Design of Nano-Catalyst for Removal of Phenolic Compounds from Wastewater by Oxidation Using Modified Digital Basket Baffle Batch Reactor: Experiments and Modeling

Abstract

Removal of phenol and phenolic compounds from wastewater using various techniques has received considerable attention in recent years. In this work, the removal of phenol from a model solution of phenol via catalytic oxidation is investigated with oxidant H₂O₂. For this purpose, we designed a new nano-catalyst (8% Fe₂O₃/AC) by loading iron oxide nanoparticles over nano-activated carbon via the impregnation process. We modified the recently developed digital basket baffle batch reactor (DBBBR) and used it for the catalytic oxidation process in order to examine the activity of the prepared nano-catalyst. The highest efficiency of phenol removal was found to be 95.35% under the following parameters: oxidation time of 120 min, oxidation temperature at 85 °C, and stirrer speed of 600 rpm. The minimization of the sum of the squared error between the experimental data and predicted results of phenol removal was considered as a base for the optimization technique to estimate the optimal parameters for the kinetic process. The predicted conversion of phenol excellently agreed with the experimental results (absolute average errors < 5%) for a wide range of process parameters.

1. Introduction

Phenol, an essential chemical, is utilized in the production of drugs, fungicides, and preservatives and is also an essential product of the petroleum industry. Nevertheless, phenolic compounds are major contaminants that are categorized as carcinogenic and teratogenic materials [1,2]. These compounds are fed into the environment by several industrial facilities such as the oil, polymer, petrochemical, pharmaceutical, paint, and dye industries [3,4,5]. Because water is a scarce commodity around the globe, it is essential to remove toxic contaminants such as phenol from wastewater to reclaim and reuse wastewater. Several techniques have been adopted in recent years to remove phenol or phenolic compounds from wastewater [6].

High acidity, salinity, low biodegradability, and chemical oxygen demand (COD) are the major properties for phenolic compounds [4]. Also, low volatilities and readily formed azeotropes and eutectics are important characterizations for these compounds [5]. Therefore, conventional treatment techniques, such as physical and biological methods, have difficulty treating phenol and its derivatives efficiently [1,6]. The catalytic oxidation processes utilizing oxygen, ozone, hydrogen peroxide (H₂O₂), or the combination of them proved to be a highly efficient process in the elimination of phenolic compounds [7]. Catalytic oxidation employing H₂O₂ is a more environmentally friendly and efficient process as compared with catalytic oxidation utilizing air, since H₂O₂ is a stronger oxidizing agent [8,9]. In this process, phenolic compounds are oxidized by H₂O₂ to water, carbon dioxide, or some short-chain acids in the presence of a catalyst under a moderate operating condition. H₂O₂ is a non-toxic oxidant, promotes the efficiency of the oxidation process, produces green byproducts, and reduces the severe operating conditions of the process. The catalytic wastewater treatment processes via oxidation are implemented employing catalysts, which leads to a reduction in the activation energy and, thus, the process takes place under mild conditions. In addition, H₂O₂ is used as an oxidant in the catalytic oxidation process in order to overcome the limitations of liquid–gas mass transfer and extremely promote the process’s performance [9]. Currently, nanomaterials are widely applied in various fields of environmental treatment owing to their unique physiochemical properties. Economically, nanotechnology is beneficial for the utilization of water resources and the conservation of energy. Nanostructured adsorbents are also employed for the treatment of wastewater, as they react at a faster rate and exhibit much higher efficiency [10]. Activated carbons (ACs) are appropriate materials for a wide field of catalytic industries, either as catalysts or catalyst support. The effectiveness of them is considerably affected by their porous structure, surface area, and the surface active sites, which have a significant role in pollutants’ removal activity. The resistance to heat and radiation, cost (relatively cheap), stability in acidic/basic solutions, and good mechanical strength are other significant specifications of these materials. The chemistry of ACs’ surface is examined by various oxygen functional groups, like lactones, carbonyls/quinones, carboxylic acids, anhydrides, and phenols. These groups of oxygen can be added or eliminated from the materials’ surface via applying the thermal treatments for liquid and gas phases [11]. The nanoparticles of iron oxide (Fe₂O₃) have been gaining the focus of researchers in addressing environmental issues. These materials have high efficiency in removing several categories of pollutants found in water via adsorption and photo-degradation processes. Also, the deterioration of water quality has resulted in the utilization of iron oxide nanoparticles as new adsorbents for wastewater treatment. The large surface-area-to-volume ratio and great biocompatibility allow surface modification and easy separation by employing an external magnetic field of iron oxide nanoparticles, presenting them as excellent adsorbents. It is comparatively low cost, is reusable, and has excellent magnetic properties [8].

