International Journal of Chemical Engineering
Volume 2020 (2020), Article ID 2813946, 12 pages
https://doi.org/10.1155/2020/2813946

Research Article

Adsorptive Desulfurization of Organic Sulfur from Model Fuels by Active Carbon Supported Mn (II): Equilibrium, Kinetics, and Thermodynamics

Jianhong Wang,1,2 Qi Zhang,1,2 Hao Yang,1,2 and Congzhen Qiao1,2

¹Henan Engineering Research Center of Resource and Energy Recovery from Waste, College of Chemistry and Chemical Engineering, Henan University, Kaifeng, China
²Puyang Lianzhongxingye Chemical Industry Co., Ltd., Puyang, China

Correspondence should be addressed to Hao Yang; hyang@henu.edu.cn

Received 8 October 2019; Revised 18 February 2020; Accepted 21 February 2020; Published 16 June 2020

Academic Editor: Iftekhar A. Karimi

Copyright © 2020 Jianhong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Mn (II)/AC adsorbents were prepared by ultrasonic impregnation. The 2 wt. % Mn/AC showed best adsorptive performance, and the optimal adsorption temperature was 313 K. Benzene, methylbenzene, and naphthalene were used to explore the adsorptive selectivity of Mn/AC, indicating that Mn could enhance the adsorptive capacity but could not improve the adsorptive selectivity. The adsorptive mechanism was mostly like to be π-complex. Adsorptive isotherms and kinetics were investigated, and the parameters were calculated. The R², RMSE, and AICc were used to assess the optimal model. The results showed that Temkin adsorptive isotherm was more suitable to describe the isothermal data; the MPnO kinetics model was more superior to other kinetic models. The order of reaction was between 1 and 2. The outcome of adsorptive thermodynamics indicated that removal of DBT onto Mn/AC was a spontaneous and exothermic process.

1. Introduction

Organic sulfurs in fuel oil burned so that they release SOX into the atmosphere, causing serious environmental pollutions and health problems [1–3]. To reduce the emission of SOX, governments around the world had made more stringent laws and regulations [4, 5]. Hence, it is imperative for refineries to study new methods to produce ultralow sulfur fuels. Sulfur-containing compounds in fuel oils exist in the form of straight-chain (thiol, thioether, etc.) and cyclic-annular (thiophene (T), benzothiophene (BT), dibenzothiophene (DBT) etc.) organic sulfur compounds [6, 7].

The traditional hydrodesulfurization (HDS) process has been widely applied into industrial desulfurization fields. HDS is effective in removing straight-chain organic sulfurs, but it is hard for the removal of cyclic-annular organic sulfur compounds [8, 9]. Related studies showed that if the sulfur level in fuel oil reduces to 15 ppm, the volume of catalyst bed will have to be increased 7 times as that of the current HDS catalyst bed [10]; meanwhile, HDS could cause hydrogen consumption and the loss of octane number, because of the nonselective hydrogenation of cyclanic [11, 12]. Hence, various alternative technologies such as catalytic oxidation desulfurization (ODS) [13–15], extraction desulfurization (EDS) [16–18], adsorptive desulfurization (ADS) [19–21], and biodesulfurization (BDS) [22–24] were explored to produce ultralow sulfur fuels, among which, ADS is considered as a potential deep desulfurization technology with several advantages, such as mild conditions of temperature and pressure and selectivity of cyclic-annular organic sulfurs by unsaturated hydrocarbon [25].

Sorbent is a critical factor for ADS process. Various adsorbents have been used for the removal of sulfur from real oils or model oils, such as molecular sieve [26, 27], metal oxide [28], active carbons (ACs) [29], etc., among which ACs are suitable to obtain ultralow sulfur oils due to large specific surface area, abundant pore structures, and high density of surface functional groups [30]. However, ACs without modification have less selectivity for the removal of cyclic-annular organic sulfur compounds. Therefore, modification of ACs is vital factor to improve selectivity. Chemical modification is used to change or increase surface functional groups of ACs. C. O. Ania and Bandosz [31] and coworker adopted metal-loaded (Na, Co, Ag, and Cu) method to modify ACs. The results showed that the DBT removal capacity of metal-loaded ACs was more effective than nonmodified commercial ACs; meanwhile, Co and Cu were more effective than other metals. Fallah and Azizian [5] and coworker used HNO₃, (NH₄)₂S₂O₈, H₂SO₄, HCl, and NaOH to disposal activated carbon cloth (ACC). The results showed that the adsorption capacity of ACC- HNO₃ was higher than other adsorbents due to the highest density of oxygen containing functional groups on its surface, which indicated that modification by HNO₃ could remarkably enhance the density of oxygen containing functional groups so as to improve selectivity.

