid concentration
may range from 40-50% for a 30 -40days drying time in an arid climate for 300mm sludge layer.
2.1.5.7 ARTIFICIAL MEDIA DRYING BEDS.
In the artificial drying bed stainless steel wedge or high-density polyurethane are formed
into panels. In the wedge wire drying bed, liquid sludge is introduced onto a horizontal,
relatively open drainage medium. The medium consist of small stainless steel wedge-shaped bars
with the flat part of the wedge on top. Its advantage is: no clogging of the wedge wire, drainage
is constant and rapid, throughput is higher than sand beds, aerobically digested sludge can be
dried and bed is easy to maintain. The principal disadvantage is that its capital cost is higher than
that of conventional drying sand. In the high- density polyurethane media system, special
300mm square interlocking panels are formed for installation on a slope slab or in prefabricated
steel self-dumping trays. Each panel has an 8% open area for dewatering and contains a built-in
23
underdrain system. The system can be designed for open or covered beds. Its advantages are:
dilute sludge can be dewatered including aerobically digested waste activated sludge, filtrates
contains low suspended solids and fixed unit can be cleaned easily with a front end loader.
2.1.5.8
VACUUM-ASSISTED DRYING BEDS.
In a vacuum assisted drying beds, dewatering and drying are assisted by the application of
vacuum. Its operations involves: Preconditioning the sludge with a polymer, filling the bed with
sludge, dewatering the sludge initially by gravity drainage followed by the application of
vacuum, allowing the sludge to air dry for about 24-48hrs, removal of the dewatered sludge and
washing the surface of the porous plates with a high pressure hose to remove the remaining
sludge residue.
2.2
DRYING:
With drying, sludge is dewatered further to about 95% dry solid. This is a process which
involves reducing water content by vaporization of water to the air. There are two major drying
methods namely convection drying which involves passing heated air flue gas over a sludge
layer were it absorbs water from the wet sludge. In contact drying heat is transferred to the
sludge through a wall. Sludge can also be dried on an open air in a favorable climatic condition.
The two most important control measures in drying sludge are fly ash collection and odor
control. Sludge drying occurs at a temperature of approximately 3700C and to achieve complete
destruction of odor, the exhaust gas must reach approximately 7300C.
24
2.3 DEFINITION OF TERMS
2.3.1 SPECIFIC RESISTANCE
The term specific resistance was first proposed by Carman (1934) and was defined by
him as the pressure that is required to produce 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. In
sludge dewatering experiment 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 process continues, the resistance to flow of fluid through the medium
becomes negligible while the resistance to filtration exerted by the sludge cake steadily increases
as the porosity decreases along the cake height. The driving forces required overcoming the
resistance offered by the cake and the filter bed is provided by the difference in pressure between
the deposited zone of the sludge solid and the bottom of the filter bed.
The specific resistance of sludge depends on the characteristics of the sludge, the
chemical and physical treatment of sludge prior to filtration, the filter media and other
mechanical features of equipment design (Eugene and Mueller, 1958).
Among the characteristics of sludge which affect filtration are viscosity of filtrate, solid
concentration, compressibility of the sludge, chemical composition, and temperature of sludge
and porosity of the cake (Eugene and Mueller, 1958).
Coackley (1958) showed experimentally that the specific resistance decreases with
decreasing solid content in a digested sludge filtration. It has been found that specific resistance
of suspension comprised of irregular shaped particles increases with the initial concentration of
25
the suspension while the specific resistance of suspension of spherical particles was constant and
independent of concentration. Dick, (1968)
Heerjets (1964) adduced that the variation of specific resistance with solid concentration
could be explained as due to filter blinding. In very dilute solution particles will either enter a
filter pore or cover the pore opening thereby blocking the filter causing increase in resistance.
In terms of chemical nature of sludge, Turovskil (1974) suggested that the presence of iron,
chromium, copper, acids and alkalines improve filtration while fats, oil and petroleum products
inhibits filtration.
Genter (1958) reviewed the effect of chemical composition on sludge filtration. Since the
chemical composition of a sludge controls the amount of chemical required for conditioning,
hence its filterability indirectly depends on its chemical demand.
Hawkins (1964) reported that limes softening of sludge high in magnesium content are
more difficult to dewater by vacuum filtration than sludge low in magnesium content.
Parkes, et al (1972) remarked that the presence of chlorine in sludge is detrimental to
sludge filterability. The effect of phosphate precipitate present in some sludges on dewaterability
was found by O’shoughnessy (1974).
Eugene et al (1958) have indicated that specific resistance is more easily reduced when
Ferric chloride is added first to the sludge before lime.
Coackley (1956) has shown that freezing alone gives only a small decrease in specific
resistance but when Ferric chloride is added before freezing it is possible to obtain sludge having
a specific resistance of the order of 1,000 times less than that of the original sludge.
Christensen and Donald (1979) on investigating the chemical reactions affecting
filterability of iron- lime sludge conditioning Ferric and ferrous salt discovered that Ferric ions
26
gives the best performance used alone or with lime. The combination of ferrous sulphate and
lime provides the poorest conditioning.
The effect of aging on the sludge filterability in Ferric chloride conditioned sludge was
also part of Christensen and Donald’s investigation.
Nelson and Tavery (1978) remarked from their research findings that polymers are a cost
effective means of conditioning sludge, but that maximum yield is much more effectively
achieved when Ferric chloride and lime are used to condition raw sludge mixture.
Other chemicals that have been used by various workers in filtration include
polyelectrolyte (Dick, 1968) and fly ash (Dick, 1968). Physical factors that influence specific
resistance includes shear, filter medium, pressure, hydrolysis and rainfall.
Filter medium blinding affect specific resistance of sludge. The probability of cloth
blinding occurring and its degree will largely depend on the initial concentration of fine in the
sludge, the mesh size of the filter medium and the efficiency of the conditioning chemical in
flocculated fine (White and Baskerville 1974).
White and Baskerville, 1974) reported that the problem of blinding of vacuum filter
cloths could be caused by a high grease content in the sludge. Lime and Ferric chloride
conditioner could however eliminate such blinding.
Coackley (1958) has experimentally shown that specific resistance of digested sludge
increase with the pressure and that if the initial pressure was greater than the pressure applied in
later stages, the rate of filtration would be lower than that obtained by allowing the pressure to
build up slowly to the filtration pressure.
27
Randall and Koch (1969) working on the dewatering characteristics of aerobically
digested sludge found that the dewatering time of a sludge containing hygroscopic fiberous
material could be prolonged considerably by rainfall effects thereby affecting specific resistance.
2.3.2
COMPRESSIBILITY OF SLUDGE
The compressibility of a sludge is another parameter believed to be affecting sludge
filtration 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 filtrate.
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. In a
sludge mass having its void filled with incompressible water, decrease in volume or compression
can take place when water is expelled out of the voids. Such a compression resulting from a long
time static load and the consequent escape of pore water is termed as consolidation.
When the pressure is applied on the sludge mass, the entire load is carried by pore water
in the beginning. As the water starts escaping from the voids, the hydrostatic pressure in water
gets gradually dissipated and the load is shifted to the sludge solids which increases effective on
them, as a result the sludge mass decrease in volume. The rate of escape of water depends on the
permeability and compressibility of the sludge. Carman defined the parameter through the
relation
R = KPS and Ruth (1933) suggested
2.1
R = r(1 + r2ps)
2.2
28
Both equation are empirical and has been criticized as not given a qualitative definition of
compressibility.
Ademiluyi agued that the persistent controversy in sludge filtration equations is due to
the inapplicability of Darcy’s law to compressible or non rigid materials. The compressibility of
sludge must be accounted for before the present controversy can be resolved (Anazodo, 1974,
white and Gale 1975). It is for this reason that the dimensional equation and modified equation
can not be accepted as valid.
Neither Carman (1935) nor Ruth (1933) gave a qualitative definition of compressibility
coefficient S . S was first evaluated by first determining r at varying pressures. The slope of the
log r versus log P then gives the compressibility coefficient. From the carefully investigated
work of Ademiluyi et al (1983) this definition does not hold for all degree of dilutions.