In this study, a novel nano-catalyst was prepared using 8% Fe as the active metal and activated carbon (AC) (8% Fe/AC) by employing the Incipient Wetness Impregnation (IWI) method. A digital basket baffled batch reactor (DBBBR) was recently designed by Humadi et al. [11], which was used for oxidative desulfurization of fuel. The DBBBR was found to be more effective than a conventional batch reactor by Humadi et al. In this work, we used a different version of the DBBBR (in terms of the size of different components of the reactor) to facilitate the catalytic oxidation of phenol using hydrogen peroxide. A series of experiments were then carried out in the reactor under various operating conditions and the efficiency of the reactor and the catalyst was then evaluated. A mathematical modeling technique was applied to estimate the best values of kinetic parameters for the catalytic phenol oxidation process. Finally, the optimization process was implemented so as to calculate the optimal parameters for the catalytic phenol oxidation process, at which point the removal of phenol was maximized. The novelty of this work is in conducting the catalytic phenol oxidation process in the recently designed reactor in the presence of a new homemade nano-catalyst (8% Fe/AC). Note that this type of reactor has not been used so far for the oxidation of phenol. Also, the mathematical model was built for the catalytic phenol oxidation process to find the optimal operating condition to maximize the removal of phenolic compounds.

2. Materials Used and Experimental Design

2.1. Material Application

2.1.1. Feedstock

The feedstock was a model wastewater which was prepared by injecting phenol (provided by Alpha Chemika Company—Maharashtra, India, purity of 99%) into demineralized water with a total phenol content of 839 ppm, which refers to the initial phenol concentration in the wastewater.

2.1.2. Ferric Nitrate Nonahydrate

Ferric nitrate nonahydrate (Fe(NO₃)₃.9H₂O) (obtained from Himedia, India) was utilized as the active metal in the designed nano-catalyst (8% Fe/AC) with purity 98%.

2.1.3. Activated Carbon (AC)

Commercial AC (Supplied from Alpha Chemika Company—Maharashtra, India) was utilized as catalyst support in the homemade prepared nano-catalyst.

2.1.4. Hydrogen Peroxide (30% H₂O₂)

H₂O₂ (Sigma-Aldrich (Burghausen, Germany), purity above 99.99%) was utilized to oxidize phenol to CO₂ and H₂O.

2.2. Incipient Wetness Impregnation (IWI) Process

Incipient Wetness Impregnation (IWI) [12,13,14,15,16] technology was employed in preparing the novel nano-catalyst. At first, AC was treated and dried so as to eliminate any impurities before being utilized in the IWI process. Physical activation of activated carbon and drying under inert operating conditions were carried out to remove any moisture from porosity before using it in the preparation of the nano-catalyst. Temperature of physical activation was 110 °C.

After that, the active metal solution was prepared by treating 2 g (of the metal salt) of active metal (Fe(NO₃)₃.9H₂O) with 50 mL of deionized water in a magnetic stirrer with rotational speed of 450 RPM for 1.5 h in order to make sure there was complete dissolution of the active metal in the solvent. The produced materials were then filtered in absence of heating to eliminate any further impurities. The active metal solution was then slowly added to 9.2 g of support (AC) with continuous stirring for 1 h in order to make sure that the dispersion of active metal over the support was completed. Finally, calcination process of the product was performed by utilizing the furnace with a gradual increase in temperature to 150 °C for 1.5 h. Then, the temperature of calcination was raised to 350 °C for 2 h and finally to 560 °C for 1.5 h in order to obtain the nano-catalyst (8% Fe₂O₃/AC). Figure 1 illustrates the steps of the homemade nano-catalyst (8% Fe₂O₃/AC) preparation using IWI technology.

2.3. Experimental Procedure

2.3.1. Digital Basket Baffled Batch Reactor (DBBBR)

For the convenience of the readers, we briefly describe the configuration of DBBBR here. The DBBBR was designed in the Petroleum and Gas Refinery Engineering Department, College of Petroleum Process Engineering, Tikrit University/Iraq by Humadi et al. [11] to produce greener fuel by removing sulfur from the fuel via oxidation reaction. In this work, we have redesigned the reactor in terms of different components of the reactor. Evaluation of the effectiveness of the reactor in the context of wastewater treatment via catalytic oxidation process is one of the aims of this work in addition to testing the effectiveness of the new homemade catalyst for such purpose. The design of basket baffled batch reactor enhanced distribution of 8% Fe₂O₃/AC in feedstock and achieved excellent mass transfer rate in the catalytic oxidation process. The DBBBR design involved digital mixer (range of speed from (0 to 5000) RPM), which was linked to a rod, and the end of the rod was connected to the four baskets’ impeller. Also, the baskets involved good equal distribution for the circular holes along the baskets’ surfaces in a hexagonal form, resulting in mixing channels enhancing inside the catalyst and reactor, thus improving the efficiency of oxidation technology. Four baffles were installed on the reactor wall to minimize stagnant zones in it and promote string of reactants. Baffles were distributed inside the surface of the reactor in equal dimensions (38 cm between every two baffles) and a protrusion of 2.5 cm woolen material (for high temperature conditions above 1000 °C) was used for insulating the reactor. The reactor was made of stainless steel. The specifications of the DBBBR are listed in

Table 1. The specifications of the DBBBR.

