# Modeling and Optimization for Production of Rice Husk Activated Carbon and Adsorption of Phenol

Authors: Y. S. Mohammad; E. M. Shaibu-Imodagbe; S. B. Igboro; A. Giwa; C. A. Okuofu
Journal: Journal of Engineering
 (2014)

---

## Abstract

Modeling of adsorption process establishes mathematical relationship between the interacting process variables and process optimization is important in determining the values of factors for which the response is at maximum. In this paper, response surface methodology was employed for the modeling and optimization of adsorption of phenol onto rice husk activated carbon. Among the action variables considered are activated carbon pretreatment temperature, adsorbent dosage, and initial concentration of phenol, while the response variables are removal efficiency and adsorption capacity. Regression analysis was used to analyze the models developed. The outcome of this research showed that 99.79% and 99.81% of the variations in removal efficiency and adsorption capacity, respectively, are attributed to the three process variables considered, that is, pretreatment temperature, adsorbent dosage, and initial phenol concentration. Therefore, the models can be used to predict the interaction of the process variables. Optimization tests showed that the optimum operating conditions for the adsorption process occurred at initial solute concentration of 40.61 mg/L, pretreatment temperature of 441.46°C, adsorbent dosage 4 g, adsorption capacity of 0.9595 mg/g, and removal efficiency of 97.16%. These optimum operating conditions were experimentally validated.


---

## Body

## 1. Introduction

The increase in industrial, agricultural, and domestic activities has led to the discharge of large amounts of wastewater containing toxic pollutants. The growing awareness of the adverse effects of the presence of these water pollutants has led to increased strict regulation of water pollution, hence making the treatment of wastewater generated from industrial activities a high priority [1]. Phenols are among the most common water pollutants that can cause hazards including health hazard which may lead to death. Amongst hydrocarbons present in refinery wastewater, phenol is one of the main dissolved components and it is also one of the difficult hydrocarbons to degrade biologically [2, 3]. Consequently, pollution control and management have evolved many technologies for the treatment of wastewater [4, 5]. These technologies and methodologies which differ in their performance and effectiveness include coagulation, filtration, ion exchange, sedimentation, solvent extraction, adsorption, electrodialysis, chemical oxidation, disinfection, chemical precipitation, and membrane separation [6, 7]. Among the various available technologies for water pollution control, adsorption process is considered relatively better because of its convenience, ease in operation and simplicity of design [8–10]. The process can remove different types of pollutants due to the availability of wide range of adsorbents especially activated carbon which make it to have a wider applicability in water pollution control [7, 11–13]. Rice husk is an agricultural waste that is readily available as a by-product of rice processing but requires pretreatment to produce activated carbon for better performance as an adsorbent.Response Surface Methodology (RSM) had been known as a collection of mathematical and statistical techniques for modeling and analyzing problems in which a response of interest is influenced by several variables. Basically, it had been used in multivariate experimental design, statistical modeling and process optimization [14, 15]. Thus process optimization was observed to be important in determining the values of factors for which the response is at maximum. The application of statistical experimental design techniques in adsorption process was found to result in reduced process variability combined with the requirement of less resources (time, reagents and experimental work) [16, 17]. It had been reported that RSM has several classes of designs, among which are; central composite design, box-behnken design and three-level factorial design being the most widely used and the experimental data required are dependent on the chosen design [18, 19]. There is little or no information on the optimization of carbonization temperature for the production of rice husk activated carbon for phenol adsorption using response surface methodology. In addition, the usual approach to modeling and optimization has been on either the process variable for the production of activated carbon or that of the batch adsorption process. This paper, however, highlights a novel approach involving the simultaneous modeling and optimization of process variables for the production of rice husk activated carbon and batch adsorption of phenol using response surface methodology.


## 2. Methods

### 2.1. Production of Activated Carbon

The natural precursor used in the preparation of adsorbent was rice husk which was collected from National Cereal Research Institute, Badeggi. When collected from NCRI Rice Mill, the rice husk was washed with distilled water to remove dirt and surface impurity, then oven-dried at 100°C for 24 h in accordance with the procedure of Kudaybergenov et al. [20]. In the thermal pretreatment, rice husk was placed on a ceramic flat surface, charged into a furnace and heated to a temperature of 300°C at a heating rate of 20–25°C/min and residence time of 1 h. The charred residue was collected and cooled at room temperature. The procedure above was repeated for 400°C and 500°C. The thermal pretreated rice husks were labeled RH300, RH400 and RH500. In the chemical pretreatment, each of the carbonized rice husk (charred residue) was activated with 1 M H3PO4 for 3 h at impregnation ratio of 2 : 1 (volume mL of acid/mass g of rice husk) and later oven-dried overnight at 200°C to ensure proper drying [21, 22]. The material was then removed from the oven, cooled for 2 h and then washed with distilled water to bring the pH to 7.0 and again oven-dried overnight at 100°C [21].


### 2.2. Preliminary Batch Experiment

In the preliminary Batch Adsorption experiment, 2 g of the pretreated adsorbent was added to 100 mL of standard solution of phenol with initial concentration of 10, 30, and 50 mg/L in 250 mL conical flask. The mixture in the flask was placed on magnetic stirrer at 150 rpm [23, 24] for 90 min at ambient temperature. Using a 5 mL syringe, samples were withdrawn at predetermined time interval (90 min) and centrifuged at 3000 rpm for 20 min. The supernatant solution was collected from the centrifuge by decantation and filtered using a micro filter attached to a 5 mL syringe. The procedure above was repeated for 3 and 4 g of pretreated adsorbents. The analysis of phenol in each sample filtrate was carried out using UV spectrophotometer set at wave length of 270 nm.


### 2.3. Determination of Adsorption Capacities and Removal Efficiency

Adsorption capacityq
e at equilibrium was determined using the equation [25, 26]:
(1)
q
e
=
C
o
-
C
t
V
m
.
Adsorption removal efficiency was determined using the equation [27–29]:
(2)
RE
=
C
o
-
C
e
C
o
×
100
,
where q
e = adsorption capacity at equilibrium (mg/g), C
o = initial concentration of solute (mg/L), C
e = equilibrium concentration of solute (mg/L), V = volume of solution (L), m = mass of activated carbon used (g), and RE = removal efficiency (%).


