Journal of Minerals & Materials Characterization & Engineering, Vol. 11, No.5, pp.543-558, 2012
jmmce.org Printed in the USA. All rights reserved
543
Optimal Evaluation of Coag-Flocculation Factors for Alum-Brewery
Effluent Syst em by Response Surface Methodology
M.C. Menkiti1*, M.C. Aneke2, E.B. Ogbuene3, O.D. Onukwuli1, E.O. Ekumankama4
1Department of Chemical Engineering, Nnamdi Azikiwe University, Awka, Nigeria
2School of Built and Natural Environment, Northumbria University, Ellison Building, New
Castel Upon Tyne, United Kingdom
3Centre for Environmental Management and Control, University of Nigeria, Enugu Campus,
Nigeria.
4Department of Food Science and Technology, Ebonyi State University, Abakaliki, Nigeria
*Corresponding Author: cmenkiti@yahoo.com
ABSTRACT
This work investigates coag-flocculation optimization treatment of alum-brew ery effluent s ystem
via response surface methodology (RSM). To minimize suspended and dissolved particles (SDP),
experiments were carried out using nephelometric jar test and 23-factorial design with three
star-points, six-center-points and two replications. A central composite design, which is the
standard design of RSM, was used to evaluate the effects and interactions of three major factors
(coagulation pH, coagulant dosage, settling time) on the treatment efficiency. Multivariable
quadratic model developed for the response studied indicates the optimum conditions to be 9,
500mg/l and 20minutes for coagulation pH, coagulant dosage and settling time, respectively. At
optimum, the SDP was reduced from 10831.490mg/l to 801.451mg/l, representing 92.601%
removal efficiency. RSM has demonstrated to be appropriate approach for the optimization of
the coag-flocculation process by statistical evaluation.
Keywords: Coag-flocculation, Brewery effluent, Alum, Response surface methodology, Central
composite design
544 M.C.Menkiti, M.C.Aneke, E.B. Ogbuene Vol.11, No.5
1. INTRODUCTION
Brewer y effluent (BRE), a major waste product from lager production, is a notorious pollutant
deleterious to the aquifers of brewery bearing communities in Nigeria. The characteristics of the
BRE is a major determinant for the most suitable technique and remedial implementation
options available for the treatment of the effluent [1,2,3]. Depending on the process route, the
quality and characteristics of BRE fluctuate significantly. The organic components of BRE
consist of sugars, soluble starch, ethanol, volatile fatty acids and solids which are mainly spent
grains, yeast and trub [4,5]. Typically, untreated BRE contains suspended solids (100-1500mg/l),
chemical oxygen demand (300-800mg/l), nitrogen (30-100mg/l) and phosphorus (10-30) [6].
Physiochemical treatment processes are effective in the purification of young and freshly
produced BRE.
Coag-flocculation is a widely applied and relatively simple physiochemical technique commonly
used for water and wastewater treatment. The removal mechanisms of this process mainly
consists of charge neutralization of negatively charged colloids by cationic hydrolysis product,
followed by incorporation of impurities in an amorphous hydroxide precipitate through
flocculation. The aggregated particles form visible flocs that settle out under gravity [7-12].
Inorganic salts such as ferrous sulfate, ferric chloride, ferric chloro-sulfate and aluminium
sulfate (alum) are generally used in coag-flocculation. Among these inorganic coagulants, alum
is most widely used in our locality, having proven to be very efficient in operation. It has been
reported based on conventional experiments that alum optimally remove 80-90% of suspended
and dissolved particles (SDP) from BRE [3,13].
Though these limited documented results are encouraging, there are associated disadvantages in
the conventional method (one factor at a time, OFAT) usually applied in the search for the
operational optimal variables. The major disadvantage is the individual optimization of variables
through the single-dimensional search which are time consuming and incapable of reaching the
true optimum as interaction among variables is not taken into consideration [7,14,15]. As a
solution, the statistical method of response surface methodology (RSM) has been proposed to
include the influence of individual factors as well as their interactive influences. RSM, which is a
technique for designing experiment helps researchers to build models, evaluate the effects of
several factors and achieve the optimum conditions for desirable responses in addition to
reducing the number of experiments [7,16,]. Analysis of variance (ANOVA) provides the
statistical results and diagnostic checking test which provide the means to evaluate the adequacy
of the models.