Adsorption selectivity of ADS will be a hot topic. In this study, Mn (II)/AC prepared by impregnating KMnO₄ on HNO₃/AC were studied with respect to adsorption and adsorbents selectivity performance on DBT in model oils. The adsorption mechanism of Mn (II)/AC was discussed by comparing to HNO₃/AC in model oil with competitive components (benzene, toluene, and naphthalene). Three adsorptive isothermal models (Langmuir, Freundlich, and Temkin) were used to fit the experimental data. The kinetic data was fitted by three kinetic models (PFO, PSO, and MPnO). The R², RMSE, and AICc were applied to assess the goodness-of-fit of the models. Thermodynamics were discussed by static adsorption test.

2. Experimental Section

2.1. Reagents

Dibenzothiophene (DBT, 98%) and nitric acid were obtained from Kermel Co. Ltd., China. Coconut-shell-based active carbon (AC) (20 to 40 meshes) was purchased from KeXing Factory China. Naphthalene (Nap), benzene, methylbenzene, and potassium permanganate (KMnO₄) were purchased as commercial analytical grade reagents. The calibration table samples of sulfur (sulfur concentration: 100, 200, and 500 ppmwS) were purchased from Jiangsu Jiangfen Electroanalytical Instrument Co. Ltd., China.

2.2. Preparation of Adsorbent

The impregnation method was adopted in the experiments. Firstly, AC was boiled for 2 h by deionized water, then screened for 20 to 40 meshes, and stored. Secondly, 50 g AC after washing and 30 wt. % HNO₃ was mixed and agitated for 4 h at 298 K, then extensively washed to neutral, and dried at 383 K for 24 h, which were marked HNO₃/AC. Finally, the HNO₃/AC and solution of KMnO₄ were mixed in water bath oscillator (T = 313 K, r = 90 rpm) for 12 h and then ultrasound for 0.5 h and dried at 383 K for 24 h. The samples were calcined by 773 K in N₂ for 4 h and screened (20 to 40 meshes), which were represented by Mn/AC.

2.2.1. Characterization of Adsorbents

Nitrogen adsorption isotherms were investigated on Automated Physics and Chemisorption Analyzers (Autosorb-iQ-MP-C) from Quantachrome American. All adsorbents were outgassed at 573 K for 4 h, and each adsorbent was measured with 0.040 to 0.045 g. The specific surface area (SBET) and total pore volume (Vt) were calculated by Brunauer-Emmett-Teller (BET) method. The narrow micropores with 0.6 nm to 1.2 nm (Vnarrow) and pore size distribution were obtained by density functional theory (DFT) method. X-ray diffraction (XRD) was tested on Bruker D 8 Advance equipped with a copper anode (Cu Kα = 1.5406 Å) from Germany, which was operated at 30 kV and 30 mA. Adsorbents were scanned 2θ from 10 to 90° with a step rate for 0.2 s⁻¹. The results of XRD were compared with Power Diffraction File (PDF) database. X-ray fluorescence was used to test the content of Mn in the carbons. To achieve this purpose, X-ray fluorescence analysis was used to measure the content of Mn in the ACs. To reach this purpose, S2 RANGER from Germany Bruker AXS GmbH was used.

2.3. Adsorption from Model Oils

2.3.1. Model Oil Sample

Model oil was made by adding DBT into n-octane solution with an initial sulfur concentration (c₀) for 9.38 mmol·L⁻¹ and represented by DM0. To study the effects of Nap, benzene, and methylbenzene on competitive adsorption over Mn/AC, several kinds of model oil were prepared by adding 5 wt. % benzene, methylbenzene, and nap with c₀ for 9.38 mmol·L⁻¹, respectively [32], which were represented by DM1, DM2, and DM3. Mode oils were made with different c₀ of 6.25, 7.81, 9.37, 12.50, 15.63, 18.75, and 21.88 mmol·L⁻¹. In this paper, c₀ was tested in each experiment. The analytical precision reached ± 0.01 mmol·L⁻¹.