### 2.4. Modeling and Optimization

#### 2.4.1. Experimental Design

The Central Composite Design (CCD) was applied in this work to study the interaction of variables involved in the preparation of rice husk activated carbon as well as batch adsorption process of phenol using the activated carbon prepared. The CCD is widely used for modeling and optimization and it requires only a minimum number of experiments. Generally, the CCD consists of three kinds of runs; they are factorial runs (2
n), axial runs (2
n) and center runs (n
c) [30, 31]. This design consist of a 2
n factorial (coded to the usual ±1 notation) augmented by 2
n axial points (
±
α
,
0,0
), (
0
,
±
α
,
0
), (
0,0
,
±
α
), and n
c center points (
0,0
,
0
) [1, 32], where α is the distance of the axial point from the center [33]. The center points are used to determine the experimental error and reproducibility of the data [34, 35] and the axial points are chosen such that they allow rotatability which ensures that the variance of the model prediction is constant at all points equidistant from the design center [36]. Therefore, according to Abbas [37] and Arulkumar et al., [38], the number of experimental runs required is given by the equation:
(3)
N
=
2
n
+
2
n
+
n
c
,
where N = total number of experimental runs, n = number of independent variables (factors), and n
c = number of center points.Three variables were considered in this study, they are (i) pretreatment temperature “A”, a rice husk activated carbon production variable, (ii) initial phenol concentration “B”, a batch adsorption process variable, and (iii) adsorbent dosage “C”, a batch adsorption process variable.For three variables, the number of center run was six, therefore number of experimental run required was computed as:(4)
N
=
2
n
+
2
n
+
n
c
=
2
3
+
2
3
+
6
=
8
+
6
+
6
=
20
.
This implied that 20 experimental runs consisting of 8 factorial runs, 6 axial runs and 6 center runs were required. The two response variables considered in the study were: (i) removal efficiency (Y
1) and (ii) adsorption capacity (Y
2).


#### 2.4.2. Regression Model

Each response was used to develop an empirical model that correlate the response to the three factors that is, rice husk activated carbon preparation variable (A) and batch adsorption process variables (B, C), using second-order polynomial equation [39–41]:
(5)
Y
=
b
o
+
∑
i
=
1
n
b
i
X
i
+
∑
i
=
1
n
b
i
i
X
i
2
+
∑
i
=
1
n
-
1
∑
j
=
i
+
1
n
b
i
j
X
i
X
j
,
,
where Y is the predicted response, b
o is the constant coefficient, b
i is the linear coefficient, b
i
j is the interaction coefficient, b
i
i is the quadratic coefficient, and X
i, X
j are the coded values for the factors.


#### 2.4.3. Statistical and Graphical Analysis

Significance of the model equations and their terms were evaluated using statistical tools such as coefficient of determination (R-squared), Fisher value (F-value), probability (P value), and residual [42–44]. Graphs were employed to analyze the combined effect of factors on responses using 3D plots and to also analyze the predicted versus actual value plots of the response variables.


#### 2.4.4. Optimization

Optimization technique was employed to determine the optimum operating conditions for the process variables under consideration. To achieve this, goals were set with constraints. For each of the factors, goal was set “in range” with constraints 300–500, 10–50, and 2–4 of lower-upper level for factorsA, B, and C, respectively. For the response surface, the goal for Y
2 was also set “in range” with constraint 0.18–2.393 as lower-upper levels, while the goal for Y
1 was set “maximize” at 100. Therefore removal efficiency becomes the objective function or performance index.


#### 2.4.5. Model Validation

Model validation was carried out by conducting batch experiment under optimum operating conditions. In order to evaluate the validity of the model, experimental values obtained were compared with the model predicted values.


#### 2.4.6. Software Application

Design Expert Software (version 8) was used for the design of the experiment, regression, statistical analysis, optimization, and graphical analysis.


## 2.1. Production of Activated Carbon

The natural precursor used in the preparation of adsorbent was rice husk which was collected from National Cereal Research Institute, Badeggi. When collected from NCRI Rice Mill, the rice husk was washed with distilled water to remove dirt and surface impurity, then oven-dried at 100°C for 24 h in accordance with the procedure of Kudaybergenov et al. [20]. In the thermal pretreatment, rice husk was placed on a ceramic flat surface, charged into a furnace and heated to a temperature of 300°C at a heating rate of 20–25°C/min and residence time of 1 h. The charred residue was collected and cooled at room temperature. The procedure above was repeated for 400°C and 500°C. The thermal pretreated rice husks were labeled RH300, RH400 and RH500. In the chemical pretreatment, each of the carbonized rice husk (charred residue) was activated with 1 M H3PO4 for 3 h at impregnation ratio of 2 : 1 (volume mL of acid/mass g of rice husk) and later oven-dried overnight at 200°C to ensure proper drying [21, 22]. The material was then removed from the oven, cooled for 2 h and then washed with distilled water to bring the pH to 7.0 and again oven-dried overnight at 100°C [21].


## 2.2. Preliminary Batch Experiment

In the preliminary Batch Adsorption experiment, 2 g of the pretreated adsorbent was added to 100 mL of standard solution of phenol with initial concentration of 10, 30, and 50 mg/L in 250 mL conical flask. The mixture in the flask was placed on magnetic stirrer at 150 rpm [23, 24] for 90 min at ambient temperature. Using a 5 mL syringe, samples were withdrawn at predetermined time interval (90 min) and centrifuged at 3000 rpm for 20 min. The supernatant solution was collected from the centrifuge by decantation and filtered using a micro filter attached to a 5 mL syringe. The procedure above was repeated for 3 and 4 g of pretreated adsorbents. The analysis of phenol in each sample filtrate was carried out using UV spectrophotometer set at wave length of 270 nm.


## 2.3. Determination of Adsorption Capacities and Removal Efficiency

Adsorption capacityq
e at equilibrium was determined using the equation [25, 26]:
(1)
q
e
=
C
o
-
C
t
V
m
.
Adsorption removal efficiency was determined using the equation [27–29]:
(2)
RE
=
C
o
-
C
e
C
o
×
100
,
where q
e = adsorption capacity at equilibrium (mg/g), C
o = initial concentration of solute (mg/L), C
e = equilibrium concentration of solute (mg/L), V = volume of solution (L), m = mass of activated carbon used (g), and RE = removal efficiency (%).