It was because of the importance of this parameter that Nebiker et al (1968) suggested
that the factors which affect specific resistance should be investigated whether such factor also
affect compressibility coefficient. Since the compressibility coefficient of sludge were only
evaluated by previous workers, Ademiluyi, Anazodo and Egbuniwe (1983) investigated the
effect of dilution and chemical conditioning on compressibility coefficient using Carman’s
equation. They concluded that the decrease in compressibility coefficient with increasing dilution
as noted fro investigation indicates that with certain systems and concentration Carman’s
empirical relationship r = ( KPS) may not be obeyed.
Trawinski (1980) argued that the compressibility of cake is one of the reason why
filtration equation is limited. A universal definition based on Terzaghi 1966, Lamb, 1969)
definition of compressibility coefficient cannot be overstressed. This will be more acceptable to
the academic world than the empirical equation by Carman and Ruth.
29
2.4
LIMITATION OF CARMAN’S EQUATIONS
Carman’s equation was formulated from a combination of poiseuill’s law and Darcy’s
law and can largely be classified as belonging sperry’s group of equations. It is this equation that
is been used to solve filtration problem today.
The general lack of agreement (Heertjets 1964,
Anazodo 1974) between experimental data of Ruth and his coworkers has led these workers
including Heertjes (1964) to conclude that a valid theoretical basis for the treatment of filtration
problems has not been established. This view was also reiterated by purchas (1981). Recently it
has been suggested that all equation based on sperry’s theory or which contain the same
variables as Carman’s equation might not describe the filtration process well enough if certain
parameters that are influencing filtration phenomenon are missing ( Ademiluyi, 1981).
Also the
dimensional equation as derived by Anazodo cannot be accepted in view of the objections raised
by white and Gale (1975).
2.4.1 THE VARIABILITY OF (R) DURING FILTRATION PROCESS
The only apparent problem in the laboratory Buchner funnel technique of Coackley (1958) is the
mode of evaluating the assumed average specific resistance r. This is due to the Carman’s
equation on which the design of the apparatus was based.
Filtrate volume are measured only few minutes or seconds after the start of filtration and
before cake cracking. Hence only the parabolic portion of the plot of t/v versus v is measured.
Early workers also submitted that the specific resistance increase from the surface to the
cake to the septum since the porosity decreases from the surface of the filter septum (Grace,
1953, Tiller, 1964, Hemnant, 1981). There is no laboratory apparatus which measures specific
resistance parameter, neither is there any theory simple in concept which enables the direct
evaluation of specific resistance during vacuum filtration in available literature.
30
2.4.2 THE PROBLEM OF VARIABLE HYDROSTATIC HEAD
In vacuum filtration, before the application of vacuum it is a common experience that
dewatering takes place especially for highly conditioned sludge. The only driving force at this
period is nothing but the hydrostatic pressure. When vacuum is eventually applied the effect of
hydrostatic pressure as a component of the total operating pressure cannot be reasonably
considered as negligible.
Willis and Tosun (1980) showed that deviations from the parabolic behavior (a common
phenomenon in all sludge filtrations) may be due to variability of preasure. This shows that the
pressure operating in vacuum filtration is not the constant pressure due to vacuum alone but ther
is another contributory variable which brings about the none parabolic relationship of the plot of
t/v versus v. This may be the hydrostatic pressure.
It is this pressure only that operates in gravity dewatering on dry beds, and hence it can
not be taken to be negligible in vacuum filtration
Hermant (1974) hinted that the hydrostatic head should be accounted for in the basic
equation for industrial vacuum sludge filtration. He also poin variation until the constant pressure
of the vacuum is reached.
2.4.3 RELATIONSHIP BETWEEN VOLUME AND TIME
Carman (1943, 1935) presented the relationship between V and t to be parabolic but, Willis et al
(1980) presented a deviation parabolic relationship and suggested that this deviation from
parabolic relationship might be due to variability of operating pressure.
31
2.4.4 RELATIONSHIP BETWEEN VOLUME AND AREA OF FILTRATION
Carman’s equation predicts that v is proportional to absolute area A but from carefull
experimental investigation by Ademiluyi et al (1982) it has been shown that v is proportional to
the area A raised to the power 0.91 plus or minus 0.02 and 1.38 plus or minus 0.02 when total
area and effective areas of the filter are used respectively. ( Ademiluyi, Anazodo Egbuniwe,
1982)
2.4.5 THE CONCENTRATION TERM
In Carman’s equation C is the mass of dry cake per unit filtrate volume and this
parameter is difficult to measure experimentally as stated by Ademiluyi and hence it is taken as
the initial solid content of the sludge which is inconsistent with theoretical prediction.
2.4.6 THE RELATIONSHIP BETWEEN R AND P
In Carman’s equation, R increases with P but from practical experience more filtrate
volume is procured at higher pressure than at lower pressure which shows that the resistance
should decrease with increasing pressure.
2.4.7 THE AREA OF FILTRATION
The filtration area has brought up controversies among previous researchers (Ademiluyi,
1981). Some believe that the total area should be assumed while others school of thought
advocate effective area of filtration. . Some take the effective area as being equal to the area of
the filter medium while some define it as the total area of the concentric holes of the Buchner
funnel.
32
2.5
APPARATUS USED IN FILTRATION EXPERIMENT
Coackley (1956) presented a filtration apparatus called Buckner Funnel apparatus using
carman’s theory. Sludge is filtered using a vacuum pump. With the aid of the apparatus the
volume of filtrate at specific time can be collected and used to plot t/v versus v as required by
carman’s Theory. It is this apparatus that is used in the laboratory evaluation of specific
resistance both in chemical engineering and public health engineering laboratories.
Swanwick and Davidson, (1961) examined the relationship between specific resistance
and area for sludge. They drew attention to the large uncertainty in the value used for the
effective filtration area of the buckner funnel.
Coackley (1958) had assumed that the effective filtration area of the buckner funnel was
equal to the area of the filter paper. However, Swanwick et al (1961) argued that this
overestimated the true filtration area by more than 25%.
Kavanagh (1980) contributed to resolve the forgoing conflicts by arguing that the use of
the filter paper area as a measure of the effective filtration area of the burkner funnel which was
not supported by Swanwick et al, is in fact justified and does not introduce significant error into
the determination of specific resistance.
Because r is evaluated by first measuring t and v, Wuhrman (1977) designed and
described a device which can be used to automate the measurement of r. The Wuhrmann
apparatus simply measures the period taken for the accumulation of a fixed volume of filtrate
between two set of volume, thus b is calculated from the values of t and v. While recognizing the
problems associated with initial none- linearity of typical plot of t/v against v. Wuhrmann
assumes that the non-linear portions of the graph always fall at the same volumes. Knapp
(1981), criticized this assumptions and concluded that the use of a two point graph is unsound.
33
To this end, an accurate level indicator for the measurement of specific resistance was
made by Knapp et al (1981) based on Carman’s equation. Knapp et al claimed that the apparatus
could be used to overcome the intrinsic problems of the Wuhrmann apparatus and allows
accurate automatic determination of time and volume.
The Knapp apparatus is a u tube receiver with one arm fitted with a series of electrodes
and the other being connected to the filter outlet which record and plots t/v versus v on a chart.
They however, admitted that the cost of the apparatus is very low both the electrode
assembly and the electrical circuit are cheap and easy to make. A simple power supply was
found to be adequate. They however submitted that the chart recorder is expensive. Also the
incorporation of Knapp’s apparatus into vacuum filter has not been tested and its possibility may
be doubtful.
The capillary suction time apparatus was invented by Baskerville et al (1968). The CST
determination has proved very popular (Eden,1983) as a rapid method of assessing the ease of
dewatering of sludge and hence of the relative efficiency of conditioners. The CST test is
however entirely arbitrary (Eden, 1983).
2.6
FILTRATION THEORIES
2.6.1 ALMY AND LEWIS (1912)
The theory of filtration was first proposed by Almy and Lewis who filtered chromium
hydroxide at a series of constant pressures. Their equation is given below:
2.3
Were n and m are indefinite powers, P= pressure, V = Volume and K is a constant of
proportionality which varies with the material to be filtered.
34
2.6.2
SPERRY (1916)
Sperry used the analogy between ground water flow and the filtration process to derive
his filtration equation. He assumed that since Poiseuille's law holds for groundwater flow, then it
should also represent the basic law of filtration.
