Residence time distribution analysis and optimization of photocatalysis of phenazopyridine using immobilized TiO2 nanoparticles in a rectangular photoreactor

Journal of Industrial and Engineering Chemistry 19 (2013) 1525–1534

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Residence time distribution analysis and optimization of photocatalysis of phenazopyridine using immobilized TiO2 nanoparticles in a rectangular photoreactor M. Fathinia, A.R. Khataee * Research Laboratory of Advanced Water and Wastewater Treatment Processes, Department of Applied Chemistry, Faculty of Chemistry, University of Tabriz, Tabriz, Iran

A R T I C L E I N F O

Article history: Received 9 September 2012 Accepted 16 January 2013 Available online 5 February 2013 Keywords: TiO2 nanoparticles Photocatalyst Pharmaceutical wastewater Response surface methodology Flow pattern

A B S T R A C T

Optimization of photocatalytic degradation of phenazopyridine (PhP) under UV light irradiation using immobilized TiO2 nanoparticles was studied. The effect of operational parameters was investigated using response surface methodology (RSM). Maximum removal efficiency was achieved at the optimum conditions: initial drug concentration of 10 mg/L, UV light intensity of 47 W/m2, flow rate of 200 mL/min, and reaction time of 150 min. The residence time distribution (RTD) analysis was studied to find the effect of flow rate on the drug removal efficiency. The tracer (PhP) pulse injection response was studied with UV–vis measurements and was used to prepare RTD curves. ß 2013 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.

1. Introduction Pharmaceutical waste disposal procedure involves a number of traditional techniques, such as sewer and incineration [1]. Despite the widespread utilization of these techniques, they do not help to remove drugs from contaminated waters. Waste drugs are flowed into water through wastewaters or direct disposal of pharmaceutical producers. Therefore, strategies should be adopted to prevent disposing waste drugs into environment before suitable treatment [2,3]. The heterogeneous photocatalytic process is one of the ideal techniques to degrade drugs. TiO2 is the most widely studied photocatalyst due to its high chemical stability, low cost, noncorrosive, and high activity under UV illumination [4]. When a semiconductor like TiO2 is illuminated with l < 390 nm, an electron excites out of its energy level and consequently leaves a hole in the valence band. As electrons are moved up from the valence band to the conduction band, they generate electron–hole pairs. These charges can either recombine or participate in different reactions [5–8]. Many studies have focused on the chemical pathways or degradation kinetics of photocatalysis, but there have been few reports based on the design of photocatalytic reactors [9]. Using the rectangular reactor in this work, the effective parameters of photocatalytic degradation of PhP

* Corresponding author. Tel.: +98 411 3393165; fax: +98 411 3340191. E-mail addresses: [email protected], [email protected] (A.R. Khataee).

such as initial concentration, UV light intensity, reaction time and the flow rate can be optimized. RSM is a mathematical and statistical tool to assess the effect of input variables on an output response [10,11]. It has been widely employed in optimizing and modeling of various photocatalytic processes due to its capability of analyzing the interactions amongst factors, and determining the optimum region of the factors level [4,12]. The most commonly selected methods in RSM are the Box–Behnken and central composite design (CCD) [12–14]. In the present study, CCD was applied in order to obtain the optimum condition of photocatalytic degradation of PhP using a rectangular photoreactor. TiO2 nanoparticles were employed as an immobilized film due to the advantages of reactors operated with immobilized semiconductors [11,15]. In photoreactors operated with immobilized TiO2 nanoparticles, the reaction rate is mainly determined by the light intensity radiated on the surface, the adsorption features of the reacting constituents in the solution, and mass transfer from the bulk of the fluid to the catalyst surface [5]. However, little consideration has been given to the use of the RTD in investigating the performances of photoreactors. In actual field of chemical engineering, the type of the reactors is often very different from the ideal reactors (the perfectly mixed, batch, the plug flow tubular reactors) [11]. In most studies idealized plug flow or batch reactors are used, where all the flow elements in the reactor have the same residence time. The RTD of a reactor is a distinctive of flow regime in the reactor, being one of the most informative characterizations of the reactor [16]. The liquid RTD is important for accurate kinetic modeling of the

1226-086X/$ – see front matter ß 2013 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jiec.2013.01.019