## 2.4. Modeling and Optimization

### 2.4.1. Experimental Design

The Central Composite Design (CCD) was applied in this work to study the interaction of variables involved in the preparation of rice husk activated carbon as well as batch adsorption process of phenol using the activated carbon prepared. The CCD is widely used for modeling and optimization and it requires only a minimum number of experiments. Generally, the CCD consists of three kinds of runs; they are factorial runs (2
n), axial runs (2
n) and center runs (n
c) [30, 31]. This design consist of a 2
n factorial (coded to the usual ±1 notation) augmented by 2
n axial points (
±
α
,
0,0
), (
0
,
±
α
,
0
), (
0,0
,
±
α
), and n
c center points (
0,0
,
0
) [1, 32], where α is the distance of the axial point from the center [33]. The center points are used to determine the experimental error and reproducibility of the data [34, 35] and the axial points are chosen such that they allow rotatability which ensures that the variance of the model prediction is constant at all points equidistant from the design center [36]. Therefore, according to Abbas [37] and Arulkumar et al., [38], the number of experimental runs required is given by the equation:
(3)
N
=
2
n
+
2
n
+
n
c
,
where N = total number of experimental runs, n = number of independent variables (factors), and n
c = number of center points.Three variables were considered in this study, they are (i) pretreatment temperature “A”, a rice husk activated carbon production variable, (ii) initial phenol concentration “B”, a batch adsorption process variable, and (iii) adsorbent dosage “C”, a batch adsorption process variable.For three variables, the number of center run was six, therefore number of experimental run required was computed as:(4)
N
=
2
n
+
2
n
+
n
c
=
2
3
+
2
3
+
6
=
8
+
6
+
6
=
20
.
This implied that 20 experimental runs consisting of 8 factorial runs, 6 axial runs and 6 center runs were required. The two response variables considered in the study were: (i) removal efficiency (Y
1) and (ii) adsorption capacity (Y
2).


### 2.4.2. Regression Model

Each response was used to develop an empirical model that correlate the response to the three factors that is, rice husk activated carbon preparation variable (A) and batch adsorption process variables (B, C), using second-order polynomial equation [39–41]:
(5)
Y
=
b
o
+
∑
i
=
1
n
b
i
X
i
+
∑
i
=
1
n
b
i
i
X
i
2
+
∑
i
=
1
n
-
1
∑
j
=
i
+
1
n
b
i
j
X
i
X
j
,
,
where Y is the predicted response, b
o is the constant coefficient, b
i is the linear coefficient, b
i
j is the interaction coefficient, b
i
i is the quadratic coefficient, and X
i, X
j are the coded values for the factors.


### 2.4.3. Statistical and Graphical Analysis

Significance of the model equations and their terms were evaluated using statistical tools such as coefficient of determination (R-squared), Fisher value (F-value), probability (P value), and residual [42–44]. Graphs were employed to analyze the combined effect of factors on responses using 3D plots and to also analyze the predicted versus actual value plots of the response variables.


### 2.4.4. Optimization

Optimization technique was employed to determine the optimum operating conditions for the process variables under consideration. To achieve this, goals were set with constraints. For each of the factors, goal was set “in range” with constraints 300–500, 10–50, and 2–4 of lower-upper level for factorsA, B, and C, respectively. For the response surface, the goal for Y
2 was also set “in range” with constraint 0.18–2.393 as lower-upper levels, while the goal for Y
1 was set “maximize” at 100. Therefore removal efficiency becomes the objective function or performance index.


### 2.4.5. Model Validation

Model validation was carried out by conducting batch experiment under optimum operating conditions. In order to evaluate the validity of the model, experimental values obtained were compared with the model predicted values.


### 2.4.6. Software Application

Design Expert Software (version 8) was used for the design of the experiment, regression, statistical analysis, optimization, and graphical analysis.


## 2.4.1. Experimental Design

The Central Composite Design (CCD) was applied in this work to study the interaction of variables involved in the preparation of rice husk activated carbon as well as batch adsorption process of phenol using the activated carbon prepared. The CCD is widely used for modeling and optimization and it requires only a minimum number of experiments. Generally, the CCD consists of three kinds of runs; they are factorial runs (2
n), axial runs (2
n) and center runs (n
c) [30, 31]. This design consist of a 2
n factorial (coded to the usual ±1 notation) augmented by 2
n axial points (
±
α
,
0,0
), (
0
,
±
α
,
0
), (
0,0
,
±
α
), and n
c center points (
0,0
,
0
) [1, 32], where α is the distance of the axial point from the center [33]. The center points are used to determine the experimental error and reproducibility of the data [34, 35] and the axial points are chosen such that they allow rotatability which ensures that the variance of the model prediction is constant at all points equidistant from the design center [36]. Therefore, according to Abbas [37] and Arulkumar et al., [38], the number of experimental runs required is given by the equation:
(3)
N
=
2
n
+
2
n
+
n
c
,
where N = total number of experimental runs, n = number of independent variables (factors), and n
c = number of center points.Three variables were considered in this study, they are (i) pretreatment temperature “A”, a rice husk activated carbon production variable, (ii) initial phenol concentration “B”, a batch adsorption process variable, and (iii) adsorbent dosage “C”, a batch adsorption process variable.For three variables, the number of center run was six, therefore number of experimental run required was computed as:(4)
N
=
2
n
+
2
n
+
n
c
=
2
3
+
2
3
+
6
=
8
+
6
+
6
=
20
.
This implied that 20 experimental runs consisting of 8 factorial runs, 6 axial runs and 6 center runs were required. The two response variables considered in the study were: (i) removal efficiency (Y
1) and (ii) adsorption capacity (Y
2).


## 2.4.2. Regression Model

Each response was used to develop an empirical model that correlate the response to the three factors that is, rice husk activated carbon preparation variable (A) and batch adsorption process variables (B, C), using second-order polynomial equation [39–41]:
(5)
Y
=
b
o
+
∑
i
=
1
n
b
i
X
i
+
∑
i
=
1
n
b
i
i
X
i
2
+
∑
i
=
1
n
-
1
∑
j
=
i
+
1
n
b
i
j
X
i
X
j
,
,
where Y is the predicted response, b
o is the constant coefficient, b
i is the linear coefficient, b
i
j is the interaction coefficient, b
i
i is the quadratic coefficient, and X
i, X
j are the coded values for the factors.


## 2.4.3. Statistical and Graphical Analysis

Significance of the model equations and their terms were evaluated using statistical tools such as coefficient of determination (R-squared), Fisher value (F-value), probability (P value), and residual [42–44]. Graphs were employed to analyze the combined effect of factors on responses using 3D plots and to also analyze the predicted versus actual value plots of the response variables.


## 2.4.4. Optimization

Optimization technique was employed to determine the optimum operating conditions for the process variables under consideration. To achieve this, goals were set with constraints. For each of the factors, goal was set “in range” with constraints 300–500, 10–50, and 2–4 of lower-upper level for factorsA, B, and C, respectively. For the response surface, the goal for Y
2 was also set “in range” with constraint 0.18–2.393 as lower-upper levels, while the goal for Y
1 was set “maximize” at 100. Therefore removal efficiency becomes the objective function or performance index.


