Advances in Chemical Engi neering and Science , 2011, 1, 125-132
doi:10.4236/aces.2011.13019 Published Online July 2011 (http://www.SciRP.org/journal/aces)
Factorial Optimization and Kinetics of Coal Washery
Effluent Coag-Flocculation by Moringa Oleifera Seed
Biomass
Matthew Chukwudi Menkiti1*, Chukwuka Ikechukwu Nwoye2,
Chinenye Adaobi Onyechi1, Okechukwu Dominic Onukwuli1
1Department of Chemical Engineering, Nnamdi Azikiwe University, Awka, Nigeria
2Department of Material and Metallurgical Engineering, Nnamdi Azikiwe University, Awka, Nigeria
Received March 6, 2011; revised April 10, 2011; accepted April 26, 2011
Abstract
Factorial optimization and kinetics of coal washery effluent (CWE) coag-flocculation by Moringa oleifera
seed has been investigated at room temperature based on standard method of bench scale jar test. Moringa
oleifera coag-flocculant (MOC) was produced according to work reported by Ghebremichael. A 23 full fac-
torial central composite design was employed for the experimental design and analysis of results with respect
to optimization. The combined effects of pH, dosage and settling time on the particle (turbidity) removal
were studied using response surface methodology. Kinetic data generated were confronted with specified
kinetic models for the evaluation of functional kinetics parameters. The optimal values of pH, dosage and
settling time were recorded at 8400 mg/l and 25 min, respectively. The results of the major kinetic parame-
ters recorded are 20.002 l/mg·min, and 0.79 min for order of reaction, coag-flocculation reaction rate con-
stant and coagulation period, respectively. The minimum removal efficiency recorded was 95% at 3 mins of
coag- flocculation. The results, while re affirming MOC as efficient coag-flocculant, confirmed that theory
of perikinetics holds for the studied system at the conditions of the experiment.
Keywords: Moringa Oleifera, Effluent, Coagulation/Flocculation, Optimization
1. Introduction
Coag-flocculation process is an established technology
for the protection of environmental and human health
with wide applications in water and waste water treat-
ment facilities. Coag-flocculation is a core and usually
the first unit process in water treatment and it is very
important for the removal of suspended and dissolved
particles (SDP). It is the act of destabilizing stable col-
loidal particles in suspension, such that they can ag-
glomerate into settleable flocs. Readily, coag-floccula-
tion is optimized for the removal of inorganic colloids,
dissolved natural organic load, microbes and color which
are typical composition of coal washery effluent [1-4].
Conventionally, coag-flocculation treatment technique
entails the use of metal salts (Al and Fe salts) and syn-
thetic organic polymers. Although the chemicals are very
effective and widely used, there are inherent draw backs:
they impact on the pH value of water, increase the solu-
ble residues volume and metal content of sludge. With
Alum, there is risk of Alzheimer’s disease and similar
health related problems [5-7]. Obviously, the issues of
cost and availability of the chemicals are major draw-
backs since they have to be imported in hard currency.
In order to alleviate the prevailing challenges, ap-
proaches should focus on sustainable water treatment
that are low cost, eco-friendly, robust and require mini-
mal maintenance and operator skills. MOC among other
natural materials such as Brachestegia eurycoma , Afze-
lia bella and Mucuna seeds posses these qualities and
provide the required remedy for the identifiable deficien-
cies associated with non natural coagulants [8]. The
Moringa oleifera is a small, fast growing drought de-
ciduous tree that ranges in height from 5 - 12 m. The seed
kernel contain positively charged water soluble proteins
that act like magnets and attracting the predominantly
negatively charged particles (SDP) to form settleable
flocs [9].

