Publisher: Taylor & Francis Journal: Environmental Technology DOI: 10.1080/09593330.2014.994041
t
Degradation of antidepressant drug Fluoxetine in aqueous media by
rip
ozone/H2O2 system: Process optimization using central composite
us c
design
Abbas Aghaeinejad-Meybodi1, Amanollah Ebadi1 *, Sirous Shafiei1,
1
M
an
Alireza Khataee2, Mohammad Rostampour1
Environmental Engineering Research Centre, Department of Chemical Engineering,
2
ed
Sahand University of Technology, Tabriz, Iran.
Research Laboratory of Advanced Water and Wastewater Treatment Processes,
*
ce
Iran.
pt
Department of Applied Chemistry, Faculty of Chemistry, University of Tabriz, Tabriz,
Corresponding author: assistant prof. of Chemical Engineering,
Ac
Email: [email protected], Tel: (+98) 41 33459140 , Fax: (+98) 41 33224950
Abbas Agaheinejad-Meybodi: PhD student of chemical engineering, Email: [email protected] Sirous Shafiei: Associate Prof. of chemical engineering, Email: [email protected] Alireza Khataee: Associate Prof. of applied chemistry, Email: [email protected]
1
Mohammad Rostampour: MSc. Student of Chemical Engineering, Email:
Ac
ce
pt
ed
M
an
us c
rip
t
[email protected]
2
Degradation of antidepressant drug Fluoxetine in aqueous media by ozone/H2O2 system: Process optimization using central composite design
rip
t
Abstract
The main objective of this work is the modelling and optimization of
antidepressant drug Fluoxetine degradation in aqueous solution by ozone/H2O2
us c
process using central composite design (CCD). The operational parameters were
ozone concentration, initial hydrogen peroxide concentration, reaction time and initial Fluoxetine concentration. A good agreement between the predicted values of Fluoxetine removal and experimental results were observed (R2=0.976 and
an
Adj-R2= 0.955). Pareto analysis indicated that all selected factors and some interactions were effective on the removal efficiency. It was found that the
M
reaction time is the most effective parameter in the ozone/H2O2 process. The maximum removal efficiency (86.14 %) was achieved at ozone concentration of 30 mg L-1, initial H2O2 concentration of 0.02 mM, reaction time of 20 min and
ed
initial Fluoxetine concentration of 50 mg L-1 as the optimum conditions. Keywords: Fluoxetine; Pharmaceutical wastewater; Central composite design;
ce
pt
Ozonation, Response surface methodology.
Ac
Introduction
Currently, there are great scientific and public attention on pharmaceuticals as
environmental pollutants [1]. In recent years, pharmaceuticals have been identified in aqueous solutions because ordinary water and wastewater treatment is not completely effective for removing many drugs [2, 3]. Generally, pharmaceuticals are highly resistant to biodegradation and usually remain intact after water and wastewater treatment plants (WWTPs). For this reason, their existence in aqueous systems and in 3
the environment is a serious problem [3, 4]. Pharmaceutical waste may have hazardous and toxicity complications on humans and living micro-organisms [5]. Therefore, appropriate methods should be adapted to impede the spread of pharmaceutical waste in the environment after the secondary treatment [6, 7]. In the past decade, Fluoxetine has been proposed as one of the most widely used
t
antidepressants and has attracted a lot of attention. [8]. Fluoxetine and its principal
rip
metabolite Norfluoxetine have been detected in surface waters due to imperfect
us c
destruction after therapeutic use [9].
Concentrations of Fluoxetine in wastewater effluents have been identified in the range of 30-82 ng L-1 [10] and in surface water as high as 12 ng L-1 in the USA [11] and
an
as high as 99 ng L-1 in Canada [12]. Some studies have suggested a range of potential aquatic ecosystem effects of this antidepressant drug in the environment.
