EFFECT OF RAW WATER QUALITY ON COAGULANT DOSAGE AND
OPTIMUM pH
YANNIE ANAK BENSON
A project report submitted in partial fulfillment of
the requirements for the award of the degree of
Master of Engineering (Civil-Environmental
Management)
Faculty of Civil Engineering
Universiti Teknologi Malaysia
16 NOVEMBER 2006
iii
Praise the LORD GOD because of the blessed and strength HE gave unto me,
Sincere thanks to my lovely husband, Johnny and daughter, Jwelyn Ystefanie
because of your moral support, sacrifice and became my backbone,
Thanks Apak and Mama for your love all these years,
In loving memory brother, Jeruslavin Benson (18th June 2003); You always in our
heart and this is a gift for you..
iv
ACKNOWLEDGEMENT
I would like to thank Dr. Azmi Aris for his patience, dedication and excellent
supervision. Without him, my Master Project would not excellent and succesful
completed. I also would like to extend my gratitude to all Environmetal Lab’s
technician especially Mdm. Rosmawati because she always be there when I need the
assist in laboratory work.
Special thanks to Ooi Boon Siew because of her dedication in teaching me
the basic to explore MINITABTM statistical software. Not forget to Jini Anak Gilbert
Malandang, Nadiah and Zul Said, thank you for their companionship and advice.
My sincere thanks to all who involved in this project that I did not mentioned their
name. Lastly to all my family members; thank you so much for their companionship
and sporting all these years.
v
ABSTRACT
Removal of turbidity, suspended solids (SS) and natural organic matter
(NOM) using coagulation are well known because of the ability of the process in
destabilizing the colloids particles and reducing the repulsion force between the
particles. The objectives of the study are to explore the effect of the selected water
quality parameters (i.e initial pH, initial temperature and SS) and to develop a
statistical relationship between the water quality parameters and the optimum
dosage and pH. The study was conducted using jar test procedures using synthetic
water prepared using kaolin as the source of SS. The experiments were designed
using Response Surface Method (RSM) with final turbidity as the response. RSM
was found to be better approach than one-factor-at-a-time (OFAT) in determining
the optimum dose and pH. Initial pH and SS was found to have significant effect to
optimum dose at 90% confidence level (α = 0.1) and temperature was the only
factor having significant effect on optimum pH at 80% confidence level (α = 0.2).
Probably due to the complexity of the nature of the coagulation process, the
relationship between the parameters and the response was only developed for
optimum pH.
vi
ABSTRAK
Penggunaan proses pengentalan untuk menyingkirkan kekeruhan, bendasing
terampai dan jirim semulajadi organik didalam air sangat popular kerana
kebolehannya dalam menidakstabilkan zarah-zarah koloid dan mengurangkan daya
tolakan di antara zarah.
Objektif utama kajian ini adalah untuk melihat kesan
daripada parameter kualiti air yang terpilih (pH awal, suhu awal dan kepekatan
pepejal) dan juga untuk menghasilkan hubungkait statistik antara parameter kualiti
air dengan dos optimum dan pH optimum. Kajian telah dijalankan menggunakan
prosedur Ujian Balang dengan penggunaan air sintetik yang telah disediakan
menggunakan kaolin sebagai pepejal terampai air.
Ujikaji telah direkabentuk
menggunakan Kaedah Response Surface (RSM) dengan mengambilkira kekeruhan
adalah sebagai hasil tindakbalasnya. Didapati bahawa RSM adalah jauh lebih bagus
berbanding dengan pendekatan menggunakan Satu-Faktor-Pada-Satu-Masa (OFAT)
dalam menentukan pH optimum dan dos optimum. Adalah didapati bahawa pada
90% tahap keyakinan (α = 0.1), pH awal dan nilai awal pepejal terampai mempunyai
kesan yang penting terhadap dos optimum manakala hanya suhu sahaja didapati
memberi kesan penting terhadap pH optimum pada 80% tahap keyakian (α = 0.2).
Hubungkait antara parameter dan hasil tindakbalas hanya boleh dibangunkan untuk
pH optimum, kemungkinan besar disebabkan oleh tindakbalas pengentalan yang
agak kompleks.
vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
TITLE PAGE
i
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xiii
LIST OF SYMBOL
xvi
INTRODUCTION
1.1
Preamble
1
1.2
Problem Statement
2
1.3
Aim
3
1.4
Objectives
3
1.5
Scope and Limitation of The Study
3
LITERATURE REVIEW
2.1
Introduction
5
viii
2.2
Colloidal Stability
5
2.3
Theory of Coagulation
8
2.4
Common Chemical Used As Coagulant
10
2.5
Factor Affecting Coagulation
11
2.5.1
Coagulant Dose
12
2.5.2
Turbidity
13
2.5.3
Natural Organi Matter
14
2.5.4
Alkalinity and pH
15
2.5.5
Temperature
15
2.5.6
Mixing Speed
16
2.5.7
Treatmnet process
17
2.6
Common Experiment For Coagulation
17
2.7
Experimental Design
18
2.7.1
One-Factor-At-A-Time and Matrix
18
2.7.2
Response Surface Method
20
2.7.2.1
21
Factorial / Fractional Factorial
Design
2.7.2.2
3
Central Composite Rotatable Design
25
METHODOLOGY
3.1
Equipments and Materials
29
3.2
Experimental Procedure
30
3.2.1
Preliminary Study
30
3.2.1.1
One-Factor-At-A-Time
30
3.2.1.2
Response Surface Method
32
ix
3.2.2
Raw Water Quality - Alum Dosage and pH
33
Relationship
4
5
RESULTS AND DISCUSSION
4.1
Preliminary Study
37
4.2
Preliminary Response Surface Method
39
4.3
Water Quality - Optimum Dose And pH Relationship
40
4.3.1
Response Surface Analysis
41
4.3.2
Lowest FTU Approach
42
4.3.2.1 Factorial Analysis
44
4.3.2.2 Response Surface Analysis
47
CONCLUSIONS AND RECOMMENDATIONS
5.1
Conclusions
56
5.2
Future Study Recommendations
57
REFERENCES
58
APPENDIX A (DESIGN TABLE FOR 20 SET)
63
APPENDIX B (DETAILS FOR FACTORIAL ANALYSIS)
74
APPENDIX C (RESPONSE SURFACE ANALYSIS FOR FACTORS
THAT AFFECT COAGULATION - FULL
76
QUADRATIC TERMS)
APPENDIX D (RESPONSE SURFACE ANALYSIS FOR FACTORS
THAT AFFECT COAGULATION - LINEAR +
SQUARED TERMS)
79
x
LIST OF TABLES
TABLE NO.
TITLE
PAGE
CHAPTER 1
INTRODUCTION
CHAPTER 2
LITERATURE RIVIEW
2.1
Settling Velocity of various sizes of colloidal particles*
(Source: Peavy et. al., 1985)
6
2.2
Guideline of the nature of NOM and expected TOC
removals (Source: Edzwald and Tobiason, 1999)
14
2.3
Typical pattern of a 2-level, 3-factor full factorial design
24
2.4
An example of fully expanded 23 factorial
24
2.5
Guide to the Central Composite Rotatable Design and as
for a 2k Full Factorial (Diamond, 2001)
25
CHAPTER 3
METHODOLOGY
3.1
Experimental run for OFAT approach
31
3.2
Experimental run in RSM approach
33
3.3
Setting of water characteristics used in the study
35
3.4
Design table for range 20 mg/L to 120 mg/L of alum
dosage
36
3.5
Design table for range 40 mg/L to 200 mg/L of alum
dosage
36
xi
CHAPTER 4
RESULTS AND DISCUSSIONS
4.1
Results of the OFAT experiment on the turbidity removal
(Initial turbidity = 31 FTU)
38
4.2
Turbidity results from the RSM experiment in preliminary
works (Initial turbidity = 31 FTU)
40
4.3
The summary of response surface regression for 20 sets of
experiment
42
4.4
Optimum pH and dosage for the experiments based on
Lowest FTU approach
43
4.5
ANOVA for turbidity removal at optimum dose and
optimum pH
44
4.6
The summary of the response surface analysis for the water
quality effect on optimum dose
48
4.7
The summary of the response surface analysis for the water
quality effect on optimum pH
48
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
APPENDICES
A-1
Design table of RSM for Set 1
64
A-2
Design table of RSM for Set 2
64
A-3
Design table of RSM for Set 3
65
A-4
Design table of RSM for Set 4
65
A-5
Design table of RSM for Set 5
66
A-6
Design table of RSM for Set 6
66
A-7
Design table of RSM for Set 7
67
A-8
Design table of RSM for Set 8
67
xii
A-9
Design table of RSM for Set 9
68
A-10
Design table of RSM for Set 10
68
A-11
Design table of RSM for Set 11
69
A-12
Design table of RSM for Set 12
69
A-13
Design table of RSM for Set 13
70
A-14
Design table of RSM for Set 14
70
A-15
Design table of RSM for Set 15
71
A-16
Design table of RSM for Set 16
71
A-17
Design table of RSM for Set 17
72
A-18
Design table of RSM for Set 18
72
A-19
Design table of RSM for Set 19
73
A-20
Design table of RSM for Set 20
73
xiii
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
CHAPTER 1
INTRODUCTION
CHAPTER 2
LITERATURE RIVIEW
2.1
A negative colloid particle with its electrostatic field
(Source: Reynolds and Richards 1996; McGhee, 1991)
7
2.2
Ionic compression or repulsion force: (a) Charge system
in a colloidal suspension which shows the reduction of
thickness in diffused layer (b) Reduction of net force
8
2.3
Schematic actions of forces acting on hydrophobic
colloids in stable suspension
9
2.4
Conceptual view of reaction on coagulation mechanism
(Source: Pernitsky, 2003; Pernitsky, 2001; Dennett et.
al., 1996)
10
2.5
The alum coagulation diagram and its relationship to zeta
potential (Source: AWWA and ASCE, 1990)
13
2.6
Diagram of One-Factor-At-A-Time shows of the
turbidity versus alum dose (Source: Adopted from
Czitrom, 1999)
19
2.7
Matrix in 3D view. (Source: Aris, 2004)
20
2.8
Full Factorial Design with 2-level and 3 factors in 3D
view
22
2.9
One-factor-at-a-time vs factorial (Source: Czitrom, 1999)
22
2.10
Central composite rotatable design in 3D view
26
xiv
2.11
The view of 3D CCRD with 2 factors (F: 4 runs of full
factorial points or cube; S: 4 axial points or star points;
C: 1 centre point). (Source: Czitrom, 1999)
26
2.12
Central composite rotatable design for three factors used
in effect of raw water quality on coagulant dosage study
28
CHAPTER 3
METHODOLOGY
3.1
Flow chart of OFAT experiment
31
3.2
Flow chart of experimental design
34
CHAPTER 4
RESULTS AND DISCUSSIONS
4.1
Effect of alum dose on final turbidity (pH 7)
38
4.2
Effect of pH on final turbidity (Alum dose = 40 mg/L)
39
4.3
Pareto chart for (a) Optimum Dose and (b) Optimum pH
based on final turbidity (A: Temperature; B: pH; C: SS)
45
4.4
Main effect plot for water quality parameters at (a)
Optimum Dose (b) Optimum pH
46
4.5
Interaction effect plot for water quality parameters at
optimum dose
46
4.6
Interaction effect plot for water quality parameters at
optimum pH
47
4.7
(a) Contour and (b) response surface plots representing
relationship between pH and temperature at optimum pH
50
4.8
(a) Contour and (b) response surface plots representing
relationship between temperature and SS at optimum pH
51
4.9
(a) Contour and (b) response surface plots representing
relationship between pH and SS at optimum pH
52
4.10
(a) Contour and (b) response surface plots representing
relationship between pH and temperature at optimum
dose
53
xv
4.11
(a) Contour and (b) response surface plots representing
relationship between temperature and SS at optimum
dose
54
4.12
(a) Contour and (b) response surface plots representing
relationship between pH and SS at optimum dose
55
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
APPENDICES
xvi
LIST OF SYMBOL
mg
-
milligrams
g
-
grams
L
-
litre
mL
-
millilitre
°C
-
Degree Celsius
FTU
-
Formazin Turbidity Unit
NTU
-
Nephelometric Turbidity Unit
p-value
-
level of confidence in percentage
CaCO3
-
calcium carbonate
CHAPTER 1
INTRODUCTION
1.1
Preamble
In drinking water treatment, coagulation process is use to destabilize colloidal
materials or contaminants. Followed by solid-liquid separation processes such as
flocculation, sedimentation, or dissolved air flotation (DAF) and filtration, the
processes are capable to remove the colloidal particles from the water (Pernitsky,
2001).