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system, and facilitating reactor design to achieve or preserve a desired flow pattern. RTD allows a more thorough comparison between systems with different zones of the reactor. Also RTD allows the process engineer to diagnose the flow pattern in the reactor and represents a tool in successful process scale-up [17,18]. Therefore, in the present work, our aim is to investigate the flow regime inside the photoreactor in each flow rate via RTD curves, also the effect of different flow rates on RTD curves and on removal efficiency of PhP has been studied. 2. Experimental 2.1. Materials PhP (C11H11N5HCl, molar mass of 249.7 g/mol), is a commonly used analgesic drug in urinary tract treatment and other medical prescriptions. Its structure and characteristics are given in Table 1. It was chosen here, due to the presence of the azo group which made it a resistant compound to biodegradation. PhP has also a sharp color which made it a suitable tracer for RTD studies. PhP was purchased from Tabriz pharmaceutical company (Iran). The investigated photocatalyst was TiO2 PC-500 (anatase > 99%) (Millennium Inorganics, Brussels, Belgium) the crystallites mean size was 8 nm, the BET surface area and total pore volume were 320.76 m2/g and 0.3104 cm3/g, respectively. These characteristics were proved by XRD and TEM analyses which have been reported previously [5,10]. 2.2. Immobilization of TiO2 nanoparticles on ceramic plates TiO2 nanoparticles were immobilized on the ceramic plates by sol–gel dip-coating method. Organically modified silica (Ormosil) was used as the hydrophobic binder. The immobilization procedure was reported in our previous work [13]. The main advantage of this kind of immobilization is that the use of binder removed the need for high temperatures which was provided by furnace. The obtained films have good mechanical anchoring due to the chemical bonding, in comparison with films made with the dried mixture of TiO2 and water. Fig. 1a and b, respectively, shows the SEM images of the ceramic plate before and after immobilization of TiO2 nanoparticles on it. As shown in Fig. 1b, the available points in the surface of the ceramic plate are coated with TiO2 nanoparticles. The coated plates were thoroughly washed with deionized water for the removal of free TiO2 particles. 2.3. Photocatalysis experiments The experimental set-up is based on a rectangular photocatalytic reactor of workable area 15 cm  90 cm, made out of stainless steel (Fig. 2). The wastewater to be treated is falling as a thin film from the top of the chamber onto titanium dioxide nanoparticles immobilized on ceramic plates. The angle of slant was set at 58 to achieve a homogeneous distribution of the liquid. The sample to be treated (2000 mL of drug solution) was stored in a reservoir and was continuously circulated in the system by a

Fig. 1. SEM images of ceramic plates: (a) before and (b) after immobilization of TiO2 nanoparticles.

peristaltic pump at an adjustable flow rate. The reservoir was open to air to insure sufficient oxygenation. The solution in the reservoir was continuously stirred to keep the solution homogeneous. Artificial irradiation was provided by three 30 W UV-C lamp (Philips, The Netherlands) with peak intensity at 254 nm, positioned above the reactor. The lamps were turned on at the beginning of each experiment. The distance between the solution and the UV source was adjusted according to the experimental conditions. The radiation intensity was measured by a UV radiometer purchased from Cassy Lab Company (Germany). At different reaction times obtained from the experimental design, samples of 2 mL were taken and the remaining PhP was determined using a spectrophotometer at lmax = 436 nm and drawing the calibration curve. Using this method, the percent of removal efficiency (RE (%)) could be obtained. The RE (%) was expressed as the percentage ratio of removed drug concentration to that of the initial one.

Table 1 Characteristics of the phenazopyridine. Chemical structure

Molecular formula

Mw (g/mol)

lmax (nm)

CAS number

Trade name

C11H11N5HCl

249.7

436

94-78-0

Pyridium

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Fig. 2. The experimental set-up of rectangular photocatalytic reactor.