In this present study, central composite design (CCD) and RSM was used to design the
experiments, build models and determine the optimum conditions. It monitored how SDP
Vol.11, No.5 Optimal evaluatio n of coag-flocculation factors 545
removal (as response) were affected by changes in the levels of alum dose, coagulation pH and
settling time (as factors). Quantitative measurement of efficiency and speed of the coag-
flocculation were also determined.
2. MATERIALS AND METHODS
2.1 Effluent Sampling and Characterization
Effluent sample was taken from brewery site in Enugu, Nigeria. Sample collection, preservation
and characterization were done in accordance with the standard method for the examination of
water [17]. Characterization was carried out immediately after sample arrived in the laboratory.
Table 1 shows the characteristics of BRE sampled.
Table 1: Characteristics of Brewery Effluent
Paramet er s Values
pH
6.940
Turbidity (NTU)
9538.700
Total hardness(mg/l)
68.000
Ca hardness (mg/l)
51.000
Mg hardness (mg/l)
18.000
Fe2+(mg/l)
0.180
Cl-(mg/l)
18.994
E.cond(µm/m2)
480.000
TDS (mg/l)
7235.340
TSS (mg/l)
10000.335
BOD3 1021.011
2.2 Coag-Flocculation
In this present work, alum (a metal salt) was used as a coagulant. The alum used in this study
was in powder form with chemical formula, Al2(SO4)3.18H2O (M=666.42g/mol, 51-59%
Al2(SO4)3,, pH 2.5-4). Coagulant sample was sourced from the staple of Merck, Germany.
In order to carry out the study, jar tests were used to perform the coagulation-flocculati on (coa g-
flocculation) process. The experiments were carried out using 2L square jars, with six paddle
stirrers, manufactured by Phipps and Birds, VA USA. The coag-flocculation pH was adjusted
using 0.1M H2SO4 or 0.1MNaOH just before dosing of the coagulant. The time and speed for
rapid and slow mixing were set with an automatic controller as follow: Rapid mixing at
250rpm(G=550 sec-1) for 1 minutes after alum addition, followed by slow mixing at 30
546 M.C.Menkiti, M.C.Aneke, E.B. Ogbuene Vol.11, No.5
rpm(G=22 sec-1 ) for 30 minutes, and then settling for 3- 30 minutes range. During settling,
samples were withdrawn using pipette from 2cm depth and analyzed for optimization with
SDP(mg/l) removal as a response.
2.3 Experimental Design and Data Analysis
In this study, CCD and RSM were applied to optimize three important operating variables: pH,
coagulant dosage and settling time. Experiments were initiated as a preliminary study for
determining a narrower range of pH, coagulant dosage and settling time prior to designing the
experimental runs. Accordingly, pH from 1-12 were tried and the increment continued until
appreciable reductions were observed in the process response(SDP). Likewise, a wide dosage
and time range of 100-1000mg/l and 5-50 minutes, respectively were examined to search for a
narrower and more effe ctive range. The prelimin ary search ran ge of settling time was pegged at
5-50minutes. As a result, the study ranges and levels displayed in table 2 were chosen. Table 3
shows the CCD in the form of a 32 full factorial design with three star points, six center points
and two replications to generate 34 runs and responses.
The cente r-points replicates verify changes in the midd le of the plan and measures o f the degree
of precision property, while star-points verify the non-linear suspected curvature. In order to
obtain the optimum pH, dosage and settling time, SDP reduction response was studied and
interpreted by MATLAB 7.0. The behavior of the system is explained by the generic
multivariable polynomial equation 1 below [18]:
∑∑ ∑∑=<= ++++= m
jjjj
ji jiijj
m
jjXbXXbXbbY 1
2
1
0
ε
(1)
With respect to this current particular study, equation 1 transforms to generic equation 2 for the
23-CCD of the system under consideration.
