Catalytic process modeling and sensitivity analysis of alkylation of benzene with ethanol over MIL-101(Fe) and MIL-88(Fe)

Abstract

A solvothermal method was used to synthesize MIL-101(Fe) and MIL-88(Fe), which were used for alkylation of benzene. The synthesized catalysts were characterized by X-ray diffraction, Fourier transform infrared spectroscopy, field emission scanning electron microscope, dynamic light scattering, and BET techniques. Metal-organic frameworks (MOFs) were modeled to investigate the catalytic performance and existence of mass transfer limitations. Calculated effectiveness factors revealed absence of internal and external mass transfer. Sensitivity analysis revealed best operating conditions over MIL-101 at 120°C and 5 bar and over MIL-88 at 142°C and 9 bar.

Key words： MOFs; alkylation; ethylbenzene; catalysts pellet model; kinetic model; sensitivity analysis

Introduction

Metal-organic frameworks (MOFs) have been widely applied in gas storage and separation, sensors, catalysis, and drug delivery [¹–⁴]. MOFs consist of an organic linker, such as terephthalic acid, and a metal ion, which makes them an infinite porous material [⁵,⁶]. They have high surface area, controllable geometry, adjustable pores, and structural variety, compared with conventional microporous and mesoporous materials [⁷]. They are frequently applied as an catalyst in Aldol condensation [⁸], Knoevenagel condensation [⁹,¹⁰], photocatalysis [¹¹,¹²], hydrogenation/isomerization [¹³,¹⁴], cyanosilylation of aldehydes [¹⁵], oxidation [¹⁶,¹⁷], acylation/alkylation of aromatics [¹⁸,¹⁹], and other condensation reactions [²⁰].

Alkylation and acylation reactions are widely used in chemical and petrochemical processes to produce organic products such as solvents, pharmaceuticals, fragrance, dyes, and agrochemicals [²¹]. Traditionally, the alkylation process is carried out using chloride acids such as AlCl₃, FeCl₃ or TiCl₄, but the use of them may lead to problems such as catalyst stability, equipment corrosion, and environment pollution [²²]. Hence, enormous attempts have been made to expand alternative heterogeneous catalytic systems (e.g., zeolites), in which utilizing solid acid catalysts would facilitate product separation and catalyst recovery and reduce product contamination by lowering metal leaching [²³,²⁴]. Various heterogeneous components such as zeolites, modified clays, MCM-41, ion-exchange resins, mesoporous sulfated zirconia or nafion/silica composite materials have been considered for alkylation or acylation processes [²⁶,²⁷]. However, the industrial alkylation process was carried out using zeolites under license by companies such as UOP, Mobil Badger or Eni, where this process was carried out at elevated temperature (e.g., 400°C) with high by-products [²¹]. As is known to all, high temperature results in a high tendency of carbon deposition on the catalyst and increases utility costs. Recently, MOFs such as IRMOF-8 [²²], MOF-5 [¹⁸], Cu-MOF-74 [²³], MIL-101(Fe) [²⁴], and MIL-88(Fe) [²⁴] have been used in both alkylation and acylation processes at low temperature in comparison to conventional catalysts.

In this work, we synthesized MIL-101(Fe) and MIL-88(Fe) using a conventional solvothermal method, and used the alkylation process to evaluate the catalytic activity of the synthesized catalysts. We performed the kinetic study at various temperatures and space velocities over MIL-101 and MIL-88. The proposed kinetic model was used in pellet modeling and investigation into catalyst performance, where mass transfer limitations over MIL-101(Fe) and MIL-88(Fe) have been evaluated in the alkylation process.

Materials and methods

Synthesis of MIL-101(Fe)

A previously reported solvothermal method was used for the synthesis of MIL-101. FeCl₃·6H₂O, N,N-dimethylformamide (DMF) and terephthalic acid (1,4-benzene dicarboxylic acid, BDC) were used as the iron source, solvent, and organic linker, respectively. FeCl₃·6H₂O (5 mmol) was dissolved in 30 mL DMF to form a clear solution, and 2.5 mmol terephthalic acid was dissolved in the solution. The prepared mixture was then transferred to a teflon-lined stainless steel autoclave at 110°C for 20 h. After that the autoclave was allowed to cool to room temperature, and the light orange powder of MIL-101 was recovered and washed with water three times for 30 min and with ethanol once for 1 h to extract DMF and unreacted BDC. Finally, MIL-101(Fe) was dried at 100°C and activated in a vacuum oven at 150°C.

Synthesis of MIL-88(Fe)

For the synthesis of MIL-88(Fe), FeCl₃·6H₂O, DMF, BDC, and NaOH were used as the metal source, solvent, organic linker and source of the hydroxyl group. Firstly, 6 mmol FeCl₃·6H₂O was dissolved in 30 mL DMF, and 6 mmol BDC was added to the solution under stirring to form a clear solution. Afterwards, 5 mL of 2 mol∙L^–1 NaOH was added to the solution, and the prepared solution was transferred to a teflon-lined stainless steel autoclave at 100°C for 12 h. After 12 h, the solution was centrifuged to recover light yellow MIL-88 powder and washed with water three times for 30 min and with ethanol once for 1 h. Finally, MIL-88 powder was dried at 100°C and activated at 150°C in a vacuum oven.