He stated that, the rate of flow was considered to be strictly proportional to the first
power of P and V and in which provision was made for the effect of filter base resistance and
variation in filtrates viscosity. This is his modified Poiseuille's law equation.
2.4
were R is given as the resistance to flow of filtrate through the filter cake and the filter medium.
The above equation has been criticized by previous workers as been more of theoretical than
practical.
2.6.3
BAKER (1921)
Baker’s work was in disagreement with that of Almy and Lewis as regards the
relationship between rate of flow been proportional to independent powers (n and m) of pressure
and volumes and this led to his deriving of another equation of the form given below:
2.5
The integrated expression is
2.6
2.6.4 WEBER AND HERSHEY (1926)
The original equation of Almy and Lewis was modified by Weber and Hershey into the
form below
2.7
35
Underwood (1926) criticized the above equation on the ground that it contains error and went
forward to propose the concept of specific resistance. His equation is of the form
r=
2.8
were r" is the resistance of unit cube of cake when under unit pressure, with unit rate of filtrate
flow passing through it. r is average resistance per unit cube of cake. Because this equation was
derived through modification of an equation that already has been proved to be in error, it was
not also accepted by researchers as been valid.
2.6.5 CARMAN (1934, )
Carman was the first to propose the cake filtration theory based on the concept of
specific resistance. He approximated compressible cake to a non-compressible sand bed and
derived the equation stated below:
t=
+μRV
2.9
He declared that if the total filtration Pressure P is made up of a part which overcomes cake
resistance and a part which overcomes initial resistance of the filter septum, then for a rigid cake
of thickness L and assuming that filter septum also obeys Darcy’s law, the rate of filtration is
given as
U=
2.10
Since cake permeability is defined as the ease with which liquid is passed, cake resistance is
conversely defined as the difficulty with which liquid is passed and from this assumption that
L =CV/A
2.11
Another equation was derived thus:
2.12
36
where 'R' is the initial resistance due to the filter septum and 'r' is the resistance of the cake.
Integrating the above equation we arrive at the final form shown below:
t=
2.13
2.6.6 RUTH (1933,)
The idea of specific resistance was given more light by Ruth who demonstrated
experimentally that the plot of Volume per unit area V versus time t followed a parabolic relation
as shown by Carman and Ruth 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 in theory that for
constant pressure filtration the relationship between V and t were not perfect parabolas rather, 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 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.
37
2.6.8 GRACE (1953)
Grace theory showed that specific resistance rp for a cake with uniformly applied pressure
stress could be obtained by consolidating the cake at that pressure and subsequently determining
its permeability. He obtained an expression for average specific resistance of the cake which
depends on the pressure drop across cake P2-P1 and on the pressure drop across the septum P1-P.
The filter medium resistance is determined from a separate permeability experiment thus:
2.14
2.15
r is obtained by integrating the left hand side by Simpson’s rule. Grace remarked that the
average specific resistance at any particular pressure within the needed range could be calculated
and that the determination of permeability over a complete range of pressure could be completed
in a day. He asserted that in the filtration of compressible cake the mechanical pressure on the
cake particle varies through the cake depth, causing a variation in the cake porosity and specific
resistance through the depth of the deposited cake.
Grace also asserted that the pressure that is causing physical compression of the cake
result in the cumulative drag of filtrate flowing through pores, component of existing
gravitational field acting on cake solid in direction of filtrate flow through cake, and kinetic
energy change in filtrate flowing through the cake. Since the overall pressure stress increases in
the direction of filtrate flow, the specific cake resistance increases in the same direction.
38
2.6.9 RUSHTON ET AL (1973)
Rushton and others modifying Caman’s Equation took into account the part played by
particle sizes during filtration to arrive at the equation given below:
=μc/
2.16
The above equation gave a better agreement between theory and experimental results
than the yield equation based on Carman's theory.
2.6.10 ANAZODO (1974)
Carman’s equation for sludge filtration which was based on poiseuille’s and Darcy’s law
was criticized by Anazodo who argued that the approximation of filter cake to a rigid bundles of
capillary tubes or to a non compressible sand bed is incorrect. 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,
and t. Finally, he combined Force and Mass
creating FMLX LY LZ system of dimensional analysis to derive the equation below. Where x, y
and z are three mutually perpendicular axes in space.
V =〔
2.17
Since the relationship between V and t has been established to be parabolic, Anazodo,(1974)
substituted f = 1/2 to obtain a dimensional equation for sludge filtration as:
2.18
39
2.6.11 GALE AND WHITE (1975)
Gale and White, (1975) rejected Anazodo’s (1974) derivation using dimensional equation
on the ground that, Anazodo,(1974) 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 5/4.and also that
Anazodo need not assume f = 1/2.
Carman’s equation was preferred because it predicted the relationship between volume of filtrate
and just area. Gale and White (1975) went forward to modify Anazodo’s (1974)equation to the
one below:
V2 = P u-1 A2b t (Cr)2b-3
2.19
It was concluded that V and A should be determined experimentally so that, If b = 1,
Caman's equation should be accepted, and if b= 5/4, Anazodo's (1974) equation holds. 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.
2.6.12 HEMANT (1981)
Hemant,(1981) analyzed Ruth’s (1933) cake 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 (1933) theory that at constant pressures
filtrates volume versus time plot on a Log – Log scale would yield a slope of 0.5 was too definite
(it has been found to be between 0.25 and 0.5).His equation is given below.
+
2.20
Commenting on the variability of specific resistance, Hemant (1981) 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
40
with time and so do pressure across the medium. As the total pressure drops 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. The problem with his equation was that he did not account for this
variable pressure in his derivation because he used the constant pressure P. His view therefore, is
that the pressure can only be assumed constant indeed when the hydrostatic head is zero.
2.6.13 ADEMILUYI, ANAZODO AND EGBUNIWE (1982)
In 1982, an investigation was conducted to find out the true value of b (an exponent of
area) in the modified equation of Gale and White (1975). This was necessary because of
controversies amongst researchers as to the correct relationship between volume of filtrate and
area. In establishing the value of b they varied the area and measured the value of the filtrate
volume at various time interval and keeping all other terms in the equation constant At the end,
‘b’ was found to be 0.91± 0.02, if calculations were made with the total area of filtration while
the value of 'b' was 1.38±0.02, if the effective area of filtration was used in the analysis of
experimental data. Their suggestion was that the total area of filtration should be used in
Caman's (1934) equation while the effective area of filtration should be used in Anazodo’s
(1974) dimensional equation. Their findings are presented below:
V2 =
2.21
and
V2 =
2.22
Where A and Aeff are the total Area and the effective Area of the Buchner funnel respectively.
41
Because of the obvious limitation of Carman’s equation and the general lack of agreement
between researchers on an acceptable equation to describe sludge filtration,
2.6.14 ADEMILUYI (1984)
Ademiluyi (1984) developed an equation for compressible sludge to be used in routine
laboratory investigation. The equation has been suggested to replace the traditional Carmans
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 Carmans equation. The equation is given below:
2.23
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 s which is not a
dimensionless pure number.
2.6.15 J O ADEMILUYI ET AL (1982,)
Ademiluyi (1982) and coworkers developed a dimensionless number as an index of
sludge filtration. A concept referred to as sludge filterability number was proposed. It considers
both the ease by which a filtrate is collected and the quality of the cake. The formulated equation
is given bellow.
=
2.24
were
is initial height of sludge in the manometer after the filtration process, ∆H is the drop in
head,
is the concentration of sludge, C is the concentration of cake,
velocity and t is the time taken to obtain filtrate.
42
is the initial constant
2.6.16 AGUNWAMBA ET AL, (1988)
A new model of filtration equation using the method of material balance and regression
analysis was derived by Agunwamba and coworkers (1988). In this model the input variable,
sludge concentration (C0); the state variable, specific resistance (R); and the output variables,
cake concentration C and filtrate concentration (CF) were incorporated. The derived equation is
given below:
+
2.25
Another contribution by Agunwamba et al (1989), was the application to geometric
programming to sludge filtration using the optimization technique. This was applied to the
minimization of the filtrate concentration and the resistance. For the resistance, it was found that
to achieve better dewaterability the value of R the specific resistance should be reduced through
dilution as the equation shows below:
R = 7200P
7200(C -
7200p/
2.26
Similarly for the filtrate minimization they showed that it is desirable to achieve a high cake
quality during the process of filtration. In conclusion, they stated that the filtrate minimization
problem is the problem of meeting the effluent quality discharge standard while maintaining the
cake concentration C as high as possible. The objective function used is given below:
dµR/ 7200P (1 +
).