M
A scientific report shows that prescription of Fluoxetine has ultimately led to some unexpected environmental consequences through discharge of the drug (e.g. the
ed
fraction of Fluoxetine non-metabolized by the liver) in various ecosystems [13].
pt
Fluoxetine and Norfluoxetine have been detected in fish samples obtained from an effluent-dominated stream, this information being an indicator of their bioaccumulation
ce
potential [14]. Fluoxetine induce spawning in some crustaceans and bivalves [15]. In a
Ac
research work, Brooks et al. [16] evaluated the environmental hazard of fluoxetine to select benthic and pelagic toxicity test organisms. This study provided novel waterborne fluoxetine toxicity data for Pseudokirchneriella subcapitata, Ceriodaphnia dubia, Daphnia magna, Pimephales promelas and Oryias latipes, and sediment toxicity information for Hyalella Azteca and Chironomus tentans. US EPA’s ECOSAR (ecological structure– activity relationship (SAR)) was used to predict the toxicity of antidepressant pharmaceuticals to algae and they were ranked in the top 10 most toxic
4
of 49 pharmaceutical classes warranting further toxicity testing of algae with selective serotonin reuptake inhibitors (SSRIs) [17]. Johnson et al. [18] investigated the toxicity of SSRIs (Fluoxetine, Sertraline, and Fluvoxamine) to algae/phytoplankton using the US EPA ECOSAR, acute single-species growth inhibition assays, species sensitivity distributions (SSDs), and an outdoor microcosm mixture experiment. Because many
t
pharmaceuticals and personal care products have been detected in aqueous
rip
environmental compartments, understanding their fate under natural water conditions is
us c
important.
Kwon and Armbrust indicated that the Fluoxetine has low biological degradability in WWTPs. Their experimental studies also described that Fluoxetine is
an
partly resistant to the hydrolysis and photolysis and rebellious versus microbial decomposition [19].
M
Among all of the studied methods, advanced oxidation processes (AOPs) have been used successfully to eliminate a wide variety of pollutants including
ed
pharmaceuticals in water and wastewater treatment [20, 21]. In AOPs, hydroxyl free
pt
radicals (HO• ) and other powerful oxidants are formed that are capable of removing contaminants with high chemical stability or resistant to mineralization [22, 23].
ce
Among the different oxidants, hydroxyl radicals (HO• ) are powerful oxidants
Ac
that can increase the rate of pollutants degradation significantly [24]. UV/H2O2, UV/O3, O3/H2O2, UV/ O3/H2O2, Fenton and photo-Fenton, catalytic ozonation and
photocatalytic processes such as UV/TiO2 are the most commonly used AOPs for treatment of wastewaters [25-42]. In ozone based AOP such as O3/H2O2 process, micropollutants can be oxidized by both molecular ozone (directly) and •OH radicals (indirectly). The •OH radicals are extremely powerful oxidants whose reaction rate constants with organic molecules are generally in
5
the range 108 to 1010 M-1.s-l. This means that AOP treatment of typical organic substrates will be practical, even if the steady-state concentration of •OH is only between 10-10 to 10-12 M [43]. Dissolved organic matters might act as radical scavengers, which would significantly decrease the efficiency of ozone treatment on target compounds [44].
t
Considering the investment and operation costs, ozonation still is not a cheap
rip
technology. Although safe operation is no longer a problem, ozonation systems require
us c
considerable safety precautions, thus increasing the investment costs [45].
The number of studies conducted for Fluoxetine degradation using AOPs is very limited. Mendez-Arriaga et al. [9] reported the Fluoxetine photooxidation by catalytic-ozonation
processes
in
aquatic
solution.
an
combined
Degradation
of
contaminants mixture containing Fluoxetine with membrane reactor was investigated by
M
Benotti et al.[46].