Description	Specification
Dimension of reactor	Height = 12 cm, Diameter = 10 m
Length of the rod	37 cm
Type of impeller (Stainless steel)	Four basket impeller
Height of basket	1.2 cm
Length of basket	1.2 cm
Width of basket	1.2 cm
Impeller diameter	94 mm
Height of baffle (Stainless steel)	10 cm
Width of baffle	1.5–1.8 cm

and the schematic of the DBBBR system is illustrated in Figure 2.

2.3.2. Catalytic Oxidation of Phenol Process

In order to examine the performance of the designed nano-catalyst in the modified version of the DBBBR, the catalytic oxidation of phenol used for the model solution of phenol treatment was implemented by using H₂O₂ as oxidant (25 mL fuel/1 mL H₂O₂). Phenol as a model of phenolic compounds was injected in the model solution of phenol with an initial concentration of 839 ppm. The designed 8% Fe₂O₃/AC as charged into the basket with 1.25 g of catalyst in each basket. In the catalytic phenol oxidation process, 100 mL of the feedstock was charged into the DBBBR for each run. For all experiments, the ratio of the amount of feedstock to oxidizing agent (H₂O₂) was 25 and the catalyst weight was 5 g. The catalytic phenol oxidation was processed at mild parameters, where the oxidation time was 30, 60, 90, and 120 min; the reaction temperature was 25, 45, 65, and 85 °C; the magnetic speed was 200, 400, 600, and 800 RPM. Constant pressure of 1 atm was used for all cases. In the chemical reaction, gases were evaporated through the process, which were condensed after that. The treated product was analyzed using a UV spectrophotometer instrument to estimate the final concentration of phenol.

2.3.3. UV Spectrophotometer Analysis

Considering UV-visible spectroscopy was an important suitable technique for determination of phenolic and phenol compounds in model solution. Concentrating the amount of compounds, in fact, depended on two reasons. Firstly, UV light has the ability to absorb phenol and phenolic compounds. Secondly, estimation of the compounds depended on the colored nature that could lead to absorption features in the visible range. The wavelength of phenol was between 210–225 nm.

2.3.4. Characterization of the Prepared Nano-Catalyst (8% Fe₂O₃/AC)

Brunauer–Emmett–Teller (BET)

Surface area, pore volume, and pore size of the AC support and 8% Fe₂O₃/AC were measured by utilizing the Brunauer–Emmett–Teller (BET) test and the results are explained in

Table 2. BET results for AC and prepared nano-catalyst.

Property	Support (AC)	Nano-Catalyst (8% Fe2O3/AC)
Surface area, m2g−1	908.880	778.107
Total pore volume, cm3g−1	0.512	0.4416
Mean pore diameter, nm	2.255	2.3824

. In the catalytic oxidation process, specific surface area and pore volume of the prepared nano-catalyst (8% Fe₂O₃/AC) were very substantial factors influencing the process, where increases in surface area caused enhanced phenol removal. The large surface area contributed to excellent contact area between phenol and H₂O₂, providing a high rate of elimination of phenol. In addition, the high specific surface area reinforced the diffusion of phenol molecules to the surface-active sites of the catalyst [17].

Scanning Electron Microscope with Energy Dispersive X-ray (SEM-EDX)

The SEM image of 8% Fe₂O₃/AC is displayed in Figure 3A and

Table 3. The amount of element on nano-catalyst.

Element	Line Type	Weight %	Weight % Sigma	Atomic %
C	K series	57.77	0.35	70.37
O	K series	26.80	0.33	24.51
Fe	K series	10.46	0.19	2.74

. As shown in the figure, a high and excellent distribution of Fe₂O₃ over the AC surface was noticed, where metal oxide is represented by the white regions while AC support is represented by the dark regions. The results of EDX obviously show the elemental composition of the designed nano-catalyst, as illustrated in Figure 3B. The percentage compositions were 10.46%, 26.80%, and 57.77% for iron (Fe), oxygen (O), and carbon (C), respectively. The EDX image displays a regular and good dispersion of active metal on the surface of the nano-catalyst. The results are in good agreement with the theoretical calculations of Fe amount in the designed nano-catalyst.

Fourier Transform Infrared (FTIR) Spectroscopic Analysis

The FTIR test spectrum displays the functional groups of the AC and 8% Fe₂O₃/AC, as referred to in Figure 4. The band at ~3450 cm⁻¹ was ascribed to O-H stretching vibration of hydroxyl groups. The bands at 1650–1500 cm⁻¹ were attributed to an aromatic C=C ring stretching [18]. The absorption band at 1350 cm⁻¹ was attributed to the C-H asymmetric and symmetric bending and the band between 1178 and 1088 cm⁻¹ to the C-O [19]. The absorption peaks at 700–400 cm⁻¹ corresponded to C-C bond stretching vibration [19]. After the loading process of Fe₂O₃ over AC, the absorption bands at ~470 cm⁻¹ and ~550 cm⁻¹ were increased, which was ascribed to Fe–O stretching [20,21].