2.27
43
2.6.17 ADEMILUYI (1991).
A mathematical relationship between CST and SDN to be used in the evaluation of the
SDN using the CST apparatus was formulated by Ademiluyi. The equation can be used in
assessing the effect of conditioning on sludge filterability. It was found that when an
unconditioned sludge is used, the CST is high and this indicates a decrease in velocity. He
explained that, the reason for the above situation was that a longer time has been spent to cover
the distance between sludge reservoir and the reference mark of the filter paper. However, in a
conditioned sludge, the CST decreases with the increase in chemical dosage and this indicates an
increase in velocity of the filtrate towards the reference mark and therefore there is an increase in
filterability.
In summary, there has been lack of agreement amongst researchers in respects of
equations presented in other to improve the performance of the sludge filtration process .
Anazodo (1974) proposed a dimensional equation but it was not accepted by Gale and
White (1975) who stated that Carman’s (1934) equation was preferable because the relationship
between volume of filtrate and area of filtration gave a linear one. In addition, Gale and White
(1975) argued that, Anazodo (1974) need not assume (f) = 1/2 in his dimensional equation. This
lack of agreement amongst researchers has led to the conclusion by Heerjes and Purchas that
equations that contain the same parameters with that of Carman’s equation, may not adequately
describe the filtration process if some parameters believed to affect filtration processes are
missing ( Ademiluyi, 1981)
It can be stated that, any equation that will fully describe the
filtration phenomenon should incorporate the compressibility coefficient as this will be more
acceptable to previous workers.
44
CHAPTER THREE
METHODOLOGY
3.1
STUDY AREA
The sludge that was used for this study was from the sewage treatment plant of the
University of Nigeria Nsukka located at about 300m from the junior staff quarters. There are
two Imhoff tanks, each measuring about 6.667m
4.667m
10m, designed for a population of
over 3,000 students and lecturers. Sludge is discharged from the Imhoff tank to the drying bed
once every 10 days Effluent from the Imhoff tank enters the waste stabilization ponds. The plant
treats mainly domestic wastewater.
3.2 MATERIALS AND METHOD
The materials used for this study are listed below:
Measuring cylinder, Calibrated tape for reading the drop in sludge height, Sand and gravel for
supporting the sludge sample, Rubber buckets for collection of sludge sample, Thermometer for
measuring temperature, Stop Watch for recording time of filtration, Distilled Water for diluting
sludge sample, ,Ferric Chloride for conditioning of sludge sample, Rectangular sludge Drying
bed of X-sectional Area of 9000cm2.
Before filtration commences, the apparatus was prepared by placing gavel at the base of
the drying bed to a height of 20cm. A sand of height 20cm was immediately poured on topn of
the gravel. A known volume of the digested sludge after been mixed properly with an iron bar in
a bucket to induce homogeneity and eliminate air bubbles was poured into the filtration
apparatus to a height of 30cm and simultaneously, a stop watch was started as the sludge was
allowed to dewater under gravity . During the filtration run, the sludge continued to gasify and
within several hours a considerable portion of the sludge solid raised to the top and the dirty
45
sludge water remained below. As this water drains away the floating sludge subsides and this
leads to a decrease of sludge surface. As the filtration is going on the volume of filtrate collected
into a cylinder placed at the base of the drying bed was recorded for a period of two hours for the
first day and 24 hours for the subsequent days. The temperature of the sludge and the filtrate at
the waste water site before and after a filtration period was also noted using the thermometer
instrument and the temperature was used to compute the density of the filtrate and dynamic
viscosity of the sludge. At the end of filtration, the specific resistance was calculated for the
entire periods of filtration.
To determine the response of pretreatment on the specific resistance of the sludge, five
portions of sludge were conditioned with (10g,20g,30,40g,50g) of Ferric chloride and the
mixture
were allowed to undergo filtration. The volume of filtrate collected after every
20minute was recorded. The relationship between volume of filtrate V and time t was used to
plot t/v versus v and the result used to calculate the specific resistance of the sludge. Before this
filtration, a known volume of the conditioned sludge was taking to the laboratory and was oven
dried at a temperature of 1050C so that the Initial solid content (M) can be determined. Also,
after the filtration run a known volume of the wet sludge was taken to the laboratory for the
determination of void ratio. This procedure was done for all the five portions of conditioned
sludge and the results were used to evaluate the compressibility coefficient of the sludge. The
result of the five experiments to check the response of specific resistance to pretreatment is
shown in appendix 111 while the record for the laboratory computation of void ratio is shown in
appendix iv.
46
Sludge
30cm
Sand
20cm
Gravel
20cm
Drain pipe
Orifice
Measuring cylinder
Fig 3.1 diagram of the sludge filtration set up
3.3
DIMENSIONAL ANALYSIS
Dimensional analysis is a mathematical technique which makes use of the study of
dimensions for solving engineering problems. Each physical phenomenon can be expressed by
an equation given relationship between different quantities. It helps to determine a systematic
arrangement of the variables in the physical relationships. It is based on the principle of
dimensional homogeneity and uses the dimensions of relevant variables affecting the the
phenomenon. The various physical quantities used in the fluid phenomenon can be expressed in
terms of the fundermental quantities ( M, L, T).
47
3.4 METHOD OF DIMENSIONAL ANALYSISThe theory of experiment is based on the
dimensional analysis method developed by Anazodo in 1974. Anazodo combined FORCE and
MASS dimensional units and differentiated the LENGTH into three mutually perpendicular axis
in space LXLYLZ .
Table 3.1 Filtration Variables and FMTLxLYLZ units:
VARIABLES
SYMBOLS
FMTLXLYLZ
VOLUME OF FILTRATE
V
LXLYLZ
TIME OF FILTRATION
T
T
MASS OF DRY CAKE PER
M
MLX-1LY-1LZ-1
HYDROSTATIC PRESSURE
P
FLX-1LY-1
DYNAMIC VISCOSITY
µ
FTLZ-2
SPECIFIC RESISTANCE
R
LZ/M
AREA OF FILTRATION
A
LXLY
VOLUME
The dimensional relationship between volume of filtrate and various parameters affecting sludge
filtration process is given as:
2.28
48
For Dimensional homogeneity we have that
For condition on:
: 1 = a- b - d
2.29
: 1 =-2c - d + f
2.30
: 0=d-f
2.31
:
0=b+c
2.32
: 0=c+e
2.33
From the above, we have five simultaneous equations in six unknowns and can easily be solved
using normal equation.
Therefore from equation (29)
f=d
2.34
From equation (28)
1 = -2c from which c =-1/2.
2.35
Also from equation (31), e = -c therefore, e = 1/2
From equation (30)
0 = b - ½ and so b =1/2
2.36
From equation (27)
a = 1 + b +d
2.37
a=1+½+d
2.38
a = 3/2 + d
2.39
Finally, from equation (29), f = d which brings our equation into the form
49
2.40
.
2.41
were t is the time of filtration and V is the volume of filtrate.
A plot of
versus
gave a straight line and therefore equating powers of
and
Fig 2: graph of the plot of t/v versus initial solid content of sludge( M)
we have that,
1 = -2d which implies that,
d = -1/2
2.42
Substituting all the computed unknown values we have the equation below:
2.43
50
Accounting for compressibility coefficient we have that, pressure P which is the hydrostatic
were ρ is the density of water, g is the
pressure can be represented by the relation P =
gravitational acceleration, and H is the sludge height at the end of a filtration time which can also
be written as
were
is the initial sludge height and
is the change in sludge
height between two successive time of filtration.
Substituting the above transformation into our equation, we have:
2.44
Inverting equation (2.44)
2.45
2.46
But M =
where
is the volume of sludge. if we substitute it into the equation above we
have:
were ∆p = ρg∆H, and
= P1
Dividing through by A
2.47
Also replacing
by
in equation we have;
2.48
Were
percentage of solid content expressed in decimal,
Specific gravity of sludge and
= density of filtrate. So substituting:
2.49
Were
51
2.50
2.51
= ∆e
Were
2.52
2.53
Equation (2.53) is the modified dimensional equation
3.5 METHOD OF EVALUATING PARAMETERS IN THE MODIFIED EQUATION.
3.5.1 INITIAL SOLID CONTENT (M)
A known volume of the conditioned sludge before filtration commences was taken to the
laboratory and weighed in a can, after which the sludge and the can were placed inside the oven
for drying at 1050C for twenty four (24hrs) and after which the dry weight was evaluated.
