Diffusion of heavy oil in well-defined and uniform pore-structure catalyst under hydrodemetallization reaction conditions

Chemical Engineering Journal 231 (2013) 420–426

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Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej

Diffusion of heavy oil in well-defined and uniform pore-structure catalyst under hydrodemetallization reaction conditions Ai-cheng Chen, Sheng-Li Chen ⇑, De-run Hua, Zheng Zhou, Zhi-gang Wang, Jun Wu, Jun-hui Zhang State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, PR China

h i g h l i g h t s  Well-defined pore-structure catalysts were used to study the intraparticle diffusion.  Reliable intrinsic and bulk diffusivity at reaction condition were gained.  Well-defined pore-structure catalyst is an ideal media for intrinsic diffusion study.

a r t i c l e

i n f o

Article history: Received 31 January 2013 Received in revised form 9 July 2013 Accepted 11 July 2013 Available online 20 July 2013 Keywords: Diffusion Porous materials Petroleum Catalyst support Intrinsic diffusivity Uniform pore structure catalyst

a b s t r a c t Intraparticle diffusion was investigated over well-defined and uniform pore-structure (WDUPS) model catalysts under reaction conditions for hydrodemetallization of heavy oil. Based on the intrinsic reaction rate constant and the apparent reaction rate constant, the intraparticle effective diffusivity was calculated. The intrinsic diffusivity and the bulk diffusivity under reaction conditions were obtained from the measured intraparticle effective diffusivity, and the porosity and tortuosity of the catalyst. The intrinsic diffusivity obtained using the WDUPS model catalyst was greatly different from that obtained using the conventional catalysts. Owing to its well-defined and uniform pore-structure and therefore definite porosity and tortuosity, the WDUPS model catalyst is more advantageous in intraparticle diffusion study than conventional catalysts, furthermore, the intrinsic diffusivity and the bulk diffusivity obtained in this research work are more reliable than those obtained before by using conventional catalysts with vague tortuosity and wide range of pore-size distribution. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Intraparticle diffusion of heavy oil occurs inside the catalyst during the heavy oil hydrodemetallization (HDM) process. Many investigators have studied the intraparticle diffusion behavior of heavy oil by the diaphragm cell [1–3], adsorptive [4–7] and reaction–diffusion kinetic methods [7–12] on porous materials. Generally, the intraparticle effective diffusivity can be described as Eq. (1) [7–10,13,14].

De ¼ Db  e  FðkÞ=s

ð1Þ

where De and Db are the intraparticle effective diffusivity and bulk diffusivity of solute, respectively. e and s are the porosity and tortuosity of the catalyst, respectively. F(k) is the restrictive factor, where k is the ratio of molecule size to pore size, and many expressions of the restrictive factor have been put forward by researchers [1,7,13– 17]. The diffusion rate inside a pore is strongly dependent on the pore size and pore structure, and therefore catalysts with uniform ⇑ Corresponding author. Tel.: +86 10 89733396. E-mail addresses: [email protected], [email protected] (S.-L. Chen). 1385-8947/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cej.2013.07.035

pore structure are needed for research of intraparticle diffusion. However, the pore structure of catalysts prepared by the conventional method is not uniform at all, and actually is a random network porous structure with various pore size and pore tortuosity. Due to the agglomeration of microporous alumina particles during preparation, macro- and micro-pores are formed in conventional catalyst [11,18], and the diffusivities in macro- and micro-pores are quite different. Ruckenstein et al. [19] have reported that the diffusivities in the macro- and micro-pores can be quite different in the order of magnitude. Hashimoto and Smith [20] reported that the diffusivity of n-butane in macropores was about 100 times that in micropore at 30 °C for a alumina pellet with the macro- and micro-mean pore radii of 120 and 1.7 nm, respectively. In addition, it is almost impossible to accurately evaluate the tortuosity of a conventional catalyst, and varied tortuosities have been reported for conventional catalysts [8,9,21–23]. Chen reported that, even for the same catalyst, the tortuosity obtained by hydrodesulfurization (HDS) was different from that obtained by hydrodemetallization (HDM) [9,22]. Therefore, conventional catalyst is unsuitable for the investigation of intraparticle diffusion. Catalysts with uniform pore size, definite pore volume and tortuosity should be utilized in the study of catalyst intraparticle