In order to develop a cost effective and to enhance the removal efficiency,
ed
especially for practical applications, experimental conditions and concentration of
pt
components must be optimized [2]. The study of the effect of variables on the response with using classical optimization methods, changing one factor at a time, is expensive
ce
and time-consuming and require a lot of experiments, as well as the interaction between
Ac
variables on the response cannot be determined [26, 36]. For this purpose, to minimize the number of experiments and optimization of the effective parameters, an alternative approach can be used as central composite design (CCD) based on response surface methods (RSM) [25-27, 34-36, 47-50]. The main objective of RSM is to obtain an optimal response using designed experiments [36]. In RSM by using an appropriate experimental design, the number of required experiments will be reduced. Furthermore,
6
the modeling of system facilitates interpreting of multivariate phenomena and provides the possibility of process scaling [49]. There were no reported activities in literature about optimization of AOPs using CCD based on RSM for elimination of Fluoxetine in aquatic solutions. Therefore, the main objective of our research is to treat pharmaceutical wastewater containing
t
Fluoxetine by Ozone/H2O2 process. Finally, the RSM method with CCD is used to
rip
predict the optimum experimental conditions for Fluoxetine degradation in aqueous
us c
media.
Experimental
an
Chemicals and procedures
Fluoxetine hydrochloride (C17H18F3NO. HCl) typically marketed under the trade
M
name Prozac, is one of the most frequently used antidepressant pharmaceuticals. In Table 1, the characteristics and structure of Fluoxetine are provided. Fluoxetine and
ed
hydrogen peroxide (35%) were purchased from Arya pharmaceutical company (Iran)
pt
and Merck (Germany), respectively.
Table 1
ce
Ozonation experiments were performed in a semi-continuous reactor. In Figure
Ac
1, schematics of the experimental setup is shown. In all experiments, initially the reactor is filled with 250 mL pharmaceutical solution with desired concentration of Fluoxetine and H2O2 and then a gasous ozone stream, produced by an ozone generator (ozomatic, model Lab 802, Germany) using pure O2 as the feed gas, is continuously injected into reactor using a sinter glass sparger. Also, the reaction mixture is stirred completely using a magnetic stirrer during the reaction time. The residual ozone in the output gas stream from reactor is eliminated catalytically.
7
Figure 1 Samples were taken at regular time intervals. The remaining concentration of the Fluoxetine in the reaction mixture was obtained by measuring absorbance at maximum wavelength
(λmax=227
nm)
using
spectrophotometer
(Unico
S2100
UV/Vis
spectrophotometer, USA) and computing the concentration from calibration curve. The
FXT
− FXT × 100 FXT
rip
Removal efficency %R =
t
removal percentage of Fluoxetine (%R) as a function of time is given by: (1)
us c
Where [FXT]0 is the initial Fluoxetine concentration (mg L-1) and [FXT] is the Fluoxetine concentration at different reaction times (mg L-1).
an
Experimental design
M
In this study, a CCD based on RSM was used to obtain an appropriate mathematical model for prediction of the behavior of the process. For ozone/H2O2
ed
process, effective variables such as ozone concentration, initial H2O2 concentration, reaction time and initial Fluoxetine concentration were selected as the independent
pt
variables. As shown in Table 2, the ozone concentration (X1) ranged from 10 to 30 (mg
ce
L-1), initial H2O2 concentration (X2) ranged from 0.02 to 0.18 (mM), reaction time (X3) ranged from 4 to 20 (min) and initial Fluoxetine concentration (X4) ranged from 10 to
Ac
50 (mg L-1). It should be noted that preliminary experiments were conducted for determining the range of the process variables. Table 2
The actual values of the independent variables (Xi) were coded to xi for statistical calculations using the following equation: x =
X −X δX
(2)
8
where Xi, xi δX and X0 are the actual value (uncoded) of an independent variable, the coded value of the independent variable, the step change and the actual value of the independent variable at the center point respectively [4]. In this work, CCD including sixteen cubic points, seven replicates at the centre point (α=0) and eight axial points (α= ±2) which lead to a total number of 31 experiments were used for CCD
rip
t
modelling. Minitab 14 software was used for statistical analysis of experimental results.
us c
Results and discussion CCD modelling
The 4-factors five-level CCD matrix, predicted results by CCD model and
an
observed results in the Fluoxetine removal experiments are listed in Table 3.