Chemicals that are used for coagulation process is called coagulant.
Currently, there are many types of coagulant available in wastewater treatment but
the most frequently used are alum or ferric sulphate. These chemical coagulants are
in positive charged and it will react with colloidal suspension of organic and
inorganic solids that are usually negatively charged.
Besides the man-made
coagulant, other traditional coagulants originated from the plant origin such as
Moringa Olerfera seeds which can be found in India and Strychnos Potatorum are
seldomly used. The uses of other traditional coagulant from soil origin include
bentonite or clay, algae, chitosan and dough from millet bread are also reported
(Anselme and Narasiah, 1998).
2
Many factors have been reported to affect the coagulation process. These
include turbidity, organic matter and pH, ultraviolet (UV), alkalinity or acidity and
temperature (Pernitsky, 2003). While some studies have been conducted to relate
these parameters to coagulant dosage, the standard method commonly used to
determine the coagulant dosage is by using Jar Test.
1.2
Problem Statement
The effectiveness of the coagulation process is highly dependent on the
dosage of the coagulant and the pH of the water during the process. However the
effectiveness of this process and the relationship between the raw water quality and
the coagulant dosage and optimum pH can hardly be predicted until today mainly
due to the complexity of the chemistry of the coagulation process. Hence, the dose
of coagulant and pH of the process mainly depend on the results of the Jar test which
is conducted at the water treatment plant. Typically, the Jar Test will be carried out
in a daily basis and also in the event of changes in raw surface water characteristics.
Since Jar Test is a tedious experimental process and time consuming, this
study intends to develop a relationship between raw water quality parameters and the
optimum coagulant dosage and the pH based on statistical approach.
Such
relationship is anticipated to ease the operator in plant to determine the optimum
dosage and pH in the coagulation process.
3
1.3
Aim
The aim in this study is to ease the process of determining the optimum
chemical dosage and pH for coagulation process in water treatment.
1.4
Objectives
There are two main objectives of the study:
a) To explore the effect of the selected water quality parameters on the optimum
dosage of coagulant and pH.
b) To develop a statistical relationship between the selected water quality
parameters with the optimum coagulant dosage and pH.
1.5
Scope and Limitation of The Study
The study covers a comprehensive experimental works at laboratory scale.
Synthetic water prepared by using kaolin was used in the study. The experimental
work was designed using Response Surface Method (RSM). Three independent
water quality variables were chosen, namely initial turbidity, pH and temperature.
Optimum coagulant dosage and pH were used as the response variables based on the
4
lowest turbidity achieved after the jar test. Aluminium sulphate (Alum) was used as
the coagulant.
CHAPTER 2
LITERATURE REVIEW
2.1
Introduction
Coagulation is one of the important processes in water treatment. It is an
effective method in removing natural organic matters (NOM) and colloidal
particles in high and intermediate molecular weight ranges (Sinsaubaugh et. al.,
1986). This process has a direct impact on the reliability of plant operations and
final water quality and has significant contribution to the operational cost of the
treatment plant (Hooge, 2000). This chapter discuss on coagulation process, the
phenomenon of coagulation, the mechanism involved, important of water
parameter in coagulation process and the coagulants.
2.2
Colloidal Stability
A large number and variety of substances that produce turbidity can be
found in the waters. Examples of these include clay particles, organic matter
6
from decaying vegetation and animal. These particles especially colloids, range in
size from 1 millimicrons to 500 millimicrons (nanometers) and it is not visible when
using an ordinary microscope and do not easily settle ion of solution (Hammer and
Hammer Jr., 2005).
The terms stable are used for colloidal suspensions that do not agglomerate
naturally. It is stable as the individual particle has such a large surface area relative
to its weight that gravity forces do not influence its suspension (Peavy et. al., 1985).
Table 2.1 illustrates the setting velocity of different particles with respect to their
diameter.
Table 2.1: Settling Velocity of various sizes of colloidal particles* (Source: Peavy et.
al., 1985)
Particle diameter (mm)
Size typical of
Settling velocity
10
Pebble
0.73 m/s
1
Coarse Sand
0.23 m/s
0.1
Fine Sand
1.0 x 10-2 m/s (0.6 m/min)
0.01
Silt
1.0 x 10-4 m/s (8.6 m/d)
0.0001
Large colloid
1.0 x 10-8 m/s (0.3 m/yr)
0.000001
Small colloid
* Spheres with specific gravity of 2.65 in water at 20°C.
1.0 x 10-13 m/s (3 m/million yr)
There are two types of colloids, namely hydrophobic and hydrophilic.
Hydrophobic colloids are those that do not have affinity with water while hydrophilic
are colloids that have affinity with water. Its particles depend on electrical charge for
their stability in suspension. For hydrophobic colloids, individual particles are held
apart by electrostatic compression or repulsion forces by positive ions adsorbed onto
their surfaces from solution (Reynolds and Richards 1996; McGhee, 1991). Figure
2.1 on the next page illustrates the theory of double layer of electrostatic. This
7
colloidal type may be found in the bulk of inorganic and also organic matter in turbid
waters.
Rigid or Fixed Layer / Stern Layer attached to
particles
Stern potential
Surface/ Nerst
potential
Figure 2.1: A negative colloid particle with its electrostatic field. (Source: Reynolds
and Richards 1996; McGhee, 1991)
Hydrophilic colloids are stable because of their attraction for water molecules
rather than because of the slight charge that they might posses. The typical examples
of the hydrophilic colloid are as soap, soluble starch, synthetic detergents and blood
serum. These colloids are not easy to remove from suspension and thus required 10
to 20 times more coagulant than the dosage normally the used in the conventional
water treatment (Hammer and Hammer Jr., 2005).
Natural forces of attraction also exist between two particles and are called
Brownian movement and Van Der Waals’ force. Brownian movement is a random
8
motion of colloids caused by bombardment of water molecules which is tend to
enhance this physical force of attraction in pulling the particles together (Pushkin,
2004). In both cases, if the repulsion is over the attraction, the particles are not
allowed to contact each other and these hinder the flocculation process (Figure 2.2).
Figure 2.2: Ionic compression or repulsion force: (a) Charge system in a colloidal
suspension which shows the reduction of thickness in diffused layer
(b) Reduction of net force
2.3
Theory of Coagulation
Coagulation process in raw water treatment is the process of charge
neutralization of colloidal particles using the addition of a chemical reagent or the
process of conditioning suspended solids particles to promote their agglomeration
thus produces larger particles that can be more readily removed in subsequent
treatment processes (AWWA and ASCE, 1990; Jin, 2005).
9
The effectiveness of the coagulation process in water treatment practice
depends on the interaction of the coagulant species with particles and dissolved
organic material in the raw water. If both of the surface charges are similar, the
molecules of the contaminants will repel with each other (Sawyer et. al., 1978). The
basis examining coagulation can be referring by a conceptual overview of the
reactions that occur during the coagulation process on Figure 2.3 (Pernitsky, 2001).
Attraction
Repulsion
Figure 2.3: Schematic actions of forces acting on hydrophobic colloids in stable
suspension
There are four mechanisms that contribute the coagulation process, namely
enmeshment or sweep-floc particles, charge neutralization or destabilization,
complexation or precipitation and adsorption. Figure 2.4 illustrates the conceptual of
possibly reaction occur during coagulation mechanism. All these mechanisms were
categorizing as primary reaction mechanisms and they may exists either by
themselves or they also may exists in combination due to the complexity of the
nature of the coagulation process coagulation process when chemical coagulant was
added (Edzwald and Van Benscoten, 1990).
Details discussions on these
mechanisms are given in Pernitsky, 2003; Amirtharajah and Mills, 1982; Dempsey
et. al., 1985; Randtke, 1988; Edzwald and Van Benschoten, 1990; Dempsey, 1994.
10
ACTIVE COAGULANT
SPECIES
COAGULANT
Alum
Hydrolysis
CONTAMINANTS
PRODUCTS
MECHANISM
Al(OH)3 (am) +
Colloids
A: Enmeshment
NOM +
Al(OH)3 (am)
B: Adsorption
Al=Colloid
C: Charge Neutralization/
Desztabilization
Al=NOM
Al+NOM(am)
D: Complexation/
Precipitation
Colloids
Al(OH)3
(am)
NOM
3+
Al ,
AlOH2Al(OH)4-
Al3+, SO42-
3+
H+
Alkalinity
consumption
Al ,
Al(OH)2+
Colloids
NOM
Figure 2.4: Conceptual view of reaction on coagulation mechanism (Source:
Pernitsky, 2003; Pernitsky, 2001; Dennett et. al., 1996)
2.4
Common Chemical Used As Coagulant
Most widely used coagulant in drinking water treatment is based on
aluminium, called aluminium sulphate (Al2 (SO4)3) or alum, filter alum or alumina
sulphate. Coagulants react with available alkalinity such as carbonate, bicarbonate
and hydroxide or phosphate to form insoluble aluminum salts. Equation 2.1 shows
the reaction between aluminium and natural alkalinity. As metal salts, alum will
react with alkalinity in the water to produce an insoluble metal hydroxide floc which
incorporates the colloidal particles. The addition of alum was also found to remove a
large proportion of the high molecule weight of NOM compounds with the decrease
in the number-average of molecule weight values (Ho, 2005).
Al2(SO4)3.14.3H2O + 3Ca(HCO3)2
= 2Al (OH)4 + 3CaCO4 + 14.3H2O + 6CO2
Equation 2.1
11
Iron-based coagulant in the form of ferrous sulphate or copperas
(FeSO4.7H2O), ferric sulphate (Fe2(SO4)), ferric chloride (FeCl3) and the mixture of
Fe2(SO4) and FeCl3 are also commonly used in water treatment. In commercial
product, ferric sulphate is available in the form of a reddish-brown granular material
and it is readily soluble in water (Tebbuti, 1973). While aluminium-based coagulant
in the form of alum and it can be found in round-white granular.
Alum not only becomes a favourite coagulant but also no need to add lime or
soda ash along with its usage. Ferric sulphate is effective over a wide range of pH.
It is successful on colour removal at low pH values and may be used for iron and
manganese removal and as well as a coagulant in precipitation softening at high pH
(Hammer and Hammer Jr., 2005). Equation 2.2 shows the reaction between ferric
sulphate and the natural alkalinity of water.
Fe2(SO4)3 + 3Ca(HCO3)2
= 2Fe(OH)3 ↓ + 3CaSO4 + 6CO2
2.5
Equation 2.2
Factor Affecting Coagulation
There are seven factors found likely to affect the coagulation process in
removing the NOM and colloid particles or turbidity. These are coagulant dose,
turbidity or SS, natural organic carbon (NOC), pH and alkalinity, temperature,
mixing speed and the treatment process.
12
2.5.1
Coagulant Dose
Coagulant dose is a key of process-control factors because of the different
water quality conditions can have an effect on different dose of coagulant (Budd et.
al., 2004). It was found that coagulant doses are controlled by dissolved organic
carbon (DOC) concentration rather than by turbidity in most surface waters (Edzwald
and Van Benschoten, 1990). These makes an adjustment on coagulant dosage is
important to ensure the effectiveness for maintaining settled raw water quality in
plants.
High concentrations of coagulant would reduce the time of particles to
destabilise by increasing the collision-attachment efficiency which makes bulky
precipitate enmeshes particles settles rapidly to form the ‘sweep-floc’ region of
coagulation (Reed et. al., 1999; Sanks 1979). Usage of alum dose less than 5 mg/l is
believed to result in charge neutralization (destabilization) would be the primary
mechanism while at more than 5 mg/L, an entrapment mechanism would be
predominant.
In considering of turbidity and NOM removal, the optimum of alum
coagulants required is 1 mg/L which it was absolute depend on both Specific
Ultraviolet Absorbance (SUVA) and NOM concentration (Pernitsky, 2001). Figure
2.5 depicts some of the aluminum species involved in alum coagulation and the
conditions of aluminum concentration and pH under which they occur (AWWA and
ASCE, 1990).
13
Figure 2.5: The alum coagulation diagram and its relationship to zeta potential
(Source: AWWA and ASCE, 1990)
2.5.2
Turbidity
Turbidity is a very important factor in water treatment and it may control the
coagulation process if low concentration of total organic carbon (TOC) in raw water.