3.5.2 THE AREA OF FILTRATION (A)
The model that was used as the drying bed is a rectangular structure having the dimensions
120cm X 75cm X 80cm. The cross section Area of the sludge is taken as the cross sectional Area
of the rectangular model. It was measured to be 120 cm by 75 cm respectively giving a value of
9000cm2.
3.5.3 THE COMPRESIBILITY COEFFICENT(S) M2/KN
The compressibility coefficient parameter was measured in the laboratory using the
oedometer test. It was defined as the ratio
using the soil mechanic concept of soil deformation
as presented by Terzaghi. The result of the measurement is tabulated in appendix IV.
52
3.5.4 DENSITY OF FILTRATE (ρ) Kg/M3
The density of the filtrate was approximated to be the density of water at an average
temperature of the filtrate.
3.5.5 DYNAMIC VISCOSITY (µ) N.S/M2
The dynamic viscosity of the filtrate was calculated using the formula below:
µ = 0.0168
T-0.88 were ρ is the density and T is the average temperature of the filtrate
before and after filtration. -0.88 and 0.0168 are constant.
3.5.6 WEIGHT OF DRY SOLID
)
A known volume of conditioned sludge was oven dried in the laboratory at a temperature
of 1050C for twenty four hours then the residue was weighed in a balance to evaluate the dry
weight of the sludge.
3.5.7 SPECIFIC RESISTANCE OF SLUDGE (R) M/Kg
The parameter cannot be measured in the laboratory. It is actually the main bases of
sludge filtration phenomenon and can only be evaluated from the values of other parameters.
3.5.8 INITIAL SLUDGE HEIGHT (HS ) m
This parameter was evaluated by recording the height of the sludge after an interval of
time.
3.5.9 TIME OF FILTRATION (t) s
This parameter was evaluated using a stop watch. It is the time it takes to collect a
volume of filtrate in a cylinder.
3.5.10 VOLUME OF FILTRATION (V) M3
53
This parameter was evaluated by allowing filtrate at a given time interval to collect into a
cylinder placed at the base of the drying bed.
3.5.11 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 filtrate is arrived at. It is calculated by subtracting the volume of water from the volume of
sludge and determining the percentage of the result.
54
CHAPTER FOUR
RESULTS AND DISCUSSION
4.1
EXPERIMENTAL VALIDATION OF THE MODIFIED EQUATION
The results of the natural filtration for the unconditioned and conditioned sludge are
captured in tables 2 – 28. Tables 3 - 10 records the data used to validate the modified filtration
equation. Table 11-15 contains the data used to show the effect of pretreatment on the specific
resistance of the sludge while tales 19 – 28 shows the data used for evaluating the void ratio and
compressibility coefficient of the sludge.
The modified equation which predicts an equation of a straight line can be presented in the
form t/v = bV + C were b and C are slope and intercept of the equation. Figure 3- 6 shows the
theoretical and experimental plots of t/v versus v .The values of the experimental slopes and
intercepts for the four experiments conducted using the unconditioned sludge are: (1260913.48
s/m6 , 4872.53 s/m3) , (5359604.57 s/m6, 844882.56 s/m3), (112117050.4 s/m6, -2135816.16
s/m3), and (145562880 s/m6, -30497917.03 s/m3) while the theoretical values of slopes and
intercepts
are (1257426.75 s/m6, 5270.26 s/m3),( 4579418.42 s/m6, 905658.24 s/m3),
(112117075 s/m6, -21358166.74 s/m3),and (206699290.5 s/m6, -4589555.58 s/m3) respectively.
55
Fig 3 Graph of theoretical and experimental plot of t/v versus v at variable pessure
(Experimental slope =1260913.48 s/m6 , Intercept = 4872.53 s/m3)
( Theoretical slope = 1257426.75 s/m6, Intercept = 5270.26 s/m3)
Fig 4 Graph of theoretical and experimental plot of t/v versus v at variable pessure
(Experimental slope =5359604.57 s/m6, Intercept = 844882.56 s/m3)
(Theoretical slope = 4579418.42 s/m6, Intercept = 905658.24 s/m3)
56
Fig 5
Graph of theoretical and experimental plot of t/v versus v at variable pressure
(Experimental slope = 112117050.4 s/m6, Intercept = -2135816.16 s/m3
(Theoretical slope = 112117075 s/m6, Intercept
= -21358166.74 s/m3
Fig 6: Graph of theoretical and experimental plot of t/v versus v at variable pressure
(Experimental slope = 145562880 s/m6, Intercept = -30497917.03 s/m3
(Theoretical slope = 206699290.5 s/m6, Intercept = -4589555.58 s/m3)
57
Figure 3-6 shows the theoretical and experimental plots of t/v versus v using the modified
equation. The two plots are linear as predicted by the equation and the coefficient of correlation
was found to be high (0.94 to 0.99 ).The close agreement between theoretical values and
experimental values are all shown in the figures above.
The specific resistance of the unconditioned sludge tested were computed using the slopes
and intercepts evaluated above from the raw data and its values were found to be 1.0859173970
x 1012kg/m3 , 9.814795569 x 1012 kg/m3, 9.61973249 x 1013 kg/m3, and 1.110792216 x 1014
kg/m3 respectively. The data used to plot the above graphs are recorded in appendix II.
4.2
EFFECT OF CHEMICAL CONDITIONER ON THE SPECIFIC RESISTANCE
The result of experiments conducted to determine the effect of chemical conditioner on the
specific resistance and the compressibility coefficient of the sludge are shown in table 11-15 and
the data generated from observation is shown in appendix111.
Fig 7: Graph of t/v versus v for 10g of Ferric Chloride Conditioner.
58
59
Fig 11: Graph of t/v versus v for 50g of Ferric Chloride Conditioner
Figure 7-11 show the variation of specific resistance to different weight of ferric chloride
conditioner using the modified equation for the digested sludge. From the result it was found out
that the specific resistance decreases as the weight of ferric chloride conditioner increases.
60
4.3
VARIATION OF INITIAL SOLID CONTENT WITH SPECIFIC RESISTANCE
The result of the plot of specific resistance against the Initial solid content is displayed
below in figure 12.
Fig 12 Variation of specific resistance versus Initial solid content(M).
From the Figure above, initial solid content increases as specific resistance decreases as
discovered by Ademiluyi and Coackley (1958) using Carman equation.
4.4
VARIATION OF PRESSURE WITH SPECIFIC RESISTANCE
From the plot of pressure against specific resistance, we observed that as the hydrostatic
pressure increases, the specific resistance also increases which is an agreement with Ademiluyi’s
findings presented in his work on constant vacuum filtration equation of compressible sludge.
This relationship can be explained thus: As filtration continues, more and more solid settles
reducing the porosity of particles so that the pressure of water increases and also specific
resistance.
61
Fig 13: Variation of Specific Resistance versus pressure
Fig 14: Variation of pressure with void ratio for conditioned sludge.
From the experiment conducted using the oedometer we observed from the graph above
that as the hydrostatic pressure increases, the void ratio decreases. This is because as filtration
continues, more suspended solids settles down to the sludge body blocking the pores of the
62
sludge particles thereby reducing the porosity of the sludge. The data used to plot figure 14 is
shown in appendix1V.
From the same measurement also the graph of fig 15 was plotted. The graph indicated that
compressibility initially increased with increase in hydrostatic pressure and later it starts to
decrease with increase in hydrostatic pressure. The explanation of figure 15 is that the initial
increase of compressibility with increase of pressure is because initially the solid particles is
loosely packed and so porosity is high leading to increase in compressibility while as the
pressure continues to increase, the solid particles become more compressed together reducing
porosity and also reducing compressibility coefficient.
Fig 15: variation of Compressibility Coefficient with pressure for conditioned sludge.