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Nomenclatures CNi-OEP(f) CNi-OEP(p) De Db D M P H2 Ro Sa 0 ks ks i

ks

Ni-OEP concentration in feed (mol/m3) Ni-OEP concentration in product (mol/m3) effective diffusivity of solute (m2/s) bulk diffusivity of solute (m2/s) intrinsic diffusivity of solute defined in Eq. (8), =DbF(k) (m2/s) solute molecular weight (g/mol) hydrogen pressure (Pa) radius of catalyst pellet (m) specific surface area of catalyst (m2/g) rate constant on catalyst surface area (m3n2 mol1n/ Paa s) rate constant on catalyst surface area defined in Eq. (3), 0 ¼ ks PaH2 (m3n2 mol1n/s) intrinsic first-order rate constant on catalyst surface area (m/s)

diffusion. Nevertheless, it is difficult to prepare this type of ideal catalyst by conventional catalyst synthesis methods. Recently, our research group [6,24–26] has prepared a well-defined and uniform pore-structure (WDUPS) catalyst as follows: first, ordered packing of monodisperse SiO2 microspheres to prepare WDUPS SiO2 support, then coating the WDUPS SiO2 support with Al2O3 by the NH3/water vapor-induced internal hydrolysis (VIH) method [27] to prepare WDUPS Al2O3/SiO2 support, and finally loading active components on the WDUPS Al2O3/SiO2 support to prepare WDUPS model catalyst. Thus the prepared WDUPS model catalyst has uniform pore size distribution. This WDUPS model catalyst has more advantages for the investigation of intraparticle diffusion than the conventional catalysts. But to our knowledge, no literature has reported on the studies of intraparticle diffusion over the WDUPS catalysts by the reaction–diffusion kinetic method. In the present work, the WDUPS CoMo/Al2O3/SiO2 model catalysts were used for the study of intraparticle diffusion, to investigate the relationship of intraparticle intrinsic diffusivity of nickel octaethylporphyrin (Ni-OEP) and catalyst pore size using four pore-sized WDUPS model catalysts, and to compare the intraparticle intrinsic diffusivities obtained through model catalysts with that obtained through conventional catalysts.

2. Materials and methods 2.1. Preparation of catalyst Four different pore-sized WDUPS CoMo/Al2O3/SiO2 model catalysts (CAT-11, CAT-17, CAT-47 and CAT-65) were used in this work. The detail preparation procedure are referred to our previous reports [6,24–26]. The brief preparation procedures were described as follows. The monodisperse SiO2 microspheres were prepared by hydrolysis and condensation of tetraethyl orthosilicate in a methanol solution and in the presence of ammonia and water by the seed particle growth method [28,29]. Then, the SiO2 microspheres suspension was kept at 50 °C and 90% relative humidity, and self-assembled into the SiO2 opal support after the water was evaporated. After the SiO2 opal supports were dried at 100 °C for 24 h and calcined at 700 °C for 2 h, Al2O3 was coated onto the internal surface of SiO2 opal support: Al(NO3)3, the precursor of Al2O3, was deposited on the support by the incipient wet impregnation method and hydrolyzed in ammonia/water

a

ks

n r Ni-OEP

apparent first-order rate constant on catalyst surface area (m/s) order of reaction with respect to Ni-OEP HDNi reaction rate of Ni-OEP based on unit surface area of catalyst (mol/m2 s)

