Testing conditions for CoMo HDS catalyst in the kinetic region: integrated approach using the math calculations and catalytic experiments published by Ural Federal University eISSN 2411-1414 chimicatechnoacta.ru ARTICLE 2023, vol. 10(2), No. 202310208 DOI: 10.15826/chimtech.2023.10.2.08 1 of 9 Testing conditions for CoMo HDS catalyst in the kinetic region: integrated approach using the math calculations and catalytic experiments Polina P. Mukhacheva , Yuliya V. Vatutina, Ivan A. Mik * , Ksenia A. Nadeina, Maksim O. Kazakov , Oleg P. Klenov, Oleg V. Klimov , Aleksandr S. Noskov Boreskov Institute of Catalysis SB RAS, Novosibirsk 630090, Russia * Corresponding author: mikluha.ia@gmail.com This paper belongs to a Regular Issue. Abstract The main idea of the investigation was to define testing parameters with the lowest influence of internal and external diffusion on catalytic activity in hydrodesulfurization of dibenzothiophene. Traditional experimental methods were used to determine the conditions for the influence of inter- nal and external diffusion. Simultaneous change of a linear feedstock rate and a catalyst loading at constant weight hour space velocity were used to determine the process temperature (240–260 °C) at which the impact of external diffusion is minimal. Catalytic tests, including the variation of the catalyst fraction size, were carried out to define the conditions with the lowest influence of internal diffusion. It was found that when the catalyst with the fraction size of 0.1–0.25 mm was used, the fluctuation of sulfur conversion was the smallest. Besides, to validate experimental results, the calculations were performed with mass balance equations and expressions used for HDS modeling. The resulting data and catalytic experiments demonstrated that the lowest influence of internal and external diffusion is achieved at a temperature process less than 260 °C and a catalyst frac- tion of 0.1–0.25 mm. Keywords diffusion limitation kinetic region hydrodesulfurization dibenzothiophene CoMo HDS catalysts Received: 15.03.23 Revised: 12.04.23 Accepted: 15.04.23 Available online: 24.04.23 Key findings ● Testing conditions were consistent with the requirements of the ideal plug flow. ● Conditions with the lowest influence of internal and external diffusion were defined. ● Experimental results are in good agreement with the calculations. © 2023, the Authors. This article is published in open access under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). 1. Introduction Typical hydrotreating catalysts of diesel fraction are CoMo/Al2O3 catalysts with trilobe or quadrilobe granular shape [1–5]. Nowadays, most of the solutions for improving the hydrotreating catalysts are aimed at tuning active com- ponent properties, namely, at the selective formation of the active phase [6–9]. To directly estimate the effect of changes in properties of the active component on catalytic activity, catalytic tests should exclude most of the process interfer- ence parameters. When the liquid feedstock contacts with a solid catalyst during hydrotreating, the following processes occur in the reactor: mass transferring of reagents from the liquid volume to the external surface of a catalyst granule (external diffusion), and diffusion of reagents from external catalyst surface into pores and then to active sites that carry out the reaction (internal diffusion). Internal diffusion has the greatest influence on hydrotreating reactions, since these reactions proceed over solid catalysts via contact of feedstock molecules and active sites in pores of a catalyst [10, 11]. It is obvious that the influence of diffusion limitations greatly de- pends on textural properties of a catalyst, size of granules, reaction conditions and feedstock. So, it is necessary to carry out catalytic tests with low influence of internal and external diffusion on catalytic activity for reliable evaluation of the impact of active component properties on catalytic activity. There is a good theoretical background [10–13] for de- scribing approaches for testing heterogeneous catalysts in http://chimicatechnoacta.ru/ https://doi.org/10.15826/chimtech.2023.10.2.08 mailto:mikluha.ia@gmail.com http://creativecommons.org/licenses/by/4.0/ https://orcid.org/0000-0002-5005-0781 https://orcid.org/0000-0002-8336-1797 https://orcid.org/0000-0001-6401-0011 https://orcid.org/0000-0002-8089-2357 https://orcid.org/0000-0002-7038-2070 https://crossmark.crossref.org/dialog/?doi=https://doi.org/10.15826/chimtech.2023.10.2.08&domain=pdf&date_stamp=2023-04-24 https://journals.urfu.ru/index.php/chimtech/rt/suppFiles/6670/0 