Characterization techniques

A Cu-Kα X-ray diffractometer (XRD, INEL, Equniox 3000, France) in the range of 5°–120° at a speed of 0.5°∙min^–1 was used to investigate the crystallinity of the synthesized MIL-101 and MIL-88. Chemical bonding of the catalysts was studied in the range of 400–4000 cm^–1 by Fourier transform infrared spectroscopy (FTIR, Thermo Scientific Nicolet iS50, USA). Field emission scanning electron microscopy (FESEM, TESCAN, MIRA II, Czech Republic) was used to investigate the crystalline morphology of the MOFs. The surface area, pore volume, and pore diameter of the catalysts were evaluated using the Brunauer-Emmett-Teller and Barrett-Joyner-Halenda (BET-BJH, Quantachrome, NOVA 1000, USA) method. Dynamic light scattering method (DLS, VASCO2, CORDOUAN, France) was used to evaluate particle size distribution.

Kinetic evaluation

The catalytic performance of MIL-101 and MIL-88 was evaluated using gas-phase alkylation of benzene with ethanol. A stainless steel gas-phase microreactor with a 2 cm catalyst holder in diameter was used to evaluate the catalytic performance of the synthesized catalysts in the temperature range of 100°C–200°C. Different weight hourly space velocity (WHSV, h^–1) at a constant temperature was used to feed a mixture of benzene/ethanol (2 : 1 molar ratio) on the catalyst bed. The products were analyzed by means of a gas chromatograph (GC, Younglin, Republic of Korea) equipped with a helium ionization detector (HID) and TRB-5MS (60 m, 0.25 mm, 0.25 mm) column and gas chromatography-mass spectroscopy (Agilent, GC 6890, MS 5973, USA) equipped with DB WAX column. The reaction rate and activation energy were calculated using the reaction data.

Mathematical model of the pellet

The schematic of the assumed geometry for catalyst pellets is shown in Fig. 1. Accordingly, the general form of material balance at steady-state condition can be written as

(1)D_{\mathrm{eff}}{\displaystyle \frac{\mathrm{1}}{r^q}}{\displaystyle \frac{\partial }{\partial r}}\left(r^q{\displaystyle \frac{\partial C_{\mathrm{A}}}{\partial r}}\right)+r_{\mathrm{A}}=\mathrm{0},\mathrm{\hspace{0.17em}}{r}_{\mathrm{A}}=r_{\mathrm{A}}(C_{\mathrm{A}},C_{\mathrm{B}},\dots ,T),

\{\begin{array}{l}q=\mathrm{0},\mathrm{\hspace{0.17em}}\mathrm{Cartesian},\\ q=\mathrm{1},\mathrm{\hspace{0.17em}}\mathrm{cylindrical},\\ q=\mathrm{2},\mathrm{\hspace{0.17em}}\mathrm{spherical}.\end{array}

where D_eff is the effective diffusion coefficient, C_A is the concentration of reactant and r_A is the reaction rate of component A.

The boundary conditions are as follows:

(2)r=R,\mathrm{\hspace{0.17em}}\mathrm{\hspace{0.17em}}{C}_{\mathrm{A}}=C_{\mathrm{A0}},

(3)r=\mathrm{0},\mathrm{\hspace{0.17em}}\mathrm{\hspace{0.17em}}{\displaystyle \frac{\partial C_{\mathrm{A}}}{\partial r}}=\mathrm{0.}

Fig.1 Schematic of MOF catalyst particles as a porous medium.

Full size|PPT slide

Dimensionless concentration and radius can be written as

(4)f={\displaystyle \frac{C_{\mathrm{A}}}{C_{\mathrm{A0}}}},\mathrm{\hspace{0.17em}}\rho ={\displaystyle \frac{r}{R}}.

So the differential equation and boundary conditions are rewritten as

(5)D_{\mathrm{eff}}{\displaystyle \frac{\mathrm{1}}{{\rho }^q}}{\displaystyle \frac{\partial }{\partial \rho }}\left({\rho }^q{\displaystyle \frac{\partial f_{\mathrm{A}}}{\partial \rho }}\right)+R^{\mathrm{2}}{r}_{\mathrm{A}}=\mathrm{0},\mathrm{\hspace{0.17em}}{r}_{\mathrm{A}}=r_{\mathrm{A}}(f_{\mathrm{A}},f_{\mathrm{B}},\dots ,T),

(6)\rho =\mathrm{1},\mathrm{\hspace{0.17em}}\mathrm{\hspace{0.17em}}{f}_{\mathrm{A}}=\mathrm{1},

(7)\rho =\mathrm{0},\mathrm{\hspace{0.17em}}\mathrm{\hspace{0.17em}}{\displaystyle \frac{\partial f_{\mathrm{A}}}{\partial \rho }}=\mathrm{0.}

However, D_eff evaluation consists of molecular diffusion and Knudsen diffusion, where these two parameters are evaluated as follows. The molecular diffusion equation [²⁵] is