Higher coagulants doses, longer flocculation time and lower filtration rates are much
required in high water turbidity (≥ 100 NTU) (Pernitsky, 2003). The optimum
turbidity removal and solid-liquid separation often occurs in low solubility of
coagulant’s pH (Eikebrokk, 1990; Edzwald and Van Benschoten 1990; Bell-Ajy et.
al., 2000). However, turbidity has less effects on coagulant dose when the colloidal
particles removal through adsorption onto or sweep-floc mechanism (Pernitsky,
2001).
14
2.5.3
Natural organic matter
Natural organic matter also may contribute to poor water quality. It was
characterizing by SUVA and the concentration was measures by TOC, DOC or
ultraviolet (UV) (Pernitsky, 2001). Natural organic matter completely predominant
in water supplies which has SUVA more and equal to 2 but have less effect on
coagulation as the decreasing of SUVA. At this condition, coagulant dose seems to
increase with increasing of TOC. Table 2.2 shows the guidelines for interpretation of
SUVA value in NOM.
Table 2.2: Guideline of the nature of NOM and expected TOC removals (Source:
Edzwald and Tobiason, 1999)
SUVA
<2
Composition
Coagulation
DOC Removals
Mostly non-humics
NOM has little influence
< 25% for alum,
Low hydrophobicity,
Poor DOC removals
Little greater for ferric
Mixture of aquatic
humics and other NOM,
NOM influences
25-50% for alum,
Mixture of hydrophobic
and hydrophilic NOM,
DOC removals should be
fair to good
Little greater for ferric
NOM controls
> 50% for alum,
Good DOC removals
Little greater for ferric
Low molecular weight
2–4
Mixture of molecular
weights
>4
Mostly aquatic humics,
High hydrophobicity,
High molecular weight
15
2.5.4
Alkalinity and pH
Alkalinity and pH are two different things because alkalinity is a measured of
water capacity to neutralize acids while pH is the unit in measuring the level of
acidic in water. Addition of 1 mg/L of alum might neutralize 0.5 mg/L of hydrogen
ions (Tang et al, 1998). Low concentration of alkalinity might destroy a buffering
capacity and also makes rapidly dropping in water pH. In maintaining the optimum
pH, it is required an artificial buffer because pH was emphasized as a critical process
condition for coagulation (Peavy et. al., 1985; Amirtharajah & Mills, 1982). While a
high alkalinity water would be highly buffered and exhibit a limited pH decrease
after coagulant (Budd et. al., 2004).
A level of response in water varies depending on alkalinity and it is
dominated by the dissolve inorganic carbon species (carbonate and bicarbonate) in
the range of pH in most natural waters. At 20°C, a pH for minimum polyaluminum
solubility was in ranged 6.0 to 6.7 (Pernitsky, 2001). Coagulation at pH less than 7.5
with alum would decrease and become a significant problem for high alkalinity water
and it is recommended to maximize TOC removal of alum when the pH is very low
(less than pH 5.5) (Pernitsky, 2003).
Although sweep coagulation occur when
negatively-charged forms of alum predominate in range pH 6 to 8, an optimum pH
for coagulation is within the range of 5.5 to 7.5, while 5.0 to 8.5 in the treated water
with ferric, respectively.
2.5.5
Temperature
Low temperature in water affects the chemical properties of water (reaction
rates, solubility of solids and liquids), pH and hydrolysis species of coagulants and
mostly in sedimentation. Reaction rates and reaction kinetics decrease with reducing
16
temperature which the relationship is expressed with Arrenius empirical rate law
(Snoeyink and Jenkins 1980).
Solubility may be considered as a function of
temperature in which pH of minimum solubility for aluminum and of most solids
decrease as the temperature decreases (Al-Laya and Middlebrooks, 1974; Odegard
et. al., 1990; Dempsey, 1994; Edzwald et. al., 1994). However, an increase of
temperature in endothermic reactions and a positive enthalpy data and also in
equilibrium makes the solubility increase (Bagwell et al., 2001, Pernitsky, 2003).
Decreasing in water temperature was accompanied by a decreasing in
turbidity removal because of the deposition of Al(OH)3 on the particulates surface
significantly reduced with decrease of temperature (Kang et al., 1995; Hooge, 2000).
Recommendation on slow hydrolysis and precipitation reactions of metal coagulants
in cold water was beneficial to flocculation loading rates, perhaps by permitting
hydrolysis species to react more extensively with turbidity and with humic
substances (Schultz et al,. 1984; Shea et al., 1971; Adhin et al., 1974).
2.5.6
Mixing Speed
Rapid mixing is utilized as part of the coagulation process to distribute the
coagulant chemicals throughout the water stream. When alum or ferric chloride is
used to achieve destabilization through charge neutralization, it is extremely
important that the chemical coagulant is efficiently distributed because the
intermediate products of the coagulant reaction are the destabilizing agents. Thus,
because of the short life of these intermediate species; coagulant must be contact
with the solids particles if the destabilization is to be achieved. However, in some
cases, excessive rapid mixing may serve to break-up coagulant molecules or floc
particles, thereby reducing the effectiveness of subsequent solids removal processes
(EPA, 1999).
17
Mixing intensity is typically quantified with a number known as the velocity
gradient or G value and this value is a function of the power input into the rapid
mixing process and the volume of the reaction basin. Typical G values for rapid
mixing coagulation were in range from 300 to 8000 sec–1 (Hudson, 1981). Time
required to achieve efficient coagulation varies were depending on the coagulation
mechanism involved. When the charge neutralization is involved, the detention time
required may be one second or less but if the sweep-floc or entrapment involved, a
longer detention times (1 - 30 seconds) may be appropriate (Kawumara, 1991;
AWWA and ASCE, 1998; Hudson, 1981)
2.5.7
Treatment Process
A physical forces also to be believe, one of the affecting factor involved with
the effectiveness of the raw water treatment for different of it treatment processes
(Pernitsky, 2001). As for direct filters, it is needs or requires the effective charge of
neutralization and the production of small floc particles. This element is important to
minimize the headloss of the filters. On the other hand, sedimentation requires the
precipitation of a dense, strong and rapidly settling floc. While treatment using
dissolves air flotation (DAF) approach requires effective charge neutralization but at
the same time, it may tolerate reasonably large amounts of precipitation floc.
2.6
Common Experiment For Coagulation
Jar Test is a common laboratory procedure to determine the optimum
coagulant dosages for water and wastewater treatment.
This test simulates the
coagulation and flocculation processes that encourage the removal of suspended
18
colloids and organic matter which can lead to turbidity, odor and taste problems.
The range of mixing time are 1 minutes to ensure complete dispersion of the
chemicals and then mixed slowly for 15 to 20 minutes to aid in the formation of flocs
and also approximately 30 minutes to allow settlement or until clarification has
occurred. The results from this test are used to determine the quantity of coagulant
to be used in the water treatment plant.
2.7
Experimental Design
Two methods has been preferable to solving problem in drinking water
treatment are traditional method and the statistical method. Traditional methods
were using one-factor-at-a-time (OFAT) and matrix while statistical method was
using response surface method (RSM). The purposes of these approaches usage are
to find the most effective, truly important and efficiency variables or winning
combinations variables in coagulant dosage.
2.7.1
One-Factor-At-A-Time and Matrix
One-factor-at-a-time (OFAT) approach is the most common traditional
problems solving method used by researchers nowadays as alternatives to analyse
and statistical experimental design (Figure 2.6). In this method, researcher conducts
the tests in systematically changing the levels of one factor but in the same time
keeping the others in constant and then study the behavior of the system at several
levels of those factors (Haaland, 1989).
19
Turbidity (NTU)
4
3
2
1
40
60
80
Alum Dose (mg/L)
Figure 2.6: Diagram of One-Factor-At-A-Time shows of the turbidity versus alum
dose (Source: Adopted from Czitrom, 1999)
This method will find the best value for each factor and the process of this
finding value is repeated for the remaining factors until all factors have been
considered. Although it is simple and straight forward method but it also ineffective
because it is suffers from several shortcomings which may lead to wrong conclusions
(Haaland, 1989; Hendrix, 1979). It also takes too many experiments or trial to come
out with the answer.
Eventhough it does not require many measurements in one space, in
particular OFAT not capable to identifying the interactions effects from more than
one factor because it is not fully explore the space of possible solutions and may miss
the solution (Haaland, 1989; Adrion et al., 1984). This method can be simplify said
that “A botched design gives very little information for a lot of work” (Box, 1965).
It is often called botched because the design so poor.
A second traditional approach to statistical and analyze experimental design
is with laying out the matrix of all possible combinations of the important factors.
Figure 2.7 illustrate the matrix in 3D view. If the OFAT is the simplest method,
matrix show the most complicated method because it is fully explores the
20
experimental space until the solutions are identified.
Eventhough this method
overcomes the shortcomings that occur in OFAT approach and effective, however it
is inefficient because it requires an unnecessarily large number of measurements
which this costly the implementation (Haaland, 1989; Adrion et al., 1984).
Figure 2.7: Matrix in 3D view. (Source: Aris, 2004)
2.7.2
Response Surface Method
Response Surface Method is one of the statistical methods which are
providing an advantage over traditional problem solving such as OFAT and matrix.
Response Surface Method more focus on small, well-design experiments which solve
problem on the process being studied (Haaland, 1989). Compare to OFAT and
matrix design, this statistical design method also efficient and effective because it
provides good coverage of the experimental space with as few measurements as
possible (Adrion, et al., 1984).
21
Response Surface Method explores the relationships between several
explanatory variables and one or more response variables (Box and Wilson, 1951).
The main idea of RSM is to use a sequential experimental procedure to obtain an
optimal response. Box and Wilson has suggested two of polynomial model to do this
experimental procedure. A first model is a first-degree polynomial model and the
second is a second-degree polynomial model.
2.7.2.1
Factorial / Fractional Factorial Design
First step to obtain an optimal response in sequence experimental procedure
is by using a first-degree polynomial model.
This model actually is only an
approximation but it is useful because it is easy to estimate and apply, even easy for
those who have little knowledge in the process to use it. Easiest way to estimate a
first-degree polynomial model is by using a factorial design or a fractional factorial
in fully design.
This model is sufficient to determine which of the explanatory variables have
an impact on the response variables of interest. Once it is suspected that only
significant explanatory variables are left, then this solution need more complicated
design that is a second-degree polynomial model.
Eventhough full factorial design or a full fractional factorial design are in
same field but full factorial design actually allow the researcher to explore multiple
factors simultaneously while fractional means that we do a fraction or a part of the
full factorial design.
Figure 2.8 illustrate the full factorial design.
It’s enable
researcher to do half-fraction, a quarter- fraction or an eighth-fraction (Box and
Hunter, 1961a; Box and Hunter, 1961b; Tiao and George, 2000; Box et al., 1978).
For example a half-fraction is to do half of the full factorial design, or (1/2)24 =
22
(1/2)16 = 8 runs to investigate four factors; (1/2)(25) = (1/2)32 = 16 runs to
investigate five factors; and so on.
For details, Figure 2.9 shows a graphical
Factor 2 demonstration of why factorial design is better than OFAT experiments.
Factor 3
Factor 1
Figure 2.8: Full Factorial Design with 2-level and 3 factors in 3D view
Figure 2.9: One-factor-at-a-time versus factorial (Source: Czitrom, 1999)
23
A design with all possible high and low combinations of all the input factors
in different experimental conditions is called a full factorial design with runs at nk. If
an experiment with k factors, each set at two levels, it is called a two-level factorial
design. It is also called a saturated design. k is the independent variables whose
possible influence on a response variable is to be assessed are referred to as factors
and n is refer to the number of the response level.
The high and low levels are conveniently denoted by + and − or by + 1 and −
1. The factors can be continuous (pressure, temperature, concentration, etc.) or
discrete (additive present, source of raw material, stirring used, etc.). The block with
the 1's and -1's is called the Model Matrix or the Analysis Matrix. The table or
tabular formed by the columns factor or response is called the Design Table or
Design Matrix.
For example, if there are k factors, each at 2 levels, a full factorial design has
k
2 runs and if the factor used 3, a full factorial design has 23 runs which is equal to 8
runs (Table 2.3) and the Table Matrix may be expanding to observed the presence of
interaction effect by two or more factors with few more columns as shown in Table
2.4.. The example of the run in the design always used the Standard Order which is
not in randomized order and wrote from number 1 until the run’s number will be
conducted.