## 2.4.5. Model Validation

Model validation was carried out by conducting batch experiment under optimum operating conditions. In order to evaluate the validity of the model, experimental values obtained were compared with the model predicted values.


## 2.4.6. Software Application

Design Expert Software (version 8) was used for the design of the experiment, regression, statistical analysis, optimization, and graphical analysis.


## 3. Results and Discussion

### 3.1. Responses Obtained from the Experiment

Table1 shows the design matrix consisting of types of run, coded and actual factors as randomized by the software, and respective response obtained from the experiment. From the results, it could be observed that the highest removal efficiency (Y
1) of 95.72% was obtained and this was followed by the removal efficiency of 94.17%. In terms of adsorption capacity (Y
2), the highest value of 2.39 mg/g was obtained and this was followed by adsorption capacity of 2.21 mg/g. In comparison, recent studies by Kalderis et al., [13], Kermani et al., [45], Mahvi et al., [46], and Daffalla et al., [47] on adsorption of phenol onto rice husk activated carbon shows that adsorption capacities of 27.58 mg/g, 0.886 mg/g, 0.95–1 mg/g, and 0.98–46.19 mg/g were obtained, respectively. The differences in adsorption capacities could be as a result of the influence of the processes employed in the production of the activated carbon which was reported to have significant influence on its performance in adsorption process [48].Table 1
Design matrix for the factors and respective response from experiment.
Run
Type
Coded factors
Uncoded factors
Responses
A (°C)
B (mg/L)
C (g)
A (°C)
B (mg/L)
C (g)
Y
1 (%)
Y
2 (mg/g)
1
Factorial
−1
1
−1
300
50
2
88.32
2.21
2
Factorial
1
1
1
500
50
4
94.70
1.18
3
Factorial
1
1
−1
500
50
2
95.72
2.39
4
Axial
1
0
0
500
30
3
93.86
0.94
5
Center
0
0
0
400
30
3
90.47
0.91
6
Axial
−1
0
0
300
30
3
82.57
0.83
7
Center
0
0
0
400
30
3
90.47
0.91
8
Factorial
−1
1
1
300
50
4
94.17
1.18
9
Axial
0
1
0
400
50
3
93.47
1.56
10
Center
0
0
0
400
30
3
90.47
0.91
11
Axial
0
−1
0
400
10
3
75.79
0.25
12
Axial
0
0
1
400
30
4
93.68
0.70
13
Factorial
−1
−1
−1
300
10
2
56.49
0.28
14
Factorial
1
−1
−1
500
10
2
78.25
0.39
15
Center
0
0
0
400
30
3
90.47
0.91
16
Factorial
−1
−1
1
300
10
4
71.93
0.18
17
Center
0
0
0
400
30
3
90.47
0.91
18
Center
0
0
0
400
30
3
90.47
0.91
19
Axial
0
0
−1
400
30
2
88.42
1.33
20
Factorial
1
−1
1
500
10
4
85.79
0.21


### 3.2. Development of Model Equations

Correlation between the response surface and factors were developed using CCD of the Design Expert software. According to sequential model sum of squares, the models were selected based on the highest order polynomials where the additional terms were significant and the models were not aliased [49, 50]. Correlation coefficient and standard deviation were used to evaluate the fitness of the models developed. The closer the R
2 value is to unity and the smaller the standard deviation, the better the model in predicting the response [51].Table2 shows that the quadratic model has relatively small standard deviation of 0.61 and relatively high R
2 value of 0.9979 with predicted R
2 (0.9960) in reasonable agreement with adjusted R
2 (0.9826). It was also observed on the table that the quadratic model for response Y
1 was not aliased. This implies that the quadratic model can be employed to describe the relationship between response Y
1 and the interacting variables. Table 3 also shows that the quadratic model has relatively small standard deviation of 0.036 and relatively high R
2 value of 0.9981 with predicted R
2 (0.9819) in reasonable agreement with adjusted R
2 (0.9963). It was also observed on the same table that the quadratic model for response Y
2 was not aliased. This implies that the quadratic model can be employed to describe the relationship between response Y
2 and the interacting variables.Table 2
Regression statistics for removal efficiency (model for responseY
1).
Source
Standard deviation
R
2
AdjustedR
2
PredictedR
2
Comment
Linear
5.02
0.7729
0.7303
0.5487
2FI
4.29
0.8653
0.8031
0.1189
Quadratic
0.61
0.9979
0.9960
0.9826
Suggested
Cubic
0.056
1.0000
1.0000
0.9871
AliasedTable 3
Regression statistics for adsorption capacity (model for responseY
2).
Source
Standard Deviation
R
2
AdjustedR
2
PredictedR
2
Comment
Linear
0.19
0.9173
0.9018
0.8114
2FI
0.073
0.9897
0.9850
0.9442
Quadratic
0.036
0.9981
0.9963
0.9819
Suggested
Cubic
3.00
E
-
03
1.0000
1.0000
0.9902
AliasedTheR
2 values of 0.9979 and 0.9981 implied that 99.79% and 99.81% of the variation in removal efficiency and adsorption capacity respectively can be attributed to the three factors (A-pretreatment temperature; B-initial phenol concentration; C-adsorbent dosage) considered. Therefore, the quadratic models were selected as suggested by the software and the response surface model equations in their actual values are
(6)
Y
1
=
-
0.000217641
A
2
-
0.014404
B
2
+
0.65959
C
2
-
0.00173025
A
B
-
0.018465
A
C
-
0.1137
B
C
+
0.33625
A
+
2.38714
B
+
10.1384
C
-
51.11583
,
Y
2
=
-
0.00000184545
A
2
+
0.0000113636
B
2
+
0.11355
C
2
+
0.0000030625
A
B
-
0.00031625
A
C
-
0.012256
B
C
+
0.00278124
A
+
0.070862
B
-
0.50129
C
-
0.12217
.