2.4. Analytical procedures The photocatalytic reactions were monitored by UV–vis spectrophotometer (WPA lightwave S2000, England) in the range of 200–700 nm. Scanning electron microscopy (SEM) was carried out on a scanning electron microscope of S-4200 (Hitachi, 4200 Japan) device after gold-plating of the samples. The samples used for TEM observations were prepared by dispersing the TiO2 powder in ethanol followed by ultrasonic vibration (Sonorex Bandelin Digi Tec, UK) for 15 min, then placing a drop of the dispersion onto a copper grid coated with a layer of amorphous carbon. The TEM images were recorded by a Cs-corrected high-resolution TEM (JEM-2200FS, JEOL, Japan) operated at 200 kV. To determine the crystal phase composition and average crystalline size of immobilized TiO2 nanoparticles sample, X-ray diffraction (XRD) measurements were carried out at room temperature by using Siemens X-ray diffraction D5000, with Cu Ka radiation. The accelerating voltage of 40 kV and emission current of 30 mA were used. The average crystalline size of the samples was calculated according to Debye–Scherrer formula [19]. Nitrogen sorption analyses were obtained by a sorptometer (Micrometrics, Gimini series) using standard continuous procedures at 77.15 K on calcined samples that had been degassed at 363 K for 1 h and then at 403 K under high vacuum for at least 10 h. The surface area was calculated according to the Brunauer– Emmett–Teller (BET) model over a relative pressure range of 0.05– 0.90.

Experimental data were analyzed using Minitab 15 software. For statistical calculations, the Xi variables were coded as xi according to the following equation: xi ¼

Xi  X0 dX

(1)

where X0 is the value of Xi at the center point and dX presents the step change [20]. The experimental ranges and the levels of the independent variables for PhP removal are given in Table 2. It should be mentioned that preliminary experiments were performed to determine the extreme values of the variables. 2.6. Experimental conditions of RTD studies To characterize the liquid flow pattern in the photoreactor, the liquid residence time distribution curves were determined at different flow rates of 50, 100, 150, 200 and 250 mL/min. For this purpose, a pulse input of tracer (V = 10 mL of C0 = 100 mg/L of PhP) at time t = 0 s was loaded to the initial path of the reactor (part A in Fig. 2), with a syringe. The tracer processed through the path of the reactor at part (B) of Fig. 2. The samples were taken from the end path of reactor (part C in Fig. 2), at the regular time intervals only in one cycle, until the concentration of the tracer reached to near 0 mg/L in each flow rate. Then PhP outlet concentrations, [PhP]out (mg/L), were measured and plotted as a function of time. In the present study, all RTD computations were conducted in MATLAB 6.5 (MathWorks, Natick, MA).

2.5. Experimental design In this work, a central composite design was used to propose a mathematical model of the process behavior. In order to assess the effect of operating parameters on the photocatalytic removal efficiency of PhP, four main factors were chosen: initial drug concentration (mg/L) (X1), reaction time (min) (X2), UV light intensity (W/m2) (X3) and flow rate (mL/min) (X4). A total of 31 experiments were employed in this work, including 24 = 16 cube points, 7 replications at the center point and 8 axial points.

Table 2 Coded and actual values of variables of the experimental design. Variables

Initial PhP concentration (mg/L) (X1) Reaction time (min) (X2) Intensity (W/m2) (X3) Flow rate (mL/min) (X4)

Ranges and levels 2

1

0

+1

+2

5 30 11 50

10 60 20 100

15 90 29 150

20 120 38 200

25 150 47 250

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Table 3 The 4-factor central composite design matrix and the value of response function (RE (%)). Run

[PhP] (mg/L)

Time (min)

Intensity (W/m2)

Flow rate (mL/min)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

0 0 0 1 0 1 0 1 1 0 1 1 1 1 2 1 1 0 0 1 0 0 0 1 2 1 0 0 1 1 1

0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 2 0 1 0 1 2 0 1 1 1

0 0 0 1 2 1 2 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1

0 2 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 2 1 1 1

3. Results and discussion 3.1. Second order polynomial model and analysis of variance (ANOVA) The 4-factor CCD matrix and experimental results attained in the photocatalytic removal runs are presented in Table 3. The experimental data from the CCD was analyzed using response surface regression and fitted to a second-order polynomial model Eq. (2): Y ¼ b0 þ b1 X 1 þ b2 X 2 þ b3 X 3 þ b4 X 4 þ b12 X 1 X 2 þ b13 X 1 X 3 þ b14 X 1 X 4 þ b23 X 2 X 3 þ b24 X 2 X 4 þ b34 X 3 X 4 þ b11 X12 þ b22 X22 þ b33 X32 þ b44 X42