3. Results and Discussion

3.1. Effect of Operating Conditions on the Catalytic Oxidation of Phenol

3.1.1. Effect of Stirrer Speed

To investigate the effect of stirrer speed on the efficiency of the phenol oxidation process, several experiments were carried out at different speed such as 200, 400, 600, and 800 RPM; at constant pressure; at different reaction times such as 30, 60, 90, and 120 min; and at different reaction temperatures such as 25, 45, 65, and 85 °C using designed catalyst (8% Fe₂O₃/AC) and H₂O₂ as an oxidant. Figure 5A–D illustrates the impact of stirrer speed on phenol removal for various operating conditions. Clearly, for each set of operating conditions, it was noted that the higher the stirrer speed the higher the conversion of phenol was, except in Figure 5D. The conversion of phenol increased from 80.45% to 94.16% (Figure 5D) when the speed was increased from 200 to 800 RPM with the time of 120 min and temperature of 85 °C [22]. However, the maximum removal of phenol was 95.35% at the best parameters (120 min, 85 °C, and 600 RPM). The influence of mixing intensity had good activity for the dispersion of the catalyst and provided excellent performance in the oxidation of phenol using H₂O₂ oxidant. When the stirrer speed was increased above 800 RPM and the temperature beyond 65 °C, the conversion of phenol decreased due to random mixing which affected the conversion of phenol.

3.1.2. Effect of Reaction Time

The impact of reaction time on phenol removal is shown in Figure 6A–D at different operating conditions. Figure 6A–D illustrates the impact of reaction time on the oxidation performance. It can be noticed that phenol removal in the BBBR reactor was dramatically promoted via raising the time of reaction as the phenol removal improved from 83.55% to 95.35% when the reaction time was enhanced from 30 min to 120 min at reaction temperature 85 °C and speed of digital 600 RPM, as shown in Figure 6C. This behavior is repeated to improve the time of contacting the oxidant and phenol, consequently supplying sufficient reaction time between phenol and hydroxyl radicals [23,24]. Therefore, oxidation technology needs sufficient time to complete as any other reaction and is improved as time is enhanced. The best oxidation performance was under the oxidation time of 120 min.

3.1.3. Influence of Reaction Temperature

Figure 7A–C shows the effect of temperature on the oxidation of phenol. At different temperatures (25, 45, 65, and 85) °C, the optimal conversion of phenol was 95.35% at the reaction temperature 85 °C. Enhancing the temperature from 25 °C to 85 °C improved the phenol removal from 36.83% to 95.35% at 600 RPM and 120 min. Oxygen free radicals were formed with enhancing temperature, and reacted with oxygen and water to generate H₂O₂ and O₃ [25]. Also, rising temperature improved the number of molecules sharing in oxidizing of phenol via enhancing the activation energy, which improved the phenol and oxygen diffusion inside the catalyst pores [16,17]. Figure 7A–C refers to the impact of the temperature on the phenol oxidation process.

4. Mathematical Model of DBBBR for Catalytic Phenol Oxidation Process

Mathematical models play a fundamental part in science and engineering in order to reinforce a conception of considerable operations and systems by employing mathematical equations. Mathematical modeling for the catalytic phenol oxidation process was applied by utilizing the gPROMS Version 7.1 (General Process Modeling System) program [14,15]. The equations provided in the mathematical modeling are listed in

Table 4. The set of equations utilized in the mathematical modeling process.