M
Table 3
ed
For calculating the predicted response, the quadratic polynomial response
β x +
β x +
β x x +ε
i ≠j
(3)
ce
Y=β +
pt
equation that includes the interaction terms was used (Eq. 3) [51]:
Ac
Where Y, xi, xj i and j represent the response variable, coded independent
variables, and index numbers for patterns respectively. i < j must be observed for interaction term (xixj), k is the number of input variables. β0, βi, βii and βij are intercept term, linear, quadratic and interaction effects, respectively. ε is the random error accounting for the differences between observed and predicted results. According to these results, an empirical relationship (the quadratic polynomial equation (Eq. 4)) between the independent variables (ozone concentration, initial H2O2 concentration,
9
initial Fluoxetine concentration and reaction time) and response (Fluoxetine removal efficiency) was obtained. = 73.6136 + 4.20682x − 0.8642x + 5.5252x − 2.8747x − 0.5183x x − 1.4709x x + 0.6170x x + 0.3767x x − 0.4414x x + 2.3200x x − 0.2857x − 0.5194x
us c
rip
t
− 1.2471x − 0.3336x
(4)
Analysis of variance (ANOVA)
an
The predicted values of Fluoxetine removal efficiency (% R) have been calculated by quadratic polynomial model (Eq. 4) and are given in Table 3. According
M
to the presented results in the Table 3, it can be observed that there is a good agreement between predicted values of Fluoxetine removal efficiency and experimental data. A
ed
comparison between the predicted results and the experimental data indicates that the model can effectively predict the process efficiency with correlation coefficient of R2 =
pt
0.976 (see Figure 2).
ce
The obtained correlation coefficient R2 indicates that quadratic polynomial
Ac
model can describe 97.6% variability in pharmaceutical removal efficiency. It also shows that only 2.4% of variation is not supported by the model. Figure 2
ANOVA results for the quadratic response surface model fitting are summarized in Table 4. The results indicates that both linear and squares parameters are highly significant (P
t
Degradation of antidepressant drug Fluoxetine in aqueous media by
rip
ozone/H2O2 system: Process optimization using central composite
us c
design
Abbas Aghaeinejad-Meybodi1, Amanollah Ebadi1 *, Sirous Shafiei1,
1
M
an
Alireza Khataee2, Mohammad Rostampour1
Environmental Engineering Research Centre, Department of Chemical Engineering,
2
ed
Sahand University of Technology, Tabriz, Iran.
Research Laboratory of Advanced Water and Wastewater Treatment Processes,
*
ce
Iran.
pt
Department of Applied Chemistry, Faculty of Chemistry, University of Tabriz, Tabriz,
Corresponding author: assistant prof. of Chemical Engineering,
Ac
Email: [email protected], Tel: (+98) 41 33459140 , Fax: (+98) 41 33224950
Abbas Agaheinejad-Meybodi: PhD student of chemical engineering, Email: [email protected] Sirous Shafiei: Associate Prof. of chemical engineering, Email: [email protected] Alireza Khataee: Associate Prof. of applied chemistry, Email: [email protected]
1
Mohammad Rostampour: MSc. Student of Chemical Engineering, Email:
Ac
ce
pt
ed
M
an
us c
rip
t
[email protected]
2
Degradation of antidepressant drug Fluoxetine in aqueous media by ozone/H2O2 system: Process optimization using central composite design
rip
t
Abstract
The main objective of this work is the modelling and optimization of
antidepressant drug Fluoxetine degradation in aqueous solution by ozone/H2O2
us c
process using central composite design (CCD). The operational parameters were
ozone concentration, initial hydrogen peroxide concentration, reaction time and initial Fluoxetine concentration. A good agreement between the predicted values of Fluoxetine removal and experimental results were observed (R2=0.976 and
an
Adj-R2= 0.955). Pareto analysis indicated that all selected factors and some interactions were effective on the removal efficiency. It was found that the
M
reaction time is the most effective parameter in the ozone/H2O2 process. The maximum removal efficiency (86.14 %) was achieved at ozone concentration of 30 mg L-1, initial H2O2 concentration of 0.02 mM, reaction time of 20 min and
ed
initial Fluoxetine concentration of 50 mg L-1 as the optimum conditions. Keywords: Fluoxetine; Pharmaceutical wastewater; Central composite design;
ce
pt
Ozonation, Response surface methodology.