(2)

where Y is the predicted response of the removal efficiency. The b0 is the intercept coefficient; bi values are the linear coefficients, bii values are the quadratic coefficients; bik values are the interaction coefficients and xi values are the coded independent variables. The fitted second-order polynomial equation illustrating the removal efficiency using response surface analysis is given in Eq. (3). Y ¼ 51:7316  5:9264X 1 þ 8:2773X 2 þ 3:6899X 3 þ 1:9234X 4 þ 1:1856X 2 X 3  0:0216X 2 X 4  0:3872X 3 X 4  3:1830X12 þ

þ

0:5949X32



1:2979X42

Experimental

Predicted

53.70 53.00 50.29 45.21 50.19 51.01 61.80 36.10 42.01 50.56 68.93 58.12 25.78 38.62 31.00 58.45 66.69 52.41 49.90 45.34 53.12 40.06 52.14 37.92 50.77 48.16 76.36 43.85 53.78 55.39 37.31

51.73 50.39 51.73 42.86 46.73 48.26 61.49 35.95 45.14 51.73 68.53 60.68 28.90 41.30 27.15 58.48 67.89 51.73 51.73 47.52 51.73 39.77 51.73 41.73 50.85 48.69 72.88 42.69 53.38 58.79 35.80

the mean square error. The F-value, also called the variance ratio, is the ratio of variance due to the effect of a factor (in this case the model) and variance due to the error term [21,22]. If the model is a good predictor of the experimental results, F-value should be greater than the tabulated value of F-distribution for a certain number of degrees of freedom in the model at a level of significance of a. The obtained F-value, 27.18, is clearly greater than the tabulated F (2.352 at 95% significance) confirming the adequacy of the model fits [22]. The ANOVA analysis also shows the lack-of-fit (LoF) of the test results, which can be used to investigate the model sufficiency. The F-value for lack of fit is greater than the tabulated F (2.352 at 95% significance), so it is not significant. Since the model lack of fit has shown to be insignificant, the resulted response surfaces plots were sufficiently explained by Eq. (3) [22,23]. In order to determine whether the model actually describes the experimental data, the various coefficients of determination, R2 was evaluated here. These R2 coefficients have values between 0 and 1. According to the results achieved from ANOVA (see Table 4),

Table 4 Analysis of variance (ANOVA) for fit of removal efficiency from central composite design.

 0:6980X 1 X 2 þ 0:5595X 1 X 3 þ 1:1925X 1 X 4 1:1487X22

Removal efficiency (%)

(3)

Photocatalytic removal efficiencies (RE (%)) have been predicted by Eq. (3) and the achieved results are presented in Table 3. Table 4 indicates the results of the quadratic response surface model fitting in the form of ANOVA. The Test for significance of the regression model is performed as an ANOVA procedure by calculating the Fvalue, which is the ratio between the regression mean square and

Source of variations

Sum of squares

Degree of freedom

Adjusted mean square

F-Value

P-Value

Regression Residuals Lack of fit Pure error

3375.60 141.95 128.70 13.25

14 16 10 6

241.115 8.872 12.870 2.209

27.18 – 5.83NS –

0.000 0.000 0.021 –

Total

3517.55

30

–

–

–

R2 = 0.9582, Adj-R2 = 0.9243. Lack of fit, sum of squares (SS) = total SS  pure error SS. NS, not significant.

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Table 5 Estimated regression coefficients and corresponding t- and P-values from the data of central composite design experiments. Coefficient

Parameter estimate

Standard error

t-Value

P-Value

b0 b1 b2 b3 b4 b12 b13 b14 b23 b24 b34 b11 b22 b33 b44

51.7316 5.9264 8.2773 3.6899 1.9234 0.6980 0.5595 1.1925 1.1856 0.0216 0.3872 3.1830 1.1487 0.5949 1.2979

1.1258 0.6080 0.6080 0.6080 0.6080 0.5570 0.5570 0.5570 0.5570 0.7446 0.7446 0.7446 0.7446 0.7446 0.7446

45.951 9.747 13.614 6.069 3.164 0.937 0.751 1.601 1.592 0.029 0.520 5.715 2.062 1.068 2.330

0.000 0.000 0.000 0.000 0.000 0.363 0.463 0.129 0.131 0.977 0.610 0.000 0.056 0.301 0.033