M. C. MENKITI ET AL. 126
In recent years, there has been increasing advocacy for
the research in and the use of natural coag-flocculants
such as MOC, as an alternative to the synthetic ones, es-
pecially in developing country like Nigeria where port-
able water supply is highly limited. However, the major
challenges have been the availability of research data that
will promote the design of mini flocculator suitable for
handling effluents such as CWE usually discharge into
drinking aquifers of our communities. The focus is there-
fore directed towards the provision of kinetic data, the
mathematical relationship that predicts the interaction of
studied variables and the optimal values of the variables.
The situation in Nigeria is typical of water system in de-
veloping countries and the results of this study can be ap-
plied to a number of similar situations in order to improve
the quality of water supply and protect the environment.
2. Materials and Method
2.1. Material Collection, Preparation and
Characterization
2.1.1. Coal Washery Effluent
The effluent used in this study was taken from the coal
washery pond of moribund coal mine located in Akwuke ,
Enugu State, Nigeria. The physicochemical and biologi-
cal characteristics of the effluent presented in Table 1
were determined based on standard method [10].
2.1.2. Moringa Olei fera (MO) Sample
Dry Moringa oleifera (precursor to MOC) were sourced
from Agulu, Anambra State, Nigeria and stored at room
temperature. MOC was obtained as a by product of oil
extraction procedure reported by [3]. The analysis of MO
seed powder were performed by standard method [11]
and the characteristics presented in Table 2.
2.2. Coag-Flocculation Experiment
Experiment were carried out in a conventional jar-test
apparatus equipped with a six-unit multiple stirrer system.
Appropriate dosage of MOC in the range 100 - 500 mg/l
was added directly to 200 ml of CWE. The suspension,
tuned to pH range of 2 - 10 using H2SO4 and NaOH were
subjected to 2 minutes of rapid mixing (250 rpm), 20 min
of slow mixing (40 rpm), followed by 30 minutes of set-
tling. During settling, samples were withdrawn using
pipette from 2 cm depth and analyzed for turbidity (con-
verted to SDP in mg/l) changes with a view to determin-
ing optimal conditions (pH, dosage, settling time via
23-CCD) and kinetics parameters. Independent variables
range and levels for the coag-flocculation process opti-
mization are given in Table 3 while Table 4 displays the
full 23-CCD factorial design matrix with output response.
Table 1. Characteristics of coal washery effluent.
Parameters Values
pH 2.5200
Turbidity (NTU) 5387.0000
Total hardness (mg/l) 358.0000
Ca hardness (mg/l) 306.0000
Mg hardness (mg/l) 52.0000
Ca2+ (mg/l) 122.4000
Mg2+ (mg/l) 15.6000
Fe2+ (mg/l) 0.2500
SO42– (mg/l) 72.0000
NO32– (mg/l) Nil
Cl– (mg/l) 184.3400
E.cond (µm/m2) 805.2000
TDS (mg/l) 450.9120
TSS (mg/l) 109.6000
T. Coliform Nil
Plate Count 4.0000s
E-Coli Nil
BOD5 1001.0110
Table 2. Characteristics of MOC precursor.
Parameter MOC
Moisture content (%) 2.0200
Ash content (%) 2.1200
Lipid content (%) 30.4700
Crude protein (%) 39.3400
Carbohydrate (%) 23.7100
Crude fibre (%) 2.1600
Table 3. Experimental range and le vels of independent pro-
cess variables.
Independent
Variable Lower
limit (–1) Base
level (0) Upper limit (+1)
pH 2.0000 6.0000 10.0000
Dosage 100.0000 300.0000 500.0000
Settling time 10.0000 20.0000 30.0000
The experimental results of the 23-CCD were studied and
interpreted by software, MATLAB 7.0 to estimate the
response of the dependent variable. The kinetics of coag-
flocculation and extent of aggregation were monitored at
optimal conditions at 3,5,10,15,20,25 and 30 min. The
data were subsequently fitted in appropriate kinetic model.
The experiments were carried at room temperature.
3. Theory
3.1. Coag-Flocculation Optimization
Optimization was studied specifically by central com-