Ac
Introduction
Currently, there are great scientific and public attention on pharmaceuticals as
environmental pollutants [1]. In recent years, pharmaceuticals have been identified in aqueous solutions because ordinary water and wastewater treatment is not completely effective for removing many drugs [2, 3]. Generally, pharmaceuticals are highly resistant to biodegradation and usually remain intact after water and wastewater treatment plants (WWTPs). For this reason, their existence in aqueous systems and in 3
the environment is a serious problem [3, 4]. Pharmaceutical waste may have hazardous and toxicity complications on humans and living micro-organisms [5]. Therefore, appropriate methods should be adapted to impede the spread of pharmaceutical waste in the environment after the secondary treatment [6, 7]. In the past decade, Fluoxetine has been proposed as one of the most widely used
t
antidepressants and has attracted a lot of attention. [8]. Fluoxetine and its principal
rip
metabolite Norfluoxetine have been detected in surface waters due to imperfect
us c
destruction after therapeutic use [9].
Concentrations of Fluoxetine in wastewater effluents have been identified in the range of 30-82 ng L-1 [10] and in surface water as high as 12 ng L-1 in the USA [11] and
an
as high as 99 ng L-1 in Canada [12]. Some studies have suggested a range of potential aquatic ecosystem effects of this antidepressant drug in the environment.
M
A scientific report shows that prescription of Fluoxetine has ultimately led to some unexpected environmental consequences through discharge of the drug (e.g. the
ed
fraction of Fluoxetine non-metabolized by the liver) in various ecosystems [13].
pt
Fluoxetine and Norfluoxetine have been detected in fish samples obtained from an effluent-dominated stream, this information being an indicator of their bioaccumulation
ce
potential [14]. Fluoxetine induce spawning in some crustaceans and bivalves [15]. In a
Ac
research work, Brooks et al. [16] evaluated the environmental hazard of fluoxetine to select benthic and pelagic toxicity test organisms. This study provided novel waterborne fluoxetine toxicity data for Pseudokirchneriella subcapitata, Ceriodaphnia dubia, Daphnia magna, Pimephales promelas and Oryias latipes, and sediment toxicity information for Hyalella Azteca and Chironomus tentans. US EPA’s ECOSAR (ecological structure– activity relationship (SAR)) was used to predict the toxicity of antidepressant pharmaceuticals to algae and they were ranked in the top 10 most toxic
4
of 49 pharmaceutical classes warranting further toxicity testing of algae with selective serotonin reuptake inhibitors (SSRIs) [17]. Johnson et al. [18] investigated the toxicity of SSRIs (Fluoxetine, Sertraline, and Fluvoxamine) to algae/phytoplankton using the US EPA ECOSAR, acute single-species growth inhibition assays, species sensitivity distributions (SSDs), and an outdoor microcosm mixture experiment. Because many
t
pharmaceuticals and personal care products have been detected in aqueous
rip
environmental compartments, understanding their fate under natural water conditions is
us c
important.
Kwon and Armbrust indicated that the Fluoxetine has low biological degradability in WWTPs. Their experimental studies also described that Fluoxetine is
an
partly resistant to the hydrolysis and photolysis and rebellious versus microbial decomposition [19].