Greek letters g effectiveness factor a order of reaction with respect to H2 U Thiele modulus k ratio of molecule diameter to pore diameter e porosity of catalyst s tortuosity factor qcat density of catalyst (g/m3)

vapor at 100 °C for 7 h [27,30], followed by calcining at 500 °C for 5 h. The amount of Al2O3 coating was 0.046 g per 100 m2 support surface [31]. At last, the transition metals molybdenum (5.42 lmol/m2) and cobalt (3.61 lmol/m2) were loaded on the support by two-step incipient wetness impregnation [32,33]. Ammonium molybdate was incipiently impregnated on the model support and then it was held at room temperature for 12 h, followed at 110 °C for 6 h, and finally calcined at 500 °C for 5 h. After that, cobalt nitrate was loaded with the same procedure just as molybdenum. The support of the WDUPS catalyst is a hexagonal closedpacking of monodisperse microspheres (face-center cubic structure or opal structure). Theoretically, the pore size of the opals can be calculated from the size of the monodisperse microspheres, and pore volume and pore tortuosity of the opals are constant and can be calculated geometrically from the FCC structure [34,35]. For comparison, two types of conventional catalysts (CAT-A and CAT-B) were utilized in this work. The supports of CAT-A and CATB, commercial c-Al2O3 and supplied by Qilu Catalyst Factory of Sinopec, China, are prepared by the conventional method. Co and Mo were loaded on the c-Al2O3 by two-step incipient wetness impregnation, and the amounts of Co and Mo were the same to that of WDUPS catalysts, i.e., 3.61 lmol/m2 and 5.42 lmol/m2 for Co and Mo respectively. Before catalytic performance testing, the prepared WDUPS model and the conventional catalysts CAT-A and CAT-B were crushed and then sieved to different sizes of catalyst pellet (0.675, 0.365, 0.230 and 0.127 mm). 2.2. Characterization of catalyst The characteristics of these four catalysts are given in Table 1. All of the characteristic data were obtained using 1.45 mm catalyst pellet. The surface areas of these catalysts were determined by the BET method. The pore size distributions of the CAT-11, CAT-17, CAT-A and CAT-B catalysts were obtained through low temperature N2 adsorption–desorption on a Micromeritics ASAP2020M instrument (Micrometritics Instrument Corp., USA). Owing to the large average pore size, the pore size distributions of the CAT-47 and CAT-65 catalysts were obtained by the mercury penetration method using an Auto Pore IV9500 Mercury Porosimeter (Micro-

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2.3. Catalytic activity measurements

Table 1 Characteristics of WDUPS model catalysts and conventional catalysts. Items

CAT-11 CAT-17 CAT-47 CAT-65 CAT-A CAT-B a b

Specific surface areaa (m2/g)

Pore volumeb (cm3/g)

Average pore size (nm)

Porosity

64.80 43.06 18.64 13.47 168.90 218.70

0.18 0.19 0.22 0.22 0.39 0.77

11.1 17.6 47.2 65.3 9.2 14.1

0.29 0.30 0.33 0.33 0.60 0.73

e

Catalyst pellet density (g/cm3) 1.58 1.56 1.48 1.49 1.53 1.01

Data obtained by the BET method. Data obtained by the n-butanol impregnation method.

metritics Instrument Corp., USA). The average pore diameters of these model catalysts ranged from 11.1 to 65.3 nm, and the average pore diameters of CAT-A catalyst and CAT-B catalyst are 9.2 and 14.1 nm, respectively. As shown in Fig. 1, each of the four WDUPS model catalysts showed a monodisperse and narrow pore size distribution. The CAT-A catalyst had a monomodal pore size distribution, and the CAT-B catalyst had a bidispersed pore structure. Due to agglomeration of microporous alumina nano-particles during preparation of the conventional catalysts [11,18], macropores were formed during the preparation of catalysts CAT-A and CAT-B. But this type of macropore is difficult to be characterized by the low temperature N2 adsorption–desorption method for its too large average pore size, and also difficult to be characterized by the mercury penetration method for its too small pore throat size. Fig. 2 shows the SEM image of WDUPS catalyst CAT-65, which was taken using a FEI Quanta 200F electron microscope operating at 20 kV. It can be seen that the CAT-65 catalyst was threedimentional ordered materials. The monodisperse microspheres were closely packed into the face-center-cubic structure (or opal structure). The pores in the catalyst were uniform and well defined. The small pore volume and the large density of the WDUPS catalyst pellets, as shown in Table 1 also indicated that the SiO 2 microspheres were self-assembled into the facecenter-cubic structure.