Chimica Techno Acta 2023, vol. 10(2), No. 202310208 ARTICLE 2 of 9 DOI: 10.15826/chimtech.2023.10.2.08 a flow tube reactor to determine the influence of diffusion limitations on catalyst activity. Catalytic experiments, in- cluding proportional changes of a linear feedstock velocity and volume of a catalyst at constant liquid hour space ve- locity (LHSV), are usually carried out. The influence of ex- ternal diffusion is considered to be minimal, when the var- iation of a linear feedstock velocity and catalyst volume does not cause a change in the conversion of the addressed reagent. The influence of diffusion can be indirectly esti- mated by calculating liquid–solid mass transfer coefficient (ks, cm s–1) [11, 14]. When the impact of internal diffusion is the lowest, ks can be determined by mass balance equations of liquid and solid phases. These equations include effective diffusivity and the mass transfer coefficient. The higher ks, the greater impact of external diffusion [14, 15]. After that, catalytic tests are performed to define the in- fluence of internal diffusion on catalytic activity. The tests include the decrease of catalyst’s granular size and activity measurements. When the reduction in granular size does not affect the conversion, the influence of internal diffusion is minimal. [12]. The indirect characteristic used for defin- ing the internal diffusion impact is the catalyst effective- ness factor (ƞ) [11, 14]. When the effectiveness factor is much less than 1, there is an influence of internal diffusion. For example, the effectiveness factor for hydrotreating cat- alysts with trilobe shape is about 0.3–0.8 for processing model sulfur-containing molecules [14]. When catalysts are tested in hydrotreatment of the real feedstock, the effec- tiveness factor is usually less than 0.6 [16]. The effective- ness factor should be close to 1 to conduct a correct inves- tigation in the development of hydrotreating catalysts, for example, for the determination of the reaction rate con- stant, activation energy, etc. This report presents the testing conditions for CoMo/Al2O3 hydrotreating catalysts in hydrodesulfuriza- tion (HDS) of dibenzothiophene (DBT) at the lowest influ- ence of internal and external diffusion. Catalytic experi- ments were carried out in conditions of ideal plug flow. Therefore, the obtained results can be used by the research- ers working in the field of hydrotreating catalysts and can be adapted to their catalysts test conditions. The mass transfer coefficient and the effectiveness factor of the cata- lyst were defined using the results of catalytic experiments. They were calculated using the mass balance equations and mathematical expressions. These parameters were calcu- lated with known mathematical expressions previously used in HDS modeling [2, 17–27]. 2. Experimental 2.1. Catalyst preparation and characterization The CoMo/Al2O3 catalyst has been prepared by the follow- ing procedure. To prepare impregnating solution, the rea- gents were sequentially added into the water under stirring in the following order: cobalt hydroxide (Baltic Enterprise, Ltd., Russia, pure), molybdenum oxide (Alfa Aesar, USA, pure) and phosphoric acid (OJSC “TK Spectr-Khim”, Russia, 98%). The reagents were dissolved at 70 °C. After complete dissolution of the reagents, the obtained solution was used for vacuum impregnation of γ-Al2O3 support (produced by OOO «NPK «Synthesis», Russia). Then, the catalyst was dried at 120 °С during 4 h in air flow. Investigation of the catalyst by nitrogen adsorption-de- sorption was made according to the procedure described in [28]. The catalyst was calcined at 550 °C before analysis. High-resolution transmission electron microscopy (HRTEM) and X-ray photoelectron spectroscopy (XPS) studies were performed for the catalyst sulfided in H2S flow. The descrip- tion of the sulfidation procedure is given in [28, 29]. 