M
Among all of the studied methods, advanced oxidation processes (AOPs) have been used successfully to eliminate a wide variety of pollutants including
ed
pharmaceuticals in water and wastewater treatment [20, 21]. In AOPs, hydroxyl free
pt
radicals (HO• ) and other powerful oxidants are formed that are capable of removing contaminants with high chemical stability or resistant to mineralization [22, 23].
ce
Among the different oxidants, hydroxyl radicals (HO• ) are powerful oxidants
Ac
that can increase the rate of pollutants degradation significantly [24]. UV/H2O2, UV/O3, O3/H2O2, UV/ O3/H2O2, Fenton and photo-Fenton, catalytic ozonation and
photocatalytic processes such as UV/TiO2 are the most commonly used AOPs for treatment of wastewaters [25-42]. In ozone based AOP such as O3/H2O2 process, micropollutants can be oxidized by both molecular ozone (directly) and •OH radicals (indirectly). The •OH radicals are extremely powerful oxidants whose reaction rate constants with organic molecules are generally in
5
the range 108 to 1010 M-1.s-l. This means that AOP treatment of typical organic substrates will be practical, even if the steady-state concentration of •OH is only between 10-10 to 10-12 M [43]. Dissolved organic matters might act as radical scavengers, which would significantly decrease the efficiency of ozone treatment on target compounds [44].
t
Considering the investment and operation costs, ozonation still is not a cheap
rip
technology. Although safe operation is no longer a problem, ozonation systems require
us c
considerable safety precautions, thus increasing the investment costs [45].
The number of studies conducted for Fluoxetine degradation using AOPs is very limited. Mendez-Arriaga et al. [9] reported the Fluoxetine photooxidation by catalytic-ozonation
processes
in
aquatic
solution.
an
combined
Degradation
of
contaminants mixture containing Fluoxetine with membrane reactor was investigated by
M
Benotti et al.[46].
In order to develop a cost effective and to enhance the removal efficiency,
ed
especially for practical applications, experimental conditions and concentration of
pt
components must be optimized [2]. The study of the effect of variables on the response with using classical optimization methods, changing one factor at a time, is expensive
ce
and time-consuming and require a lot of experiments, as well as the interaction between
Ac
variables on the response cannot be determined [26, 36]. For this purpose, to minimize the number of experiments and optimization of the effective parameters, an alternative approach can be used as central composite design (CCD) based on response surface methods (RSM) [25-27, 34-36, 47-50]. The main objective of RSM is to obtain an optimal response using designed experiments [36]. In RSM by using an appropriate experimental design, the number of required experiments will be reduced. Furthermore,
6
the modeling of system facilitates interpreting of multivariate phenomena and provides the possibility of process scaling [49]. There were no reported activities in literature about optimization of AOPs using CCD based on RSM for elimination of Fluoxetine in aquatic solutions. Therefore, the main objective of our research is to treat pharmaceutical wastewater containing
t
Fluoxetine by Ozone/H2O2 process. Finally, the RSM method with CCD is used to
rip
predict the optimum experimental conditions for Fluoxetine degradation in aqueous
us c
media.
Experimental
an
Chemicals and procedures
Fluoxetine hydrochloride (C17H18F3NO. HCl) typically marketed under the trade
M
name Prozac, is one of the most frequently used antidepressant pharmaceuticals. In Table 1, the characteristics and structure of Fluoxetine are provided. Fluoxetine and
ed
hydrogen peroxide (35%) were purchased from Arya pharmaceutical company (Iran)
pt
and Merck (Germany), respectively.
Table 1
ce
Ozonation experiments were performed in a semi-continuous reactor. In Figure
Ac
1, schematics of the experimental setup is shown. In all experiments, initially the reactor is filled with 250 mL pharmaceutical solution with desired concentration of Fluoxetine and H2O2 and then a gasous ozone stream, produced by an ozone generator (ozomatic, model Lab 802, Germany) using pure O2 as the feed gas, is continuously injected into reactor using a sinter glass sparger. Also, the reaction mixture is stirred completely using a magnetic stirrer during the reaction time. The residual ozone in the output gas stream from reactor is eliminated catalytically.