Y=b0+b1X1+b2X2+b3X3+b12X1X2+b13X1X3+b23X2X3+b11X21+b22X22+b33X23 (2)
Where Y is the predicted response, b0, bj and bjj are constants coefficients; Xi and Xj are the
coded independent factors; ε is the random error. X1, X 2, and X 3 are coagulation pH, coagulant
dosage and settling time, respectively. The polynomial coefficients are determined by the
following relationships expressed below(equations 3-6):
∑ ∑∑
= ==
+=
M
j
N
iuju
N
u
XPYuab
1
2
1
0
(3)
u
N
uiui
YXeb
=
=
1
(4)
Vol.11, No.5 Optimal evaluatio n of coag-flocculation factors 547
uju
N
uiuij YXXgb
=
=1
(5)
∑ ∑∑∑= ===
++= M
j
N
iu
N
iuuju
N
uujuii YPXdYXcb 1
2
1
2
(6)
Where a(0.40625); e(0.1000); g(0.125); c(0.40625); d(-0.09375); p(-0.15625)
Analysis of variance (ANOVA) was used for graphical analyses of the data to obtain the
interactions between the process variables and the responses. The quality of the fit polynomial
model w as express ed by the coefficien t o f det erminat io n R2, and its statistical significance/model
adequacy was checked by the Fisher’s F-test in the same programme. Model terms were
evaluated by the p-value (probability) with 95% confidence level. Homogeneity of the variance
and significance of the polynomial coefficients were tested by G-test and CSI-test, respectively.
Three dimensional surface plots and their respective contour plots were obtained for alum driven
coag-flocculation based on the effects of the three factors (pH, coagulant dosage and settling
time) at two levels. Furthermore, the optimum region was identified based on the interpretation
of the final form of equation 2 by MATLAB 7.0.
Table 2: Levels and range of variables tested in 23 -CCD.
Independent Variable
Lower limit (-1)
Base level (0)
Upper limit (+1)
pH
2.000
6.000
10.000
Dosage (mg/l)
100.000
300.000
500.000
settling time (min)
10.000
20.000
30.000
Table 3: Full design matrix and response result for the experimental variables.
S/NO X1 X2 X3 X1X2 X1X3 X2X3 X
2
1 X
2
2 X
2
3 Yave
1
0
0
0
0
0
0
0
0
0
812.8885
2
-1
-1
-1
1
1
1
1
1
1
663.969
3
1
-1
-1
-1
-1
1
1
1
1
525.8948
4
-1
1
-1
-1
1
-1
1
1
1
688.9848
5
1
1
-1
1
-1
-1
1
1
1
231.945
6
0
0
0
0
0
0
0
0
0
777.2038
7
-1
-1
1
1
-1
-1
1
1
1
295.4538
8
1
-1
1
-1
1
-1
1
1
1
323.0663
9
-1
1
1
-1
-1
1
1
1
1
394.8588
10
1
1
1
1
1
1
1
1
1
171.1975
11
0
0
0
0
0
0
0
0
0
577.959
12
-1
0
0
0
0
0
1
0
0
397.62
548 M.C.Menkiti, M.C.Aneke, E.B. Ogbuene Vol.11, No.5
13
1
0
0
0
0
0
1
0
0
185.0038
14
0
-1
0
0
0
0
0
1
0
463.091
15
0
1
0
0
0
0
0
1
0
498.1178
16
0
0
-1
0
0
0
0
0
1
1005.389
17
0
0
1
0
0
0
0
0
1
457.1103
3. RESULTS AND DISCUSSION
3.1 Statistical Analysis
The relationship between the three variables (pH, dosage and time) and the single process
response (SDP removal) for the coag-flocculation process was analyzed using RSM. The CCD
shown in table 3 permitted the generation of array profile for all factors effect estimate (table 4)
and factors effects estimate chart (figure 1). Figure 1, which is a representation of effects of
factors on response variable, is presented to imitate pareto graphic. According to figure 1 and
table 3, the effects estimates are presented in absolute values (to verify which were positive and
negative). According to figure 1, quadratic variables have the highest effects at 175.23 while
interaction variable(X2X3) is the most trivial at -22.91. The statistical implication is the
repres entation of X21, X22 and X23 as the most significant on the response of the dependent
variable. Figure 1 presents more of positive affecting factors (example, squared pH, dosage and
time) than negative affecting ones (example, pH). These positive affecting factors appear in
equation 1 with a positive sign. On the other hand, negative affecting factors represent the
contrary. Also , positive bars indicate that by varying the variable, the response increases.