Fig. 1. Pore-size distributions of the WDUPS model catalysts and the conventional catalysts. (–j–, –N–, –h– and –M– obtained by the BET method. –– and –r– obtained by the mercury penetration method).

Most metal-containing compounds in crude oil is porphyrin type compounds and up to 50% of the metal in the porphyrin of crude oil exists in the form of etio-I- and octaethyl-type porphyrins [36]. Therefore, nickel 2,3,7,8,12,13,17,18-octaethylporphyrin (Ni-OEP) (purchased from Frontier Scientific Inc (USA)), a kind of etio-I- and octaethyl-type porphyrins, was used as model metal compound in this work. The molecular diameter of Ni-OEP is estimated by Dn = 0.0403  M0.537 (nm) [37] to be 1.24 nm. The Ni-OEP was dissolved in a nickle-free lube base oil, which was supplied by Sinopec Shanghai Gaoqiao Petrochemical Corp., China, at room temperature to reach a content of 20 mg/g. The Ni-OEP concentration of the lube base oil before and after hydrodenickelation was analyzed with an UNICO-UV-2102 PCS UV–Vis photometer at a wavelength of 552.2 nm. Hydrodenickelation (HDNi) experiments were carried out in a bench-scale trickle-bed hydrotreating reactor with an inner diameter of 9.00 mm. The catalyst was mixed with quartz sand (inert materials) and added into the reactor to form a catalyst bed with height of 45 mm. According to the criteria reported by Doraiswamy and Tajbl [38], the reactor was almost a plug-flow one. Prior to HDNi experiment, the catalyst was presulfided at 300 °C and 4.0 MPa for 4 h with 3 wt.% carbon disulfide in cyclohexane. Each HDNi experiment was run for 20 h at 300 °C and 6.0 MPa to ensure the catalyst to reach a stabilized state before measuring the HDNi kinetic data. After that, HDNi experment was carried out under the conditions shown in Table 2. In the HDNi reaction, the reactants diffuse from bulk solution onto the outside surface of the catalyst pellets, then diffuse from the outside surface into the internal surface of the catalyst pellets, are adsorbed on the internal surface and finally react to form products. In order to investigate the intraparticle diffusion, the external diffusion resistance must be negligible in compared with the intraparticle diffusion resistance and chemical reaction resistance. Through changing the catalyst-loading amount and the reactant feeding rate, we performed the HDNi reaction under different superficial velocities of reactant in the packed bed, and found that the same conversion of Ni-OEP was achieved at the same weight hourly space velocity but different superficial velocities, indicating that the external diffusion resistance was eliminated in the experiment. Under the circumstance of external diffusion resistance free, the chemically intrinsic reaction rate constant and the apparent reaction rate constant were

Fig. 2. SEM image of WDUPS catalyst CAT-65.

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Table 2 Reaction conditions of the HDNi experiments. Processes

Catalyst presulphurization

Catalyst stabilization

HDNi reaction

Temperature (°C) Pressure (MPa) Catalyst bed volume (mL) Liquid feed flow rate (g/h) H2/Oil ratio (V/V)

300 4.0 2.5

300 6.0 2.5

270–330 6.0 2.5

10.0

5.0

2.0–9.0

140

1000

1000

determined over different size catalyst pellets. The intraparticle diffusivities were calculated on the basis of the intrinsic rate constant, the apparent rate constant, pore volume and pore tortuosity. Fig. 3. Relationship between Ni-OEP conversion and catalyst pellet diameter over CAT-11 at 270–330 °C and 6.0 MPa.