Eq. (3) has a coefficient of determination (R2) of 0.9582 [22,24]. The coefficient of determination (R2) obtained for the above quadratic equation indicates that 95.82% of variation in removal efficiency can be explained by independent variables of initial PhP concentration (mg/L) (X1), reaction time (min) (X2), radiation intensity (W/m2) (X3) and flow rate (mL/min) (X4). The p-value of (p  0.05) for any factor in the ANOVA test indicates a significant effect of the corresponding variable on the response (see Table 5). Regression analysis of the experimental data (Table 5) shows that all of the operational parameters had significant linear effect on removal efficiency. This was evident from the p-value obtained from the regression analysis [23]. Just initial concentration of PhP was found to have the negative linear effect of 5.9264 on removal efficiency (Table 5). The insignificant terms can be removed from the CCD model. Finally the reduced and best fitted model for the removal efficiency (RE (%)), developed from the regression procedure and supported by ANOVA is shown in coded form in Eq. (4). Y ¼ 51:7316  5:9264X 1 þ 8:2773X 2 þ 3:6899X 3 þ 1:9234X 4 

3:1830X12



1:2979X42

(4)

The adequacy of the model is also evaluated by the residuals [22,24]. The residuals, which are the difference between the observed responses and the predicted responses, are examined using the normal probability plots of the residuals and the plots of the residuals versus the fitted values. If the model is reasonable, the points on the normal probability plots of the residuals should form a straight line. On the other hand, the plots of the residuals versus the fitted response should be randomly scattered [22]. The observed residuals are plotted against the fitted values, given by a normal distribution (see Fig. 3), which reveals that the residuals were randomly scattered.

3.2. Effect of variables as response surface and counter plots 3.2.1. Effect of UV light intensity Fig. 4a demonstrates the effect of UV light intensity and reaction time on photocatalytic removal efficiency (RE (%)) for initial drug concentration of 15 mg/L and flow rate of 150 mL/min. As it is obvious from Figure 4a, removal efficiency increased with increasing UV light intensity and reaction time [13,15]. The proposed reason is that the incident UV light intensity determines the rate of electron–hole pairs (e/h+) generation and concentration in an illuminated semiconductor. The photocatalytic removal efficiency of organic pollutants in the aqueous solution was least at lower intensities, which is due to the lower rate of (e/h+) formation by lower photon energy absorption. On the other hand, the photocatalytic removal efficiency was very high at high intensities. The reason of this observation is that the high light intensity provides more energy to produce (e/h+) in most of TiO2 nanoparticles, leading to higher RE (%). 3.2.2. Effect of initial drug concentration To study the effect of initial drug concentration on photocatalytic removal efficiency (%), the experiments were carried out with initial drug concentration varying from 5 to 25 mg/L at constant flow rate (150 mL/min) and UV light intensity (29 W/m2). The results are displayed in Fig. 4b. It can be seen that the photocatalytic removal efficiency increases with an increase in the initial amount of drug to a certain level (from 5 to 12 mg/L) and a further increase in its initial concentration (from 12 to 25 mg/L) leads to decrease the decolorization efficiency. The photocatalytic removal efficiency relates to the probability of OH radicals formation and to the probability of OH radicals reaction with drug molecules. As the initial concentration of the PhP increases up to certain level (12 mg/L in our work), the probability of the reaction between PhP

Fig. 3. Residual plots for photocatalytic removal efficiency of PhP.

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Fig. 4. The response surface and contour plots of photocatalytic removal efficiency RE (%) as the function of (a) reaction time (min) and UV light intensity (W/m2); (b) initial drug concentration (mg/L) and reaction time (min); and (c) flow rate (mL/min) and reaction time (min).

molecules and oxidizing species also increases, leading to an enhancement in the removal efficiency [20]. The further increase of drug concentration consequently decreases the photocatalytic activity. Different explanations are proposed, some of which are based on the adsorption of contaminant molecules on the solid surface in a Langmuir–Hinshelwood model [5,25]. One acceptable explanation is the fact that at high drug concentration, the drug molecules may compete with oxygen or the adsorbed intermediates which decrease degradation efficiency [26]. Another reason may be due to the absorption of light photons

by the drug itself leading to a lesser availability of photons for generation of electron–hole pairs and subsequently hydroxyl radicals [2]. 3.2.3. Effect of flow rate and RTD studies Fig. 4c shows the response surface and contour plots of photocatalytic removal efficiency (%) as a function of flow rate and reaction time. An improvement in photocatalytic removal efficiency with increasing flow rate has been observed. So, in order to analyze the effects of liquid flow rates on removal efficiency and