### 3.3. Statistical Analysis

The model equations selected were further evaluated using ANOVA component of the software. Table4 shows that response surface quadratic model for removal efficiency has F-value of 529.68 indicating that the model is significant. For the model terms, P value less than 0.05 implies that model term is significant [52–55] and largest F-value signifies the model term having the most significant effect on the response [50, 56]. In this case, the significant model terms are A, B, C, A
B, A
C, B
C, A
2, and B
2 while C
2 is the insignificant model term. The model term having the most significant effect on the response is B with F-value of 2589.51 and the effect is in the order B
>
A
>
C
>
A
B
>
B
2
>
B
C
>
A
C
>
A
2. Table 5 shows that response surface quadratic model for adsorption capacity has F-value of 570.02 indicating that the model is significant. In this case, the significant model terms are A, B, C, A
C, B
C, and C
2 while A
B, A
2, and B
2 are insignificant model terms. The model term having the most significant effect on the response is B with F-value of 3947.85 and the effect is in the order B
>
C
>
B
C
>
C
2
>
A
>
A
C.Table 4
ANOVA table for removal efficiency (model for responseY
1).
Source
Sum of squares
df
Mean square
F-value
P value
Comment
Model
1773.14
9
197.02
529.63
<0.0001
Significant
A
300.64
1
300.64
808.29
<0.0001
Significant
B
963.17
1
963.17
2589.51
<0.0001
Significant
C
109.47
1
109.47
294.33
<0.0001
Significant
A
B
95.8
1
95.8
257.56
<0.0001
Significant
A
C
27.28
1
27.28
73.33
<0.0001
Significant
B
C
41.13
1
41.13
110.59
<0.0001
Significant
A
2
13.07
1
13.07
35.02
0.0001
Significant
B
2
91.28
1
91.28
245.42
<0.0001
Significant
C
2
1.2
1
1.2
3.22
0.1031
Residual
3.72
10
0.37Table 5
ANOVA table for adsorption capacity (model for responseY
2).
Source
Sum of squares ×10−2
df
Mean square ×10−2
F-value
P value
Comment
Model
674
9
75
570.02
<0.0001
Significant
A
2
1
2
15.28
0.0029
Significant
B
518
1
518
3947.56
<0.0001
Significant
C
99
1
99
751.81
<0.0001
Significant
A
B
0.03
1
0.03
0.23
0.6429
A
C
0.8
1
0.8
6.09
0.0332
Significant
B
C
48
1
48
366.07
<0.0001
Significant
A
2
0.094
1
0.094
0.71
0.4181
B
2
0.0057
1
0.0057
0.043
0.8394
C
2
3.5
1
3.5
27
0.0004
Significant
Residual
1.3
10
0.13Therefore, removing the insignificant model terms, the quadratic models for the responses become:(7)
Y
1
=
-
0.000217641
A
2
-
0.014404
B
2
-
0.00173025
A
B
-
0.018465
A
C
-
0.1137
B
C
+
0.33625
A
+
2.38714
B
+
10.1384
C
-
51.11583
,
Y
2
=
0.11355
C
2
-
0.00031625
A
C
-
0.012256
B
C
+
0.00278124
A
+
0.070862
B
-
0.50129
C
-
0.12217
.
The residual of the response surface models presented in Tables 5 and 6 shows that the highest-lowest error (residual) for response Y
1 is 1.02–0.03% and that of Y
2 is 0.07–0.00027 mg/g. This also signifies the quality of the models in terms of predicting the responses.Table 6
Actual-predicted values and residual.
Run
ResponseY
1 (%)
ResponseY
2 (mg/g)
Actual
Predicted
Residual
Actual
Predicted
Residual
1
88.32
88.06
0.25
2.21
2.20
0.0082
2
94.70
94.19
0.51
1.18
1.18
0.001
3
95.72
95.8
0.083
2.39
2.36
0.028
4
93.86
93.74
0.12
0.94
0.93
0.0093
5
90.47
90.44
0.03
0.91
0.90
0.0016
6
82.57
82.78
0.21
0.83
0.84
0.014
7
90.47
90.44
0.03
0.91
0.90
0.0016
8
94.17
93.84
0.34
1.18
1.14
0.033
9
93.47
94.49
1.02
1.56
1.63
0.07
10
90.47
90.44
0.03
0.91
0.90
0.0016
11
75.79
74.86
0.93
0.25
0.19
0.065
12
93.68
94.41
0.72
0.70
0.70
0.00027
13
56.49
56.98
0.49
0.28
0.28
0.00021
14
78.25
78.56
0.31
0.39
0.42
0.31
15
90.47
90.44
0.03
0.91
0.90
0.0016
16
71.93
71.82
0.11
0.18
0.21
0.027
17
90.47
90.44
0.03
0.91
0.90
0.0016
18
90.47
90.44
0.03
0.91
0.90
0.0016
19
88.42
87.79
0.63
1.33
1.33
0.0051
20
85.79
86.02
0.23
0.21
0.22
0.0069The plots of actual versus predicted values of responseY
1 and Y
2 in Figures 1 and 2, respectively, show very minimal divergence of points from the diagonal indicating that these response surface model equations can be used to adequately represent the interaction of the three factors.Figure 1
Actual-predicted plot for responseY
1.Figure 2
Actual-predicted plot for responseY
2.


### 3.4. Combined Effect of Factors on Response

#### 3.4.1. Combined Effect of Temperature and Initial Concentration at Constant Adsorbent Dosage

Figure3 shows the combined effect of temperature and initial concentration on removal efficiency. It was observed that the two factors have significant combined effect on removal efficiency and increase in any of the factors reasonably increases the removal efficiency. The combined effect was observed to be greater at higher values of the two factors. The combined effect of temperature and initial concentration on adsorption capacity is as shown in Figure 4. The figure shows that the combined effect is almost completely as a result of the singular effect of initial concentration with temperature having very small effect. It was also observed that adsorption capacity is significantly increased with increase in initial concentration whereas increase in temperature results in relatively very small increase in adsorption capacity.Figure 3
Combined effect of factorsA-B on response Y
1.Figure 4
Combined effect of factorsA-B on response Y
2.


#### 3.4.2. Combined Effect of Temperature and Adsorbent Dosage at Constant Initial Concentration

Figure5 shows that temperature and adsorbent dosage have relatively small combined effect on removal efficiency. It was observed that the effect of temperature is relatively higher than that of adsorbent dosage and increase in any of the two factors increases the removal efficiency. Figure 6 shows the combined effect of temperature and adsorbent dosage on adsorption capacity. It was observed that adsorbent dosage greatly controls the combined effect of the two factors with temperature having very little effect. It was also observed that increasing the adsorbent dosage decreases the adsorption capacity.Figure 5
Combined effect of factorsA-C on response Y
1.Figure 6
Combined effect of factorsA-C on response Y
2.