(8)D_{\mathrm{AB}}={\displaystyle \frac{\mathrm{0.001858}{T}^{\mathrm{3}/\mathrm{2}}{[(M_{\mathrm{A}}+M_{\mathrm{B}})/M_{\mathrm{A}}{M}_{\mathrm{B}}]}^{\mathrm{1}/\mathrm{2}}}{P{\sigma }^{\mathrm{2}}{\Omega }_{\mathrm{D}}}},

where T, M_A, M_B, P, s_AB, and W_D are temperature, the molecular weight of component A, the molecular weight of component B, pressure, effective collision diameter Å, and collision integral, respectively. For diffusion in porous material with smaller pore size than normal mean free path, the Knudsen diffusion is described as [²⁶]

(9)D_{\mathrm{K}}=\mathrm{9700}r\sqrt{{\displaystyle \frac{T}{M}},}

where r is pore radius (cm) and M is molecular weight. Whatever, D_pore is as follows:

(10)D_{\mathrm{pore}}^{-\mathrm{1}}={\displaystyle \frac{\mathrm{1}}{D_{\mathrm{AB}}}}+{\displaystyle \frac{\mathrm{1}}{D_{\mathrm{K}}}}.

Meanwhile, D_eff is a function of tortuosity (t) and porosity (e) of porous material, so D_eff is written as [27]

(12){\displaystyle \frac{D_{\mathrm{eff}}}{D_v}}={\displaystyle \frac{\epsilon }{\tau }},

where t is a function of e too, which is normally expressed in the form of \tau ={\epsilon }^{-\mathrm{0.5}}.

Diffusional resistance was measured using the effectiveness factor, which in the present work for alkylation agent is defined by

(13)\eta ={\displaystyle \frac{\mathrm{Actual}\mathrm{\hspace{0.17em}}\mathrm{overall}\mathrm{\hspace{0.17em}}\mathrm{reaction}\mathrm{\hspace{0.17em}}\mathrm{rate}}{\begin{array}{l}\mathrm{Reaction}\mathrm{\hspace{0.17em}}\mathrm{rate}\mathrm{\hspace{0.17em}}\mathrm{that}\mathrm{\hspace{0.17em}}\mathrm{would}\mathrm{\hspace{0.17em}}\mathrm{result}\mathrm{\hspace{0.17em}}\mathrm{if}\mathrm{\hspace{0.17em}}\mathrm{the}\mathrm{\hspace{0.17em}}\mathrm{entire}\mathrm{\hspace{0.17em}}\mathrm{interior}\\ \mathrm{surface}\mathrm{\hspace{0.17em}}\mathrm{was}\mathrm{\hspace{0.17em}}\mathrm{exposed}\mathrm{\hspace{0.17em}}\mathrm{to}\mathrm{\hspace{0.17em}}\mathrm{external}\mathrm{\hspace{0.17em}}\mathrm{pellet}\mathrm{\hspace{0.17em}}\mathrm{surface}\mathrm{\hspace{0.17em}}\mathrm{conditions}\end{array}}}{\displaystyle \frac{-r_{\mathrm{A}}}{-r_{\mathrm{A,s}}}}={\displaystyle \frac{A_{\mathrm{p}}{D}_{\mathrm{eff}}\partial C_{\mathrm{A}}/\partial r}{-r_{\mathrm{A,s}}{V}_{\mathrm{p}}}}.

\eta \to \mathrm{1} illustrates surface reaction limited regime and \eta \ll \mathrm{1} indicates dominant diffusion limited regime.

Moreover, internal mass transfer limitation was also evaluated using the Weisz-Prater criterion [28]:

(14)C_{\mathrm{wp}}={\displaystyle \frac{-{r^{\prime }}_{\mathrm{A,obs}}{\rho }_{\mathrm{c}}{R}^{\mathrm{2}}}{D_{\mathrm{eff}}{C}_{\mathrm{As}}}},

where –r_A,obs, r_c, and C_As are observed reaction rate, catalyst density and reactant concentration at the surface of catalyst, respectively. With C_{\mathrm{wp}}\ll \mathrm{1} there is not any internal mass transfer limitation over the catalyst, while C_{\mathrm{wp}}>\mathrm{1} indicates the existence of internal mass transfer limitation. Moreover, the presence of external mass transfer limitation was checked as follows [28]:

(15){\displaystyle \frac{\mathrm{observed}\mathrm{\hspace{0.17em}}\mathrm{rate}}{\mathrm{rate}\mathrm{\hspace{0.17em}}\mathrm{of}\mathrm{\hspace{0.17em}}\mathrm{film}\mathrm{\hspace{0.17em}}\mathrm{resistance}\mathrm{\hspace{0.17em}}\mathrm{control}}}={\displaystyle \frac{-r_{\mathrm{A,obs}}{V}_{\mathrm{p}}}{A_{\mathrm{p}}{C}_{\mathrm{Ag}}{k}_{\mathrm{g}}}},

where V_p, A_p, C_Ag, and k_g are pellet volume, pellet surface, reactant concentration at gas phase and local mass transfer coefficient, respectively. Local mass transfer coefficient (k_g) can be calculated as follows:

(16)Sh={\displaystyle \frac{k_{\mathrm{g}}d}{D_{\mathrm{AB}}}}={\displaystyle \frac{\mathrm{1}}{\mathrm{0.8237}-\ln {(Pe)}^{\mathrm{0.5}}}},\mathrm{\hspace{0.17em}}\mathrm{\hspace{0.17em}}Pe=ReSc,

where Sh, d, Pe, Re, and Sc are Sherwood number, catalyst diameter, Peclet number, Reynolds number, and Schmidt number, respectively.