2.3.2. Adsorption Experiment

For each experiment, the common agent oil ratio (10/1 g·L⁻¹) was adopted. All static adsorption experiments were run in a water bath shaker (SHA-C, YuHua Instrument Co. Ltd. in Henan, China, 90 rpm). All sulfur concentrations were analyzed by JF-TS-2000 Fluorescence Sulfur Analyzer (Jiangsu Jiangfen Electroanalytical Instrument Co. Ltd., China). Samples were burned in quartz tube at 1273 K with high purity oxygen (350 mL·min⁻¹) and argon (120 mL·min⁻¹). Before determination, the standard curve was plotted by the testing of standard samples, and the correlation coefficient (R²) reached 0.9999.

The mole adsorption capacity, qt (mmol S g⁻¹ adsorbents), was used to describe the performance of adsorption desulfurization, which was calculated as

In order to eliminate the influence of initial concentration and guarantee the unity of experimental conditions, the desulfurization rate was also used to describe the performance of adsorption desulfurization, being given as follows:

where c₀ and ct are the sulfur concentrations of the moment t = 0 and t, respectively. and m are the volume of model oil and the mass of adsorbents, respectively, and M is the molar mass of sulfur atom.

3. Results and Discussions

3.1. Effects of Mn-Loaded Amount

Effects of different Mn-loaded amounts were investigated, and the results are shown in Figure 1. According to Figure 1, It is apparent that adsorptive capacity increased and then decreased and reached a maximum at 2 wt. %. The reason might be that the number of activate sites increased with Mn-loaded amount increasing. When Mn-loaded amount was higher than 2 wt. %, the adsorption capacity deduced, which might be the cause of the aggregation of Mn so that the activate sites reduced (Figure 2). The 2 wt. % Mn-loaded showed best adsorption capacity and qe reached 0.434 mmol·g⁻¹.

Figure 1: Effects of Mn-loaded amount (model oil: 10 mL; DBT, 9.38 mmol·L⁻¹; adsorbents, 0.1 g 2 wt. % Mn/AC; adsorption temperature, 313 K; adsorption time, 4 h).

Figure 2: Nitrogen adsorption isotherm plots of adsorbents with different Mn-loaded amount.

Textural properties of adsorbents are significant for adsorption performance. In this paper, various Mn-loaded amounts were measured by Automated Physics and Chemisorption Analyzers. The nitrogen adsorption isotherms were described in Figure 3, showing that all adsorbents were type-I shape [33], which indicated that pore size with all adsorbents was mainly micropore, and Mn-loaded might almost keep original textural properties.

Figure 3: Pore size distribution curves of different Mn-loaded amount.

Pore size is critical factor for adsorption process. The corresponding DFT pores size distribution is shown in Figure 2, and SBET, Vt, and Vnarrow are calculated and shown in Table 1. According to Figure 2, the proportion of pore size around 0.5 nm reduced with the Mn-loaded increasing; however, the proportion of pore size (around 0.6 nm) increased. The most likely reason was that high temperature (773 K) metal penetration caused the partial collapse of micropores around 0.5 nm, and the skeleton contraction led to forming new micropores [34, 35]. According to Table 1, after Mn-loaded, SBET and Vt were lower than HNO₃/AC because the proportion of pore size around 0.5 nm reduced (Figure 2). Surprisingly, SBET and Vt of 5 wt. % were higher than those of 2 wt. % and 3 wt. %. This is because metal crystal agglomeration blocked channel to form new micropores (0.4 to 0.5 nm from Figure 2), when the Mn-loaded amount was 5 wt. %. Reportedly, the molecule diameter of DBT is 0.65 nm [36]; therefore, the proportion of pore size (0.6 to 1.2 nm) is critical factor for adsorption DBT. According to Table 1, the increase order of Vnarrow was 1 wt. % (0.121), 2 wt. % (0.113), HNO₃/AC (0.106), 5 wt. % (0.104), and 3 wt. % (0.100). Mn-loaded amount with 1 wt. % was optimal choice, but the adsorptive capacity of 2 wt. % was higher than that of 1 wt. % because the active sites of 2 wt. % Mn/AC were more than those of 1 wt. %. Interestingly, qe of 3 wt. % was higher than 5 wt. %, but Vnarrow with 5 wt. % was higher than 3 wt. %. The most likely reason is that mental aggregation degree of 5 wt. % was more serious than that of 3 wt. % so that the active sites with 3 wt. % were more than 5 wt. %.

Table 1: Corresponding parameters of texture properties with different Mn-loaded amount.