Parameter (Symbol)	Equations/Values	Equation No.
Rate of reaction ($-{\mathrm{r}}_{\mathrm{ph}}$)	$(-{\mathrm{r}}_{\mathrm{ph}})={\mathsf{ƞ}}_0{\mathrm{k}}_{}{\mathrm{C}}_{\mathrm{ph}}{}^{\mathrm{n}}$	(1)
Arrhenius equation (k)	k = k0${\mathrm{e}}^{(-\frac{\mathrm{EA}}{\mathrm{RT}})}$	(2)
The final phenol content (${\mathrm{C}}_{\mathrm{ph}}$)	${\mathrm{C}}_{\mathrm{ph}}={[{\mathrm{C}}_{\mathrm{ph},\mathrm{t}}{}^{(1-\mathrm{n})}+(\mathrm{n}-1).\mathrm{t}.{\mathrm{K}}_{\mathrm{in}}{\mathsf{ƞ}}_0]}^{(\frac{1}{1-\mathrm{n}})}$	(3)
The effectiveness factor (${\mathsf{ƞ}}_0$)	${\mathsf{ƞ}}_0=\frac{3(\mathsf{ɸ}\cot \mathrm{h}\mathsf{ɸ}-1)}{{\mathsf{ɸ}}^2}$	(4)
Thiele modulus ($\mathsf{ɸ}$)	$\mathsf{ɸ}=\frac{{\mathrm{V}}_{\mathrm{P}}}{{\mathrm{S}}_{\mathrm{P}}}\sqrt{(\frac{\mathrm{n}+1}{2})\frac{{\mathrm{k}}_{\mathrm{in}}{\mathrm{C}}_{\mathrm{ph}}{}^{(\mathrm{n}-1)}{\mathsf{\rho }}_{\mathrm{p}}}{{\mathrm{D}}_{\mathrm{ei}}}}$	(5)
The catalyst effective diffusivity (${\mathrm{D}}_{\mathrm{ei}}$)	${\mathrm{D}}_{\mathrm{ei}}=\frac{{ℇ}_{\mathrm{B}}}{\mathcal{T}}\frac{1}{\frac{1}{{\mathrm{D}}_{\mathrm{mi}}}+\frac{1}{{\mathrm{D}}_{\mathrm{ki}}}}$	(6)
The porosity of catalyst (${ℇ}_{\mathrm{B}}$)	${ℇ}_{\mathrm{B}}={\mathrm{V}}_{\mathrm{g}}{\mathsf{\rho }}_{\mathrm{p}}$	(7)
Particle density (${\mathsf{\rho }}_{\mathrm{p}}$)	${\mathsf{\rho }}_{\mathrm{p}}=\frac{{\mathsf{\rho }}_{\mathrm{B}}}{1-{ℇ}_{\mathrm{B}}}$	(8)
The tortuosity factor ($𝒯$)	Tortuosity factor ($𝒯$) of the pore network (2 to 7)	----
The Knudsen diffusivity (${\mathrm{D}}_{\mathrm{ki}}$)	${\mathrm{D}}_{\mathrm{ki}}=9700{\mathrm{r}}_{\mathrm{g}}{(\frac{\mathrm{T}}{{\mathrm{M}}_{\mathrm{w},\mathrm{ph}}})}^{0.5}$	(9)
Mean pore radius (${\mathrm{r}}_{\mathrm{g}}$)	${\mathrm{r}}_{\mathrm{g}}=\frac{2{\mathrm{V}}_{\mathrm{g}}}{{\mathrm{S}}_{\mathrm{g}}}$	(10)
The molecular diffusivity (${\mathrm{D}}_{\mathrm{mi}}$)	${\mathrm{D}}_{\mathrm{mi}}=8.93\ast {10}^{-8}(\frac{{\mathrm{v}}_{\mathrm{l}}{}^{0.267}\mathrm{T}}{{\mathrm{v}}_{\mathrm{ph}}{}^{0.267}{\mathsf{\mu }}_{\mathrm{ph}}})$	(11)
The molar volume of the liquid (${\mathrm{v}}_{\mathrm{l}}$)	${\mathrm{v}}_{\mathrm{l}}=0.285{({\mathrm{v}}_{\mathrm{cl}})}^{1.048}$	(12)
The molar volume of the phenol compound (${\mathrm{v}}_{\mathrm{ph}}$)	${\mathrm{v}}_{\mathrm{ph}}=0.285{({\mathrm{v}}_{\mathrm{cph}})}^{1.048}$	(13)
The external volume of the catalyst (For sphere particle) (${\mathrm{V}}_{\mathrm{p}}$)	${\mathrm{V}}_{\mathrm{p}}=\frac{4}{3}\mathsf{\pi }{({\mathrm{r}}_{\mathrm{p}})}^3$	(14)
The external surface of the catalyst (For sphere particle) (Sp)	${\mathrm{S}}_{\mathrm{p}}=4\mathsf{\pi }{({\mathrm{r}}_{\mathrm{p}})}^2$	(15)
The phenol viscosity (${\mathsf{\mu }}_{\mathrm{ph}}$)	${\mathsf{\mu }}_{\mathrm{ph}}=\exp {[\ln ({\mathsf{\alpha }\ast \mathsf{\mu }}_{\mathrm{ph},\mathrm{b}})\ast \frac{\ln ({\mathsf{\mu }}_{\mathrm{ph},\mathrm{b}})}{\ln ({\mathsf{\alpha }\ast \mathsf{\mu }}_{\mathrm{ph},\mathrm{b}})}]}^{\mathsf{\varphi }}$	(16)
Constant factor ($\mathsf{\alpha })$	0.1175 for alcohols and 0.248 for other materials.	----
Molecule volume fraction ($\mathsf{\varphi }$)	$\mathsf{\varphi }=\frac{1-(\mathrm{T}/{\mathrm{T}}_{\mathrm{c}})}{1-({\mathrm{T}}_{\mathrm{b}}/{\mathrm{T}}_{\mathrm{c}})}$	(17)

[26,27,28,29,30,31,32,33,34,35,36,37,38,39].