Kinetic models

Alkylation of benzene with ethanol was used to evaluate the catalytic activity of MIL-101(Fe) and MIL-88(Fe) at the gas phase and atmospheric pressure. Carbonium ion-type mechanism is commonly used to explain the alkylation reaction as an electrophilic reaction (Scheme 1). The reaction is initiated by producing an electrophilic group by bridging a proton from the acidic site with alkylation agents (e.g., ethanol or anisole) and attacking the electrophilic group to the aromatic ring, where the protonated ring is formed on the surface and the alkyl is built by returning a proton to the surface [²⁹].

Fig.2 Scheme 1 Alkylation of benzene over MIL-101(Fe) and MIL-88(Fe).

Full size|PPT slide

Several kinetic models were used to illustrate the alkylation of light hydrocarbons. Langmuir-Hinshelwood (LH) or Rideal-Eley (RE) mechanisms are widely used to show the kinetic model of the alkylation process. As a typical example, Ruckenstein and Smirniotis (1995) [³⁰] and Pradhan et al. (2001) [³¹] have exhibited benzene alkylation with both LH and RE mechanisms. Furthermore, power law, LH and RE models were utilized by Sotelo et al. (1993) to investigate the kinetic mechanism of alkylation of toluene. However, by the assumption of absorption of both reactants on the active phase of catalyst (according to Scheme 1), LH mechanism can achieve

(17)-r_i={\displaystyle \frac{k_{\mathrm{S}}{K}_{\mathrm{A}}{K}_{\mathrm{B}}{C}_{\mathrm{A}}{C}_{\mathrm{B}}}{{(\mathrm{1}+K_{\mathrm{B}}{C}_{\mathrm{B}}+K_{\mathrm{A}}{C}_{\mathrm{A}})}^{\mathrm{2}}}}.

On the other hand, the RE mechanism can be written by the assumption of alkylation agent absorption as follows:

(18)-r_i={\displaystyle \frac{k_{\mathrm{S}}{K}_{\mathrm{A}}{C}_{\mathrm{A}}{C}_{\mathrm{B}}}{\mathrm{1}+K_{\mathrm{A}}{C}_{\mathrm{A}}}},

where k_s, K_A, and K_B are kinetic rate constant, equilibrium constant of the alkylation agent, and equilibrium constant of the aromatics, respectively. C_A and C_B are concentration of the alkylation agent and concentration of the aromatics, respectively. In this work, all of the rate equations were written based on the alkylation agent (r_A).

On the other hand, k_s can be defined with the Arrhenius equation:

(19)k_{\mathrm{S}}=k_{\mathrm{0}}\exp \left({\displaystyle \frac{-E}{\mathrm{R}T}}\right).

Furthermore, the observed reaction rate at the gas phase for plug flow reactor can be written as follows:

(20)-r_{\mathrm{A,obs}}={\displaystyle \frac{\mathrm{d}X}{\mathrm{d}(W/F_{\mathrm{A}\mathrm{o}})}}.

In this paper, bi-reactant adsorption was assumed on the catalyst active phase, so the LH model was used as the kinetic model.

Solution procedure

One-dimensional boundary value problem (BVP, Eq. (5)) has been solved by applying MATLAB software and a discretization method, such as the finite difference method. The nonlinear least square method was used for parameter estimation of the kinetic equation. r_A,obs for evaluation of external and internal limitations was evaluated using conversion as low as 8%. Meanwhile, sensitivity analysis using LH model was carried out on the ASPEN HYSYS simulator.

Results and discussion

Catalyst characterization

Powder XRD was used to verify the structure of MIL-101(Fe) and MIL-88(Fe). Figure 2 displays the XRD results for the synthesized MIL-101(Fe) and MIL-88(Fe). The peaks between 8 and 10.7 indicate the formation of MIL-101(Fe) with good crystallinity. Furthermore, significant peaks at 9.3–15 reveal the formation of MIL-88. The XRD results also indicate appropriate crystallinity of the synthesized MIL-88(Fe).

Fig.3 Powder XRD for the synthesized MIL-101(Fe) and MIL-88(Fe).

Full size|PPT slide

Fourier transform infrared spectroscopy (FT-IR) results for MIL-101 and MIL-88 are illustrated in Fig. 3. The results for MIL-101 indicate the peak at 545 cm^–1 belongs to Fe‒O. The peaks between 735 and 1000 cm^–1 attributed to C‒H bonding reveal the presence of an organic linker in the structure of MIL-101(Fe). Furthermore, strong vibrations at 1400 and 1600 indicate the C‒O and COO bonds belong to the organic linker at MIL-101. Additionally, FT-IR results for MIL-88 show that peaks at 620–720 cm^–1 belong to Fe‒O bonding, and vibrations around 1396–1595 cm^–1 are attributed to symmetric and asymmetric of C‒O carboxyl group. The peak at 1685 cm^–1 indicates C=O bond related to the organic linker in the MIL-88 structure.