Mn-loaded amount (wt. %)
SBET (m² g⁻¹)
Vt (cm³ g⁻¹)
Vnarrow (cm³ g⁻¹)

0
932
0.423
0.106

1
916
0.410
0.121

2
801
0.379
0.113

3
787
0.376
0.100

5
853
0.408
0.104

The result of XRF is shown in Figure 4 (EDX patterns), which indicated that Mn was successfully supported on ACs by impregnation method. Meanwhile, the content of Mn on ACs was calculated. The result showed that the content of Mn on ACs reached 1.59 wt. %. The theoretical (2 wt. %) and practical (1.59 wt. %) load difference reached 20.5%, and comparison result showed that Mn was well supported on ACs by impregnation method.

Figure 4: EDX patterns for the 2 wt. % Mn/AC.

XRD spectra of 10 wt. % Mn/AC were carried out to identify the elemental form on ACs, and the result is shown in Figure 5. The intensity peaks centered for 2θ = 23.3 (002) and 43.3 (100) were the characteristic peaks of AC [37]. 2θ = 34.91°, 40.55°, 58.72°, 70.18°, and 73.79° were detected (Figure 5), which was based on JCPDS 07-0230. The results showed that Mn mainly existed in the form of two valence manganese oxide on HNO₃/AC.

Figure 5: XRD patterns of 10 wt. % Mn/AC.

3.2. Effects of Adsorption Time

The effects of adsorption time are shown in Figure 6. As can be seen, the adsorption amount of DBT (qt) in the initial stage increased quickly and then increased slightly after 120 min, which might be the reason that concentration difference between the inner and outer surface and the number of active sites of adsorbent gradually decreased with time elapsed. The adsorption equilibrium amount (qe) is reached at 4 h.

Figure 6: Effects of adsorption time onto Mn/AC (model oil DM0, 20 mL; DBT, 9.38 mmol·L⁻¹; adsorbents, 0.2 g 2 wt. % Mn/AC; adsorptive temperature, 313 K).

3.3. Effects of Adsorption Temperature

The effect of adsorption temperature was explored, using model oil DM0 with c₀ of 9.38 mmol·L⁻¹, and the results are shown in Figure 7. It is apparent that desulfurization rate increased and then decreased with temperature increasing and reached a maximum at 313 K. The reason might be that the diffusion of adsorbate increased with adsorption temperature increasing because the viscosity of solution decreased. When adsorption temperature was higher than 313 K, the adsorption capacity deduced, which might be the cause of desorption rate increasing sharply [38]. According to Figure 7, desulfurization rate reached max at 313 K.

Figure 7: Effects of adsorption temperatures onto Mn/AC (model oil DM0, 20 mL; DBT, 9.38 mmol·L⁻¹; adsorbents, 0.2 g 2 wt. % Mn/AC; adsorption time, 4 h).

3.4. Effects of Initial Concentration on Adsorption

The effect of different initial concentrations was studied at 313 K (Figure 8). It is apparent that the rate of adsorption for DBT removal varied with different c₀. However, their trends were consistent. The adsorption amount of DBT (qt) in the initial stage increased quickly with increasing adsorption time and reached balance, which indicated that an increase in c₀ caused an increase in qe.

Figure 8: Effects of initial concentration onto Mn/AC (model oil with different c₀:6.25, 12.50 and 18.75 mmol L⁻¹; : 20 mL; adsorbents, 0.2 g 2 wt. % Mn/AC; adsorptive temperature, 313 K).

3.5. Competitive Adsorption

Influences of benzene, methylbenzene, and nap (5 wt. %) on ADS were investigated, and the results are shown in Figure 9. According to Figure 9, for removal of DBT with model oil DM0, Mn/AC had higher desulfurization rate than that of HNO₃/AC, indicating that Mn/AC improved its performance of removal of DBT.

Figure 9: Effect of competitive adsorption (: 10 mL; c₀, 9.38 mmol·L⁻¹; adsorbents, 0.1 g; adsorption temperature, 313 K; adsorption time: 4 h; model oil: DM0, DM1, DM2, and DM3).

Competitive adsorption of benzene on Mn/AC and HNO₃/AC was studied, respectively. It was apparent that there was an obvious decrease of removal rate compared to that of DM0 without benzene. The loss of desulfurization rate decreased by the order Mn/AC (9.39%) > HNO₃/AC (5.97%), which indicated that Mn could not improve the selectivity of HNO₃/AC for DBT removal in model oil with benzene. DBT removal in model oil DM1 with methylbenzene was investigated onto Mn/AC and HNO₃/AC. The similar results were obtained. The loss of desulfurization rate showed decrease in order of Mn/AC (13.77%) > HNO₃/AC (10.08%), indicating that Mn could not improve the selectivity of HNO₃/AC for removal of DBT in model oil with methylbenzene. The existence of nap in model oil (DM3) would strongly decrease for removal of DBT. The similar results showed decrease in order of Mn/AC (34.81%) > HNO₃/AC (31.96%), which demonstrated that Mn could not improve the selectivity of HNO₃/AC for removal of DBT in model oil with nap.