#### 3.4.3. Combined Effect of Initial Concentration and Adsorbent Dosage at Constant Temperature

Figure7 shows that initial concentration and adsorbent dosage have significant combined effect on removal efficiency with initial concentration exhibiting the greatest effect though adsorbent dosage shows reasonable effect too. The combined effect was observed to be greater at higher values of the two factors. It was also observed that increasing any of the factors increases the removal efficiency. Figure 8 shows that the two factors have significant combined effect on adsorption capacity. It was observed that, at higher initial concentration, increase in adsorbent dosage greatly decreases the adsorption capacity than at lower initial concentrations. Increase in initial concentration was also observed to increase the adsorption capacity but with much effect at lower adsorbent dosage.Figure 7
Combined effect of factorsB-C on response Y
1.Figure 8
Combined effect of factorsB-C on response Y
2.


### 3.5. Optimization

Optimization of the two responses under the same condition is difficult because the interest regions of factors are different. WhenY
1 increases, Y
2 decreases and vice versa. Therefore the function of desirability was applied and the operating condition with the highest desirability was considered as selected by the software. Hence, the optimum operating conditions for the production of rice husk activated carbon and batch adsorption of phenol using the rice husk activated carbon are as follows.Factors
A-temperature of pretreatment = 441.46°C,
B-initial phenol concentration = 40.61 mg/L,
C-activated carbon dosage = 4 g.Response
Y
1-removal efficiency = 97.1608%,
Y
2-adsorption capacity = 0.9595 mg/g.


### 3.6. Model Validation

Table7 compares the results of experimental values with predicted values under optimum operating condition. It can be seen from the table that the percentage error of experimental against predicted value for adsorption capacity and removal efficiency are 1% and 1.777%, respectively. Therefore, this shows that the models and optimum operating condition developed for the factors are valid and applicable in predicting the response variables.Table 7
Model validation.
Tp  (°C)
m (g)
C
o (mg/L)
Experimental
Theoretical
Percentage error
q
e (mg/g)
RE (%)
q
e (mg/g)
RE (%)
q
e
RE
441.46
4
40.61
0.969
95.464
0.960
97.160
1.000
1.777


## 3.1. Responses Obtained from the Experiment

Table1 shows the design matrix consisting of types of run, coded and actual factors as randomized by the software, and respective response obtained from the experiment. From the results, it could be observed that the highest removal efficiency (Y
1) of 95.72% was obtained and this was followed by the removal efficiency of 94.17%. In terms of adsorption capacity (Y
2), the highest value of 2.39 mg/g was obtained and this was followed by adsorption capacity of 2.21 mg/g. In comparison, recent studies by Kalderis et al., [13], Kermani et al., [45], Mahvi et al., [46], and Daffalla et al., [47] on adsorption of phenol onto rice husk activated carbon shows that adsorption capacities of 27.58 mg/g, 0.886 mg/g, 0.95–1 mg/g, and 0.98–46.19 mg/g were obtained, respectively. The differences in adsorption capacities could be as a result of the influence of the processes employed in the production of the activated carbon which was reported to have significant influence on its performance in adsorption process [48].Table 1
Design matrix for the factors and respective response from experiment.
Run
Type
Coded factors
Uncoded factors
Responses
A (°C)
B (mg/L)
C (g)
A (°C)
B (mg/L)
C (g)
Y
1 (%)
Y
2 (mg/g)
1
Factorial
−1
1
−1
300
50
2
88.32
2.21
2
Factorial
1
1
1
500
50
4
94.70
1.18
3
Factorial
1
1
−1
500
50
2
95.72
2.39
4
Axial
1
0
0
500
30
3
93.86
0.94
5
Center
0
0
0
400
30
3
90.47
0.91
6
Axial
−1
0
0
300
30
3
82.57
0.83
7
Center
0
0
0
400
30
3
90.47
0.91
8
Factorial
−1
1
1
300
50
4
94.17
1.18
9
Axial
0
1
0
400
50
3
93.47
1.56
10
Center
0
0
0
400
30
3
90.47
0.91
11
Axial
0
−1
0
400
10
3
75.79
0.25
12
Axial
0
0
1
400
30
4
93.68
0.70
13
Factorial
−1
−1
−1
300
10
2
56.49
0.28
14
Factorial
1
−1
−1
500
10
2
78.25
0.39
15
Center
0
0
0
400
30
3
90.47
0.91
16
Factorial
−1
−1
1
300
10
4
71.93
0.18
17
Center
0
0
0
400
30
3
90.47
0.91
18
Center
0
0
0
400
30
3
90.47
0.91
19
Axial
0
0
−1
400
30
2
88.42
1.33
20
Factorial
1
−1
1
500
10
4
85.79
0.21


## 3.2. Development of Model Equations

Correlation between the response surface and factors were developed using CCD of the Design Expert software. According to sequential model sum of squares, the models were selected based on the highest order polynomials where the additional terms were significant and the models were not aliased [49, 50]. Correlation coefficient and standard deviation were used to evaluate the fitness of the models developed. The closer the R
2 value is to unity and the smaller the standard deviation, the better the model in predicting the response [51].Table2 shows that the quadratic model has relatively small standard deviation of 0.61 and relatively high R
2 value of 0.9979 with predicted R
2 (0.9960) in reasonable agreement with adjusted R
2 (0.9826). It was also observed on the table that the quadratic model for response Y
1 was not aliased. This implies that the quadratic model can be employed to describe the relationship between response Y
1 and the interacting variables. Table 3 also shows that the quadratic model has relatively small standard deviation of 0.036 and relatively high R
2 value of 0.9981 with predicted R
2 (0.9819) in reasonable agreement with adjusted R
2 (0.9963). It was also observed on the same table that the quadratic model for response Y
2 was not aliased. This implies that the quadratic model can be employed to describe the relationship between response Y
2 and the interacting variables.Table 2
Regression statistics for removal efficiency (model for responseY
1).
Source
Standard deviation
R
2
AdjustedR
2
PredictedR
2
Comment
Linear
5.02
0.7729
0.7303
0.5487
2FI
4.29
0.8653
0.8031
0.1189
Quadratic
0.61
0.9979
0.9960
0.9826
Suggested
Cubic
0.056
1.0000
1.0000
0.9871
AliasedTable 3
Regression statistics for adsorption capacity (model for responseY
2).
Source
Standard Deviation
R
2
AdjustedR
2
PredictedR
2
Comment
Linear
0.19
0.9173
0.9018
0.8114
2FI
0.073
0.9897
0.9850
0.9442
Quadratic
0.036
0.9981
0.9963
0.9819
Suggested
Cubic
3.00
E
-
03
1.0000
1.0000
0.9902
AliasedTheR
2 values of 0.9979 and 0.9981 implied that 99.79% and 99.81% of the variation in removal efficiency and adsorption capacity respectively can be attributed to the three factors (A-pretreatment temperature; B-initial phenol concentration; C-adsorbent dosage) considered. Therefore, the quadratic models were selected as suggested by the software and the response surface model equations in their actual values are
(6)
Y
1
=
-
0.000217641
A
2
-
0.014404
B
2
+
0.65959
C
2
-
0.00173025
A
B
-
0.018465
A
C
-
0.1137
B
C
+
0.33625
A
+
2.38714
B
+
10.1384
C
-
51.11583
,
Y
2
=
-
0.00000184545
A
2
+
0.0000113636
B
2
+
0.11355
C
2
+
0.0000030625
A
B
-
0.00031625
A
C
-
0.012256
B
C
+
0.00278124
A
+
0.070862
B
-
0.50129
C
-
0.12217
.