Negative bars indicate the contrary.
Table 4: Non-discriminatory array profile for factor effect estimate.
Factors
Effects
Effect
Estimate
% Estimate
Cumulative
Estimate (%)
X2
3
C33
175.23
34.32517
34.32517
X2
2
C22
175.23
34.32517
68.65034
X2
1
C11
175.23
34.32517
102.9755
X
3
C3
98.24
19.24388
122.2194
X
1
X
3
C13
42.57
8.338883
130.5583
X2X3
C23
22.91
4.487757
135.046
X
2
C2
-34.075
-6.67483
128.3712
X
1
X
2
C12
-60.55
-11.8609
116.5103
X
1
C1
-84.285
-16.5103
100
Sum
510.500
100.0000
Vol.11, No.5 Optimal evaluatio n of coag-flocculation factors 549
Legend description: X23≡ X23 ,X22≡ X22, X21≡X21 , X3≡X3 , X1≡X1, X1X2≡X1X2, X1X3≡X1X3, X2≡X2 ,X2X3≡X2X3
Fig.1: Non-discriminatory factor effects estimate chart.
Furthermore, the CCD shown in table 3 allowed the development of mathematical equation
where predicted results,(Y) were assessed as a function of coagulation pH(X1), coagulant
dosage(X2) and settling time(X3) and cal culat ed as the su m of con stant , thr ee firs t ord er eff ects (
terms in X1,X2,X3), three interactive effects (X1X2, X1X3, X2X3) and three second order
effects(X12, X22, X32) according to equation 2.The results obtained were then analyzed b y means
of ANOVA to asses the “goodnesss of fit”. Equation from the initial ANOVA analysis was
modified by eliminating the terms found statistically insignificant via CSI-test. Equation 7
depicts the reduced quadratic model in terms of coded factors. Table 5 shows ANOVA results
due to statistical testing of the model equation 7.
Y=955.45+592.54X21+142.00X22-131.34X23 (7)
Equation 7 indicates that only the coefficients of quadratic interaction proved to be significant at
CSI of 73, since the magnitude of the other coefficients were less than 73. Data given in table 5
demonstrate that the model is significance at 5% confidence level since p-value is less than
0.05.The F-test indicates that the model equation is adequate since 0.008 is less than F-
table(22.036). This describes the variation of the data around the fitted model. The results
affirmed that there is significant model correlation between the variables and process response.
The R2 coefficient gives the proportion of the total variation in the response predicted by the
550 M.C.Menkiti, M.C.Aneke, E.B. Ogbuene Vol.11, No.5
model, indicating ratio of sum of squares due to regression(SSR) to total sum of square(SST). A
high R2 value, close to one is desirable and reasonable agre ement with adjusted R2 is a ne ces si ty.
A hi gh R 2 coefficient ens ures a satisfactory adjustment of the multivariable polynomial model to
the experimental data [7,19,]. The fact that ANOVA report gives high R2 correlation factor
allows us to present the CCD model and DOE procedures as a consistent statistical method for
analyzing the system under study at the conditions of the experiment. This aspect is very
important in order to scale up the results of the current investigation on the bases that model
applied to this phenomena explains properly the behavior of the system [20]. The Chochrain’s
test(G-test) indicates that holistically the variance is homogeneous since G is less than 0.4383.