63
CHAPTER FIVE
CONCLUSSIONS AND RECOMMENDATION
A Modified FMTLXLYLZ dimensional equation using sludge drying bed method has been
presented. The equation incorporates the compressibility coefficient believed to affect sludge
dewatering phenomenon. The equation was verified using data from the filtration experiment
gotten from the sludge disposal site of the University of Nigeria Nsukka. There was a close
agreement between experimental and theoretical values of the variable pressure filtration. For the
experimental plot the slopes and intercept are (1260913.48 s/m6 , 4872.53 s/m3) , (5359604.57
s/m6, 844882.56 s/m3), (112117050.4 s/m6, -2135816.16 s/m3), and (145562880 s/m6, 30497917.03 s/m3) while the theoretical values of slopes and intercepts are (1257426.75 s/m6,
5270.26 s/m3),( 4579418.42 s/m6, 905658.24 s/m3), (112117075 s/m6, -21358166.74 s/m3),and
(206699290.5s/m6,-4589555.58s/m3) respectively.; the correlation coefficient ranged from (
0.94-0.98)
A series of filtration experiments using conditioned sludge, has demonstrated the
response of the specific resistance to changes in pretreatment given the values (6.160002033 x
1011 m/kN, 5.03438889 x 1011 m/kg, 4.221393301 x 1011 m/kg , 3.830709783 x 1011 m/kg and
1.65123474 x 1011 m/kg).
RECOMMENDATIONS
The close agreement between experimental and theoretical values arrived at using the
sludge drying bed filtration at variable pressures makes the equation unique and ok. The equation
also incorporates the compressibility coefficient believed to affect sludge filtration phenomenon.
It is therefore recommended that and also with the incorporation of the compressibility
coefficient In view of the satisfactory performance of the natural filtration process we are
64
recommending that the equation be tested and compared to previous equations to determine its
validity for use in solving sludge filtration problems.
65
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67
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69
APPENDIX I
Table 2: EXPERIMENTAL RESULT OF THE NATURAL FILTRATION OBSERVATION
TIME OF
VOLUME OF
HEIGHT OF
TEMPRATURE
TEMPRATURE
DENSITY OF
OF FILTRATE
OF SLUDGE
FILTRATE
SLUDGE
FILTRATION
FILTRATE
SURFACE
(S)
(M3)
(M)
0
0
C
Kg/M3
C
0
0
0.300
-
7200
0.0717
0.145
24
24
997.296
14400
0.1034
0.141
25
26
996.783
21600
0.1283
0.141
26
26
996.783
28800
0.1505
0.140
28
28
996.232
36000
0.1709
0.120
29
30
995.646
43200
0.1805
0.100
30
30
995.646
86400
0.1820
0.100
25
28
996.232
172800
0.1860
0.100
25
28
996.232
259200
0.1890
0.098
26
28
996.232
345600
0.1920
0.096
23
25
997.044
432000
0.2000
0.094
23
26
996.783
518400
0.2060
0.090
26
28
996.232
604800
0.2120
0.085
25
26
996.783
691200
0.2160
0.083
26
28
996.232
777600
0.2200
0.083
26
28
996.232
864000
0.2250
0.083
26
28
996.232
950400
0.2280
0.083
26
28
996.232
1036800
0.2310
0.083
25
28
996.232
1123700
0.2350
0.083
26
28
996.232
1209600
0.2380
0.083
26
28
996.232
1296000
0.2430
0.080
26
28
996.232
1382400
0.2460
0.080
26
27
996.512
1468800
0.2490
0.080
26
27
996.512
1555200
0.2520
0.080
26
27
996.512
1641600
0.2550
0.080
25
27
996.512
1728000
0.2580
0.080
25
28
996.232
1814400
0.2590
0.080
26
28
996.232
70
24
-
APPENDIX II
CALCULATIONS OF SPECIFIC RESISTANCE
Table 3: Data used to calculate experimental slope and intercept for validation of equation
V(m3)
t(s)
t/v (s/m3)
V2(m6)
v.t/v(s)
0
7200
0
0.0717
0
100,488.49
0
0.0051
0
7200
14400
0.1034
139,264.99
0.0107
14400
21600
0.1283
168,421.05
0.0165
21600
28800
0.1505
191,362.12
0.0227
28800
36000
0.1709
210,649.50
0.0292
36000
43200
0.1805
239,335.18
0.0326
43200
∑
0.8053
1,049,521.33
0.1168
151200
Volume of sludge (V) = 0.27 m3, Initial Height of sludge Hs = 0.3m, Average Height of sludge H
= 0.155m, Initial hydrostatic pressure Pi = 684.3 N/m2, Average Applied pressure Pav ρgh =
1514.82 N/m2 , Average Temp. (oc)= 26oc, Density of water = 996.23kg/m3, Area (A) = 0.9 m2,
Dynamic Viscosity µ = 0.892N.s/m2, Weight of dry solid Wd = 0.0157 kg, Initial Solid Content
(M) = 0.058 kg/m3, Percentage of solid expressed in decimal Ps = 0.05, Specific gravity of sludge
Ssl = 1.05, Acceleration due to gravity (g) = 9.81 m/s2,
From Regression Analysis, we know that the slope b is given by the formula below
b=
s/m6
71
C=
= 149931.62 - 145059.09
= 4872.53 s/m3
Solving for the specific resistance and the compressibility coefficient of the sludge we have from
R=
=
= 1.154645622 X 1012 m/Kg
S=
=
= 0.000005 m2/KN.
t(s)
V(m3)
t/v(s/m3)
V2(m6)
V.t/v(s)
86400
0.182
474725.27
0.0331
86400
172800
0.186
929032.26
0.0346
172800
259200
0.189
1371428.57
0.0357
259200
345600
0.192
1800000.00
0.0369
345600
432000
0.200
2160000.00
0.0400
432000
518400
0.206
2516504.85
0.0441
518400
604800
0.212
2852830.19
0.0449
604800
1.155
12104521.14
0.2693
2419200
Volume of sludge (V) = 0.27 m3, Initial Height of sludge Hs = 0.1 m , Initial pressure P1 = 977.84
KN/M 2, Average pressure PAV = Average height of sludge H = 0.09 m, Average Temp. = 25oc,
Density of water = 996.78kg/m3, Area (A) = 0.9 m2, Dynamic Viscosity µ = 0.952N.s/m2,
72
Weight of dry solid Wd = 0.0157kg, Initial solid Content (M) = 0.058 kg/m3, Percentage of solid
expressed in decimal Ps = 0.05, Acceleration due to gravity (g) = 9.81 m/s2,
From Regression Analysis, the slope b is given by the formula below
b=
=
= 5359604.57 s/m6
= 844882.56 s/m3
C=
R=
=
= 1.532861179 x 1012 m/Kg
S=
=
= 0.00006 M2/KN .
73
t(s)
V(m3)
t/v(s/m3)
V2(m6)
V.t/v(s)
691200
0.216
3200000.00
0.0467
691200
777600
0.220
3534545.46
0.0484
777600
864000
0.225
3840000.00
0.0506
864000
950400
0.228
4168421.05
0.0519
950400
1036800
0.231
4488311.69
0.0534
1036800
1123700
0.235
4781702.13
0.0552
1123700
1209600
0.238
5082352.94
0.0566
1209600
1.593
29,095,333.27
0.3628
6,653,300
Volume of sludge (V) = 0.27 m3, Initial Height of Sludge Hs = 0.083m, Average pressure PAV =
694.27 KN/M 2, Average Temp. = 25oc, Density of water = 996.78kg/m3, Area (A) = 0.9 m2,
Dynamic Viscosity µ = 0.952N.s/m2, Weight of dry Solid Wd = 0.0157kg, Initial solid Content
(M) = 0.058 kg/m3 , Acceleration due to gravity (g) = 9.81 m/s2, Percentage of solid expressed in
decimal Ps = 0.05,Specific gravity of sludge SSl = 1.05,
From Regression Analysis, the slope b is given by the formula below
b=
s/m6
=
C=
= -21358161.15 s/m3
74
R=
=
= 7.367464785X 1012 m/Kg
S=
=
= 0.003M2/KN
t(s)
V(m3)
t/v(s/m3)
V2(m6)
V.t/v(s)
1296000
0.244
5311475.41
0.0595
1296000
1382400
0.246
5619512.19
0.0605
1382400
1468800
0.249
5898795.18
0.0620
1464800
1555200
0.252
6171428.57
0.0635
1555200
1641600
0.255
6437647.06
0.0650
1641600
1728000
0.258
6697674.42
0.0666
1728000
1814400
0.259
7005405.41
0.0671
1814400
1.763
43141938.24
0.4442
10886400
Volume of sludge (V) = 0.27 m3, Initial Height of sludge Hs = 0.08m, Initial pressure P1=
781.84 KN/M2, Average Temp.= 26oc, Density of water = 996.23 kg/m3, Area (A) = 0.9 m2,
Dynamic Viscosity µ = 0.892N.s/m2,Weight of dry solid Wd = 0.0157kg, Initial Solid Content
(M) mass/vol of sludge= 0.058( kg/m3 , Acceleration due to gravity (g) = 9.81 m/s2, Percentage
of solid expressed in decimal Ps = 0.05, Specific gravity of sludge SSl 1.05,
From regression analysis, the slope b is given by the formula below.