Reportedly, HNO₃/AC improved its ADS selectivity performance by increasing the number of the oxygen containing groups on the AC surface [39], and the ADS mainly was π-H interaction which was the one of weak hydrogen bonds [40], indicating the sequence of π electron density with competitive components played a critical factor for adsorptive selectivity. In this paper, the order of π electron density with competitive components was nap (two benzene rings) > methylbenzene (containing electron donating group-CH₃) > benzene (a benzene ring). The experimental data showed the same influence sequence, which indicated that π-H interaction played an important role on HNO₃/AC removal of DBT over. Mn/AC showed higher desulfurization rate than HNO₃/AC because Mn-loaded increased the number of active sites on surface of HNO₃/AC. However, experimental data indicated that Mn could not improve the adsorptive selectivity, demonstrating that the adsorptive mechanism of Mn/AC might be π-complexation type. Similar result was obtained for Al-Ghouti [41].

3.6. Adsorption Isotherms

In this paper, the equilibrium isothermal adsorption was studied by using different c₀ (6.25, 7.81, 9.38, 12.50, 15.63, 18.75, and 21.88 mmol·L⁻¹ DBT) with a contact time of 4 h at 313, 323, and 333 K. The results are shown in Figure 10. As Figure 10 showed, qe increased sharply with the increase of the equilibrium concentration (ce) and subsequently increased slightly, which indicated that a majority of DBT could be adsorption onto Mn/AC for lower c₀.

Figure 10: Equilibrium isothermal adsorption of DBT over Mn/AC (adsorbent: 0.2 g 2 wt. %; : 20 mL; c₀: 6.25, 7.81, 9.38, 12.50, 15.63, 18.75, and 21.88 mmol·L⁻¹ DBT; adsorption time: 4 h).

In this paper, three isothermal models (Langmuir, Freundlich, and Temkin) were used to describe the relationship between the adsorbed and the equilibrium concentrations.

Basic assumption of Langmuir isotherm is that the adsorbed layer is one molecule in thickness (monolayer adsorption), and all sites possess equal affinity for each adsorbate (homogeneous sites) [42, 43]. The Langmuir isotherm was given as follows:

where KL is the Langmuir constant and is the theoretical maximum adsorption capacity.

Freundlich isotherm is the earliest proposed relationship describing the heterogeneous surface and not restricted to the formation of monolayer adsorption process. The Freundlich isotherm was shown in the following:

At the Freundlich isotherm, Kf is the indicative isothermal parameters of adsorption intensity. The value of 1/n gets closer to 0, which indicated that the surface of adsorbent gets more heterogeneity [44, 45].

Temkin assumes that decreases in heat of adsorption of all molecules are linear; meanwhile its derivation is based on a uniform distribution of binding energies. The Temkin isotherm was described in the following:

where R and T are the gas constant (8.314 JK⁻¹·mol⁻¹) and the absolute temperature, repetitively. KT (L g⁻¹) is equilibrium binding constant, b (J mol⁻¹) is related to adsorption heat [46].

The correlation coefficients (R²) [47] and the root-mean-square error (RMSE) [32] were used to estimate the fitness of isothermal models; R² and RMSE were given as follows:

where m is the number of the experimental data and i is an index; qexp,i and qcal,i are the adsorption capacity of experiment and calculation, respectively. is the mean of measured q values. The value of R² is closer to 1, which indicated that the model is more suitable to describe the experimental data. A RMSE of 0 indicates a perfect fit to the data.

In the following, three adsorption isothermal models (Langmuir, Freundlich, and Temkin) were evaluated to fit the experimental data about the adsorption process on Mn/AC. Figure 11 shows the nonlinear fitting results by Langmuir adsorption isothermal model. Maximum monolayer adsorption capacities with different adsorption temperatures (313, 323, and 333 K) were obtained to be 0.699, 0.660, and 0.647 mmol·g⁻¹, respectively (Table 2). Figure 12 shows the nonlinear fitting results by Freundlich adsorption isothermal model. The values of 1/n with different adsorption temperatures (313, 323, and 333 K) were 0.178, 0.193, and 0.212, respectively (Table 2). They lied between 0 and 1, which indicated favorable removal of DBT onto Mn/AC. The results of nonlinear fitting by Temkin adsorption isothermal model are given in Figure 13. The values with b were obtained to 25.796, 26.490, and 26.121 kJ·mol⁻¹, which indicated that adsorption process was mainly physical adsorption.