Response F inal Equat i on in terms of coded fact ors
PF-Test R
2
Ad j. R
2
SD G CSI
SDP remova l955.45+592.54X
2
1+142X
2
2- 131.34X
2
30.00310.0080.9612 0.91014.570.40173
Parameters*
Table 5 : ANOVA results for response parameters
*Parameters :- P:Probability of error ; SD:Standard deviation; G:Chochrain’s test; CSI:coeff icient signif icance index
3.2 Process Optimization and Analysis
The optimization results obtained by solving equation 7 as interpreted by MATLAB 7.0 are
presented in table 6. W ith the objective of minimiz ing SDP, the optimal pH, dosage and settling
time were recorded at 9, 500mg/l and 20 minutes, respectively. It can be deduced that at optimal
operation, the SDP was reduced from initial 10831.490mg/l to 801.451 mg/l. This translates to
about 92.601% SDP removal from the BRE at the conditions of the experiment. The high
performance recorded at pH 9 is expected since alum is known to perform well in alkaline
medium.
The most important graphical representation in RSM is the surface (3D) plots shown in figures
2-4. It plots equation 7 and allows to evaluate from qualitative point of vie w how the beh avior of
the whole system is. Contour plots (figures 5-7) are drawn as well for a better comprehension of
the system.
With SDP removal as the response, the obvious trough in the response surfaces indicates that the
optimal conditions for the two interacting variables were exactly located inside the design
boundary. The corresponding contour plots (figures 5-7) show a considerable curvature in
contour curves, implying that these two factors were interdependent. In other words, there were
significant interactive effects on SDP removal between pH and settling time, pH and dosage as
well as dosage and settling time. It is pertinent to note that the values of output responses are tied
to the intensity of the color of the plots. Hence, for the surface responses (figures 2-4) and their
corresponding contours, the best(minimal) results are 900, 1000 and 850mg/l, respectively. For
interaction of pH and time, figure 2 posted the best result at pH(6-9) and entire time range.
Equally, similar results are recorded for figure 3 and the corresponding contour plot. Figure 4,
Vol.11, No.5 Optimal evaluatio n of coag-flocculation factors 551
indicating the interaction between dosage and settling time, shows that at the conditions of the
experiment, the minimal SDP removal is achieved at pH( 6-10) and settling time(10-20).
Another area of good performance is recorded at pH(6-10) and time(30min). These areas of l ocal
minima are in agreement with the optimization results. Like earlier observed, the saddle contours
(figures 5 and 7) and symmetrical sunken contour (figure7) show that the pairs of the interacting
variables have substantial influence on the minimization of the SDP, in additi on to obtaining the
minimization at optimal region.
In general, the 3-D plots provide routine avenue to observe the surface areas of the plot within
which the process performs at optimal level based on the effects of the interactions of the
variables under consideration. The significan ce o f th ese i nt era cti on effe ct s bet ween th e va ri abl es
would have been lost if the experiments were carried out by traditional (OFAT) method of study.
Table 6: Process optimization results for SDP removal.
Sample X1(pH) X2(Dosage) X3(Settling time)
Y(SDP
removal)(mg/l)
CV*
RV**
CV*
RV**(mg/l)
CV*
RV**(min)
BRE
0.750
9.000
1.000
500.000
0.000
20.000
955.451
*Coded Value
**Real value
Fig. 2: Surface graph of SDP removal showing interaction of pH and Settling time
552 M.C.Menkiti, M.C.Aneke, E.B. Ogbuene Vol.11, No.5
Fig. 3: Surface graph of SDP removal showing interaction of pH and dosage.
Fig. 4: Surface graph of SDP removal showing interaction of dosage and settling time.
Vol.11, No.5 Optimal evaluatio n of coag-flocculation factors 553
900
1000
1100
1200
1300
1400
1500
-1 -0.500.5 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
pH
S ett li ng tim e(m i ns)
Fig. 5: Contour plot of SDP removal showing interaction of pH and settling time
1000
1100
1200
1300
1400
1500
1600
-1 -0.5 00.5 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
pH
Dosage(mg/l)
Fig. 6: Contour plot of SDP removal showing interaction of pH and dosage.
554 M.C.Menkiti, M.C.Aneke, E.B. Ogbuene Vol.11, No.5
850
900
950
1000
1050
-1 -0.500.5 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Dosage(m g/l)
S ett li ng tim e(m i ns)
Fig. 7: Contour plot of SDP removal showing interaction of dosage and settling time.