BET-BJH test was used to evaluate the surface area, pore volume, and pore diameter of the catalysts. BET results show a surface area of 1800 m²·g^–1, a pore volume of 1.7 cc·g^–1, and a pore diameter of 2 nm for MIL-101 at 77 K. Furthermore, due to highly flexible solids, MIL-88 had close pores during drying and cooling to 77 K, and as a consequence, N₂ adsorption in pores of MIL-88 was very low, so simulated BET was performed to evaluate the surface area of MIL-88 to be 3040 m²·g^–1. BET test was carried out for MIL-88, revealing a surface area of 26 m²·g^–1. The simulated results indicated MIL-88 had a pore diameter of 9 nm [32].

Fig.4 FT-IR spectra for the synthesized MIL-101(Fe) and MIL-88(Fe).

Full size|PPT slide

The morphology and crystal structure of synthesized catalysts were studied using FESEM micrographs. Figure 4 shows the synthesized crystals of MIL-101 and MIL-88. MIL-101 had crystals with an octahedral shape (Fig. 4(a)), while MIL-88 had crystals with a hexagonal bi-pyramid structure (Fig. 4(b)). Furthermore, FESEM results indicate high crystallinity of MIL-88 and MIL-101, which is in good agreement with the XRD results.

Fig.5 FESEM micrographs of (a) MIL-88(Fe) and (b) MIL-101(Fe).

Full size|PPT slide

Figure 5 shows the DLS results for particle size distribution of the synthesized MOFs. The detected average size for MIL-101(Fe) and MIL-88(Fe) was about 685 and 567 nm, respectively.

Fig.6 DLS results for (a) MIL-101(Fe) and (b) MIL-88(Fe).

Full size|PPT slide

Table 1 summarizes the properties of MIL-101(Fe) and MIL-88(Fe) that were used for the alkylation and acylation reactions.

Tab.1 Summarized properties of the synthesized MOFs

Catalyst	Particle size /nm	Surface area /(m2·g–1)	Pore diameter /nm	Porosity /e
MIL-101	685	1800	2	0.55
MIL-88	567	3040	0.9	0.75

Catalytic performance

Benzene alkylation was carried out for the kinetic study over MIL-101 and MIL-88 catalysts. Typically, the weight of catalysts was varied to change the space velocity of reactants to catalysts (W/F_Ao), while the mole ratio of benzene to ethanol was adjusted as 2:1. Figure 6 illustrates ethanol conversion changes over MIL-101 and MIL-88 at various temperatures as a function of 1/WHSV (h^–1). Langmuir-Hinshelwood (LH) mechanism based on the surface reaction was used to express the reaction rate based on the illustrated isotherms. Ethanol conversion was decreased at various temperatures by decreasing the weight of catalysts, and more significant decrease of conversion was observed over MIL-101 than that over MIL-88.

Fig.7 Conversion of the alkylation agent over (a) MIL-101(Fe) and (b) MIL-88(Fe).

Full size|PPT slide

The estimated kinetic parameters are listed in Table 2 based on Eqs. (14) and (15) and Fig. 6. R² between 0.96 and 0.98 reveals the reliability of the estimated rate constants of experimental data utilizing the LH model for both catalysts.

Tab.2 Parameter estimation results for the LH equation^a)

Catalyst	Temperature /°C	Model parameter			Activation energy /(kJ·mol–1)	R2
		ks /(mol·g–1·min–1)	KB /(mL·mol–1)	KA /(mL·mol–1)
MIL-101(Fe)	125	1.429×104	1.97	543.2	49.9	0.96
	150	1.359×104	0.46	386.4		0.97
	175	2564.0	0.14	218.1		0.96
MIL-88(Fe)	150	2980.0	0.59	537.5	172.3	0.98
	175	4.582×104	0.30	299.0		0.96
	200	2.020×104	0.16	283.0		0.98

a) These data were previously reported in reference [24].

Figure 7 illustrates concentration profiles of the key components in the alkylation reaction over MIL-101 and MIL-88 with pellet radius at typical conditions. Ethylbenzene and toluene concentration steadily increased through both catalysts. The concentration profile for MIL-88 indicated a sharp decrease in benzene and ethanol content, while at this typical condition (150°C, WHSV= 3.34 h^–1), the concentration changes showed lower reactant consumption over MIL-101. By contrast, the concentration profile for MIL-101 showed relatively high benzene concentration at all positions. Simulation results also showed higher ethylbenzene concentration for MIL-88 compared with that for MIL-101. Moreover, from the concentration profile, it can be found that the main reaction zone for MIL-88 and MIL-101 was located at r/R≈ (0.6, 1) and (0.4, 1), respectively. Higher ethylbenzene concentration over MIL-88 is attributed to its lower acidic site strength that suppressed alkylation agent cracking, which leads to less toluene production rate as the other main products of alkylation reaction using MIL-88. By contrast, the strong acid sites of MIL-101 generated more ethyl groups, leading to lower selectivity of MIL-101 to ethylbenzene due to higher toluene production.

Fig.8 Concentration profiles of ethanol (EtOH), benzene (Bz), ethylbenzene (EB), and toluene (Tol) over MIL-101 (150°C) (a) and MIL-88 (175°C) (b) utilizing the LH model.