7
Figure 1 Samples were taken at regular time intervals. The remaining concentration of the Fluoxetine in the reaction mixture was obtained by measuring absorbance at maximum wavelength
(λmax=227
nm)
using
spectrophotometer
(Unico
S2100
UV/Vis
spectrophotometer, USA) and computing the concentration from calibration curve. The
FXT
− FXT × 100 FXT
rip
Removal efficency %R =
t
removal percentage of Fluoxetine (%R) as a function of time is given by: (1)
us c
Where [FXT]0 is the initial Fluoxetine concentration (mg L-1) and [FXT] is the Fluoxetine concentration at different reaction times (mg L-1).
an
Experimental design
M
In this study, a CCD based on RSM was used to obtain an appropriate mathematical model for prediction of the behavior of the process. For ozone/H2O2
ed
process, effective variables such as ozone concentration, initial H2O2 concentration, reaction time and initial Fluoxetine concentration were selected as the independent
pt
variables. As shown in Table 2, the ozone concentration (X1) ranged from 10 to 30 (mg
ce
L-1), initial H2O2 concentration (X2) ranged from 0.02 to 0.18 (mM), reaction time (X3) ranged from 4 to 20 (min) and initial Fluoxetine concentration (X4) ranged from 10 to
Ac
50 (mg L-1). It should be noted that preliminary experiments were conducted for determining the range of the process variables. Table 2
The actual values of the independent variables (Xi) were coded to xi for statistical calculations using the following equation: x =
X −X δX
(2)
8
where Xi, xi δX and X0 are the actual value (uncoded) of an independent variable, the coded value of the independent variable, the step change and the actual value of the independent variable at the center point respectively [4]. In this work, CCD including sixteen cubic points, seven replicates at the centre point (α=0) and eight axial points (α= ±2) which lead to a total number of 31 experiments were used for CCD
rip
t
modelling. Minitab 14 software was used for statistical analysis of experimental results.
us c
Results and discussion CCD modelling
The 4-factors five-level CCD matrix, predicted results by CCD model and
an
observed results in the Fluoxetine removal experiments are listed in Table 3.
M
Table 3
ed
For calculating the predicted response, the quadratic polynomial response
β x +
β x +
β x x +ε
i ≠j
(3)
ce
Y=β +
pt
equation that includes the interaction terms was used (Eq. 3) [51]:
Ac
Where Y, xi, xj i and j represent the response variable, coded independent
variables, and index numbers for patterns respectively. i < j must be observed for interaction term (xixj), k is the number of input variables. β0, βi, βii and βij are intercept term, linear, quadratic and interaction effects, respectively. ε is the random error accounting for the differences between observed and predicted results. According to these results, an empirical relationship (the quadratic polynomial equation (Eq. 4)) between the independent variables (ozone concentration, initial H2O2 concentration,
9
initial Fluoxetine concentration and reaction time) and response (Fluoxetine removal efficiency) was obtained. = 73.6136 + 4.20682x − 0.8642x + 5.5252x − 2.8747x − 0.5183x x − 1.4709x x + 0.6170x x + 0.3767x x − 0.4414x x + 2.3200x x − 0.2857x − 0.5194x
us c
rip
t
− 1.2471x − 0.3336x
(4)
Analysis of variance (ANOVA)
an
The predicted values of Fluoxetine removal efficiency (% R) have been calculated by quadratic polynomial model (Eq. 4) and are given in Table 3. According
M
to the presented results in the Table 3, it can be observed that there is a good agreement between predicted values of Fluoxetine removal efficiency and experimental data. A
ed
comparison between the predicted results and the experimental data indicates that the model can effectively predict the process efficiency with correlation coefficient of R2 =
pt
0.976 (see Figure 2).
ce
The obtained correlation coefficient R2 indicates that quadratic polynomial
Ac
model can describe 97.6% variability in pharmaceutical removal efficiency. It also shows that only 2.4% of variation is not supported by the model. Figure 2
ANOVA results for the quadratic response surface model fitting are summarized in Table 4. The results indicates that both linear and squares parameters are highly significant (P