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M. Fathinia, A.R. Khataee / Journal of Industrial and Engineering Chemistry 19 (2013) 1525–1534

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characterize the liquid flow pattern, three sets of the experimental measurements have been carried out in the photoreactor without recirculation. The residence time distribution was evaluated using E(t) and F(t) curves, representing the variation of the tracer concentration at the exit of reactor with time. There are several types of tracers that can be used to measure RTD’s of the reactor [21]. Commonly used tracers include color, conductive or radioactive materials as they allow the easy measurement or detection in the effluent stream. The list of dyes which have been used as a tracer for RTD measurements have been reported before [27]. It is very important that the selected tracer should: (I) define the entrance and exit boundaries of the reactor adequately, (II) have properties similar to the reactor mixture, (III) be soluble in the reacting mixture and (IV)

should not absorb on the surfaces of the reactor [11]. The use of organic substances as tracers with a subsequent photometric detection is associated with the difficulty of finding substances that are stable for a sufficiently long period of time to perform a measurement [28,29]. In all of the radioactive methods reported, contamination of the bed material by the tracer often required long lag times between experiments for the tracer to decompose [30]. In the present work, PhP was selected as an ideal tracer, the reason is its good solubility and sharp color which lead to the accurate manual sampling and detection. The effect of flow rate on RTD was analyzed by the help of following parameters and their related distribution plots (see Fig. 5a–e). The area under the curve of the tracer concentration against time was normalized by dividing the concentration values

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by the total area under the curve, thus giving the E(t) values as follows: C C EðtÞ ¼ R 1 i ffi P1 i 0 C i Dt i 0 C dt

(5)

where Ci is tracer concentration appearing at the exit time of t. The parameters of the curve, such as the mean residence time (t¯m ), the variance of the residence time (s2) and the dimensionless variance (s 2D ) were calculated from the following equations [21,31,32]: t¯m ¼

Z

1 0

s2 ¼

Z

1

P X t C Dt tEðtÞ dt ffi P i i i ¼ t i Ei Dt C i Dt i 2 ðt  t¯m Þ E dt ¼

0

s 2D ¼



s

t¯m

2

P

P 2 2 t C i Dt i ðt i  t¯m Þ C i Dt i 2 P ffi Pi  t¯m C i ti C i Dt i

(6)

(7)

(8)

Mean residence time (MRT) is the mean time spent by the material under specific processing condition. A lower value of MRT indicates higher mean velocity of the flowing material. The variance s2 is the measure of the spread of distribution. The RTD dimension less variance (s 2D ) can be considered as a measure of the dispersion. A lower value of s 2D (s 2D ! 0) indicates lesser dispersion and the flow approaches to near plug flow, the higher value of s 2D indicates higher dispersion and the flow approaches to perfectly mixed flow [21]. For analyzing the performances of the non-ideal reactors, it is usual to report RTD data either directly, or in relation with flow models. There are two types of models that may fit the experimental data of the residence time distribution of tracer flowing through a reactor. These models are the multi-parameter models and the one-parameter models [33,34]. The multiparameter models can be represented by the finite stage model whereas the one-parameter models can make use of the axial dispersion model and tanks-in-series model [35,36]. To characterize the RTD quantitatively in the photoreactor the single parameter model were chosen in this work: the tanks-in-series model, where the real circulation loop is replaced by a series of consecutive, equal volume of ideally stirred tank reactors, Neq, resulting in the same longitudinal mixing effect. The degree of mixing is characterized by the number of (Neq) and could be calculated according to Eq. (9). The large numbers of (Neq), indicate that more tanks are able to fit the distribution and the flow regime inside the reactor approaches to the plug flow and vice versa [11,21,37]. It means that a low value of Neq signifies that few tanks are able to fit the distribution, hence there is comparatively more mixing and the flow regime inside the reactor approaches to the mixed flow [5]. N eq ¼

t2 s2

(9)