## 3.3. Statistical Analysis

The model equations selected were further evaluated using ANOVA component of the software. Table4 shows that response surface quadratic model for removal efficiency has F-value of 529.68 indicating that the model is significant. For the model terms, P value less than 0.05 implies that model term is significant [52–55] and largest F-value signifies the model term having the most significant effect on the response [50, 56]. In this case, the significant model terms are A, B, C, A
B, A
C, B
C, A
2, and B
2 while C
2 is the insignificant model term. The model term having the most significant effect on the response is B with F-value of 2589.51 and the effect is in the order B
>
A
>
C
>
A
B
>
B
2
>
B
C
>
A
C
>
A
2. Table 5 shows that response surface quadratic model for adsorption capacity has F-value of 570.02 indicating that the model is significant. In this case, the significant model terms are A, B, C, A
C, B
C, and C
2 while A
B, A
2, and B
2 are insignificant model terms. The model term having the most significant effect on the response is B with F-value of 3947.85 and the effect is in the order B
>
C
>
B
C
>
C
2
>
A
>
A
C.Table 4
ANOVA table for removal efficiency (model for responseY
1).
Source
Sum of squares
df
Mean square
F-value
P value
Comment
Model
1773.14
9
197.02
529.63
<0.0001
Significant
A
300.64
1
300.64
808.29
<0.0001
Significant
B
963.17
1
963.17
2589.51
<0.0001
Significant
C
109.47
1
109.47
294.33
<0.0001
Significant
A
B
95.8
1
95.8
257.56
<0.0001
Significant
A
C
27.28
1
27.28
73.33
<0.0001
Significant
B
C
41.13
1
41.13
110.59
<0.0001
Significant
A
2
13.07
1
13.07
35.02
0.0001
Significant
B
2
91.28
1
91.28
245.42
<0.0001
Significant
C
2
1.2
1
1.2
3.22
0.1031
Residual
3.72
10
0.37Table 5
ANOVA table for adsorption capacity (model for responseY
2).
Source
Sum of squares ×10−2
df
Mean square ×10−2
F-value
P value
Comment
Model
674
9
75
570.02
<0.0001
Significant
A
2
1
2
15.28
0.0029
Significant
B
518
1
518
3947.56
<0.0001
Significant
C
99
1
99
751.81
<0.0001
Significant
A
B
0.03
1
0.03
0.23
0.6429
A
C
0.8
1
0.8
6.09
0.0332
Significant
B
C
48
1
48
366.07
<0.0001
Significant
A
2
0.094
1
0.094
0.71
0.4181
B
2
0.0057
1
0.0057
0.043
0.8394
C
2
3.5
1
3.5
27
0.0004
Significant
Residual
1.3
10
0.13Therefore, removing the insignificant model terms, the quadratic models for the responses become:(7)
Y
1
=
-
0.000217641
A
2
-
0.014404
B
2
-
0.00173025
A
B
-
0.018465
A
C
-
0.1137
B
C
+
0.33625
A
+
2.38714
B
+
10.1384
C
-
51.11583
,
Y
2
=
0.11355
C
2
-
0.00031625
A
C
-
0.012256
B
C
+
0.00278124
A
+
0.070862
B
-
0.50129
C
-
0.12217
.
The residual of the response surface models presented in Tables 5 and 6 shows that the highest-lowest error (residual) for response Y
1 is 1.02–0.03% and that of Y
2 is 0.07–0.00027 mg/g. This also signifies the quality of the models in terms of predicting the responses.Table 6
Actual-predicted values and residual.
Run
ResponseY
1 (%)
ResponseY
2 (mg/g)
Actual
Predicted
Residual
Actual
Predicted
Residual
1
88.32
88.06
0.25
2.21
2.20
0.0082
2
94.70
94.19
0.51
1.18
1.18
0.001
3
95.72
95.8
0.083
2.39
2.36
0.028
4
93.86
93.74
0.12
0.94
0.93
0.0093
5
90.47
90.44
0.03
0.91
0.90
0.0016
6
82.57
82.78
0.21
0.83
0.84
0.014
7
90.47
90.44
0.03
0.91
0.90
0.0016
8
94.17
93.84
0.34
1.18
1.14
0.033
9
93.47
94.49
1.02
1.56
1.63
0.07
10
90.47
90.44
0.03
0.91
0.90
0.0016
11
75.79
74.86
0.93
0.25
0.19
0.065
12
93.68
94.41
0.72
0.70
0.70
0.00027
13
56.49
56.98
0.49
0.28
0.28
0.00021
14
78.25
78.56
0.31
0.39
0.42
0.31
15
90.47
90.44
0.03
0.91
0.90
0.0016
16
71.93
71.82
0.11
0.18
0.21
0.027
17
90.47
90.44
0.03
0.91
0.90
0.0016
18
90.47
90.44
0.03
0.91
0.90
0.0016
19
88.42
87.79
0.63
1.33
1.33
0.0051
20
85.79
86.02
0.23
0.21
0.22
0.0069The plots of actual versus predicted values of responseY
1 and Y
2 in Figures 1 and 2, respectively, show very minimal divergence of points from the diagonal indicating that these response surface model equations can be used to adequately represent the interaction of the three factors.Figure 1
Actual-predicted plot for responseY
1.Figure 2
Actual-predicted plot for responseY
2.


## 3.4. Combined Effect of Factors on Response

### 3.4.1. Combined Effect of Temperature and Initial Concentration at Constant Adsorbent Dosage

Figure3 shows the combined effect of temperature and initial concentration on removal efficiency. It was observed that the two factors have significant combined effect on removal efficiency and increase in any of the factors reasonably increases the removal efficiency. The combined effect was observed to be greater at higher values of the two factors. The combined effect of temperature and initial concentration on adsorption capacity is as shown in Figure 4. The figure shows that the combined effect is almost completely as a result of the singular effect of initial concentration with temperature having very small effect. It was also observed that adsorption capacity is significantly increased with increase in initial concentration whereas increase in temperature results in relatively very small increase in adsorption capacity.Figure 3
Combined effect of factorsA-B on response Y
1.Figure 4
Combined effect of factorsA-B on response Y
2.