M. C. MENKITI ET AL. 127
Table 4. Process design matrix and output response.
S/NO X1 X
2 X 3 Y 1 Y 2
1 0 0 0 163.71 164.01
2 –1 –1 –1 2045.67 2055.13
3 1 –1 –1 514.65 513.9
4 –1 1 –1 2134.97 2135.33
5 1 1 –1 467.56 460.05
6 0 0 0 165.86 163.81
7 –1 –1 1 1615.32 1613.33
8 1 –1 1 261.31 262.25
9 –1 1 1 847.24 849.31
10 1 1 1 195.51 197.71
11 0 0 0 164.73 164.67
12 –1 0 0 1386.5 1390.1
13 1 0 0 274.16 276.61
14 0 –1 0 157.48 158.84
15 0 1 0 232.65 235.51
16 0 0 –1 250.71 251.12
17 0 0 1 113.16 115.34
posite design (CCD). The parameters: pH, dosage and
settling time were chosen as independent variables at two
levels while particle (SDP) uptake is the output response.
A 23 full factorial experimental designs with three star
points, six centre points and two replications generated
34 experiments employed in this study. The centre points
replicates verify changes in the middle of the plan and
measures of the degree of precision property, while star
points verify the non linear suspected curvature. The
behavior of the systems is explained by the multivariable
polynomial equation presented below:
Y=
bo + b1X1 + b2X2 + b3X3 + b12X1X2 + b13X1X3 + b23X2X3
+ b11X2
1+ b22X2 2 + b33X2 3
(1)
X1 is pH, X2 is dosage, X3 is settling time.
Upon the determination of polynomial coefficients
(b0, b1, b33 e.t.c.) by the following relationships expressed
below, statistical analysis (CSI, G-test, F-test, T-test e.t.c)
were performed to developed model that is adequate, sig-
nificant and homogenous (variance wise) [12].
2
0
11
NMN
j
u
ujui
baYuPX



(2)
1
N
iiuu
u
beXY

 (3)
1
N
ijiuju u
u
bgXXY

 (4)
22
11
NMNN
iiju ujuu
uj uiui
bcXYdX PY

 

(5)
where
a(0.40625), e(0.10), g(0.125), c(0.40625), d(–0.093750),
P(–0.15625)
3.2. Coag-Flocculation Kinetic
For a coag-flocculating phase, the rate of successful col-
lision between particles of sizes i and j to form particle of
size k is [13-16].
 
1
d1,,
d2
k
B
RijBRik
ijk i
nijnn iknn
t


 


(6)
where βBR(i,j) is Brownian aggregation factor for floccu-
lation transport mechanism, n
inj is particle aggregation
concentration for particles of size i and j, respectively. It
has been established that [15-17].
8
3
B
BR p
K
T


 (7)
and
8
R
K
aD 

 (8)
where KR is the Von Smoluchowski rate constant for
rapid coagulation. KB, T and η are Boltzmann constant,
temperature and viscosity, respectively. εp is collision
efficiency factor, D

is the diffusion coefficient and a
is particle radius.
Equations (7) and (8) can be transformed to
1
2
B
Rm
K
  (9)
where Km is defined as Menkonu coag-flocculatio n rate
constant accounting for Brownian coag-flocculation
transport of destabilized particles at αth order. It can also
be shown that coag-flocculation is governed by [18-21].
d
d
t
p
Rt
N
K
N
t

  (10)
where 0.5
p
RBR
K


Thus
d
d
t
mt
N
K
N
t

 (11)
Nt is the concentration of SDP at time, t.
Empirical evidence shows that in real practice, 1 < α <
2 [8,22-26]. Graphical representation of linear form of
Equation (11) at α = 2 provides for Km from the slope of
linear equation below:
0
11
m
Kt
NN
 (12)
where N0 is the initial Nt at time = 0; N is Nt at upper
time limit > 0
Equation (12) can be solved to obtain coag-floccula-
tion period,τ1/2:

M. C. MENKITI ET AL. 128

1
1/2 0
0.5 m NK 

 (13)
Equation (6), solved exactly, results in generic expres-
sion for microscopic aggregation:
1
() 1/2
1
0
1/2
1
1
m
mt
m
N
Nt











(14)
m = 1(monomers), m = 2 (dimmers), m = 3 (trimmers)
Efficiency of coag-flocculation is expressed as:
0
0
(%) 100
t
NN
EN