24
Table 2.3: Typical pattern of a 2-level, 3-factor full factorial design
Factor
Run
X
Y
Z
1
+
+
+
2
+
+
-
3
+
-
+
4
+
-
-
5
-
+
+
6
-
+
-
7
-
-
+
8
-
-
-
Table 2.4: An example of fully expanded 23 factorial
Factor
Interaction effect or additional factor
X
Y
Z
XY
YZ
XZ
XYZ
Run
(1)
(2)
(3)
(4)
(5)
(6)
(7)
1
+
+
+
+
+
+
+
2
+
+
-
+
-
-
-
3
+
-
+
-
-
+
-
4
+
-
-
-
+
-
+
5
-
+
+
-
+
-
-
6
-
+
-
-
-
+
+
7
-
-
+
+
-
-
+
8
-
-
-
+
+
+
-
( ) denotes column no.
As shown by Table 2.5, when the number of factors is greater or 5, a full
factorial design requires a large number of runs and is not very efficient. It is
recommended that in that number of factors, applied a fractional factorial design or a
Plackett-Burman design is a better choice for 5 or more factors.
25
Table 2.5: Guide to the Central Composite Rotatable Design and as for a 2k Full
Factorial (Diamond, 2001)
a
No. of
variables/no.
of factor
No. of Hadamard
matrix trials/no. of
runs
No. of star
trials
No. of
centre
trials
ψ
2
4
4
5
1.4142
3
8
6
6
1.6820
4
16
8
7
2.0000
5
16
10
6
2.0000
6
32
12
9
2.3780
7
64
14
14
2.8280
8
128
16
20
3.3640
a
Runs with no. of variable greater than 4 are half-fraction
ψ = F0.25 where F is the number of factorial points in the design; also equal to the ratio between the
difference of star points value divided by the difference of factorial points value
2.7.2.2
Central Composite Rotatable Design
To overcome and to estimates this advance design, a second-degree
polynomial model is neede by implementd a central composite design or central
composite rotatable design (CCRD) (Figure 2.10). However, this second model is
still only an approximation but the approximation results is best than a first model.
Moreover, the model absolutely can be used to optimize which it can maximize,
minimize, or attain a specific target for a response or factor (Box and Wilson, 1951).
26
Figure 2.10: Central composite rotatable design in 3D view
As shown in Figure 2.11, CCRD in two factors in nine different runs consists
of four runs of full factorial, four axial points and one centre point. Other term for
full factorial is cube and other term for axial points is star points (Czitrom, 1999;
Aris, 2004). It has the advantage of incorporating information from a properly
planned factorial experiment. The factorial portion and centre points may serve as a
preliminary stage to fit a first order (linear) model and still provide evidence
regarding the existence of second-order contribution or curvature.
S
F
F
S
S C
F
F
S
Figure 2.11: The view of 3D CCRD with 2 factors (F: 4 runs of full factorial points
or cube; S: 4 axial points or star points; C: 1 centre point). (Source:
Czitrom, 1999)
27
A complete design enable the generation of a mathematical model which
describe the process and may be used to determine the best setting of the process
(Aris, 2004; Diamond, 2001). Table 2.5 in Section 2.7.2.1 provides a guideline for
the CCRD as a function of the number of variables involved in the study (Diamond,
2001). The example of CCRD for the three factors such as suspended solid (SS), pH
and temperature in effect of raw water quality on coagulant dosage is shown in Table
2.7.
As mentioned in Section 2.7.2.1, the number of the factorial run is
determined by 2k where k represents the number of variables involved. Any values
may be assigned to Ψ and number of replicates of the centre point run. However, the
values given in Table 2.6 provide only orthogonally blocked and rotatable designs
which improve the quality of the model prediction (Diamond, 2001; Aris, 2004). 28
Table 2.6: Central composite rotatable design for three factors used in effect of raw
water quality on coagulant dosage study
SS
(mg/L)
pH
Temperature
(°C)
SS
(mg/L)
Coded Termc
Runb
pH
Temperature
(°C)
Uncoded Termd
RSM101
-1
-1
-1
54.3
5.8
27.0
RSM 102
+1
-1
-1
54.3
5.8
33.0
RSM 103
-1
+1
-1
54.3
8.2
27.0
RSM 104
+1
+1
-1
54.3
8.2
33.0
RSM 105
-1
-1
+1
125.7
5.8
27.0
RSM 106
+1
-1
+1
125.7
5.8
33.0
RSM 107
-1
+1
+1
125.7
8.2
27.0
RSM 108
+1
+1
+1
125.7
8.2
33.0
RSM 109
-1.682
0
0
90.0
7.0
25.0
RSM 110
+1.682
0
0
90.0
7.0
35.0
RSM 111
0
-1.682
0
90.0
5.0
30.0
RSM 112
0
+1.682
0
90.0
9.0
30.0
RSM 113
0
0
-1.682
30.0
7.0
30.0
RSM 114
0
0
+1.682
150.0
7.0
30.0
RSM 115
0
0
0
90.0
7.0
30.0
RSM 116
0
0
0
90.0
7.0
30.0
RSM 117
0
0
0
90.0
7.0
30.0
RSM 118
0
0
0
90.0
7.0
30.0
RSM 119
0
0
0
90.0
7.0
30.0
RSM 120
0
0
0
90.0
7.0
30.0
RSM 101-108: factorial point run; RSM 109- RSM 114: star point run; RSM 115-120: centre point run
b
c
(-1) and (+1) represent the low- and high- level values of the factorial points; (-1.682) and (+1.682) represent the minimum and
maximum values of the star points; (0) represents the centre point value.
d
The actual value assigned to the variables translated from the coded value.
CHAPTER 3
METHODOLOGY
3.1
Equipments and Materials
Main equipments used in this study include jar test apparatus (Chemix Floctester Model CL6), turbidity meter (HI 93703 Portable Microprocessor Turbidity
Meter) (HANNA Instruments, 1998) and pH meter (Thermo Orion Model 420A+).
Chemicals used in this study include alum or aluminium sulphate
(Al2(SO4)3.14.3H2O), hydrochloride acid (HCl), natrium hydroxide (NaOH) and the
pH buffer for pH 7, pH 4 and pH 9. There are of analytical type and used without
further treatment and chemicals were used as received. Hydrochloric acid of 0.1N
concentration and NAOH of 0.1N concentration were used. Distilled water were
prepared by (Bibbly Merit W4000) were used in the study. Raw water used in
preliminary work were taken from middle part of Sungai UTM in the Universiti
Teknologi Malaysia’s campus and kaolin were taken from UTM’s Soil and Geology
Laboratory.
30
3.2
Experimental Procedure
3.2.1
Preliminary Study
The purpose of preliminary study is to confirm the findings of previous study
conducted by Jimbat (2006). In his study, Jimbat used synthetic water to compare
between OFAT and RSM experimental approach in determining the optimum
coagulant dosage and pH. While Jimbat study used synthetic water, this preliminary
work used raw surface water collected from one of the river at Universiti Teknologi
Malaysia.
3.2.1.1 One-Factor-At-A-Time
In OFAT experimental approach, the experiments were carried out by varying
one factor at a time with another factor being fixed. In this study, the approach
followed the common procedures used in Jar Test study. The flow chart of the
OFAT is shown in Figure 3.1 and the experimental design is shown in Table 3.1. A
volume of 500 mL of raw surface water were filled in six beakers (at a time). The
pH of the solutions was fixed at 7, while the alum solutions at six different dose (i.e.
20 mg/L, 40 mg/L, 60 mg/L, 80 mg/L, 100 mg/L and for 120 mg/L) were used and
added into each beaker.
31
SET I
Alum dosage varied from 20 mg/L - 120 mg/L; pH set at 7.
SET II
pH varied from 4.5 – 7.0; Alum set at best dosage from SET I.
Figure 3.1: Flow chart of OFAT experiment
Table 3.1: Experimental run for OFAT approach
Run
pH
Alum Dose (mg/L)
OFAT11
7.0
20
OFAT12
7.0
40
OFAT13
7.0
60
OFAT14
7.0
80
OFAT15
7.0
100
OFAT16
7.0
120
OFAT27
4.5
40
OFAT28
5.0
40
OFAT29
5.5
40
OFAT210
6.0
40
OFAT211
6.5
40
OFAT212
7.5
40
* OFAT11 – OFAT 212; refer to beaker number 1 in first run of the jar test and so on.
The water was initially rapid mixed at approximately 80 rpm for one minute
and then followed by slow mixing at 30 rpm for approximatly 15 minutes. After 15
32
minutes of slow mixing, the mixer was turn-off and the floc was allowed to settle for
30 minutes.
Samples from the supernatant for each beaker were taken and
immediately analyzed for turbidity. The best dosage was determined based on the
lowest turbidity achieved.
The second set of experiments was conducted using the best alum dosage of
the first jar test run. The pH of the water in each beaker was set at 4.5, 5.0, 5.5, 6.0,
6.5 and 7.0. The same procedures as explained in previous paragraph were repeated
and the best pH was determined best on the lowest turbidity achieved.
3.2.1.2 Response Surface Method
As mentioned earlier, RSM consists of a collection of experimental runs
made at predetermined settings of the experimental condition. In this approach, pH
was set at 4.5, 5, 6.25, 7.5 and 8 while the alum dosage was set at 20, 35, 70, 105 and
120 mg/L. The combinations of these settings are shown in Table 3.2. Except for
the combination of alum dosage and pH setting, the rest of the experimental
procedures followed those as described in previous section of OFAT.
33
Table 3.2: Experimental run in RSM approach
Run
Alum Dose (mg/L)
pH
RSM11
35
5.00
RSM 12
105
5.00
RSM 13
35
7.50
RSM 14
105
7.50
RSM 15
20
6.25
RSM 16
120
6.25
RSM 27
70
4.50
RSM 28
70
8.00
RSM 29
70
6.25
RSM 210
70
6.25
RSM 211
70
6.25
RSM 212
70
6.25
RSM213
70
6.25
* RSM11 - RSM27; refer to beaker number 1 in first run of the jar test and so on.
3.2.2
Raw Water Quality - Alum Dosage and pH Relationship
Response Surface Method approach was used to explore the relationship
between water quality variables and optimum dosage and also pH. Three raw water
quality variables were selected in this study. They are suspended solid (SS),
temperature and pH. Synthetic water using distilled water was used with kaolin
added as the source of SS.
The characteristics of the water in term of SS,
temperature and pH were predetermined accordingly prior to the experiments and are
shown in Table 3.3.
For each water characteristic, jar test procedures as described in Section 3.2.1
(RSM approach) were conducted to determine the optimum alum dosage and pH.
34
The range of alum dosage used was depended on the initial SS of the water. For
initial SS concentration of 54.3 mg/L in the initial four sets, alum dosages between
20 mg/L to 120 mg/L were used while for SS concentration of 30.0 mg/L, 90.0 mg/L,
125.7 mg/L and 150.0 mg/L in the following sets, alum dosages between 40 mg/L to
200 mg/L were used.
The flow chart of the experiments is given in Figure 3.2. The details of the
experimental design with respect to the alum dosage and pH used in the study are
given in Tables 3.3, 3.4 and 3.5.
Water Characteristics
(Set 1 to 20)
Jar Test procedures according
to RSM approach
Repeat from each set of water
characteristics
Determination of optimum
dosage and pH
Result recorded
Figure 3.2: Flow chart of experimental design
35
Table 3.3: Setting of water characteristics used in the study
Set
Temperature (°C)
pH
SS (mg/L)
1
27.0
5.8
54.3
2
33.0
5.8
54.3
3
27.0
8.2
54.3
4
33.0
8.2
54.3
5
27.0
5.8
125.7
6
33.0
5.8
125.7
7
27.0
8.2
125.7
8
33.0
8.2
125.7
9
25.0
7.0
90.0
10
35.0
7.0
90.0
11
30.0
5.0
90.0
12
30.0
9.0
90.0
13
30.0
7.0
30.0
14
30.0
7.0
150.0
15
30.0
7.0
90.0
16
30.0
7.0
90.0
17
30.0
7.0
90.0
18
30.0
7.0
90.0
19
30.0
7.0
90.0
20
30.0
7.0
90.0
36
Table 3.4: Design table for range 20 mg/L to 120 mg/L of alum dosage
Run No.