3.3 Coag-Flocculation Performance at Optimal pH and Time
The process efficiency graphically presented in figure 8 is obtained upon evaluation of equation
8 below:
100(%)
0
0
=N
NN
E
t
(8)
Where E(%) is efficiency, C o , Ct are SDP concentrations at time zero and t, respectively. The
figure depicts at optimum pH and settling time the variation of efficiency,E(%) as a function of
coagulant dosage (100, 200,300, 400, 500mg/l). Generally, the process was apparently fast at
onset with about 92.862% efficiency recorded at 3minutes for all the dosages considered. Best
result obtained at high dosage is linked to particle enmeshment and sweep–floc effects. These
phenomena are common propert y of alum , due to its ability to achieve adsorption of SDP b y the
amorphous Al(OH)3(s). For the formation of amorphous solid-state Al(OH)3(s), it has been
readily reported that the pH range of 6-10 has been favorable because the aluminum ions
required sufficient alkalinity to form it. This is strongly reflected in this study where optimal pH
is located at pH 9 and 500mg/l dosage. If the dosage is not in excess, the controlling mechanisms
tend to be partial bridging and charge neutralization [21,22].
The implication of result presented in figure 8 is that the maximum rate of coagulation driven by
optimum rate constant, Km is achieved at 500mg dosage and pH 9. This is apparent if Km is
Vol.11, No.5 Optimal evaluatio n of coag-flocculation factors 555
evaluated by fitting the experimental data on the plot of (1/Nt) or (1/SDP) against time (Figure 9)
as can be deduced from equation 9,
0
11
N
tK
Nm+=
(9)
Where Nt, N0 are SDP concentrations at time t and zero, respectively. Km is Menkonu coag-
flocculation rate constant accounting for Brownian coag-flocculation transport of destabilized
particle at αth order [23,24]. βBR is Brownian aggregation factor for flocculation transport
mechanism. t is settling time.
Table 7 presents rate – related parameters obtained from analysis of equation 9 that strongly
influence the ability of alum to coagulate SDP. Such parameters have direct bearing on the
design, fabrication and practical implementation of this study. From table 7, 500mg/l dosage has
the highest Km (0.0004l/mg.min) in obvious support of result obtained in figure 8 and table 6.
This is the most important factor responsible for the highest efficienc y obtained at 500mg/l dose
in figure 8. Km is directly proportional to the rate of coag-flocculation.
Linear regression coefficient (R2) was employed in evaluation of the level of accuracy of fit of
experimental data on equation 9. Table 7 indicates that data (R2>0.90) were significantly
described by equation 9.
Table 7: Rate related result at optimal pH and settling time.
Paramet er s
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
2.0000
2.0000
2.0000
2.0000
2.0000
R2
0.9725
0.9621
0.9389
0.9394
0.9951
( )
min./mglKm
0.0002 0.0002 0.0002 0.0002 0.0004
0.004 0.0004 0.0004 0.0004 0.0008
556 M.C.Menkiti, M.C.Aneke, E.B. Ogbuene Vol.11, No.5
92
93
94
95
96
97
98
99
100
0510 15 20 25
Efficiency , E (%)
Time (min)
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Fig. 8: Coag-flocculation efficiency at optimum pH and settling time.
0
0.002
0.004
0.006
0.008
0.01
0.012
05 10 15 20 25
1/SDP (l/mg)
Time (min)
100mg/l
200mg/l
300mg/l
400mg/l
500mg/l
Fig. 9: Rate plot at optimum pH and settling time
4. CONCLUSION
This study has demonstrated the application of RSM in seeking optimal conditions for alum
driven coag-flocculation of BRE. In order to gain a better understanding of the considered
factors for optimal coag-flocculation performance, the built up model was presented as 3-D
response surface and 2-D contour graphs. From the statistical analysis, coagulation pH,
Vol.11, No.5 Optimal evaluatio n of coag-flocculation factors 557
coagulant dosage and settling time have significant effects on the coagulation. Effects estimate
indicates the dominance of quadratic interactions. Results reveal that the optimal conditions for
minimum SDP were coagulation pH of 9, coagulant dosage of 500mg/l, settling time of 20
minutes and removal efficiency of 92.601%.
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