(15)
4. Results and Discusion
4.1. Optimization Studies
The optimization of the coag-flocculation process with
respect to pH, dosage and settling time was achieved by
response surface methodology via 23-CCD. The analysis
focused on how the SDP uptake (dependent output vari-
able) is influenced by independent variables, i.e. CWE
pH, (X1) coag-flocculant dosage (X2) and settling time
(X3). The pH range studied was between 2 and 10, dos-
age varied between 100 and 500mg/l and settling time in
the range of 10 to 20 minutes as shown in Table 3. In
order to study the combined effect of these factors, ex-
periments were performed at different combinations of
the physical parameters using statistically designed (de-
sign matrix shown in Table 4) experiments. The main
effects of the parameters and response behavior of the
system was explained by Equation (16) shown below:
Yu =
486.04 – 1.62X1 + 7.05X2 + 0.92X3 – 9.69X1X2 +
2.89X1X3 + 2.85X2X3 – 24.042
1
X + 4.622
2
X + 0.572
3
X
(16)
The optimization results obtained from the Equation
(16) as interpreted by MATLAB 7.0 are presented in
Table 5. With the objective of minimizing SDP, the op-
timal pH, dosage and settling time were recorded at
8,400 mg/l and 25 min, respectively. It can be deduced
that at optimal operation, the SDP was reduced from
12657.85 mg/l to 65.0587mg/l. This translates to about
99.48% SDP removal from the CWE. The corresponding
optimized interactive surface response plots are pre-
sented in Figures 1-3. Figure 1 shows the interaction
effects of pH and dosage on the SDP removal. In respect
of Figure 2, the interaction effect of pH and settling time
is presented while Figure 3 shows the interaction effect
of settling time and dosage. It is pertinent to point out
that the value of output responses are tied to the intensity
of the color of the 3-D plots. Hence, the optimal values
recorded for Figures 1-3 are 80, 80 and 75 mg/l, respec-
tively. In general, the 3-D plots provide avenue to ob-
serve the surface area of the curve within which the pro-
cess can perform at optimal level based on the effects of
the interaction of the variables under consideration. The
significance of these interaction effects between the
variables would have been lost if the experimental were
carried out by conventional methods of analysis.
Coag-flocculation efficiency E, (%) calculated from
Equation (15) is graphically depicted as Figure 4. It
shows the temporal variation of SDP removal at varying
dosage and optimum pH 8 and 25 minutes settling time.
It is apparent that at 3 minutes, all the dosages had
achieved up to 95% efficiency. The dosage with best per-
formance is 400 mg/l, at E, (%) > 98%. This is in agree-
ment with result recorded in Table 5. Furthermore, the
performance of MOC was compared to that of alum as
shown in Figure 5 at optimum pH and settling time.
Apparently, MOC performed better than alum for all the
dosages considered. This re-affirms the existing assertion
that MOC is a highly efficient coag-flocculant that are
eco-friendly [3,27].
4.2. Coag-Flocculation Kinetics
A summary of the coag-flocculation functional parame-
ters at optimum conditions as determined in this study is
shown in Table 6 for varying dosages. The accuracy of
the fit of the studied model (Equation (12)) with the ex-
perimental data was based on squared linear regression
coefficient (R2). Ta ble 6 indicates that experimental data
(with R2 > 0.90) were significantly described by the lin-
earised form of Equation (12). Km is determined from the
slope of Equation (12) on plotting 1/N Vs. time. The re-
sults posted in Table 6 indicate that Km (and βBR) are in-
Table 5. Optimization results of CWE coag-flocculation based on 23 CCD.
Sample X1 (pH) X2 (Dosage) X3 (Settling time) Y (SDP removal) (mg/l)
CV* RV** CV* RV** (mg/l) CV* RV** (min)
MOC 0.500 8.0000 0.5000 400.0000 0.5412 25.4120 65.0587
*Coded value
**Real value

M. C. MENKITI ET AL. 129
Table 6. Coag-flocculation kinetic parameters of MOC in CWE @varying dosage and pH of 8.
Parameters 100 mg/l 200 mg/l 300 mg/l 400 mg/l 500 mg/l
Y 0.0002 X + 0.0018 0.0002 X + 0.001 0.0002X + 0.00180.0001X + 0.0018 0.0001X + 0.0015

2.0000 2.0000 2.0000 2.0000 2.0000
R2 0.9692 7420.0000 0.9194 0.9701 0.9096
l
mg.min
m
K