### 3.4.2. Combined Effect of Temperature and Adsorbent Dosage at Constant Initial Concentration

Figure5 shows that temperature and adsorbent dosage have relatively small combined effect on removal efficiency. It was observed that the effect of temperature is relatively higher than that of adsorbent dosage and increase in any of the two factors increases the removal efficiency. Figure 6 shows the combined effect of temperature and adsorbent dosage on adsorption capacity. It was observed that adsorbent dosage greatly controls the combined effect of the two factors with temperature having very little effect. It was also observed that increasing the adsorbent dosage decreases the adsorption capacity.Figure 5
Combined effect of factorsA-C on response Y
1.Figure 6
Combined effect of factorsA-C on response Y
2.


### 3.4.3. Combined Effect of Initial Concentration and Adsorbent Dosage at Constant Temperature

Figure7 shows that initial concentration and adsorbent dosage have significant combined effect on removal efficiency with initial concentration exhibiting the greatest effect though adsorbent dosage shows reasonable effect too. The combined effect was observed to be greater at higher values of the two factors. It was also observed that increasing any of the factors increases the removal efficiency. Figure 8 shows that the two factors have significant combined effect on adsorption capacity. It was observed that, at higher initial concentration, increase in adsorbent dosage greatly decreases the adsorption capacity than at lower initial concentrations. Increase in initial concentration was also observed to increase the adsorption capacity but with much effect at lower adsorbent dosage.Figure 7
Combined effect of factorsB-C on response Y
1.Figure 8
Combined effect of factorsB-C on response Y
2.


## 3.4.1. Combined Effect of Temperature and Initial Concentration at Constant Adsorbent Dosage

Figure3 shows the combined effect of temperature and initial concentration on removal efficiency. It was observed that the two factors have significant combined effect on removal efficiency and increase in any of the factors reasonably increases the removal efficiency. The combined effect was observed to be greater at higher values of the two factors. The combined effect of temperature and initial concentration on adsorption capacity is as shown in Figure 4. The figure shows that the combined effect is almost completely as a result of the singular effect of initial concentration with temperature having very small effect. It was also observed that adsorption capacity is significantly increased with increase in initial concentration whereas increase in temperature results in relatively very small increase in adsorption capacity.Figure 3
Combined effect of factorsA-B on response Y
1.Figure 4
Combined effect of factorsA-B on response Y
2.


## 3.4.2. Combined Effect of Temperature and Adsorbent Dosage at Constant Initial Concentration

Figure5 shows that temperature and adsorbent dosage have relatively small combined effect on removal efficiency. It was observed that the effect of temperature is relatively higher than that of adsorbent dosage and increase in any of the two factors increases the removal efficiency. Figure 6 shows the combined effect of temperature and adsorbent dosage on adsorption capacity. It was observed that adsorbent dosage greatly controls the combined effect of the two factors with temperature having very little effect. It was also observed that increasing the adsorbent dosage decreases the adsorption capacity.Figure 5
Combined effect of factorsA-C on response Y
1.Figure 6
Combined effect of factorsA-C on response Y
2.


## 3.4.3. Combined Effect of Initial Concentration and Adsorbent Dosage at Constant Temperature

Figure7 shows that initial concentration and adsorbent dosage have significant combined effect on removal efficiency with initial concentration exhibiting the greatest effect though adsorbent dosage shows reasonable effect too. The combined effect was observed to be greater at higher values of the two factors. It was also observed that increasing any of the factors increases the removal efficiency. Figure 8 shows that the two factors have significant combined effect on adsorption capacity. It was observed that, at higher initial concentration, increase in adsorbent dosage greatly decreases the adsorption capacity than at lower initial concentrations. Increase in initial concentration was also observed to increase the adsorption capacity but with much effect at lower adsorbent dosage.Figure 7
Combined effect of factorsB-C on response Y
1.Figure 8
Combined effect of factorsB-C on response Y
2.


## 3.5. Optimization

Optimization of the two responses under the same condition is difficult because the interest regions of factors are different. WhenY
1 increases, Y
2 decreases and vice versa. Therefore the function of desirability was applied and the operating condition with the highest desirability was considered as selected by the software. Hence, the optimum operating conditions for the production of rice husk activated carbon and batch adsorption of phenol using the rice husk activated carbon are as follows.Factors
A-temperature of pretreatment = 441.46°C,
B-initial phenol concentration = 40.61 mg/L,
C-activated carbon dosage = 4 g.Response
Y
1-removal efficiency = 97.1608%,
Y
2-adsorption capacity = 0.9595 mg/g.


## 3.6. Model Validation

Table7 compares the results of experimental values with predicted values under optimum operating condition. It can be seen from the table that the percentage error of experimental against predicted value for adsorption capacity and removal efficiency are 1% and 1.777%, respectively. Therefore, this shows that the models and optimum operating condition developed for the factors are valid and applicable in predicting the response variables.Table 7
Model validation.
Tp  (°C)
m (g)
C
o (mg/L)
Experimental
Theoretical
Percentage error
q
e (mg/g)
RE (%)
q
e (mg/g)
RE (%)
q
e
RE
441.46
4
40.61
0.969
95.464
0.960
97.160
1.000
1.777


## 4. Conclusions

The quadratic models developed haveR
2 values of 0.9979 and 0.9981 for removal efficiency and adsorption capacity, respectively. Therefore, 99.79% and 99.81% of the variations in removal efficiency and adsorption capacity, respectively, are attributed to the three process variables considered and the models can be used to predict the interaction of the process variables. Modeling revealed that, aside singular effect, interaction of factors also significantly affects the adsorption capacity and removal efficiency. The single effect of the three process variables on adsorption capacity is in the order: initial solute concentration > adsorbent dosage > pretreatment temperature, while that of removal efficiency is in the order: initial solute concentration > pretreatment temperature > adsorbent dosage. Optimization revealed that the optimum operating condition for the adsorption process is initial solute concentration 40.61 mg/L; pretreatment temperature 441.46°C; adsorbent dosage 4 g; adsorption capacity 0.9595 mg/g; removal efficiency 97.16%.



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*Source: 278075-2014-12-24.xml*