2.2. Catalytic experiment The CoMo/Al2O3 hydrotreating catalyst was used to define the testing conditions with the lowest influence of internal and external diffusion. Preparation of the catalyst for testing. Before testing, the catalyst fraction (dc1 = 0.1–0.25 mm, dc2 = 0.25–0.5 mm and dc3 = 0.5–1.0 mm) was sulfided in a flow-through quartz reactor in H2S flow at atmospheric pressure and a temperature of 220 °C for 2 h and 400 °C for 2 h. The cata- lyst’s fraction was cooled in helium flow. Reactor description. Testing of catalysts was carried out in the fixed-bed flow microreactor in all cases. The re- actor had the following characteristics: the diameter (DR) – 8 mm, the bed length (Lb) – 40 mm, DR/dc1 = 80–32, DR/dc2 = 32–16 and DR/dc3 = 16–8, Lb/dc1 = 400–160, Lb/dc2 = 160–80 and Lb/dc3 = 80–40. To decrease the tem- perature gradient and to improve hydrodynamics of the re- actor in the catalyst’s bed, the sulfide catalyst fraction was uniformly mixed with silicon carbide (the fraction of SiC is 0.1–0.25 mm). Total volume of the mixture of SiC and the catalyst was 4 ml in all cases. It should be noted that condi- tions of catalytic experiments complied with the ideal plug flow regime: DR/dc>10 and Lb/dc>50 [13]. Model feed description. The mixture of DBT and un- decane was used as the model feedstock. DBT was used as a sulfur-containing compound. DBT content was 14500 ppm (sulfur content is 2500 ppm). Undecane (ρ = 0.74 g/cm3) was used as a solvent. Reaction conditions. The influence of external diffu- sion was considered to be minimal, when the conversion of the reacting component does not change at variation of a linear feedstock velocity and a catalyst volume and constant LHSV during catalytic tests [12]. In our case, the catalyst fraction loaded to the reactor was less than 1 g, and it was difficult to correctly measure the volume. Therefore, the present catalytic experiments include variation of a linear feedstock velocity (ϑfeed) and catalyst loading (mс) along with the constant weight hour space velocity (WHSV, h–1) (ϑfeed·ρfeed/mc). The experiments were performed using the catalyst fraction of 0.1–0.25 mm. The catalyst loadings mс = 0.5 g, 0.4 g and 0.3 g, and the linear feedstock velocities ϑfeed = 54.0 ml h–1, 43.2 ml h–1 and 32.4 ml h–1 were chosen, https://doi.org/10.15826/chimtech.2023.10.2.08 https://doi.org/10.15826/chimtech.2023.10.2.08 Chimica Techno Acta 2023, vol. 10(2), No. 202310208 ARTICLE 3 of 9 DOI: 10.15826/chimtech.2023.10.2.08 while WHSV was 80 h–1. The testing conditions were as fol- lows: p = 4 MPa, H2/feedstock ratio = 300 Nm3/m3, T = 240 °C, 260 °C and 280 °C. The additional experiment was performed to check the influence of internal diffusion limitations. The catalyst fraction (mс = 0.4 g) with the particle sizes of 0.1–0.25 mm, which was chosen after previous experiments, was used. The following conditions were used: p = 4 MPa, H2/feed- stock ratio = 300 Nm3/m3, WHSV = 80 h–1, T = 225–280 °C. The results of the experiment were used to construct a plot of the ln(k) vs 1000/T dependence. The rate constants of hydrodesulfurization of dibenzothiophene were determined based on the assumption of the pseudo-first order of reac- tion; equation (1) was used for calculation [3]. This plot al- lows calculating the activation energy (Ea) with the Arrhe- nius equation (2): 𝑘 = −𝐹(𝐷𝐵𝑇) 𝑊 · ln (1 − XDBT 100 ), (1) where k – rate constant, mol/(g·h), F(DBT) – molar flow rate of the feedstock, mol/h, W – catalyst loadings, g, XDBT – conversion of DBT, %. k = k0·exp(–Ea/RT). (2) One of the methods of defining the influence of internal diffusion on catalytic activity consists in carrying out a set of experiments with different size of granules/fraction par- ticles of a catalyst [10, 11, 13]. To determine effect of inter- nal diffusion in HDS of DBT, the experiments were per- formed. The sizes of the catalyst fraction were dc1 = 0.1– 0.25 mm, dc2 = 0.25–0.5 mm and dc3 = 0.5–1.0 mm. The testing conditions were as follows: p = 4 MPa, T1 = 240 °С, T2 = 260 °С, ratio H2/feedstock = 300 Nm3/m3, WHSV = 80 h–1. The catalyst loadings mс = 0.5 g was chosen. In all cases, the time to achieve steady-state of the cata- lyst was about 12 h. Then, 4 liquid reaction products were sampled at each process temperature. The liquid samples were analyzed using TE Instruments XPLORER for the de- termination of the residual sulfur content. Liquid products were analyzed on a PerkinElmer gas chromatograph Clarus 580 to defined residual DBT content. The resulting DBT content was similar for the samples ob- tained at one temperature regime (the inaccuracy of the method is 5%) that indicates the absence of catalysts deac- tivation during the catalytic tests. The conversion of DBT (XDBT) was used as a characteris- tic of catalytic activity. XDBT was calculated according to equation (3): 𝑋DBT = 𝐶DBT0 − 𝐶DBT 𝐶DBT0 · 100, (3) where CDBT0 is the initial DBT content in the model mixture and CDBT is the content of DBT in the hydrotreated product. 2.3. The estimation of the HDT reactor parameters To make the qualitative estimations of the HDT reactor pa- rameters, one must consider the phenomena that can change the reactor performance. Some effects such as axial mass dispersion, catalyst wetting, and wall flow have a macroscopic effect on the mass and heat transfer. Thereby their effect must be analyzed to determine whether they should be considered or not in mass balance equations and mathematical expressions [31]. 