 0.0002 0.0002 0.0002 0.0002 0.0002

lmg.min
BR
 0.0004 0.0004 0.0004 0.0004 0.0004

lmin
R
K 7.0819 × 10–12 7.5095 × 10–12 7.70909 × 1012 7.5829 × 10-12 7.6525 × 10–12

lmg
P
 5.6481 × 107 5.3265 × 107 5.1887 × 107 5.2749 × 107 5.2269 × 107

12
min  0.7900 0.7900 0.7900 0.7900 0.7900

0mg lN 555.5600 1000.0002 555.5600 555.5600 666.6700

0
Np 3.3455 × 1023 6.022 × 1023 3.3455 × 1023 3.3455 × 1023 4.0146 × 1023
-1 -0.5 00.5 1
-1
-0. 5
0
0.5
1
50
100
150
200
250
pH
Dos age (m g / l)
SDP Remo val (mg/l)
80
100
120
140
160
180
200
220
Figure 1. Coag-flocculation surface/contour plots of MOC in CWE showing interaction effects of pH and dosage.
-1 -0.5 00.5 1
-1
-0. 5
0
0.5
1
50
100
150
200
pH
Sett ling time (mins)
SDP Re moval (mg/l)
80
100
120
140
160
180
Figure 2. Coag-flocculation surface/contour plots of MOC in CWE showing interaction effects of pH and settling time.

M. C. MENKITI ET AL. 130
-1 -0.5 00.5 1
-1
-0. 5
0
0. 5
1
70
80
90
100
110
120
Dos age (m g/ l )
Settling time (mins)
SDP Removal (mg/l)
75
80
85
90
95
100
105
110
115
Figure 3. Coag-flocculation surface/contour plots of MOC in CWE showing interaction effects of Dosage and settling time.
94.5
95
95.5
96
96.5
97
97.5
98
98.5
99
99.5
051015 20 25 30
E
(
%
)
Time (min)
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Figure 4. Coag-flocculation efficiency profile for varying
MOC dosage in CWE at Ph of 8.
variant with dosage variation. This may be explained by
the near equal efficiency (equal aggregation rate) achie-
ved by the varying MOC dosages depicted in Figure 4.
Generally, the variation of KR = fn(T,η) is minimal,
following insignificant changes in the values of tem-
perature and viscosity of the effluent medium. At ap-
proximately invariant KR, εp relates directly to 2Km =
βBR. Thus high εp results in high kinetic energy to over-
come the repulsive forces. The coagulation period, τ1/2
is determined from Equation (13). Here, τ1/2 = fn(N0).
The higher the N0, the smaller the τ1/2. This accounts
for high settling rate associated with highly turbid wa-
ter. From theoretical point of view, τ1/2 εp and KR are
considered as effectiveness factor, understood to be ac-
counting for the coag-flocculation efficiency before
flocculation sets in.
Equation (14) predicts the time evolution of aggrega-
tion (monomers, dimmers, trimmers for m = 1,2,3 re-
spectively) at microscopic/discrete level. The aggrega-
tions profile as a function of time are depicted in Figure
6.
94
94.5
95
95.5
96
96.5
97
97.5
98
98.5
99
100mg/l 200mg/l 300mg/l400mg/l 500mg/l
M0C 98.88698.811898.8118 98.7189 98.8118
A
lum 98.069197.2708 96.8438 96.2097 95.8041
E (%)M0
C
Alum
Figure 5. Comparative coag-flocculation performance at 25
mins for varying MOC and Alum dosage in CWE at Ph of 8.
0
1E+24
2E+24
3E+24
4E+24
5E+24
6E+24
7E+24
8E+24
9E+24
0510 15 20 25 30
N
o
o
p
a
c
e
s
p
e
e
Time (min)
Monomer s
Dim mers
Trimmer s
Sum
Figure 6. Time evolution of the cluster size distribution for
MOC in CWE at minimum half life of 0.79 min.
The primary particles (monomers) and total number of
particles can be seen to decrease more rapidly. This can
be accounted on the basis of sweep-floc or massive in-
stantaneous destabilization of the particles. With negligi-
ble repulsion in the system, the MOC sweeps away the
SDP from the CWE [8].
E (%)
9E+24
8E+24
7E+24
6E+24
5E+24
4E+24
3E+24
2E+24
1E+24
0
No of particles (particles/l)

M. C. MENKITI ET AL. 131
5. Conclusions
The application of MOC as an effective coag-flocculant
in the treatment of high turbid effluent such as CWE has
been established. The removal of 90% of initial value of
SDP within the first three minutes of treatment justifies
that the process was rapid with high rate constant and
low coagulation period. The system can operate opti-
mally at pH 8,400 mg/l dosage and 25 min settling time.
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