Alum Dose (mg/L )
pH
RSM1
34.6
5.00
RSM2
105.4
3.60
RSM3
34.6
17.00
RSM4
105.4
6.09
RSM5
20.0
6.00
RSM6
120.0
3.89
RSM7
70.0
4.24
RSM8
70.0
4.38
RSM9
70.0
4.64
RSM10
70.0
5.19
RSM11
70.0
4.17
RSM12
70.0
4.89
RSM13
70.0
4.72
Table 3.5: Design table for range 40 mg/L to 200 mg/L of alum dosage
Run No.
Alum Dose (mg/L )
pH
1
34.6
5.00
2
105.4
3.60
3
34.6
17.00
4
105.4
6.09
5
20.0
6.00
6
120.0
3.89
7
70.0
4.24
8
70.0
4.38
9
70.0
4.64
10
70.0
5.19
11
70.0
4.17
12
70.0
4.89
13
70.0
4.72
CHAPTER 4
RESULTS AND DISCUSSIONS
4.1
Preliminary Study
At pH 7, the lowest turbidity value was 19 FTU at 20 mg/L to 60 mg/L of
alum dose which represent 38.7% removal. When the alum dose was set at 40 mg/L,
the lowest turbidity value achieved was 6 FTU at pH 7.5 (80.6%). Figures 4.1 and
4.2 illustrate the effect of pH and alum dosage on the removal of turbidity. The
highest turbidity removal (i.e. 80.6%) was achieved at pH of 7.5 and 40 mg/L of
alum dosage. However, since the OFAT approach did not consider all the space of
experiment, these optimum pH and dosage are still arguable.
38
Table 4.1: Results of the OFAT experiment on the turbidity removal (Initial turbidity
= 31 FTU)
pH
Alum Dose
(mg/L)
Final Turbidity
(FTU)
OFAT11
7.0
20
19
OFAT12
7.0
40
19
OFAT13
7.0
60
19
OFAT14
7.0
80
20
OFAT15
7.0
100
21
OFAT16
7.0
120
20
OFAT27
4.5
40
14
OFAT28
5.0
40
12
OFAT29
5.5
40
13
OFAT210
6.0
40
14
OFAT211
6.5
40
14
OFAT212
7.5
40
6
Run
* OFAT11/OFAT27; refer to beaker number 1 or 7 in first or second run of jar test.
** 1 FTU = 1 NTU
40.0
38.7
39.0
38.7
38.7
% Removal
38.0
37.0
36.0
35.5
35.0
35.5
34.0
33.0
32.3
32.0
31.0
0
20
40
60
80
100
120
Alum dose (mg/L)
Figure 4.1: Effect of alum dose on final turbidity (pH 7)
140
39
90.0
80.6
% Removal
80.0
70.0
61.3
60.0
58.1
54.8
54.8
54.8
50.0
40.0
30.0
4
4.5
5
5.5
6
6.5
7
7.5
8
pH
Figure 4.2: Effect of pH on final turbidity (Alum dose = 40 mg/L)
4.2
Response Surface Method
The results of the RSM are shown in Table 4.2.
In this method the
determination of optimum pH and its dose was directly determined by the design of
experimental using MINITABTM statistical software. With the same ranges of alum
dose (20 mg/L-120 mg/L), the turbidity value ranges achieved were 6 FTU to 16
FTU. This range is smaller than the ranges obtained in OFAT method possibly due
to the different dosages and pH used in RSM approach.
The lowest value for final turbidity in this experiment at RSM approach was
6 NTU, similar to the value achieved in the OFAT experiment. However, to achieve
the 6 FTU, the alum dose applied was 35 mg/L at pH 7.5. Eventhough the pH value
is exactly the same as in OFAT approached, the dose of alum in this method is lesser
(as compared to 40 mg/L by OFAT), thus shows a better achievement towards the
economic of coagulant dose usage. The results confirm the findings of Jimbat (2006)
40
that RSM approach is a better alternative as compared to OFAT in determining the
optimum coagulant dosage and pH.
Table 4.2: Turbidity results from the RSM experiment in preliminary works (Initial
turbidity = 31 FTU)
pH
Alum Dose
(mg/L)
Final Turbidity
(FTU)
RSM11
5.0
35
15
RSM 12
5.0
105
13
RSM 13
7.5
35
6
RSM 14
7.5
105
16
RSM 15
6.25
20
12
RSM 16
6.25
120
13
RSM 27
4.5
70
9
RSM 28
8.0
70
12
RSM 29
6.25
70
12
RSM 210
6.25
70
12
RSM 211
6.25
70
12
RSM 212
6.25
70
12
Run
* RSM11/RSM27; refer to beaker number 1 in first run of jar / beaker number 7 in second run of jar test
** 1 FTU = 1 NTU
4.3
Water Quality - Optimum Dose And pH Relationship
As mentioned in Section 3.2.2, 20 sets of experiment using predetermined
values of initial pH, SS and temperature were carried out to determine the
relationship between the selected water quality parameters and the optimum pH and
alum dosage relationship. For each set of water quality, 12 experimental runs were
carried out to identify the optimum pH and dosage. Two types of approaches were
41
used to identify these optimum values namely Response Surface analysis and lowest
FTU approach.
4.3.1
Response Surface Analysis
The detail results from the response surface analysis for each set of
experiments are given in Appendix A. The R-squared value and the p-value of lackof-fit from the response surface analysis are summarized in Table 4.3. Only sets of
experiment with R-squared value more than 80% (i.e. Set 2, 8, 9, 10, 15, 17 and 18).
The set which are more than 80% of its R-squared value considered to be significant
and acceptable results for the set. However, in order for the results to be used in
determining the optimum dosage and pH, the p-value of the terms need to be less
than 0.1 for 90% confidence level.
As can be seen in Table 4.3, not all experimental runs fulfill these
requirements. Hence, from the overall analysis, the conclusion that can be made is
that these RSM models are unacceptable and response surface analysis approach fails
to identify the optimum pH alum dose from each set of experiment. So the other
option of analysis based on the lowest FTU obtained in the experiment was made to
determined optimum pH and alum dose.
42
Table 4.3: The summary of response surface regression for 20 sets of experiment
4.3.2
Results for Set
R-square value (%)
Lack-of-fit
RSM1
59.6
0.000
RSM2
86.8
0.215
RSM3
64.6
0.004
RSM4
77.4
0.007
RSM5
57.7
0.071
RSM6
60.1
0.010
RSM7
62.1
0.000
RSM8
84.0
0.000
RSM9
86.1
0.001
RSM10
90.4
0.000
RSM11
29.5
0.000
RSM12
36.6
0.246
RSM13
4.0
0.000
RSM14
76.9
0.051
RSM15
90.7
0.002
RSM16
50.9
0.043
RSM17
88.0
0.010
RSM18
88.8
0.000
RSM19
59.7
0.045
RSM20
59.1
0.079
Lowest FTU Approach
In this approach, the determination of the optimum pH and alum dosage was
based on the lowest FTU obtained from the experiments. This approach is rather
straight-forward. The results of this analysis are shown in Table 4.4.
43
From the table, it can be observed that the optimum pH is most monopolies
by pH 5.0, followed by pH 6.3 and 4.5, and pH 7.5. The optimum dose of alum was
monopolied by dose of 120 mg/L, followed by 176.6 mg/L, 35 mg/L, 63.4 mg/L and
both 105 mg/L and 200 mg/L.
Table 4.4: Optimum pH and dosage for the experiments based on Lowest FTU
approach
Water Quality Independent Variable
Depend, Response
Set
Initial
Temperature
(°C)
Initial pH
Initial SS
(mg/L)
Optimum pH
Optimum
Dose (mg/L)
RSM1
27.0
5.8
54.3
5.0
105.0
RSM2
33.0
5.8
54.3
5.0
35.0
RSM3
27.0
8.2
54.3
5.0
35.0
RSM4
33.0
8.2
54.3
5.0
35.0
RSM5
27.0
5.8
125.7
4.5
120.0
RSM6
33.0
5.8
125.7
7.5
176.6
RSM7
27.0
8.2
125.7
5.0
63.4
RSM8
33.0
8.2
125.7
5.0
63.4
RSM9
25.0
7.0
90.0
4.5
120.0
RSM10
35.0
7.0
90.0
4.5
120.0
RSM11
30.0
5.0
90.0
7.5
176.6
RSM12
30.0
9.0
90.0
5.0
176.6
RSM13
30.0
7.0
30.0
5.0
176.6
RSM14
30.0
7.0
150.0
4.5
120.0
RSM15
30.0
7.0
90.0
6.3
120.0
RSM16
30.0
7.0
90.0
5.0
176.6
RSM17
30.0
7.0
90.0
6.3
200.0
RSM18
30.0
7.0
90.0
5.0
176.6
RSM19
30.0
7.0
90.0
6.3
120.0
RSM20
30.0
7.0
90.0
6.3
120.0
44
4.3.2.1
Factorial Analysis
The factorial analysis was conducted on the Hadamard matrix and centre
points runs using MINITABTM statistical software. The objective in conducting
factorial analysis on the results is to determine the significance of initial temperature,
pH and SS on the optimum pH and alum dosage. The analysis was carried out at α =
0.1 (90% of significance level) and α = 0.2 (80% of significance level. The detail
results of the analysis are given in Appendix B and summarized in Table 4.5. The
significant and the effect of the factors or responses are illustrated in the Pareto chart
(Figure 4.3).
Table 4.5: ANOVA for turbidity removal at optimum dose and optimum pH
Optimum Dose
Optimum pH
P-value
Significancea
P-value
Significancea
Significanceb
Temperature
0.901
No
0.175
No
Yes
pH
0.067
Yes
0.340
No
No
SS
0.092
Yes
0.340
No
No
Temperature x pH
0.901
No
0.175
No
Yes
Temperature x SS
0.272
No
0.175
No
Yes
pH x SS
0.376
No
0.340
No
No
0.272
No
0.175
No
Yes
Effect
Main
Two-way interaction
Three-way interaction
Temperature x pH
x SS
a
significant at α = 0.1
significant at α = 0.2
b
45
(a)
(b)
Figure 4.3: Pareto chart for (a) Optimum Dose and (b) Optimum pH based on final
turbidity (A: Temperature; B: pH; C: SS)
With respect to the experimental conditions used in this study, at significance
level of 90% of the p-value indicates that only initial pH and SS have significant
effect on the optimum alum dose (< 0.1). However at this significant care level,
none of the factors have significant role on the optimum pH.
Temperature is
considered a significant factor to optimum pH only at confidence level of 80%.
Initial pH and SS were found not to have significant effect on optimum pH within the
range of the study.
From Figure 4.4, it seems that the shift of temperature from 27°C to 33°C
decreased to optimum dose but increased the optimum pH. The optimum dose and
pH decreased when the initial pH was shift from 5.8 to 8.2 but both of the responses
were instantly increased when initial SS was shift from 54.3 mg/L to 125.5 mg/L.
46
Figure 4.4: Main effect plot for water quality parameters at (a) Optimum Dose (b)
Optimum pH
Interaction effects were found to be significant only for optimum pH at 80%
confidence level. Significant interaction effects at p-value < 0.2 were for Temp x
pH, Temp x SS and the three way interaction between Temp x pH and SS. Figure
4.5 and 4.6 illustrate the interaction effect between the factors.
Mean Optimum Dose
Figure 4.5: Interaction effect plot for water quality parameters at optimum dose
47
Mean Optimum pH
Figure 4.6: Interaction effect plot for water quality parameters at optimum pH
4.3.2.2
Response Surface Analysis
A response surface analysis was conducted to quantitatively characterize the
behavior of the effect and to statistically model the relationship between both the
selected water quality parameters and the optimum pH and alum dose. The analysis
was initially carried out using the full quadratic terms. The details results are given
in Appendices C and D. The p-values are summarized as in Table 4.6 for optimum
dose and Table 4.7 for optimum pH.
From the observation on optimum dose, it found that only Temperature x
Temperature were significant. As the p-value is 0.118 in full quadratic terms, thus,
this indirectly makes main effect on temperature also significant although the p-value
was insignificant (> 0.2). Although switch to only Linear + Squared terms, the pvalue at an effect of temperature interaction still obtained the best significant value
(< 0.1).