Full size|PPT slide

Figure 8 illustrates the effect of temperature on the selectivity of ethylbenzene, showing a relatively high sensitivity of selectivity to the temperature. A significant increase in selectivity of main products (ethylbenzene and toluene) was observed due to higher diffusion rate at higher temperatures. Figure 8(a) demonstrates the superior MIL-88 selectivity to ethylbenzene at almost all temperatures due to suppression formation of the methyl group ({\mathrm{CH}}_{\mathrm{3}}^{\mathrm{+}}) compared with that of MIL-101. The best ethylbenzene selectivity over MIL-101 achieved at 150°C was about 39%, while that over MIL-88 achieved at 175°C was about 80%. In addition, as a result of low benzene conversion, the performance of MIL-101 decreased significantly after 150°C. MIL-88 EB selectivity decreased with increasing the temperature to 200°C slightly. In sum, the simulated results demonstrate best operation conditions at a low temperature and are in good agreement with experimental results.

Fig.9 Selectivity of ethylbenzene (EB) over MIL-88 (a) and MIL-101 (b) as a function of temperature.

Full size|PPT slide

The focus of the present work is to figure out the existence of internal limitations on catalytic performance. Figure 9 illustrates the effectiveness factor variations with pellet radius (r/R). The effectiveness factor in the range of 0.7–1 indicates small internal diffusion resistance for both MIL-101 and MIL-88. MIL-101 demonstrates higher effectiveness factor due to its higher surface area and pore diameter, which leads to better catalytic performance. Accelerated cracking of raw materials due to facilitated diffusion in MIL-101 structure (produce more {\mathrm{CH}}_{\mathrm{3}}^{\mathrm{+}}) can lead to low ethylbenzene selectivity. In contrast, 0.7–0.9 effectiveness factor indicates the lower catalytic performance of MIL-88 but with higher selectivity to ethylbenzene as the main product. It can be concluded that MOFs can be used as suitable catalysts with a high surface area in the absence of internal limitation.

Fig.10 Variation of effectiveness factor of MIL-101(Fe) and MIL-88(Fe) with pellet size.

Full size|PPT slide

Additionally, the Weisz-Prater criterion and the ratio of observed rate against the rate of film resistance have been used in the determination of internal and external limitations. The minimal quantity of Weisz-Prater and external criterion (\ll \mathrm{1}) occurs in the absence of internal and external restriction. The calculated criterion is shown in Table 3. Accordingly, very small quantities indicate no internal and external limitations over MIL-101 and MIL-88.

Tab.3 Calculated values for external and internal mass transfer limitations

Catalyst	Density /(g·cm–3)	Deff /(cm2·s–1)	Cwp	{\displaystyle \frac{-r_{\mathrm{A,obs}}{V}_{\mathrm{p}}}{A_{\mathrm{p}}{C}_{\mathrm{Ag}}{k}_{\mathrm{g}}}}
MIL-101(Fe)	0.62	1.93×10–3	8.86×10–4	2.47×10–4
MIL-88(Fe)	1.51	1.55×10–3	1.70×10–3	1.70×10–4

Sensitivity analysis

Temperature effect

Chemisorption and surface reaction will control the reaction over the catalysts in the absence of diffusional resistance and external limitations. The Arrhenius law k_{\mathrm{S}}=k_{\mathrm{0}}\exp \left({\displaystyle \frac{-E}{\mathrm{R}T}}\right) and LH model were used in sensitivity analysis through ASPEN HYSYS simulator software. Mole fraction variations of ethylbenzene, toluene, and benzene over MIL-101 and MIL-88 with temperature are shown in Fig. 10. The sensitivity analysis reveals higher toluene production utilizing MIL-101 catalyst at all temperatures. The results also suggest that MIL-101 optimum operating temperature with the maximum ethylbenzene concentration and benzene conversion was at about 120°C. Figure 10(a) also shows a sudden increase of benzene after 150°C due to lower conversion and toluene concentration rise after 170°C as a result of higher ({\mathrm{CH}}_{\mathrm{3}}^{\mathrm{+}}) through the active phase of the catalyst. Moreover, based on Fig. 10(b), the sensitivity analysis for MIL-88 reveals maximum ethylbenzene yield and benzene conversion at about 142°C. A similar trend was observed through MIL-88: benzene conversion declined with increasing temperature after 142°C.

Fig.11 Temperature sensitivity analysis for MIL-101 (a) and MIL-88 (b).

Full size|PPT slide

Pressure effect

The LH model using C_{\mathrm{A}}={\displaystyle \frac{y_{\mathrm{A0}}{P}_{\mathrm{t}}}{\mathrm{R}T}} can be rewritten as follows:

(18)r_{\mathrm{A}}\mathrm{=}{\displaystyle \frac{k_{\mathrm{S}}{K}_{\mathrm{B}}{K}_{\mathrm{A}}{y}_{\mathrm{A}}{y}_{\mathrm{Bz}}{P}_{\mathrm{t}}^{\mathrm{2}}}{{(RT)}^{\mathrm{2}}{(\mathrm{1}+K_{\mathrm{A}}{y}_{\mathrm{A}}{P}_{\mathrm{t}}/RT+K_{\mathrm{Bz}}{y}_{\mathrm{Bz}}{P}_{\mathrm{t}}/RT)}^{\mathrm{2}}}},

where y_A, y_Bz, P_t, R and T are alkylation agent mole fraction, benzene mole fraction, total pressure, universal gas constant, and temperature, respectively. ASPEN HYSYS simulator was used to investigate the pressure effect on the reaction rate of alkylation of benzene with ethanol using MIL-101 and MIL-88 catalysts. Figure 11 illustrates the pressure effect on the mole fraction of reactants and products of the benzene alkylation reaction. An increase in pressure to 5 bar led to the higher mole fraction of ethylbenzene using MIL-101 (Fig. 11(a)) due to better diffusion of reactants. Low adsorption and desorption rate due to reactant accumulation on the active phase utilizing MIL-101 at higher pressure led to the lower conversion of benzene. This phenomenon also led to the decline in ethylbenzene concentration as the desired product.