Figure 11: Nonlinear fitting of Langmuir model (adsorbent: 0.2 g 2 wt. %; : 20 mL; c₀: 6.25, 7.81, 9.38, 12.50, 15.63, 18.75, and 21.88 mmol·L⁻¹ DBT; adsorption time: 4 h).

Table 2: Nonlinear fitting parameters of three adsorption isothermal models (Langmuir, Freundlich, and Temkin) at different adsorption temperatures (313, 323, and 333 K).

Adsorption temperatures (K)

313
323
333

Langmuir model

KL (L mmol⁻¹)
1.027
0.869
0.690

qmax (mmol g⁻¹)
0.699
0.660
0.647

R² (nonlinear)
0.940
0.976
0.944

RMSE (nonlinear)
0.016
0.010
0.015

Freundlich model

Kf
0.424
0.380
0.346

1/n
0.178
0.193
0.212

R² (nonlinear)
0.970
0.992
0.971

RMSE (nonlinear)
0.012
0.006
0.011

Temkin model

KT (L g⁻¹)
56.372
34.864
20.383

B (kJ mol⁻¹)
25.796
26.490
26.121

R² (nonlinear)
0.975
0.995
0.972

RMSE (nonlinear)
0.011
0.004
0.010

Figure 12: Nonlinear fitting of Freundlich model (adsorbent: 0.2 g 2 wt. %; : 20 mL; c₀: 6.25, 7.81, 9.38, 12.50, 15.63, 18.75, and 21.88 mmol·L⁻¹ DBT; adsorption time: 4 h).

Figure 13: Nonlinear fitting of Temkin model (adsorbent: 0.2 g 2 wt. %; : 20 mL; c₀: 6.25, 7.81, 9.38, 12.50, 15.63, 18.75, and 21.88 mmol·L⁻¹ DBT; adsorption time: 4 h).

It was determined that best fitted adsorption isotherm models considering the R² and RMSE were obtained for three isothermal models. The results are shown in Table 2. The values of R² and RMSE with three adsorption isothermal models (Langmuir, Freundlich, and Temkin) were obtained for different adsorption temperatures (313, 323, and 333 K). When adsorption temperature was 313 K, R² values with Langmuir, Freundlich, and Temkin isothermal models were 0.940, 0.970, and 0.975 (Table 2), respectively. Meanwhile the values of RMSE were 0.016, 0.012, and 0.011, respectively. The results indicated that Temkin isotherm was superior to Langmuir and Freundlich isotherm. When the adsorption temperatures were 323 and 333 K, respectively, the trends were consistent with results of 313 K. This had fully demonstrated that Temkin isotherm was more suitable to fit the experimental data.

3.7. Adsorption Kinetics

The study of adsorption kinetics in adsorption DBT process is significant as it offers valuable insights into the reaction and mechanism. The pseudo-first-order (PFO) and pseudo-second-order (PSO) models were commonly used to describe the adsorption process [48, 49]. The equations were given as follows:

where k₁ and k₂ were the rate constant of PFO and PSO, respectively.

Though PFO and PSO were commonly used to describe the adsorption process; they had restricted the reaction order to either one or two. In general, the chemical reaction order might be a noninteger. Hence, in this paper the modified pseudo-n-order (MPnO) [50] was used to describe the adsorption process. The MPnO equation was shown in the following:

where n is reaction order and kn is the rate constant of MPnO.

The R² and RMSE were used to evaluate three kinetic models. According to equations (8)–(10), PFO and PSO have two adjustable parameters and MPnO has three adjustable parameters. In general, a model will always improve fit to some degree by adding more adjustable parameters; hence R² and RMSE could not effectively assess the pros and cons of different adjustable parameter models. In this paper, the Akaike information criterion (AICc) [51] was proposed to assess the three kinetic models. The AICc equation was given as follows:

where SSE is the sum of the squared errors, m is the number of experimental data, and is the number of the adjustable parameters.

In order to obtain a more accurate assessment, an alternative indicator is proposed by AICc, as follows [52]:

where is the difference between the AICc value of model j and the smallest AICc value for three kinetic models. The value of is higher than 10⁵², which indicated that model j is inferior to the model with the smallest AICc.