48
Table 4.6: The summary of the response surface analysis for the water quality effect
on optimum dose
Full quadratic terms
Linear + Squared terms
P-valuea
Term
Temperature
0.951
0.946
pH
0.285
0.241
SS
0.590
0.555
Temperature x Temperature
0.118
0.085
pH x pH
0.704
0.678
SS x SS
0.318
0.273
Temperature x pH
0.936
-
Temperature x SS
0.454
-
pH x SS
0.553
-
a
0.01 – 0.04: Highly significant; 0.05 – 0.1: significant; 0.1 – 0.2: less significant; > 0.2: insignificant (Vecchio, 1997)
Table 4.7: The summary of the response surface analysis for the water quality effect
on optimum pH
Full quadratic terms
Linear + Squared terms
P-valuea
Term
Temperature
0.288
0.319
pH
0.043
0.052
SS
0.674
0.695
Temperature x Temperature
0.037
0.045
pH x pH
0.415
0.446
SS x SS
0.082
0.098
Temperature x pH
0.173
-
Temperature x SS
0.173
-
pH x SS
0.351
-
a
0.01 – 0.04: Highly significant; 0.05 – 0.1: significant; 0.1 – 0.2: less significant; > 0.2: insignificant (Vecchio, 1997)
At full quadratic, it was found that pH (p-value = 0.043), Temperature x
Temperature (p--value = 0.037) and SS x SS (p-value = 0.082) were significant to
49
optimum pH.
Since two-way interaction of temperature and from SS were
respectively significant, this has resulted the main effect of temperature (p-value =
0.288) and SS (p-value = 0.674) also significant. Although in e Temperature x pH
and Temperature x SS are less significant but it still can be considered. When the
terms switch to Linear + Squared terms only, clearly seen that p-value of all
significant effect obtained the reducing value.
To improve the quality of the model, another analysis was carried out with
the insignificant terms omitted from the model. The detail results of this analysis are
given in Appendix D. If the analysis eliminate three additional terms from the
model, the R-square term for optimum dose were found < 50% while lack-of-fit and
an adjustable R-square was increase up to 0.134 and 1.6%, respectively.
However, these eliminating terms from the model found that R-square,
adjustable R-square and lack-of-fit in optimum pH were decrease. It was better to
optimum pH without any elimination terms which it brought to 69.1% in R-square,
41.2 in adjustable R-square and 0.384 lack-of-fit, respectively. From these analyses,
the acceptable statistical model for this system based on the experimental condition
of the study for water quality parameters is only at optimum pH and the equation for
the model is:
Optimum pH = -53.5591 + 3.59795 Temperat + 1.72582 pH - 0.0103599 SS
-.0516633 Temperat2 + 0.114604 pH2 - .000289329 SS2
-0.106066 Temperat*pH + 0.00353553 Temperat*SS
-0.00589256 pH*SS
Where; Temperat = temperature in °C; pH = pH of the water; SS = suspended
solid in mg/L. The response surface and contour plots of the modal are given in
Figures 4.7 through 4.12.
50
Hold values: SS (mg/L: 90.0)
9
8
pH
5
7
6
6
5
7
25
26
27
(a)
28
29
30
31
32
33
34
35
T emperature
Hold values: SS (mg/L: 90.0)
7
6
Optimum pH
5
9
4
8
7
25
(b)
Temperature
6
30
pH
5
35
Figure 4.7: (a) Contour and (b) response surface plots representing relationship
between pH and temperature at optimum pH
51
Hold values: pH: 7.0
150
3.7
4.2
4.7
5.2
100
SS (mg/L)
5.7
50
25
26
27
28
29
30
31
32
33
34
35
T emperature
(a)
Hold values: pH: 7.0
6
5
Optimum pH
4
150
3
100
25
(b)
Temperature
SS
50
30
35
Figure 4.8: (a) Contour and (b) response surface plots representing relationship
between temperature and SS at optimum pH
52
Hold values: T emperat: 30.0
150
5.0
100
SS (mg/L)
6.0
6.5
7.0
5.5
50
5
6
7
8
9
pH
(a)
Hold values: Temperat: 30.0
7
6
Optimum pH
5
150
4
100
5
(b)
6
pH
7
SS
S
50
8
9
Figure 4.9: (a) Contour and (b) response surface plots representing relationship
between pH and SS at optimum pH
53
Hold values: SS (mg/L: 90.0)
9
65
90
8
115
pH
140
7
6
165
5
25
26
27
28
29
30
31
32
33
34
35
T emperature
(a)
Hold values: SS (mg/L: 90.0
150
100
Optimum Dose (mg/L)
50
9
8
7
25
(b)
Temperature
6
30
pH
5
35
Figure 4.10: (a) Contour and (b) response surface plots representing relationship
between pH and temperature at optimum dose
54
Hold values: pH: 7.0
150
100
SS (mg/L)
145
120
95
50
70
45
25
26
27
28
(a)
29
30
31
32
33
34
35
T emperature
Hold values: pH: 7.0
150
100
Optimum Dose (mg/L)
50
150
0
100
25
(b)
Temperature
SS
S
50
30
35
Figure 4.11: (a) Contour and (b) response surface plots representing relationship
between temperature and SS at optimum dose
55
Hold values: Temperat: 30.0
150
150
SS (mg/L)
100
130
110
90
50
70
5
6
7
(a)
8
9
pH
Hold values: Temperat: 30.0
150
Optimum Dose (mg/L) 100
150
50
100
5
6
pH
7
(b)
SS
S
50
8
9
Figure 4.12: (a) Contour and (b) response surface plots representing relationship
between pH and SS at optimum dose
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
5.1
Conclusions
From the study, the conclusions that could be made are as followings:
a) Response Surface Method approach provides a better results in jar test
procedures compared to OFAT. While the initial turbidity of the two
approaches is the same, the optimum dosage obtained in RSM is lower
than the one obtained by OFAT and hence, contribute to the economy of
the process.
b) At 90% confidence level, only pH and SS have significant effect on the
optimum alum dose. No interaction effect was observed. Effects of water
quality parameters on optimum pH were observed only at 80%
confidence level.
At this level, temperature, temperature x pH,
temperature x SS and three-way interactions were significant on optimum
pH
57
c) Relationship between initial temperature, pH and SS could only be
developing for optimum pH. The R-square and p-value for lack-of-fit for
this relationship were 69.1% and 0.384, respectively.
5.2
Future Study Recommendations
Based on the findings of the study, the followings are recommended for
further study.
a) To use others sources of suspended solid such as laterite, bentonite clay
and peat. The usage of these suspended solid must in powder form to
ease the experimental work.
b) To include other water quality parameters in developing the relationship.
This may include alkalinity, conductivity and dissolved oxygen content.
c) To determine the relationship based on secondary data collected from jar
test exercise at water treatment plant.
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Ph.D. Dissertation.
Pernitsky, D. J. (2003). Coagulation 101. Associated Engineering, Calvary,
Alberta: Ph. D Thesis.
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of Illinois, Urbana-Champaign: Ph. D. Thesis.
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Process Combination. Journal of American Water Works Association. 80(5): 4056.
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Vaughan and David Masciola (1999). Physicochemical Process. Water
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63
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APPENDIX A
(DESIGN TABLE FOR 20 SET)
Table A-1: Design table of RSM for Set 1
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM11
RSM12
RSM13
RSM14
RSM15
RSM16
27.0
RSM17
RSM18
RSM19
RSM110
RSM111
RSM112
RSM113
Best FTU = 3.60
5.8
54.3
Alum
Dose
(mg/L)
35
105
35
105
20
120
70
70
70
70
70
70
70
Variable
Alum
Amount
(mL)
17.5
17.5
17.5
17.5
10.0
20.0
35.0
35.0
35.0
35.0
35.0
35.0
35.0
Alum
Dose
(mg/L)
35
105
35
105
20
120
70
70
70
70
70
70
70
Variable
Alum
Amount
(mL)
17.5
17.5
17.5
17.5
10.0
20.0
35.0
35.0
35.0
35.0
35.0
35.0
35.0
Response
pH
Turbidity
(FTU)
5.00
5.00
7.50
7.50
6.25
6.25
4.50
8.00
6.25
6.25
6.25
6.25
6.25
5.00
3.60
17.00
6.09
6.00
3.86
4.24
4.38
4.64
5.19
4.17
4.89
4.72
Table A-2: Design table of RSM for Set 2
Run
Initial Water characteristic
Suspended
Temperature
Solid, SS
pH
(°C)
(mg/L)
RSM21
RSM22
RSM23
RSM24
RSM25
RSM26
33.0
RSM27
RSM28
RSM29
RSM210
RSM211
RSM212
RSM213
Best FTU = 1.75
5.8
54.3
Response
pH
Turbidity
(FTU)
5.00
5.00
7.50
7.50
6.25
6.25
4.50
8.00
6.25
6.25
6.25
6.25
6.25
1.75
2.67
4.93
4.26
2.32
3.96
2.31
4.48
3.18
3.57
3.96
4.12
3.68
65
Table A-3: Design table of RSM for Set 3
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM31
RSM32
RSM33
RSM34
RSM35
RSM36
27.0
RSM37
RSM38
RSM39
RSM310
RSM311
RSM312
RSM313
Best FTU =1.81
8.2
54.3
Alum
Dose
(mg/L)
35
105
35
105
20
120
70
70
70
70
70
70
70
Variable
Alum
Amount
(mL)
17.5
17.5
17.5
17.5
10.0
20.0
35.0
35.0
35.0
35.0
35.0
35.0
35.0
Response
pH
Turbidity
(FTU)
5.00
5.00
7.50
7.50
6.25
6.25
4.50
8.00
6.25
6.25
6.25
6.25
6.25
1.81
4.27
2.05
4.02
2.83
3.62
5.22
7.16
4.76
4.03
4.71
4.79
4.57
Table A-4: Design table of RSM for Set 4
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM41
RSM42
RSM43
RSM44
RSM45
RSM46
33.0
RSM47
RSM48
RSM49
RSM410
RSM411
RSM412
RSM413
Best FTU = 3.66
8.2
54.3
Variable
Alum
Alum
Dose
Amount
(mg/L)
(mL)
35
17.5
105
17.5
35
17.5
105
17.5
20
10.0
120
20.0
70
35.0
70
35.0
70
35.0
70
35.0
70
35.0
70
35.0
70
35.0
Response
pH
Turbidity
(FTU)
5.00
5.00
7.50
7.50
6.25
6.25
4.50
8.00
6.25
6.25
6.25
6.25
6.25
3.66
3.86
5.45
4.84
6.47
4.28
4.36
6.45
6.05
6.36
6.04
5.76
6.05
66
Table A-5: Design table of RSM for Set 5
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM51
RSM52
RSM53
RSM54
RSM55
RSM56
27.0
RSM57
RSM58
RSM59
RSM510
RSM511
RSM512
RSM513
Best FTU = 7.59
5.8
125.7
Alum
Dose
(mg/L)
63.4
176.6
63.4
176.6
40.0
200.0
120.0
120.0
120.0
120.0
120.0
120.0
120.0
Variable
Alum
Amount
(mL)
31.7
29.4
31.7
29.4
20.0
33.3
20.0
20.0
20.0
20.0
20.0
20.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
7.75
8.78
8.41
10.70
8.88
10.30
7.59
18.03
8.70
8.17
11.40
10.90
9.79
Table A-6: Design table of RSM for Set 6
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM61
RSM62
RSM63
RSM64
RSM65
RSM66
33.0
RSM67
RSM68
RSM69
RSM610
RSM611
RSM612
RSM613
Best FTU = 1.89
5.8
125.7
Variable
Alum
Alum
Dose
Amount
(mg/L)
(mL)
63.4
31.7
176.6
29.4
63.4
31.7
176.6
29.4
40.0
20.0
200.0
33.3