3. Results and discussion 3.1. Catalyst activity The HDNi reaction rate ðr Ni-OEP Þ based on the unit surface area of the catalyst can be expressed as

r Ni-OEP ¼ ks PaH2 C nNi-OEP 0

ð2Þ

where is the rate constant (m3n2 mol1n/Paa s). P H2 is the pressure of hydrogen (Pa). CNi-OEP is the Ni-OEP concentration (mol/ m3). a and n are the order of reaction with respect to H2 and NiOEP, respectively. In our experiments, the hydrogen pressure was kept constant during the kinetic rate measurement, so the term 0
PaH2 can be merged into the rate constant ks . Then, Eq. (2) yields 0 ks

r Ni-OEP ¼ ks C nNi-OEP 0 ks PaH2

data for the Ni-OEP over the CAT-11 catalyst with particle diameters of 0.127 and 0.675 mm at 270 °C and 6.0 MPa are shown in Fig. 4. The plot of ln(CNi-OEP(f)/CNi-OEP(p)) vs. 1/SHSV yielded a straight line, indicating that the HDNi is first order reaction with respect to the Ni-OEP and the slope of the line is the kinetic rate constant. The intrinsic and apparent kinetic first-order rate constants of the Ni-OEP of the four different pore-sized WDUPS CoMo/SiO2/Al2O3 model catalysts, determined by the same way as shown in Fig. 4, are summarized in Table 3. Table 3 showed that the values of the intrinsic and apparent first-order rate constants increased with temperature.

ð3Þ 3n2

1n

where ks ¼ (m mol /s). For convenience in calculation, the SHSV (Surface-area Hourly Space Velocity) was used in this work to describe the ratio of oil volumetric flow rate to catalyst area (m3-oil/s m2-cat.). The experimental data showed that ln(CNi-OEP(f)/ CNi-OEP(p)) was inversely proportional to the SHSV, indicating that the reaction was first-order with respect to the Ni-OEP. Therefore, the first-order rate constant of the HDNi can be determined using the following kinetic expression.

lnðC Ni-OEP ðf Þ=C Ni-OEP ðpÞÞ ¼ ks =SHSV

ð4Þ

where CNi-OEP(f), and CNi-OEP(p) are the Ni-OEP concentrations in the feedstock and product, respectively (mol/m3). The conversion of reactant over different sizes of catalyst pellets at a constant space velocity can be used to examine whether the system is under chemical kinetic control or not [39]. In order to obtain the intrinsic rate constant of HDNi reaction, the relationship between the conversion of Ni-OEP and the catalyst particle size over CAT-11 at 270–330 °C and 6.0 MPa was investigated, and the results are shown in Fig. 3. It can be seen that the Ni-OEP conversion decreased as the catalyst pellets diameter increase from 0.230 to 0.675 mm, indicating that the HDNi reaction was controlled by internal diffusion. When the catalyst pellet was smaller than 0.230 mm, the Ni-OEP conversion was nearly unchanged, indicating that the internal diffusion resistance can be negligible, and the HDNi reaction was under chemical kinetic control. The obtained rate constant is the intrinsic rate constant. The smallest catalyst pellets of 0.127 mm were utilized to acquire the intrinsic kinetic data, and the apparent kinetic data were obtained by using the largest catalyst pellets of 0.675 mm. To determine the kinetic rate constant of HDNi reaction, a series of experiments were carried out at different SHSV values over the WDUPS model catalysts at 270–330 °C and 6.0 MPa. The kinetic

3.2. Intraparticle effective diffusivity De The influence of catalyst particle shape on the Thiele modulus,

U, which is described by Eq. (5), can be neglected [40].

g ¼ ½1=tanhð3UÞ  1=ð3UÞ=U

ð5Þ

Therefore, the crushed and sieved WDUPS model catalyst particles were treated as spherical particles in the present research work. For a first-order irreversible reaction in an isothermal spherical particle, the intraparticle effective diffusivity, De, is calculated by using Eq. (6) [41].