Furthermore, the variation of pressure over MIL-88 (Fig. 11(b)) reveals that the best results (highest ethylbenzene mole fraction) were achieved at about 9 bar. Indeed, a lower diffusion rate has occurred as a result of a flexible structure of MIL-88 at higher pressures, which led to lower benzene conversion and ethylbenzene selectivity. On the other hand, the results reveal that MIL-88 produced a higher concentration of ethylbenzene as the desired product at almost all pressure compared with MIL-101.

Fig.12 Pressure sensitivity analysis for MIL-101 (a) and MIL-88 (b).

Full size|PPT slide

Conclusions

The solvothermal method was used to synthesize MIL-101(Fe) and MIL-88(Fe). XRD and FTIR results approved the formation of MIL-101 and MIL-88. BET results show a surface area of 1800 m²·g^–1 for MIL-101, and simulated results indicate a surface area of 3040 m²·g^–1 for MIL-88, but BET test reveals a surface area of 26 m²·g^–1 for MIL-88 due to its flexible structure. The alkylation process was used to evaluate the catalytic performance and Langmuir-Hinshelwood model parameter estimation over MIL-101 and MIL-88. Results indicate that the LH model with R² between 0.96 and 0.98 has proper results fitting. Furthermore, catalyst pellets were modelled and solved with proposed kinetic models to estimate catalytic performance (effectiveness factor (h)) and investigate mass transfer limitations. Results indicate the high catalytic performance of MIL-101 and MIL-88 with h = 0.7–1, which means very low internal diffusion limitations. Additionally, Weisz-Prator and external mass transfer criterion revealed very low internal and external mass transfer limitations over both catalysts. The sensitivity analysis revealed the best operating conditions at 5 bar and 120°C over MIL-101, and that at 9 bar and 142°C over MIL-88.

Acknowledgements

The authors acknowledge support of Iran Initiative Nanotechnology Council for this project and assistance of the personnel of Instrumental Analysis Laboratory and Central Laboratory of Amirkabir University of Technology (Tehran Polytechnic).

References

1 Tranchemontagne D J, Ni Z, O’Keeffe M, Yaghi O M. Reticular chemistry of metal-organic polyhedra. Angewandte Chemie International Edition, 2008, 47(28): 5136–5147

2 Kaye S S, Dailly A, Yaghi O M, Long J R. Impact of preparation and handling on the hydrogen storage properties of Zn₄O(1,4-benzenedicarboxylate)₃ (MOF-5). Journal of the American Chemical Society, 2007, 129(46): 14176–14177

3 Al-Janabi N, Alfutimie A, Siperstein F R, Fan X. Underlying mechanism of the hydrothermal instability of Cu₃(BTC)₂ metal-organic framework. Frontiers of Chemical Science and Engineering, 2016, 10(1): 103–107

4 Zhang M, Huang B, Jiang H, Chen Y. Metal-organic framework loaded manganese oxides as efficient catalysts for low-temperature selective catalytic reduction of NO with NH₃. Frontiers of Chemical Science and Engineering, 2017, 11(4): 594–602

5 Zhang X, Llabrés i Xamena F X, Corma A. Gold(III)—metal organic framework bridges the gap between homogeneous and heterogeneous gold catalysts. Journal of Catalysis, 2009, 265(2): 155–160

6 Hu Y, Zheng S, Zhang F. Fabrication of MIL-100(Fe)@SiO₂@Fe₃O₄ core-shell microspheres as a magnetically recyclable solid acidic catalyst for the acetalization of benzaldehyde and glycol. Frontiers of Chemical Science and Engineering, 2016, 10(4): 534–541

7 Li Z Q, Qiu L G, Xu T, Wu Y, Wang W, Wu Z Y, Jiang X. Ultrasonic synthesis of the microporous metal-organic framework Cu₃(BTC)₂ at ambient temperature and pressure: An efficient and environmentally friendly method. Materials Letters, 2009, 63(1): 78–80

8 Dewa T, Saiki T, Aoyama Y. Enolization and aldol reactions of ketone with a La³⁺-immobilized organic solid in water. A microporous enolase mimic. Journal of the American Chemical Society, 2001, 123(3): 502–503

9 Neogi S, Sharma M K, Bharadwaj P K. Knoevenagel condensation and cyanosilylation reactions catalyzed by a MOF containing coordinatively unsaturated Zn(II) centers. Journal of Molecular Catalysis A Chemical, 2009, 299(1–2): 1–4