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
8.80
6.72
9.26
1.89
9.03
6.55
8.44
11.10
9.28
9.39
7.75
8.58
8.75
67
Table A-7: Design table of RSM for Set 7
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM71
RSM72
RSM73
RSM74
RSM75
RSM76
27.0
RSM77
RSM78
RSM79
RSM710
RSM711
RSM712
RSM713
Best FTU = 4.39
8.2
125.7
Alum
Dose
(mg/L)
63.4
176.6
63.4
176.6
40.0
200.0
120.0
120.0
120.0
120.0
120.0
120.0
120.0
Variable
Alum
Amount
(mL)
31.7
29.4
31.7
29.4
20.0
33.3
20.0
20.0
20.0
20.0
20.0
20.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
4.39
8.89
9.80
8.85
10.63
8.92
8.95
16.80
9.00
9.08
9.45
9.89
9.35
Table A-8: Design table of RSM for Set 8
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM81
RSM82
RSM83
RSM84
RSM85
RSM86
33.0
RSM87
RSM88
RSM89
RSM810
RSM811
RSM812
RSM813
Best FTU = 1.81
8.2
125.7
Variable
Alum
Alum
Dose
Amount
(mg/L)
(mL)
63.4
31.7
176.6
29.4
63.4
31.7
176.6
29.4
40.0
20.0
200.0
33.3
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
1.81
8.28
8.66
14.60
7.56
12.20
5.76
7.97
7.75
7.19
7.53
7.31
7.44
68
Table A-9: Design table of RSM for Set 9
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM91
RSM92
RSM93
RSM94
RSM95
RSM96
25.0
RSM97
RSM98
RSM99
RSM910
RSM911
RSM912
RSM913
Best FTU = 2.38
7.0
90.0
Alum
Dose
(mg/L)
63.4
176.6
63.4
176.6
40.0
200.0
120.0
120.0
120.0
120.0
120.0
120.0
120.0
For Jar Test
Alum
Amount
(mL)
31.7
29.4
31.7
29.4
20.0
33.3
20.0
20.0
20.0
20.0
20.0
20.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
6.75
6.09
6.62
10.97
5.87
7.58
2.38
5.26
3.02
2.91
2.80
2.39
2.78
Table A-10: Design table of RSM for Set 10
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM101
RSM102
RSM103
RSM104
RSM105
RSM106
35
RSM107
RSM108
RSM109
RSM1010
RSM1011
RSM1012
RSM1013
Best FTU = 5.37
7.0
90.0
Variable
Alum
Alum
Dose
Amount
(mg/L)
(mL)
63.4
31.7
176.6
29.4
63.4
31.7
176.6
29.4
40.0
20.0
200.0
33.3
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
15.53
7.83
15.54
11.07
15.45
8.71
5.37
11.46
7.76
7.19
7.50
7.50
7.48
69
Table A-11: Design table of RSM for Set 11
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM111
RSM112
RSM113
RSM114
RSM115
RSM116
30.0
RSM117
RSM118
RSM119
RSM1110
RSM1111
RSM1112
RSM1113
Best FTU = 6.43
5.0
90.0
Alum
Dose
(mg/L)
63.4
176.6
63.4
176.6
40.0
200.0
120.0
120.0
120.0
120.0
120.0
120.0
120.0
Variable
Alum
Amount
(mL)
31.7
29.4
31.7
29.4
20.0
33.3
20.0
20.0
20.0
20.0
20.0
20.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
7.46
7.17
7.22
6.43
12.14
11.30
8.00
11.75
7.13
7.84
7.49
7.06
7.38
Table A-12: Design table of RSM for Set 12
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM121
RSM122
RSM123
RSM124
RSM125
RSM126
30.0
RSM127
RSM128
RSM129
RSM1210
RSM1211
RSM1212
RSM1213
Best FTU = 7.77
9.0
90.0
Variable
Alum
Alum
Dose
Amount
(mg/L)
(mL)
63.4
31.7
176.6
29.4
63.4
31.7
176.6
29.4
40.0
20.0
200.0
33.3
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
8.90
7.77
9.54
9.12
9.69
9.25
11.95
15.36
13.24
12.70
13.30
12.10
12.80
70
Table A-13: Design table of RSM for Set 13
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM131
RSM132
RSM133
RSM134
RSM135
RSM136
30.0
RSM137
RSM138
RSM139
RSM1310
RSM1311
RSM1312
RSM1313
Best FTU = 2.80
7.0
30.0
Alum
Dose
(mg/L)
63.4
176.6
63.4
176.6
40.0
200.0
120.0
120.0
120.0
120.0
120.0
120.0
120.0
Variable
Alum
Amount
(mL)
31.7
29.4
31.7
29.4
20.0
33.3
20.0
20.0
20.0
20.0
20.0
20.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
3.09
2.80
3.16
2.92
4.19
3.99
4.41
4.06
3.52
3.51
3.68
3.70
3.60
Table A-14: Design table of RSM for Set 14
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM141
RSM142
RSM143
RSM144
RSM145
RSM146
30.0
RSM147
RSM148
RSM149
RSM1410
RSM1411
RSM1412
RSM1413
Best FTU = 15.87
7.0
150.0
Variable
Alum
Alum
Dose
Amount
(mg/L)
(mL)
63.4
31.7
176.6
29.4
63.4
31.7
176.6
29.4
40.0
20.0
200.0
33.3
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
17.71
16.31
19.02
18.65
19.90
17.68
15.87
23.23
15.87
17.71
17.24
17.07
16.90
71
Table A-15: Design table of RSM for Set 15
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM151
RSM152
RSM153
RSM154
RSM155
RSM156
30.0
RSM157
RSM158
RSM159
RSM1510
RSM1511
RSM1512
RSM1513
Best FTU = 6.67
7.0
90.0
Alum
Dose
(mg/L)
63.4
176.6
63.4
176.6
40.0
200.0
120.0
120.0
120.0
120.0
120.0
120.0
120.0
Variable
Alum
Amount
(mL)
31.7
29.4
31.7
29.4
20.0
33.3
20.0
20.0
20.0
20.0
20.0
20.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
11.12
10.26
11.58
10.71
10.74
9.76
7.75
11.75
7.21
6.88
6.91
6.67
6.92
Table A-16: Design table of RSM for Set 16
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM161
RSM162
RSM163
RSM164
RSM165
RSM166
30.0
RSM167
RSM168
RSM169
RSM1610
RSM1611
RSM1612
RSM1613
Best FTU = 5.95
7.0
90.0
Variable
Alum
Alum
Dose
Amount
(mg/L)
(mL)
63.4
31.7
176.6
29.4
63.4
31.7
176.6
29.4
40.0
20.0
200.0
33.3
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
6.22
5.95
7.94
7.40
9.51
8,35
6.96
12.54
8.40
7.59
7.73
6.91
7.66
72
Table A-17: Design table of RSM for Set 17
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM171
RSM172
RSM173
RSM174
RSM175
RSM176
30.0
RSM177
RSM178
RSM179
RSM1710
RSM1711
RSM1712
RSM1713
Best FTU = 7.93
7.0
90.0
Alum
Dose
(mg/L)
63.4
176.6
63.4
176.6
40.0
200.0
120.0
120.0
120.0
120.0
120.0
120.0
120.0
Variable
Alum
Amount
(mL)
31.7
29.4
31.7
29.4
20.0
33.3
20.0
20.0
20.0
20.0
20.0
20.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
9.10
8.48
10.29
9.70
8.78
7.93
9.49
14.08
8.99
9.45
8.94
8.80
9.04
Table A-18: Design table of RSM for Set 18
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM181
RSM182
RSM183
RSM184
RSM185
RSM186
30.0
RSM187
RSM188
RSM189
RSM1810
RSM1811
RSM1812
RSM1813
Best FTU = 8.76
7.0
90.0
Variable
Alum
Alum
Dose
Amount
(mg/L)
(mL)
63.4
31.7
176.6
29.4
63.4
31.7
176.6
29.4
40.0
20.0
200.0
33.3
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
9.46
8.76
12.07
11.42
9.95
9.29
9.44
17.23
10.00
10.00
10.05
9.81
9.96
73
Table A-19: Design table of RSM for Set 19
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM191
RSM192
RSM193
RSM194
RSM195
RSM196
30.0
RSM197
RSM198
RSM199
RSM1910
RSM1911
RSM1912
RSM1913
Best FTU = 6.92
7.0
90.0
Alum
Dose
(mg/L)
63.4
176.6
63.4
176.6
40.0
200.0
120.0
120.0
120.0
120.0
120.0
120.0
120.0
Variable
Alum
Amount
(mL)
31.7
29.4
31.7
29.4
20.0
33.3
20.0
20.0
20.0
20.0
20.0
20.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
8.11
8.21
12.81
11.87
7.15
7.08
10.51
10.25
8.94
6.92
7.81
8.80
8.12
Table A-20: Design table of RSM for Set 20
Run
Initial Water characteristic
Suspended
Temperature
pH
Solid, SS
(°C)
(mg/L)
RSM201
RSM202
RSM203
RSM204
RSM205
RSM206
30.0
RSM207
RSM208
RSM209
RSM2010
RSM2011
RSM2012
RSM2013
Best FTU = 6.59
7.0
90.0
Variable
Alum
Alum
Dose
Amount
(mg/L)
(mL)
63.4
31.7
176.6
29.4
63.4
31.7
176.6
29.4
40.0
20.0
200.0
33.3
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
120.0
20.0
Response
pH
Turbidity
(FTU)
5.0
5.0
7.5
7.5
6.3
6.3
4.5
8.0
6.3
6.3
6.3
6.3
6.3
8.02
7.97
11.75
12.81
8.28
8.25
9.96
9.97
6.59
7.86
8.68
8.78
7.97
APPENDIX B
(DETAILS FOR FACTORIAL ANALYSIS)
Fractional Factorial Fit: Opt. Dose versus Temp, pH, SS
Estimated Effects and Coefficients for Opt. (coded units)
Term
Constant
Temp
pH
SS
Temp*pH
Temp*SS
pH*SS
Temp*pH*SS
Ct Pt
Effect
Coef
79.17
-1.67
-29.97
26.67
1.67
15.82
-12.47
-15.82
73.03
-3.35
-59.95
53.35
3.35
31.65
-24.95
-31.65
SE Coef
12.83
12.83
12.83
12.83
12.83
12.83
12.83
12.83
19.60
T
6.17
-0.13
-2.34
2.08
0.13
1.23
-0.97
-1.23
3.73
P
0.002
0.901
0.067
0.092
0.901
0.272
0.376
0.272
0.014
Analysis of Variance for Opt. (coded units)
Source
Main Effects
2-Way Interactions
3-Way Interactions
Curvature
Residual Error
Pure Error
Total
DF
3
3
1
1
5
5
13
Seq SS
12902.9
3270.9
2003.4
18283.4
6586.1
6586.1
43046.7
Adj SS
12902.9
3270.9
2003.4
18283.4
6586.1
6586.1
Adj MS
4301
1090
2003
18283
1317
1317
F
3.27
0.83
1.52
13.88
P
0.118
0.533
0.272
0.014
Fractional Factorial Fit: Opt. pH versus Temp, pH, SS (Alpha = 0.1)
Estimated Effects and Coefficients for Opt. (coded units)
Term
Constant
Temp
pH
SS
Temp*pH
Temp*SS
pH*SS
Temp*pH*SS
Ct Pt
Effect
0.7500
-0.5000
0.5000
-0.7500
0.7500
-0.5000
-0.7500
Coef
5.2500
0.3750
-0.2500
0.2500
-0.3750
0.3750
-0.2500
-0.3750
0.6167
SE Coef
0.2373
0.2373
0.2373
0.2373
0.2373
0.2373
0.2373
0.2373
0.3626
T
22.12
1.58
-1.05
1.05
-1.58
1.58
-1.05
-1.58
1.70
P
0.000
0.175
0.340
0.340
0.175
0.175
0.340
0.175
0.150
Analysis of Variance for Opt. (coded units)
Source
Main Effects
2-Way Interactions
3-Way Interactions
Curvature
Residual Error
DF
3
3
1
1
5
Seq SS
2.12500
2.75000
1.12500
1.30381
2.25333
Adj SS
2.12500
2.75000
1.12500
1.30381
2.25333
Adj MS
0.7083
0.9167
1.1250
1.3038
0.4507
F
1.57
2.03
2.50
2.89
P
0.307
0.228
0.175
0.150
75
Pure Error
Total
5
13
2.25333
9.55714
2.25333
0.4507
Fractional Factorial Fit: Opt. pH versus Temp, pH, SS (Alpha = 0.2)
Estimated Effects and Coefficients for Opt. (coded units)
Term
Constant
Temp
pH
SS
Temp*pH
Temp*SS
pH*SS
Temp*pH*SS
Ct Pt
Effect
0.7500
-0.5000
0.5000
-0.7500
0.7500
-0.5000
-0.7500
Coef
5.2500
0.3750
-0.2500
0.2500
-0.3750
0.3750
-0.2500
-0.3750
0.6167
SE Coef
0.2373
0.2373
0.2373
0.2373
0.2373
0.2373
0.2373
0.2373
0.3626
T
22.12
1.58
-1.05
1.05
-1.58
1.58
-1.05
-1.58
1.70
P
0.000
0.175
0.340
0.340
0.175
0.175
0.340
0.175
0.150
Analysis of Variance for Opt. (coded units)
Source
Main Effects
2-Way Interactions
3-Way Interactions
Curvature
Residual Error
Pure Error
Total
DF
3
3
1
1
5
5
13
Seq SS
2.12500
2.75000
1.12500
1.30381
2.25333
2.25333
9.55714
Adj SS
2.12500
2.75000
1.12500
1.30381
2.25333
2.25333
Adj MS
0.7083
0.9167
1.1250
1.3038
0.4507
0.4507
F
1.57
2.03
2.50
2.89
P
0.307
0.228
0.175
0.150
APPENDIX C
(RESPONSE SURFACE ANALYSIS FOR FACTORS THAT AFFECT
COAGULATION - FULL QUADRATIC TERMS)
Response Surface Regression: Optimum Dose versus Temperature, pH, SS
The analysis was done using coded units.