In the following, three kinetic models (PFO, PSO, and MPnO) were evaluated to fit the experimental data about the adsorption process on Mn/AC. Figure 14 shows the nonlinear fitting results with different initial concentrations (6.25, 12.50, and 18.75 mmol·L⁻¹) by PFO adsorption kinetic model. Equilibrium adsorption capacities (qe) were obtained to be 0.271, 0.487, and 0.615 mmol·g⁻¹, respectively (Table 3). Figure 15 describes the nonlinear fitting results with different initial concentrations (6.25, 12.50, and 18.75 mmol·L⁻¹) by PSO adsorption kinetic model. PSO fitting qe were 0.318, 0.592, and 0.738 mmol·g⁻¹ by model calculation, respectively. The results of nonlinear fitting by MPnO model are shown in Figure 16. MPnO fitting qe were obtained to be 0.289, 0.555, and 0.642 mmol·g⁻¹ (Table 3), respectively. qe of experimental measure were 0.282, 0.522, and 0.633 mmol·g⁻¹, respectively. In summary, comparison of three models fitting qe values and experimental measured qe showed that the MPnO model fitting qe values were closer to experimental measured values, which demonstrated that the MPnO model was superior to other models. MPnO model fitting qe values and experimental measured values were between PFO and PSO model fitting qe values, which indicated that reactive order was between 1 and 2 (noninteger). The results are given in Table 3 (n = 1.704, 1.766, and 1.435).

Figure 14: Nonlinear fitting of PFO model (adsorbent: 0.2 g 2 wt. %; : 20 mL; c₀: 6.25, 12.50, and 18.75 mmol·L⁻¹ DBT; adsorption time: 4 h; adsorption temperature: 313 K).

Table 3: Nonlinear fitting parameters of three adsorption kinetic models (PFO, PSO, and MPnO) at different adsorption c₀ (6.25, 12.50, and 18.75 mmol·L⁻¹).

Model oils (mmol L⁻¹)

6.25
12.50
18.75

PFO

bk₁
0.030
0.022
0.025

dqe
0.271
0.487
0.615

R²
0.976
0.971
0.989

RMSE
0.013
0.025
0.020

AICc
−141.234
−117.815
−125.417

PSO

ck₂
0.112
0.041
0.039

dqe
0.318
0.592
0.738

R²
0.994
0.992
0.996

RMSE
0.006
0.013
0.012

AICc
−165.267
−139.356
−141.155

MPnO

ekn
0.021
0.008
0.014

dqe
0.289
0.555
0.642

N
1.704
1.766
1.435

R²
0.998
0.997
0.998

RMSE
0.003
0.008
0.008

AICc
−181.398
−151.128
−153.326

a(mmol L⁻¹), b(min⁻¹), c(g mmol⁻¹ min⁻¹), d(mmol g⁻¹), e(mmol g⁻¹) [1−n] min⁻¹.

Figure 15: Nonlinear fitting of PSO model (adsorbent: 0.2 g 2 wt. %; : 20 mL; c₀: 6.25, 12.50, and 18.75 mmol·L⁻¹ DBT; adsorption time: 4 h; adsorption temperature: 313 K).

Figure 16: Nonlinear fitting of MPnO model (adsorbent: 0.2 g 2 wt. %; : 20 mL; c₀: 6.25, 12.50, and 18.75 mmol·L⁻¹ DBT; adsorption time: 4 h; adsorption temperature: 313 K).

The best fitted adsorption kinetic model was considered by the calculation of R², RMSE, and AICc. The results are described in Table 3. The values of R², RMSE, and AICc with three adsorption kinetic models (PFO, PSO, and MPnO) were obtained for different c₀ (6.25, 12.50, and 18.75 mmol·L⁻¹). When the initial concentration was 6.25 mmol·L⁻¹, R² values with PFO, PSO, and MPnO kinetic models were 0.976, 0.994, and 0.998, respectively (Table 3); RMSE were 0.013, 0.006, and 0.003, respectively (Table 3); AICc were −141.234, −165.267, and −181.398, respectively (Table 3), which indicated that MPnO kinetic model was superior to PFO and PSO model. Meanwhile, the smallest AICc value was MPnO kinetic model; hence the values with PFO and PSO were 40.164 and 16.131 (>10), respectively, which demonstrated that the PFO and PSO models were inferior to MPnO kinetic model. The results of 6.25 mmol·L⁻¹ were in agreement with other c₀ (12.50 and 18.75 mmol·L⁻¹), which indicated MPnO kinetic model was superior to PFO and PSO model. This had fully demonstrated that MPnO kinetic model was more suitable to fit the experimental data.