10 Gascon J, Aktay U, Hernandez-Alonso M D, van Klink G P M, Kapteijn F. Amino-based metal-organic frameworks as stable, highly active basic catalysts. Journal of Catalysis, 2009, 261(1): 75–87

11 Yu Z T, Liao Z L, Jiang Y S, Li G H, Li G D, Chen J S. Construction of a microporous inorganic-organic hybrid compound with uranyl units. Chemical Communications, 2004, (16): 1814–1815

12 Mahata P, Madras G, Natarajan S. Novel photocatalysts for the decomposition of organic dyes based on metal-organic framework compounds. Journal of Physical Chemistry B, 2006, 110(28): 13759–13768

13 Navarro J A R, Barea E, Salas J M, Masciocchi N, Galli S, Sironi A, Ania C O, Parra J B. H₂, N₂, CO, and CO₂ sorption properties of a series of robust sodalite-type microporous coordination polymers. Inorganic Chemistry, 2006, 45(6): 2397–2399

14 Llabrés i Xamena F X, Abad A, Corma A, Garcia H. MOFs as catalysts: Activity, reusability and shape-selectivity of a Pd-containing MOF. Journal of Catalysis, 2007, 250(2): 294–298

15 Schlichte K, Kratzke T, Kaskel S. Improved synthesis, thermal stability and catalytic properties of the metal-organic framework compound Cu₃(BTC)₂. Microporous and Mesoporous Materials, 2004, 73(1–2): 81–88

16 Suslick K S, Bhyrappa P, Chou J H, Kosal M E, Nakagaki S, Smithenry D W, Wilson S R. Microporous porphyrin solids. Accounts of Chemical Research, 2005, 38(4): 283–291

17 Dhakshinamoorthy A, Alvaro M, Garcia H. Metal organic frameworks as efficient heterogeneous catalysts for the oxidation of benzylic compounds with t-butylhydroperoxide. Journal of Catalysis, 2009, 267(1): 1–4

18 Phan N T S, Le K K A, Phan T D. MOF-5 as an efficient heterogeneous catalyst for Friedel-Crafts alkylation reactions. Applied Catalysis A, General, 2010, 382(2): 246–253

19 Ravon U, Domine M E, Gaudillere C, Desmartin-Chomel A, Farrusseng D. MOFs as acid catalysts with shape selectivity properties. New Journal of Chemistry, 2008, 32(6): 937–940

20 Opanasenko M, Dhakshinamoorthy A, Čejka J, Garcia H. Deactivation pathways of the catalytic activity of metal-organic frameworks in condensation reactions. ChemCatChem, 2013, 5(6): 1553–1561

21 Perego C, Ingallina P. Recent advances in the industrial alkylation of aromatics: New catalysts and new processes. Catalysis Today, 2002, 73(1–2): 3–22

22 Nguyen L T L, Nguyen C V, Dang G H, Le K K A, Phan N T S. Towards applications of metal-organic frameworks in catalysis: Friedel-Crafts acylation reaction over IRMOF-8 as an efficient heterogeneous catalyst. Journal of Molecular Catalysis A Chemical, 2011, 349(1–2): 28–35

23 Calleja G, Sanz R, Orcajo G, Briones D, Leo P, Martínez F. Copper-based MOF-74 material as effective acid catalyst in Friedel-Crafts acylation of anisole. Catalysis Today, 2014, 227: 130–137

24 Rahmani E, Rahmani M. Alkylation of benzene over Fe-based metal organic frameworks (MOFs) at low temperature condition. Microporous and Mesoporous Materials, 2017, 249: 118–127

25 Tompson R V, Loyalka S K. Chapman-Enskog solution for diffusion: Pidduck’s equation for arbitrary mass ratio. Physics of Fluids, 1987, 30(7): 2073–2075

26 Reinecke S A, Sleep B E. Knudsen diffusion, gas permeability, and water content in an unconsolidated porous medium. Water Resources Research, 2002, 38(12): 16-1–16-15

27 Pisani L. Simple Expression for the tortuosity of porous media. Transport in Porous Media, 2011, 88(2): 193–203

28 Rahmani E, Rahmani M. Al-based MIL-53 metal organic framework (MOF) as the new catalyst for Friedel-Crafts alkylation of benzene. Industrial & Engineering Chemistry Research, 2018, 57(1): 169–178

29 Emana A N, Chand S. Alkylation of benzene with ethanol over modified HZSM-5 zeolite catalysts. Applied Petrochemical Research, 2015, 5(2): 121–134

30 Smirniotis P G, Ruckenstein E. Alkylation of benzene or toluene with MeOH or C₂H₄ over ZSM-5 or. beta. Zeolite: effect of the zeolite pore openings and of the hydrocarbons involved on the mechanism of alkylation. Industrial & Engineering Chemistry Research, 1995, 34(5): 1517–1528

31 Sridevi U, Bhaskar Rao B K, Pradhan N C. Kinetics of alkylation of benzene with ethanol on AlCl₃-impregnated 13X zeolites. Chemical Engineering Journal, 2001, 83(3): 185–189

32 Dhakshinamoorthy A, Alvaro M, Chevreau H, Horcajada P, Devic T, Serre C, Garcia H. Iron(III) metal-organic frameworks as solid Lewis acids for the isomerization of α-pinene oxide. Catalysis Science & Technology, 2012, 2(2): 324–330