Estimated Regression Coefficients for Optimum dose
Term
Constant
Temperat
pH
SS (mg/L
Temperat*Temperat
pH*pH
SS (mg/L*SS (mg/L
Temperat*pH
Temperat*SS (mg/L
pH*SS (mg/L
S = 57.45
Coef
154.42
-0.98
-17.56
8.66
-25.92
-5.91
-15.92
1.67
15.82
-12.47
R-Sq = 38.7%
SE Coef
23.43
15.55
15.55
15.55
15.13
15.13
15.13
20.31
20.31
20.31
T
6.591
-0.063
-1.130
0.557
-1.713
-0.391
-1.052
0.082
0.779
-0.614
P
0.000
0.951
0.285
0.590
0.118
0.704
0.318
0.936
0.454
0.553
R-Sq(adj) = 0.0%
Analysis of Variance for Optimum dose
Source
Regression
Linear
Square
Interaction
Residual Error
Lack-of-Fit
Pure Error
Total
Observation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
DF
9
3
3
3
10
5
5
19
Optimum
105.000
35.000
35.000
35.000
120.000
176.600
63.400
63.400
120.000
120.000
176.600
176.600
176.600
120.000
120.000
176.600
200.000
176.600
120.000
120.000
Seq SS
20859
5247
12341
3271
33003
26417
6586
53862
Fit
121.586
84.623
108.068
77.805
132.197
158.535
68.779
101.817
82.757
79.457
167.238
108.177
94.850
123.964
154.424
154.424
154.424
154.424
154.424
154.424
Adj SS
20859
5247
12341
3271
33003
26417
6586
SE Fit
47.016
47.016
47.016
47.016
47.016
47.016
47.016
47.016
44.769
44.769
44.769
44.769
44.769
44.769
23.430
23.430
23.430
23.430
23.430
23.430
Adj MS
2318
1749
4114
1090
3300
5283
1317
Residual
-16.586
-49.623
-73.068
-42.805
-12.197
18.065
-5.379
-38.417
37.243
40.543
9.362
68.423
81.750
-3.964
-34.424
22.176
45.576
22.176
-34.424
-34.424
F
0.70
0.53
1.25
0.33
P
0.697
0.672
0.344
0.804
4.01
0.077
St Resid
-0.50
-1.50
-2.21R
-1.30
-0.37
0.55
-0.16
-1.16
1.03
1.13
0.26
1.90
2.27R
-0.11
-0.66
0.42
0.87
0.42
-0.66
-0.66
77
R denotes an observation with a large standardized residual.
Estimated Regression Coefficients for Optimum dose using data in uncoded
units
Term
Constant
Temperat
pH
SS (mg/L
Temperat*Temperat
pH*pH
SS (mg/L*SS (mg/L
Temperat*pH
Temperat*SS (mg/L
pH*SS (mg/L
Coef
-2382.56
158.887
55.9955
0.0757627
-2.93269
-4.17929
-0.0125048
0.473762
0.149200
-0.294039
Response Surface Regression: Optimum pH versus Temperature, pH, SS
The analysis was done using coded units.
Estimated Regression Coefficients for Optimum pH
Term
Constant
Temperat
pH
SS (mg/L
Temperat*Temperat
pH*pH
SS (mg/L*SS (mg/L
Temperat*pH
Temperat*SS (mg/L
pH*SS (mg/L
S = 0.7230
Coef
5.8626
0.2197
-0.4543
0.0849
-0.4566
0.1621
-0.3683
-0.3750
0.3750
-0.2500
R-Sq = 69.1%
SE Coef
0.2949
0.1957
0.1957
0.1957
0.1905
0.1905
0.1905
0.2556
0.2556
0.2556
T
19.881
1.123
-2.322
0.434
-2.398
0.851
-1.934
-1.467
1.467
-0.978
P
0.000
0.288
0.043
0.674
0.037
0.415
0.082
0.173
0.173
0.351
R-Sq(adj) = 41.2%
Analysis of Variance for Optimum pH
Source
Regression
Linear
Square
Interaction
Residual Error
Lack-of-Fit
Pure Error
Total
Observation
1
2
3
4
5
6
7
8
9
10
11
DF
9
3
3
3
10
5
5
19
Optimum
5.000
5.000
5.000
5.000
4.500
7.500
5.000
5.000
4.500
4.500
7.500
Seq SS
11.670
3.576
5.344
2.750
5.228
2.974
2.253
16.898
Fit
5.100
5.539
5.441
4.380
5.019
6.959
4.361
4.800
4.202
4.940
7.085
Adj SS
11.670
3.576
5.344
2.750
5.228
2.974
2.253
SE Fit
0.592
0.592
0.592
0.592
0.592
0.592
0.592
0.592
0.563
0.563
0.563
Adj MS
1.2967
1.1921
1.7814
0.9167
0.5228
0.5949
0.4507
Residual
-0.100
-0.539
-0.441
0.620
-0.519
0.541
0.639
0.200
0.298
-0.440
0.415
F
2.48
2.28
3.41
1.75
P
0.087
0.142
0.061
0.219
1.32
0.384
St Resid
-0.24
-1.30
-1.06
1.49
-1.25
1.30
1.54
0.48
0.66
-0.97
0.92
78
12
13
14
15
16
17
18
19
20
5.000
5.000
4.500
6.300
5.000
6.300
5.000
6.300
6.300
5.557
4.678
4.964
5.863
5.863
5.863
5.863
5.863
5.863
0.563
0.563
0.563
0.295
0.295
0.295
0.295
0.295
0.295
-0.557
0.322
-0.464
0.437
-0.863
0.437
-0.863
0.437
0.437
-1.23
0.71
-1.02
0.66
-1.31
0.66
-1.31
0.66
0.66
Estimated Regression Coefficients for Optimum pH using data in uncoded units
Term
Constant
Temperat
pH
SS (mg/L
Temperat*Temperat
pH*pH
SS (mg/L*SS (mg/L
Temperat*pH
Temperat*SS (mg/L
pH*SS (mg/L
Coef
-53.5591
3.59795
1.72582
-0.0103599
-0.0516633
0.114604
-0.000289329
-0.106066
0.00353553
-0.00589256
APPENDIX D
(RESPONSE SURFACE ANALYSIS FOR FACTORS THAT AFFECT
COAGULATION - LINEAR + SQUARED TERMS)
Response Surface Regression: Optimum Dose versus Temperature, pH, SS
The analysis was done using coded units.
Estimated Regression Coefficients for Optimum
Term
Constant
Temperat
pH
SS (mg/L
Temperat*Temperat
pH*pH
SS (mg/L*SS (mg/L
S = 52.82
Coef
154.42
-0.98
-17.56
8.66
-25.92
-5.91
-15.92
R-Sq = 32.7%
SE Coef
21.54
14.29
14.29
14.29
13.91
13.91
13.91
T
7.168
-0.069
-1.228
0.606
-1.863
-0.425
-1.144
P
0.000
0.946
0.241
0.555
0.085
0.678
0.273
R-Sq(adj) = 1.6%
Analysis of Variance for Optimum
Source
Regression
Linear
Square
Residual Error
Lack-of-Fit
Pure Error
Total
Observation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
DF
6
3
3
13
8
5
19
Optimum
105.000
35.000
35.000
35.000
120.000
176.600
63.400
63.400
120.000
120.000
176.600
176.600
176.600
120.000
120.000
176.600
200.000
176.600
120.000
120.000
Seq SS
17587.9
5247.0
12340.9
36274.3
29688.3
6586.1
53862.2
Fit
116.561
114.598
81.443
79.480
133.872
131.910
98.754
96.792
82.757
79.457
167.238
108.177
94.850
123.964
154.424
154.424
154.424
154.424
154.424
154.424
Adj SS
17587.9
5247.0
12340.9
36274.3
29688.3
6586.1
SE Fit
28.679
28.679
28.679
28.679
28.679
28.679
28.679
28.679
41.165
41.165
41.165
41.165
41.165
41.165
21.544
21.544
21.544
21.544
21.544
21.544
Adj MS
2931.32
1749.00
4113.64
2790.33
3711.03
1317.22
Residual
-11.561
-79.598
-46.443
-44.480
-13.872
44.690
-35.354
-33.392
37.243
40.543
9.362
68.423
81.750
-3.964
-34.424
22.176
45.576
22.176
-34.424
-34.424
F
1.05
0.63
1.47
P
0.438
0.610
0.267
2.82
0.134
St Resid
-0.26
-1.79
-1.05
-1.00
-0.31
1.01
-0.80
-0.75
1.13
1.22
0.28
2.07R
2.47R
-0.12
-0.71
0.46
0.94
0.46
-0.71
-0.71
R denotes an observation with a large standardized residual.
Estimated Regression Coefficients for Optimum
using data in uncoded units
80
Term
Constant
Temperat
pH
SS (mg/L
Temperat*Temperat
pH*pH
SS (mg/L*SS (mg/L
Coef
-2699.65
175.631
43.7448
2.49348
-2.93269
-4.17929
-0.0125048
Response Surface Regression: Optimum pH versus Temperature, pH, ...
The analysis was done using coded units.
Estimated Regression Coefficients for Optimum
Term
Constant
Temperat
pH
SS (mg/L
Temperat*Temperat
pH*pH
SS (mg/L*SS (mg/L
S = 0.7834
Coef
5.8626
0.2197
-0.4543
0.0849
-0.4566
0.1621
-0.3683
R-Sq = 52.8%
SE Coef
0.3195
0.2120
0.2120
0.2120
0.2064
0.2064
0.2064
T
18.350
1.036
-2.143
0.400
-2.213
0.785
-1.785
P
0.000
0.319
0.052
0.695
0.045
0.446
0.098
R-Sq(adj) = 31.0%
Analysis of Variance for Optimum
Source
Regression
Linear
Square
Residual Error
Lack-of-Fit
Pure Error
Total
Observation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
DF
6
3
3
13
8
5
19
Optimum
5.000
5.000
5.000
5.000
4.500
7.500
5.000
5.000
4.500
4.500
7.500
5.000
5.000
4.500
6.300
5.000
6.300
5.000
6.300
6.300
Seq SS
8.9203
3.5762
5.3441
7.9777
5.7244
2.2533
16.8980
Fit
5.350
5.789
4.441
4.880
5.519
5.959
4.611
5.050
4.202
4.940
7.085
5.557
4.678
4.964
5.863
5.863
5.863
5.863
5.863
5.863
Adj SS
8.92029
3.57616
5.34413
7.97771
5.72438
2.25333
SE Fit
0.425
0.425
0.425
0.425
0.425
0.425
0.425
0.425
0.610
0.610
0.610
0.610
0.610
0.610
0.319
0.319
0.319
0.319
0.319
0.319
Adj MS
1.48671
1.19205
1.78138
0.61367
0.71555
0.45067
Residual
-0.350
-0.789
0.559
0.120
-1.019
1.541
0.389
-0.050
0.298
-0.440
0.415
-0.557
0.322
-0.464
0.437
-0.863
0.437
-0.863
0.437
0.437
F
2.42
1.94
2.90
P
0.085
0.173
0.075
1.59
0.317
St Resid
-0.53
-1.20
0.85
0.18
-1.55
2.34R
0.59
-0.08
0.61
-0.90
0.85
-1.13
0.66
-0.94
0.61
-1.21
0.61
-1.21
0.61
0.61
R denotes an observation with a large standardized residual.
Estimated Regression Coefficients for Optimum
using data in uncoded units
81
Term
Constant
Temperat
pH
SS (mg/L
Temperat*Temperat
pH*pH
SS (mg/L*SS (mg/L
Coef
-37.1189
3.17369
-1.98649
0.0544582
-0.0516633
0.114604
-0.000289329