75
b. =
. = 145562880 s/m6
=
= -30497917.03 s/m3
C =
R=
=
= 9.478760053X 1012 m/Kg
S=
=
= 0.004M2/KN.
CALCULATION OF THEORETICAL SLOPE AND INTERCEPT
Table 7: Data used to calculate theoretical slope and intercept for validation of equation
V(m3)
t(s)
t/v (s/m3)
V2(m6)
v.t/v(s)
0
7200
0
0.0717
0
100,780.26
0
0.0051
0
7225.94
14400
0.1034
138,372.02
0.0107
14307.67
21600
0.1283
167,899.93
0.0165
21541.56
28800
0.1505
194,226.02
0.0227
29231.01
36000
0.1709
218,417.56
0.0292
37327.56
43200
0.1805
229,801.81
0.0326
41479.23
0.8053
1,049,497.6
0.1168
151112.97
By regression analysis
b1 =
= 1257426.75 s/m6
=
76
= 5270.26 s/m3
= 149928.23 – 144657.97
C1 =
t(s)
V(m3)
t/v(s/m3)
V2(m6)
86400
0.182
1509286.34
0.0331
274690.11
172800
0.186
1555042.54
0.0346
289237.91
259200
0.189
1589359.68
0.0357
300388.98
345600
0.192
1623676.83
0.0369
311745.95
432000
0.200
1715189.22
0.0400
343037.84
518400
0.206
1783823.52
0.0441
367467.65
604800
0.212
1852457.81
0.0449
392721.06
1.155
11628835.94
0.2693
2279289.5
b.1 =
s/m6
C1 =
V.t/v(s)
= 905658.24 s/ m3.
= 1661262.28 – 755604.04
77
t(s)
V(m3)
t/v(s/m3)
V2(m6)
V.t/v(s)
691200
0.216
2859121.74
0.0467
691200
777600
0.220
3307589.94
0.0484
777600
864000
0.225
3868175.19
0.0506
864000
950400
0.228
4204526.34
0.0519
950400
1036800
0.231
4540877.49
0.0534
1036800
1123700
0.235
4989345.69
0.0552
1123700
1209600
0.238
5325696.85
0.0566
1209600
1.593
29,095,333.24
0.3628
6,653,300
b.1 =
s/m6
C1 =
= 4156476.18 – 25514642.92
78
= -21358166.74 s/ m3
t(s)
V(m3)
t/v(s/m3)
V2(m6)
V.t/v(s)
1296000
0.244
5019425.69
0.0595
1382400
0.246
5310551.45
0.0605
1306395.66
1468800
0.249
5747240.09
0.0620
1431062.78
1555200
0.252
6183928.73
0.0635
1558350.04
1641600
0.255
6620617.37
0.0650
1688257.43
1728000
0.258
7057306.01
0.0666
1820784.95
1814400
0.259
7202868.89
0.0671
1865543.04
1.763
43141938.23
0.4442
10895133.77
b.1 =
s/m6
C1 =
= 6163134.03 – 52058693.61
79
= - 4589555.58 s/ m3
1224739.87
APPENDIX III
THE EFFECT OF FERRIC CHLORIDE ON SPECIFIC RESISTANCE
Table 11: Data for filtration experiment using 10g of Ferric Chloride
Time t (s)
Volume of filtrate (V) m3
V2
t/v
V.t/v
1200
0.05118
23446.65
0.002619
1200
2400
0.05470
43875.69
0.002992
2400
3600
0.05604
64239.83
0.003140
3600
4800
0.05710
84063.05
0.003260
4800
6000
0.05720
104895.1
0.003271
6000
0.2762
320520.32
0.01528
18000
Volume of sludge V = 0.063m3, Initial Hydrostatic Pressure PAV = 684.3 N/m2, Average
Hydrostatic Pressure P = gh = 210.18N/m2, Initial Height of sludge HS = 0.07m, Average
Height of sludge (HAV) =0.014m, Temp.= 26oc, Density of water = 996.23kg/m3, Area (A) =
0.9 m2, Dynamic Viscosity µ = 0.892N.s/m2, Weight of dry Solid Wd = 0.00941kg, Initial
solid content (M) =0.149kg/m3, Percentage of solid expressed in decimal PS = 0.09, Specific
gravity of sludge Ssl = 1.05,
By regression analysis,
b=
=
C=
= 64104.06 – 813292.99
s/m6
= 749188.94 s/m3
80
R=
=
= 6.805632338X 1011 m/Kg
S=
=
= 0.00118 M2/KN
t
V
t/v
V2
V.t/v
1200
0.05086
23594.18
0.002587
1200
2400
0.05183
46305.23
0.002686
2400
3600
0.05306
67847.72
0.002815
3600
4800
0.05431
88381.51
0.002950
4800
6000
0.05522
108656.28
0.003049
6000
0.26528
334784.92
0.014087
18000
Volume of sludge V = 0.063m3, Initial Height of sludge HS = 0.07m, Average height H =
0.016m, Average Temp. = 26oc, Density of water = 996.23kg/m3, Area (A) = 0.9 m2, Initial
Hydrostatic Pressure P = gh = 684.3N/m2, Average Applied Hydrostatic pressure PAV = 195.52
N/m2 , Dynamic Viscosity µ = 0.892N.s/m2, Weight of dry solid (Wd ) =0. 0110 Kg, Initial
Solid Content (M) = 0.174 kg/m3, Percentage of solid expressed in decimal PS = 0.12, Specific
gravity of sludge Ssl = 0.92,
By regression analysis,
b=
= 16975142.86 s/m6
81
= 66956.98 – 900633.18
C=
= - 833676.19 s/m3
R=
=
= 5.034388894X 1011 m/Kg
S=
=
= 0.00114 M2/KN
Time t (s)
Volume of filtrate (V) m3
V2
t/v
V.t/v
1200
0.05012
23942.53
0.002512
1200
2400
0.05304
45248.87
0.002813
2400
3600
0.05438
66200.81
0.002957
3600
4800
0.05544
86580.09
0.003074
4800
6000
0.05600
107142.86
0.003136
6000
0.26898
329115.16
0.014492
18000
Volume of sludge V (m3)= 0.063,Initial Height of sludge HS = 0.07, Average height H ( m)
=0.018, Average Temp. (oc)= 26, Density of water (kg/m3) = 996.23, Area (A) m2= 0.9, Initial
Hydrostatic Pressure P = gh (N/m2) = 684.3, Average Applied Hydrostatic Pressure PAV N/m2 =
175.91, Dynamic Viscosity µ (N.s/m2) = 0.892, Weight of dry Solid (Wd) kg = 0.0113, Initial
solid content (M) = 0.179, Percentage of solid expressed in decimal PS = 0.11, Specific gravity of
sludge Ssl = 1.03,
b=
82
s/m6
= 65823.03 – 721164.72
C=
= - 655341.69 s/m3
R=
=
= 4.221393301X 1011 m/Kg
S=
=
= 0.00113 m2/KN
t (s)
V( m3)
t/v
V2
V.t/v
1200
0.04899
24494.79
0.002400
1200
2400
0.04915
48830.11
0.002416
2400
3600
0.05072
70977.92
0.002573
3600
4800
0.05172
92807.42
0.002675
4800
6000
0.05250
114460.13
0.002748
6000
0.25308
351570.37
0.012812
18000
Volume of sludge V (m3) = 0.063, Initial Height of sludge HS = 0.07, Average Height (H1 ) m
=0.0215, Average Temp. (oc)= 27, Density of water (kg/m3) = 996.51, Area (A) m2= 0.9, Initial
83
hydrostatic pressure Pi (N/ m2 ) = 684.3, Average Hydrostatic Pressure PAV (N/m2) = 136.8,
Dynamic Viscosity µ (N.s/m2) = 0.952, Weight of dry Solid Wd (Kg) = 0.0144, Initial solid