Fig. 4. First-order kinetic plot for HDNi of Ni-OEP over CAT-11 catalyst at 270 °C i a and 6.0 MPa (ks : intrinsic first-order rate constant and ks : apparent first-order rate constant).

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Table 3 First-order rate constants of hydrodenickelation over WDUPS model catalysts at 6.0 MPa and elevated temperatures. Catalysts

Apparent first-order rate a constant ks (1011 m/s)

Intrinsic first-order rate i

constant ks (1011 m/s) Temperature (°C)

CAT-11 CAT-17 CAT-47 CAT-65

Temperature (°C)

270

300

330

270

300

330

3.91 4.83 10.58 6.96

10.89 13.30 24.27 17.10

29.50 35.20 47.21 27.99

2.84 3.77 8.85 6.36

6.51 8.87 18.44 14.72

13.86 19.11 33.00 23.51

Table 4 Intraparticle effective diffusivity of Ni-OEP over WDUPS model catalyst at 6.0 MPa and different temperatures. Intraparticle effective diffusivity De (1010 m2/s) Temperatures (°C)

Catalysts

CAT-11 CAT-17 CAT-47 CAT-65

270

300

330

0.69 0.78 1.04 1.09

0.95 1.12 1.42 1.50

1.30 1.53 1.92 2.04

i

De ¼ R2o  ks  qcat  Sa =ð9  U2 Þ

Fig. 5. Change of intrinsic diffusivity with the ratio of molecule diameter to pore diameter (k) over model catalysts at 270–300 °C and 6.0 MPa.

ð6Þ

where the Thiele modulus, U, is determined by using Eq. (5) with the effectiveness factor, g. The effectiveness factor was calculated a by dividing the apparent first-order rate constant, ks , by the intrini sic first-order rate constant, ks . Based on the intrinsic and apparent first-order rate constants in Table 3, the intraparticle effective diffusivity of Ni-OEP was calculated by Eqs. (5) and (6), and the results are given in Table 4. It can be seen that the value of the intraparticle effective diffusivity is in the range of 0.69  1010 to 2.04  1010 m2/s. Table 4 also showed that the intraparticle effective diffusivity was related to reaction temperature and catalyst pore size. The larger intraparticle effective diffusivity was obtained at higher reaction temperature, indicating that the diffusion rate increased with temperature. Due to the weakening of the diffusion resistance in larger pores, the larger intraparticle effective diffusivity would be obtained. That is, higher reaction temperature and larger pore size will lead to larger intraparticle effective diffusivity. 3.3. Bulk diffusivity Db

According to Eq. (9) and the e shown in Table 1, the s of the WDUPS model catalyst was calculated to be 1.48 ± 0.03. Fig. 5 shows the linear correlations of the intrinsic diffusivity (D) vs. the ratio of molecule diameter to pore diameter (k) for k < 0.12. The values of Db of Ni-OEP under reaction conditions were obtained by the extrapolation method, and were found to be 4.97  1010, 6.79  1010 and 9.23  1010 m2/s at 270, 300 and 330 °C, respectively. Db seems to be a linear function of temperature in the range from 270 to 330 °C. The bulk diffusivity (Db) of a substance under reaction conditions is difficult to be measured, so the Wilke–Chang [43] and Stokes–Einstein [40] formulas are often used to estimate the bulk diffusivity. These formulas are confined to the situation that the solute concentration is infinitesimal. In addition, some parameters (such as viscosity of solution, which is affected by solvent properties, temperature and the amount of hydrogen dissolved in solvent) used to estimate the bulk diffusivity cannot be obtained under reaction conditions. So the erroneous bulk diffusivity of molecules under hydrodemetallization reaction condition might be obtained when using the Wilke–Chang and Stokes–Einstein formulas. To the best of our knowledge, our research work is first time for people to obtain the bulk diffusivity under high-pressure hydrodemetallization conditions. Because of the random and non-uniform pore structure of conventional catalysts, it is impossible to know the exact value of the tortuosity factor (s) of the catalysts. Therefore the bulk diffusivity,