5. Kinetic Parameters Estimation Technique

The kinetic parameters of the catalytic phenol oxidation reaction can be determined by conducting the mathematical modeling process with careful matching of the results of practical experiments with the expected data. In order to estimate the optimal values for kinetic parameters, the minimization of the following objective function was evaluated as summarized below:

$$\mathrm{OBJ}={\displaystyle \sum }_{\mathrm{n}=1}^{\mathrm{Nt}}{\left({\mathrm{C}}_{\mathrm{phenol}}^{\exp }-{\mathrm{C}}_{\mathrm{phenol}}^{\mathrm{pred}}\right)}^2$$

(18)

In Equation (18), $\mathrm{Nt}$ is the number of experiments, ${\mathrm{C}}_{\mathrm{phenol}}^{\exp }$ means the experimental data, and ${\mathrm{C}}_{\mathrm{phenol}}^{\mathrm{pred}}$ is the mathematical model’s results.

The phenol conversion can be calculated using:

$${\mathrm{X}}_{\mathrm{phenol}}=1-\frac{{\mathrm{C}}_{\mathrm{phenol}}}{{\mathrm{C}}_{\mathrm{phenol}.\mathrm{t}}}$$

(19)

6. Optimization Problem Formulation for Evaluation of Kinetic Parameter

The problem of parameter evaluation was configured as follows:

Given—The conditions of the catalytic phenol oxidation reaction, the catalyst, and the reactor formation.

Obtain—The kinetic parameters (n, ko, and EA) for each designed catalyst.

So as to minimize—The sum of squared error (SSE).

Subjected to—Constraints of operation

Mathematically, by counting on the first approach, the optimization problem was presented as follows:

$$\begin{array}{ccc}\hfill \mathrm{Min}:& & \hfill \mathrm{SSE}\hfill \\ & n,EA,k_0\hfill & \\ & & \hfill \mathrm{S}.\mathrm{t}.\mathrm{f}(\mathrm{z},\mathrm{x}(\mathrm{z}),\mathrm{ẋ}(\mathrm{z}),\mathrm{u}(\mathrm{z}),\mathrm{v})=0\hfill \\ & & \hfill {\mathrm{C}}_{\mathrm{L}}\le \mathrm{C}\le {\mathrm{C}}_{\mathrm{U}}\hfill \\ & & \hfill n_l\le n\le n_u\hfill \\ & & \hfill E{A}_L\le EA\le E{A}_U\hfill \\ & & \hfill k_{OL}\le k_i\le k_{OU}\hfill \end{array}$$

S.t.f(z, x(z), ẋ(z), u(z), v) = 0: refers to the oxidation process model. z: the independent variable. u(z): the decision variable. x(z): represents the set of all variables. ẋ(z): represents the derivative of the variables with respect to time. v: is the control variable. C, C_L, C_U: concentration, lower and upper bounds of concentration. L, U: are lower and upper bounds.

7. Description of Mathematical Modeling

7.1. Determination of Kinetic Parameters

The optimal kinetic parameters of the catalytic phenol removal process were specified by applying the mathematical modeling technique, which minimized the error between the concentrations of phenol resulting from experimental runs and values determined by the model. The constant parameters applied in the modeling technique are reported in

Table 5. Constant parameters applied in the modeling.

Parameter, Unit	Value
Initial content of phenol (Ct), ppm	839
Reaction time 1, 2, 3, 4, min	30, 60, 90, 120
Reaction temperature (T1, 2, 3, 4), °C	25, 45, 65, 85
R, J/mole.°K	8.314
Vg, cm3/gm	0.4536
Sg, cm2/gm	7,073,700
Vp, cm3	0.0114137
Sp, cm2	0.28274
ρB. gm/cm3	1.79377
M.Wt of phenol	184
rg, nm	1.28249
${\mathrm{v}}_{\mathrm{cl}}$, cm3/gmole	55.95
${\mathrm{v}}_{\mathrm{c},\mathrm{ph}}$, cm3/gmole	229
Tc, °R	1250

and the optimal model parameters at various rotation speeds are presented in

Table 6. Oxidation model parameters (Optimal) under 200 RPM.

Parameter	Value
n (-)	1.9997
EA (KJ/mol)	28.8292
ko (${\mathrm{wt}}^{-0.999726}.{\min }^{-1})$	9989.6200
SSE (-)	1.13996 × 10−5

,

Table 7. Oxidation model parameters (Optimal) under 400 RPM.

Parameter	Value
n (-)	1.9869
EA (KJ/mol)	28.1398
ko (${\mathrm{wt}}^{-0.999726}.{\min }^{-1})$	15,712.4700
SSE (-)	7.81139 × 10−6

,

Table 8. Oxidation model parameters (Optimal) under 600 RPM.