The variations in these four parameters (t¯m , s2, s 2D and Neq) due to the change in operating conditions give rise to various degrees of mixing and differences in the corresponding flow patterns. In order to investigate the effect of flow rate on the RTD performance more closely, all the RTD distribution curves are plotted versus time data for each of the five flow rates on separate graphs as shown in Fig. 5. Each curve represents the complete set of data obtained by varying flow rate. The RTD results in Fig. 5 reveal that in lower flow rates the flow pattern inside the photoreactor is an imperfect mixed flow regime and short-circuiting is present depending on the low inlet flow rate. It is evident in the flow rate of 50 mL/min as there is an irregular peaks on the C(t) and E(t) curves.

There is also a substantial tailing effect of the curve at the flow rate of 50 mL/min, with tracer concentrations still being measured at the residence time of 300 (s). These effects demonstrate that stagnant volumes are present resulting in dead-spaces and shortcircuiting within the photoreactor in the low flow rates [38]. A study by Alkhaddar et al. [39] presented a mathematical model incorporating bypass flow and stagnant zones. This was confirmed by an experimental investigation evaluating the bypass flows and stagnant zones for different flow rates. From Fig. 5, it could be observed that residence time distribution is different for various flow rates. The increase in flow rate results in decrease of mean residence time in the reactor. Generally MRT is the most common parameter of concern and is an indicative of the average transient time of processing material. The MRT changed as a result of increasing the flow rate. The value of MRT (or the area under the curve of tE(t) vs. time) was calculated with MATLAB according to Eq. (6), and the values of 176.45, 132.42, 105.22, 58.27 and 36 s were attained for flow rates of 50, 100, 150, 200 and 250 mL/min, respectively. From these results it achieves that the tracer exits the reactor much quicker with increasing liquid flow rate and by decreasing liquid flow rate the tracer residence time increases inside the reactor which leads to the tailing effect in RTD curves (see Fig. 5(a–e)). The response curves at higher liquid flow rates become closer to plug flow in comparison with lower liquid flow rates which will be justified by the value of (s 2D ). In the present study, the value of variance (or the area under the curve of (t  t¯m )2E(t) vs. time) was calculated with MATLAB according to Eq. (7). The values of s 2D were calculated using Eq. (8) and the following results 0.104, 0.066, 0.058, 0.0450 and 0.035 were attained for flow rates of 50, 100, 150, 200 and 250 mL/min, respectively. From these results, it could be achieved that by increasing the flow rate from 50 to 250 mL/min the value of s 2D decreased from 0.104 to 0.035. These findings indicated that the flow regime inside the photoreactor changed from mixed flow to plug flow by increasing the flow rate (see Fig. 6). This observation was confirmed by the number of tank in series (Neq) in different flow rates. The Neq number was calculated by Eq. (9) which was 9.53, 15, 17.09, 22.19 and 28.52 for flow rates of 50, 100, 150, 200 and 250 mL/min, respectively. The achieved results revealed that the number of Neq increased by increasing flow rates (see Fig. 6). On the other hand as the value of s 2D decreased, the number of Neq increased, so the flow regime inside the photoreactor approached to plug flow (see Fig. 6). In this work the relationship between the RE (%) and the flow rates was studied with RTD parameters (t¯m , s2, s 2D and Neq). The results showed that the RE (%) increased while the flow rates increased from 50 to 200 mL/min as the number of Neq increased from 9.53 to 22.19 and the flow regime approaches from mixed flow to plug flow. This finding supports RTD conversion theory, as maximum conversion will be achieved as the mixing regime approaches to plug-flow mixing [17,38]. On the other hand, by further increase of the flow rate from 150 to 250 mL/min, the number of Neq was also increased and the flow regime became more closer to plug flow, but the achieved RE (%) from RSM optimization step revealed that the optimum flow rate in the photoreactor was 200 mL/min and further increase of flow rate would not lead to higher RE (%). The presumed reason is that when the drug solution flow rate is increased up to the optimum value (200 mL/min), the turbulence in the system is enhanced. It may lead to decomposition of more and more adsorbed drug molecules on the surface of TiO2 and as a result, photocatalytic removal efficiency increases. The higher removal efficiencies at the optimum flow rate of 200 mL/min were also attributed to the increase in the mass transfer coefficient. The findings in the represent work are in agreement with literature reports where higher flow rates would result in higher photocatalytic efficiency

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Number of Neq

30 25 20 15 10 5 50

100

150

200

250

200

250

Dimension less variance

Flow rate (mL/min) 0.12 0.1 0.08 0.06 0.04 0.02 50

100

150

Flow rate (mL/min) Fig. 6. The effect of flow rate on the value of dimension less Neq and dimension less variance.