As is well known, the relationship between the bulk diffusivity (Db) and intraparticle effective diffusivity can be described as

De  s=e ¼ Db  FðkÞ

ð7Þ

And the intrinsic diffusivity, D is defined as follows

D ¼ Db  FðkÞ

ð8Þ

D is independent of e and s, and Db is equal to D for F(k) = 1. The intrinsic diffusivity can be regarded as the ‘‘bulk diffusivity in the pores of a catalyst’’. When the pore size is large enough (F(k) = 1), the bulk diffusivity is equal to intrinsic diffusivity (Db = D). By combining Eqs. (7) and (8), we can calculate D in WDUPS model catalyst using De, e and s. The values of De and e are shown in Tables 4 and 1, respectively. The tortuosity factor (s) of porous materials, which was made by closed-packing of nonporous spheres, has a definite value that can be determined accurately by the following equation [42],

s ¼ 1 þ 0:41  lnð1=eÞ

ð9Þ

Fig. 6. Comparsion of experimental restrictive factor data with data reported in literatures (a and c: [21], b: [44], d: [9,22], e: [15], f: [1]).

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4. Conclusion Well-defined and uniform pore-structure model catalysts were applied for study of the intraparticle diffusion of a nickel-containing octaethylporphyrin under hydrodemetallization reaction conditions, and the more reliable intrinsic and bulk diffusivities of the Ni-contained compound were obtained. It was found that the intrinsic diffusivity increased with the increase of the temperature and pore size of catalysts. The well-defined and uniform porestructure model catalyst is more advantageous for the study of intraparticle intrinsic diffusion than the conventional catalysts.

Acknowledgements

Fig. 7. Intrinsic diffusivity over WDUPS model catalysts and conventional catalysts at 300 °C and 6.0 MPa.

Db, is more difficult to be obtained over the conventional catalysts than over the WDUPS model catalysts. The restrictive factor, F(k), was also obtained with Db, D and Eq. (8) and the results are shown in Fig. 6. For a comparison, the F(k) data from literatures [1,9,15,21,22,44] are also shown in Fig. 6. It can be seen that the F(k) from our experimental data are agree well with those reported in literature.

3.4. Comparison of the diffusivities obtained using WDUPS model catalysts and conventional catalysts Although the mean tortuosity of a porous material can be used to measure using the pulsed field gradient NMR method [45], the exact tortuosity value for each part of the conventional catalysts is unknown. Many researchers have suggested that the tortuosity of conventional catalysts is approximately 3 [41]. With the porosity and tortuosity of conventional catalysts, we can also calculate the intrinsic diffusivity. To investigate the difference between the intrinsic diffusivity determined using the model catalysts and that determined using the conventional catalysts, two types of conventional catalysts (CAT-A and CAT-B) were also used in experiments under the same conditions of 300 °C and 6.0 MPa. The obtained intrinsic diffusivity are shown in Fig. 7. It can be seen that the intrinsic diffusivity obtained using the conventional catalysts was higher than that using the model catalysts. The difference in intrinsic diffusivity is resulted from the uncertain catalyst pore structure parameters of the conventional catalysts. The conventional catalysts always have complicated pore structure with macropores formed during preparation. This type of macropores can reduce the diffusion resistance, resulting in larger intraparticle diffusivity [46]. In addition, the uncertain tortuosity of the conventional catalyst would lead to the wrong intrinsic diffusivity. Unlike the conventional catalysts, the WDUPS model catalysts have uniform pore size distribution and definite tortuosity. The intrinsic diffusivity obtained through the WDUPS model catalysts is more reliable than that obtained through the conventional catalysts. Therefore, the WDUPS model catalysts are more advantageous than the conventional catalysts in the study of intraparticle intrinsic diffusion. In addition, the difference between the intrinsic diffusivity of the CAT-B catalyst and that of the CAT-A catalyst was also resulted from their different catalyst pore structures.

The authors acknowledge the financial support provided by CNPC (China National Petroleum Company), the National Nature Science Foundation of China.

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