Parameter	Value
n (-)	1.9265
EA (KJ/mol)	25.6211
ko (${\mathrm{wt}}^{-0.999726}.{\min }^{-1})$	11,854.0200
SSE (-)	7.3293 × 10−6

and

Table 9. Oxidation model parameters (Optimal) under 800 RPM.

Parameter	Value
n (-)	1.9629
EA (KJ/mol)	25.9162
ko (${\mathrm{wt}}^{-0.999726}.{\min }^{-1})$	14,265.0800
SSE (-)	7.0075 × 10−6

.

7.2. Results of Experiment and Simulation

The experiment’s results and predicted data are summarized in

Table 10. Experiment and simulation results under 200 RPM.

Temperature (°C)	Time (min)	Phenol Concentration (ppm)		Conversion %		Error %
		Experimental	Predicted	Experimental	Predicted
25	30	730	725.39	12.99	13.54	0.63
25	60	640	633.26	23.72	24.52	1.05
25	90	566	558.64	32.54	33.42	1.301
25	120	510	497.62	39.21	40.69	2.43
45	30	660	654.52	21.34	21.99	0.831
45	60	535	523.04	36.23	37.66	2.24
45	90	441	428.62	47.44	48.91	2.81
45	120	371	359.36	55.79	57.17	3.14
65	30	574	570.53	31.59	31.10	0.60
65	60	419	408.45	50.01	51.32	2.52
65	90	314	308.15	62.57	63.27	1.86
65	120	252	243.12	69.96	71.02	3.52
85	30	487	479.45	41.95	42.86	1.56
85	60	311	303.12	62.93	63.88	2.53
85	90	215	211.06	74.37	74.84	1.83
85	120	164	158.26	80.45	81.14	3.50

,

Table 11. Experiment and simulation results under 400 RPM.

Temperature (°C)	Time (min)	Phenol Concentration (ppm)		Conversion %		Error %
		Experimental	Predicted	Experimental	Predicted
25	30	655	655.10	21.93	21.81	0.15
25	60	512	524.26	38.98	37.51	2.40
25	90	420	428.99	49.94	48.87	2.14
25	120	351	358.80	58.16	57.24	2.22
45	30	559	564.31	33.37	32.74	0.95
45	60	388	398.98	53.75	52.45	2.84
45	90	290	297.35	65.44	64.56	2.53
45	120	222	232.05	73.54	72.34	4.53
65	30	460	464.45	45.17	44.64	0.97
65	60	279	285.33	66.75	65.10	2.27
65	90	189	194.17	77.47	76.86	2.73
65	120	141	143.06	83.19	82.95	1.46
85	30	360	365.53	57.09	56.43	1.54
85	60	188	194.56	77.59	76.81	3.49
85	90	121	122.90	85.58	85.35	1.57
85	120	83	87.07	90.11	89.62	4.90

,

Table 12. Experiment and simulation results under 600 RPM.

Temperature (°C)	Time (min)	Phenol Concentration (ppm)		Conversion %		Error %
		Experimental	Predicted	Experimental	Predicted
25	30	550	547.30	34.45	34.77	0.50
25	60	392	375.16	53.28	55.29	4.30
25	90	285	271.57	66.03	67.63	4.71
25	120	216	206.50	74.26	75.39	4.40
45	30	441	422.03	47.44	49.70	4.30
45	60	269	259.08	67.94	69.12	3.69
45	90	175	169.28	79.14	79.82	3.27
45	120	123	120.62	85.34	85.62	1.94
65	30	340	339.86	59.48	59.49	0.04
65	60	174	169.83	79.26	79.76	2.40
65	90	103	102.10	87.72	87.83	0.87
65	120	70	69.65	91.66	91.70	0.50
85	30	247	249.93	70.56	70.21	1.19
85	60	109	108.22	87.01	87.10	0.72
85	90	60	61.44	92.85	92.68	2.40
85	120	39	40.91	95.35	95.12	4.90

and

Table 13. Experiment and simulation results under 800 RPM.

Temperature (°C)	Time (min)	Phenol Concentration (ppm)		Conversion %		Error %
		Experimental	Predicted	Experimental	Predicted
25	30	544	522.02	35.16	37.78	4.04
25	60	386	381.91	53.99	54.48	1.06
25	90	288	278.99	65.67	66.75	3.13
25	120	225	213.98	73.18	74.50	4.90
45	30	438	446.77	47.80	46.75	2.00
45	60	265	265.04	68.42	68.41	0.02
45	90	178	175.31	78.78	79.11	1.51
45	120	128	126.32	84.74	84.94	1.31
65	30	333	344.20	60.31	58.98	3.36
65	60	172	174.80	79.50	79.17	1.63
65	90	105	106.76	87.49	87.28	1.68
65	120	73	73.83	91.30	91.20	1.13
85	30	242	253.76	71.16	69.76	4.86
85	60	107	112.24	87.250	86.62	4.90
85	90	62	64.96	92.61	92.26	4.77
85	120	46	43.93	94.52	94.77	4.52

. The generated values of kinetic parameters from ODS modeling give error <5% for all results.