[40–42]. As an instance, Mehrotra et al. [41] explained the effect of circulation flow rates on photocatalytic degradation rate of benzoic acid. They found that if the external mass transfer resistance existed, the reaction rate would depend on the circulation flow rate, particularly when circulation flow rate was low. The external mass transfer resistance can be reduced to a minimum value by increasing mixing of fluid through stirring or increasing the circulating flow rate of the reaction medium [11]. So, it can be concluded that in flow rate of 200 mL/min the mass transfer coefficient was reached to its maximum level, so by the further increase of the flow rate the RE (%) was constant. Studies were done on the flow rate property through the photoreactor using the RTD technique and its effects on the photocatalysis of PhP as a model pollutant. It was shown that the hydrodynamic characteristics affected the RE (%) performance. It is concluded that the flow characteristics are important factors to be considered in photoreactors design. RTD analysis is a very important concept to characterize mixing and flow behavior inside a reactor, and to know whether the reactor is approaching any of an ideal reactor: plug flow reactor or mixed flow reactor and in which one of them the removal efficiency is maximum. Also, RTD analysis helps to model the real reactor as a combination of ideal reactors. In addition, RTD data can also be used to analyze any nonidealities like channeling, bypassing, and short circuiting present in a reactor [18,32,37]. By analyzing the RTD data with appropriate models such as one parameter model (the tank in series model here), the results give the model parameters. This can eventually be used to scale up or to design a reactor which could be operated in optimum flow rate to obtain higher removal efficiency [33,39]. 3.3. Determination of optimal conditions for photocatalysis of PhP The main objective of the optimization in this work is to determine the optimum values of variables for photocatalytic removal process, from the model obtained using experimental data. Using the response optimizer, the desired goal in term of removal efficiency was defined as ‘‘maximize’’ to achieve the highest treatment performance. The obtained optimum values are shown in Table 6. Optimal settings for the input variables were calculated along with individual and composite desirability values to indicate how well a combination of input variables satisfy the goals which were defined for the responses. Individual desirability

Table 6 Optimum operating conditions of the process variables. Variable

Optimum values

Initial PhP concentration (mg/L) (X1) Reaction time (min) (X2) Intensity (W/m2) (X3) Flow rate (mL/min) (X4) Experimental CR (%) Predicted CR (%)

10 150 47 200 89.10 89.03

Composite desirability = 1.00; individual desirability = 1.00.

(d) evaluates how the settings optimize a single response; composite desirability (D) evaluates how the settings optimize a set of overall responses. Desirability has a range from zero to one. One represents the ideal case; zero indicates that one or more responses are outside their acceptable limits. In this work, the composite desirability is 1.00, which indicates that the settings appear to achieve favorable results for all responses as a whole. Also the achieved individual desirability of 1.00, indicates that the settings are effective in maximizing RE (%). After verifying by a further experimental test with the predicted values, the result indicated that the maximal removal efficiency was obtained when the values of each parameter were set as the optimum values. It implies that response surface methodology is a useful mathematical tool for modeling and optimization of PhP photocatalytic removal efficiency. 4. Conclusions The photocatalytic treatment of an analgesic drug, PhP, from aqueous solution in a rectangular photocatalytic reactor was modeled and optimized with CCD. Effect of operational parameters on the removal efficiency of PhP was evaluated by the response surface and contour plots. The optimum values of initial drug concentration, UV light intensity, flow rate and reaction time were 10 mg/L, 47 W/m2, 200 mL/min, and 150 min, respectively. The achieved optimum value of flow rate has been characterized and justified through RTD studies. The resulting mean residence time and dimensionless variance were obtained and compared based on entrance flow rate conditions. For defining the performance of the photoreactor in each flow rate, the RTD data were analyzed in relation with tanks-in-series flow model. The number of tank in

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