Content (M) kg/m3 = 0.229, Percentage of solid expressed in decimal PS = 0.14, Specific gravity
of sludge Ssl = 1.03,
s/m6
= - 995018.33 s/m3
= 70314.07 – 1065332.4
C=
R=
=
= 3.830709783 X 1011 m/Kg
S=
=
= 0.00110m2/KN
Table 15: Data for filtration experiment using 50g Ferric Chloride
t(s)
V
t/v
V2
V.t/v
1200
0.04963
24178.92
0.002463
1200
2400
0.05115
46920.82
0.002616
2400
3600
0.05249
68584.49
0.002755
3600
4800
0.05355
89635.85
0.002868
4800
6000
0.05420
110701.11
0.002938
6000
0.26102
340021.19
0.01364
18000
Volume of sludge V (m3) = 0.063, Initial Height of sludge H ( m) =0.07, Average height of
sludge H (m) = 0.020, Average Temp. (oc)= 27, Density of water (kg/m3) = 996.51, Area (A)
m2= 0.9, Initial Hydrostatic Pressure P = gh (N/m2) = 684.3, Average applied hydrostatic
84
pressure PAV (N/m2 ) =156.37 , Dynamic Viscosity µ (N.s/m2) = 0.921, Weight of dry Solid
(Wd ) kg = 0.0174 Initial solid content (M) = 0.276, Percentage of solid expressed in decimal PS
= 0.17, Specific gravity of sludge Ssl = 1.03
b=
s/m6
= - 583329.41 s/m3
= 68004.24 – 651333.65
C=
R=
=
=
1.65123474 X 1011 m/Kg
S=
=
=
0.00109M2/KN
Table 16: Variation of ferric chloride Dosage on Specific Resistance
Amount of Ferric
Specific Resistance
Chloride
10g
6.160002033 X 1011
20g
30g
40g
3.830709783 X 1011
50g
1.65123474 X 1011
85
Table 17: Relationship Between Specific Resistance and Initial solid content
Amount of Ferric Chloride
Specific Resistance (m/kg)
Initial Solid Content (g)
10g
6.160002033 X 1011
0.149
20g
0.174
30g
0.179
40g
3.830709783 X 1011
0.229
50g
1.65123474 X 1011
0.276
Table 18: Relationship between Specific Resistance and Time
Coefficient of
Time of filtration (s)
Specific Resistance
Compressibility
(m/kg)
(m2/KN)
43200
1.154645622 X 1012
0.000005
604800
1.532861179 X 1012
0.00006
1029600
7.36746478 X1012
0.003
1814400
9.478760053 X1012
0.004
86
APPENDIX IV
COMPRESSIBILITY COEFFICIENT MEASUREMENT
Height of ring
= 6cm
Diameter of ring
= 1.8cm
Area of ring ( A ) = πd2/4
= 28.3cm
Specific gravity of sludge ( SSl )
= 1.05
Mass of ring + wet sludge in oven
= 63.4g
Mass of dry sludge (Wd )
= 20.5g
HS =
= 0.68cm
Table 19: Determination of Void ratio in oedometer test
Applied pressure
2
P N/cm
Final Dial reading
Change in Dial
Specimen height
At end of
Reading
H at end of
compression (mm)
∆H (mm)
compression
H = H1 + ∆H
e =
HS = 6.8(mm)
(mm)
0
0.2
20
1.94
19.89
1.925
19.66
1.891
18.91
1.781
18.50
1.721
18.36
1.70
(-) 0.11
5
0.31
(-) 0.23
10
0.54
(-) 0.75
20
1.29
(-) 0.41
40
1.7
(-) 0.14
80
1.84
87
Table 20 determination of compressibility coefficient for different pressure increment
Applied pressure
Change in Pressure
P (KN/m2)
∆P (KN/m2)
Change in
∆e
Compressibility
Mean of
Coefficient
compressibility
(cm2/KN)
5
0.015
0.003
5
0.034
0.007
10
0.11
0.011
20
0.06
0.003
40
0.02
0.0005
coefficient (cm2/KN)
5
10
20
40
80
88
0.004
Applied pressure
2
P N/cm
0
Final Dial reading
Change in
Specimen height
At end of compression
Dial
H at end of compression
(mm)
Reading
H = H1 + ∆H
∆H (mm)
(mm)
0.3
e =
HS = 7.5 (mm)
20
1.857
19.54
1.791
19.32
1.76
18.51
1.644
18.25
1.607
17.9
1.557
(-) 0.46
5
0.76
(-) 0.22
10
0.98
(-) 0.81
20
1.793
(-) 0.26
40
2.05
(-) 0.35
80
2.4
89
pplied pressure
Change in Pressure
P (KN/m2)
∆P (KN/m2)
Change in
∆e
Compressibility
Mean of
Coefficient
compressibility
(cm2/KN)
coefficient
(cm2/KN)
0
5
0.066
0.0132
5
0.031
0.006
10
0.012
0.001
20
0.037
0.002
40
0.05
0.001
5
10
20
40
80
90
0.005
Applied pressure
2
P N/cm
Final Dial reading
Change in Dial
Specimen height
At end of
Reading
compression (mm)
∆H (mm)
H = H1 + ∆H
(mm)
0
0.3
e =
HS =6.7 (mm)
20
1.985
19.71
1.942
19.46
1.904
18.72
1.794
18.4
1.746
18.15
1.709
(-) 0.29
5
0.59
(-) 0.25
10
0.84
(-) 0.74
20
1.58
(-) 0.32
40
1.9
(-) 0.25
80
2.15
91
Applied pressure
Change in
P (KN/m2)
Pressure
Change in
∆e
Compressibility
Mean of compressibility
Coefficient
coefficient (cm2/KN)
∆P (KN/m2)
(cm2/KN)
0
5
0.043
0.009
5
0.038
0.008
10
0.11
0.011
20
0.048
0.002
40
0.037
0.0009
5
10
20
40
80
92
0.006
Applied pressure
2
P N/cm
Final Dial reading
Change in Dial
Specimen height
At end of
Reading
H at end of
compression (mm)
∆H (mm)
compression
H = H1 + ∆H
e =
HS =7.1 (mm)
(mm)
0
0.2
20
1.817
19.41
1.734
19.22
1.707
18.65
1.627
18.30
1.577
18.11
1.551
(-) 0.59
5
0.79
(-) 0.19
10
0.98
(-) 0.57
20
1.55
(-) 0.35
40
1.9
(-) 0.19
80
2.09
93
Applied pressure
Change in Pressure
P (KN/m2)
∆P (KN/m2)
Change in
∆e
Compressibility
Mean of
Coefficient
compressibility
(cm2/KN)
coefficient
(cm2/KN)
0
5
0.083
0.0166
5
0.027
0.005
10
0.08
0.008
20
0.05
0.003
40
0.026
0.0007
5
10
20
40
80
94
0.007
Applied pressure
Final Dial reading
Change in Dial
Specimen height
P N/cm2
At end of compression
Reading
(mm)
∆H (mm)
H = H1 + ∆H
0
0.3
e =
(mm)
HS = 7.3 (mm)
20
1.739
19.8
1.712
19.5
1.671
18.94
1.595
18.7
1.562
17.91
1.453
(-) 0.2
5
0.5
(-) 0.3
10
0.8
(-) 0.56
20
1.36
(-) 0.24
40
1.6
(-) 0.79
80
2.39
Applied pressure
Change in Pressure
P (KN/m2)
∆P (KN/m2)
Change in
∆e
Compressibility
Mean of
Coefficient
compressibility
(cm2/KN)
coefficient
(cm2/KN)
0
5
0.027
0.005
5
0.041
0.008
10
0.076
0.007
20
0.033
0.002
40
0.109
0.003
5
10
20
40
80
95
0.005
96

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