3.8. Diffusion Study

In adsorption process, adsorption behavior sometimes might be described by the intraparticle diffusion model based on the theory proposed by Weber and Morris [53] which was used to identify the diffusion mechanism. The mathematical equation is given as equation (12):

where ki and C are the intraparticle diffusivity rate constant (min−0.5) and the intercept (mmol g⁻¹).

In the following, the diffusion study was carried out in different c₀ (6.25, 12.50, and 18.75 mmol·L⁻¹). The results are shown in Figure 17. The plots are not linear in the adsorption process with adsorption time (4 h), indicating that more than one process is controlling steps over the whole time range. Figure 17(a) shows that the experimental data (0 to 40 min) was linearly fitted at the initial stage, and the R² values were obtained to be 0.993, 0.991, and 0.988, respectively, which indicated that the boundary layer (surface or film diffusion) was control step in initial stage. The experimental data with adsorption time (50 to 120 min) was fitted by equation (13) (Figure 17(b)), and the values were 0.974, 0.937, and 0.940 that were close to 1, demonstrating that intraparticle or pore diffusion was rate-limiting. Figure 17(c) shows that the experimental data (150 to 240 min) was linearly fitted at the equilibrium stage, R² were 0.684, 0.925, and 0.938, respectively, though 0.684 with c₀ (6.25 mmol·L⁻¹) was far from 1, 0.925, and 0.938 with c₀ (12.50 and 18.75 mmol·L⁻¹) being close to 1. Hence, the results still indicated that the third section is the final equilibrium stage. In summary, the removal of DBT on Mn/AC was control for three phases [54].

Figure 17: Intraparticle diffusion plots for removal of DBT onto Mn/AC (model oil with different c₀, 20 mL; adsorbents, 0.2 g 2 wt. % Mn/AC; adsorption temperature, 313 K).

3.9. Thermodynamics

The thermodynamics were investigated in this paper. Gibbs free energy (ΔG) can be calculated by the thermodynamic equilibrium constant (K₀). K₀ equation [55] was given as follows:

where as is the activity of adsorbed and ae is the activity of solution at equilibrium; νs is the activity coefficient of adsorbed, νe is the activity coefficient of solution at equilibrium. When qe is infinitely close to 0, ν approaches unity; hence equation (14) is deduced in the following:

K₀ can be obtained as linear fitting of ln (qe/ce) versus qe, and the results are shown in Figure 18. R² values were obtained to be 0.963, 0.992, and 0.955, indicating that the experimental data could be fitted. The lnK₀ values with different adsorption temperatures (313, 323, and 333 K) were obtained to be 2.323, 1.866, and 1.197, respectively.

Figure 18: Plots of ln (qe/ce) versus qe for removal of DBT on Mn/AC.

Gibbs free energy (ΔG) can be calculated according to the following equations:

Equations (16) and (17) were rewritten as the following equations:

ΔH is the enthalpy of adsorption (kJ mol⁻¹), and ΔS is the enthalpy change of adsorption (J mol⁻¹·K⁻¹). ΔH and ΔS can be calculated by plots ln K₀ vs.1/T. The results are shown in Figure 19. The results of ΔH and ΔS are −48.763 kJ·mol⁻¹ and −135.955 J·mol⁻¹·K⁻¹, respectively. The negative values of ΔH and ΔS show the adsorption of DBT on Mn/AC is an exothermic process and a decrease in the degree of freedom with the adsorbed species. ΔG values with different adsorption temperatures (313, 323, and 333 K) were obtained to be −6.045, −5.011, and −3.314 kJ·mol⁻¹, which indicated that the adsorption process is spontaneous.

Figure 19: Plot of ln K₀ versus 1/T.

4. Conclusions

The following conclusions can be obtained from this paper.

(1)The optimal Mn-loaded amount and adsorption temperature were 2 wt. % and 313 K, respectively.(2)Adsorption capacity of Mn/AC was higher than HNO₃/AC in model oil DM0, indicating that Mn-loaded could enhance the adsorptive performance of HNO₃/AC. However, competitive compounds more seriously affected the Mn/AC than HNO₃/AC, which indicated that Mn-loaded could not improve the ability of adsorptive selectivity, and the adsorptive mechanism of Mn/AC was π-complexation type.(3)Temkin isotherm was more suitable to fit the experimental data. MPnO kinetic model best described the kinetic data; the order of reaction was between 1 and 2. Diffusion study indicated that the removal of DBT on Mn/AC was control for three phases.(4)The thermodynamics demonstrated that adsorption process over Mn/AC was spontaneous and exothermic.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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