8. Maximizing Phenol Removal Based on Optimal Operating Conditions

8.1. Formulation of Optimization Problem

The optimal kinetic parameters were employed to evaluate the best conditions for achieving the highest elimination of phenol. Therefore, the problem of optimization was created as follows:

Obtain—The optimal parameters for high conversion of phenol compounds.

So as to minimize—The phenol in wastewater.

Subjected to—Constraints in the operation.

The problem was represented mathematically as follows:

$$\begin{array}{ccc}\mathrm{Min}\hfill & & \hfill {\mathrm{C}}_{\mathrm{phenol}}\hfill \\ {\mathrm{T}}^{\mathrm{j}},{\mathrm{time}}_{\mathrm{i}}^{\mathrm{j}},{\mathrm{C}}_{\mathrm{phenol}}^{\mathrm{j}},(\mathrm{j}=\mathrm{RPM}\text{-}1,2,3,4)\hfill & & \\ \mathrm{S}.\mathrm{t}.\hfill & & \mathrm{f}(\mathrm{z},\mathrm{x}(\mathrm{z}),\mathrm{ẋ}(\mathrm{z}),\mathrm{u}(\mathrm{z}),\mathrm{v})=0\\ & & \hfill {\mathrm{time}}_{\mathrm{L}}^{\mathrm{j}}\le {\mathrm{time}}^{\mathrm{j}}\le {\mathrm{time}}_{\mathrm{U}}^{\mathrm{j}}\hfill \\ & & \hfill {\mathrm{C}}_{\mathrm{phenol}.\mathrm{tL}}^{\mathrm{j}}\le {\mathrm{C}}_{\mathrm{phenol}.\mathrm{t}}^{\mathrm{j}}\le {\mathrm{C}}_{\mathrm{phenol}.\mathrm{tU}}^{\mathrm{j}}\hfill \\ & & \hfill {\mathrm{T}}_{\mathrm{L}}^{\mathrm{j}}\le {\mathrm{T}}^{\mathrm{j}}\le {\mathrm{T}}_{\mathrm{U}}^{\mathrm{j}}\hfill \\ & & \hfill {\mathrm{X}}_{\mathrm{phenol}.\mathrm{tL}}^{\mathrm{j}}\le {\mathrm{X}}_{\mathrm{phenol}.\mathrm{t}}^{\mathrm{j}}\le {\mathrm{X}}_{\mathrm{phenol}.\mathrm{tU}}^{\mathrm{j}}\hfill \end{array}$$

The optimization technique was performed using gPROMS.

8.2. Optimal Values of Operating Conditions for Minimum Phenolic Compounds

The optimal operating conditions determined via using the optimization technique are presented in

Table 14. Optimal operating conditions for the oxidation process utilizing the designed catalyst.

Parameter, Unit	Values
	RPM-1	RPM-2	RPM-3	RPM-4
${\mathrm{C}}_{\mathrm{phenol}.\mathrm{t}}$, ppm	865	864	1104	956
T, °C	77	80	87	81
Time, min	200	193	190	180
Conversion, %	86.99	93.49	98.10	96.99

.

9. Conclusions

A novel nano-catalyst (8% Fe₂O₃/AC) was designed by employing the impregnated method in order to promote the catalytic phenol oxidation process, which was conducted in a recently developed but modified digital basket baffle batch reactor (DBBBR). There was a high morphology of metal oxide dispersed on the catalyst, as reported by SEM. The phenol oxidation process has shown dependency on the porosity of the prepared nano-catalyst, where such adsorbents’ surfaces (activated carbon) have the same base as the active metal oxides (Fe₂O₃). The designed nano-catalyst (8% Fe₂O₃/AC) was found to be a good adsorbent towards the phenolic compound, resulting in elimination of 95.35% phenol at mild operating conditions (reaction temperature 85 °C, reaction time 120 min, and speed of mixing 800 RPM). In the catalytic phenol removal process, it was observed that the utilization of nano-particles for catalyst preparation showed high performance. The IWI impregnation process is a good method for nano-catalyst preparation owing to the excellent dispersion of the active metal beside the high pore volume and surface area of the catalyst (8% Fe₂O₃/AC). The performance of 8% Fe₂O₃/AC depended, fundamentally, on the active compound and the amount of metal oxide loaded over the catalyst support (AC). The minimization of the sum of the squared error between the experimental data and predicted results of phenol removal was considered as a base for the optimization technique to estimate the optimal parameters for the kinetic process. The predicted conversion of phenol illustrated excellent agreement with the experimental results for a wide range of the operating condition, with absolute average errors less than 5%.