1. Isothermal operation. The temperature of the experimental reactor was con- trolled within ±1 °C during the collection of the experi- mental data. For this reason, the reactor was considered isothermal (only the mass balance was taken into account in the calculations. 2. Ideal plug behavior. It was determined by Chen criterion (2) [31] that the ex- perimental setup does not present plug-flow deviation, since the ratio of catalytic bed length to particle diameter is high enough to avoid back mixing effects. The right-hand side in expression of inequality (4) was 87 , and the left- hand side – 69 (87>69). 𝐿b 𝑑e > √20𝑛 Boa.m 𝑓 ln ( 1 1 − 𝑋 100⁄ ) , (4) where Lb – reactor-bed length, cm, de – equivalent size of a catalyst particle, cm, Bofa.m – axial mass Bodenstein number for f phase, n – order of reaction. 3. Incomplete wetting. Complete irrigation of the catalytic bed was ensured by Gierman and Harmsen criterion (W, equation (5)), since the wetting number equal to 2·10–1 was obtained. 𝑊 = µL ρL𝑑e 2𝑔 > 5 · 10−6 (5) where μL – viscosity of the liquid phase, mPa s, ρL – liquid density at process conditions, lb ft–3, g – gravitational con- stant, cm s–2 4. Wall flow effect. The experimental reactor presents the ratio of the reac- tor diameter to equivalent diameter of particles equal to 64. It meets the Sie criterion ( 𝐷𝑅 𝑑𝑒 , equation (6)) [31], decreasing the hydrodynamic problems associated with liquid distribu- tion and wall flow. 𝐷R 𝑑e > 25. (6) 3. Description of the mathematical calculations 3.1. Characteristics of the catalyst bed and physi- cal properties of the feed No effect of internal and external diffusion was confirmed through dependences of estimated HDS parameters (𝑘s and η) for some of the conditions presented in the work. Esti- mations below were obtained from isothermal small reac- tor (in this study, DR = 8 mm) [2, 15, 24, 25, 32, 33]. https://doi.org/10.15826/chimtech.2023.10.2.08 https://doi.org/10.15826/chimtech.2023.10.2.08 Chimica Techno Acta 2023, vol. 10(2), No. 202310208 ARTICLE 4 of 9 DOI: 10.15826/chimtech.2023.10.2.08 Mathematical calculations in these works are based on ki- netic experimental data, characteristics of the catalyst bed, mass balance equations and other proven chemical engi- neering expressions. A set of assumptions is assumed in cal- culating the estimations. The HDS reactor is considered iso- thermal and steady state operated. Catalyst deactivation was thought to be insignificant. The reaction is assumed to occur only in the porous solid catalyst, which is uniformly wetted by the liquid. Gas and liquid velocities are constant across the reactor. Gas–liquid mass transfer was neglected. The particle diameter of the catalyst was taken as the equiv- alent diameter of the sphere with the same volume and sur- face area as those of our catalyst. The diffusion effects for different conditions can be estimated from the values of the sulfur content in the product and the catalyst effectiveness factor. Therefore, below are the equations for simulation of an isothermal HDS reactor that include the conditions for testing and the other ones. The bed porosities (εB) of the catalyst were calculated from the weights of loadings, particles densities and the height of bed in the graduated cylinder (inner diameter 8 mm) [34]. The expressions (7)–(9) can be used to calculate the physical properties of oil and gas at process conditions. The oil density (ρL) as a function of temperature and pressure can be estimated by the Standing–Katz equation as pub- lished in [25, 35]: ρL = ρ0 + ∆ρP − ∆ρT, (7) ∆ρP = [0.167 + 16.181 ∙ 10 −0.0425ρ0 ] ∙ [ 𝑃 1000 ] − 0.01 ∙ ∙ [0.299 + 263 ∙ 10−0.0603ρ0 ] ∙ [ 𝑃 1000 ] 2 , (8) ∆ρT = [0.0133 + 152.4 ∙ (ρ0 + ∆ρP) −2.45] ∙ (𝑇R − 520) − −[8.1 ∙ 10−6 − 0.0622 ∙ 10−0.764(ρ0+∆ρP)] ∙ (𝑇R − 520) 2, (9) where ρ0 – density of oil at 15.6 °C and 101.3 kPa, lb ft–3, Δρp – pressure dependence of liquid density, lb ft–3, ΔρT – temperature correction of liquid density, lb ft–3, 𝑃 – the pressure, 𝑇R is the temperature, °R. Glaso’s equation, as presented in [18, 19, 35], was used as a generalized mathematical equation for oil viscosity. Equations (10)–(12) are the following: μL = 3.141 ∙ 10 10(𝑇 − 460)−3.444[log10(API)] 𝑎 , (10) 𝑎 = 10.313[log10(𝑇 − 460)] − 36.447, (11) API = 141.5 d15.6 − 131.5, (12) where a – dimensionless number, API – American Petro- leum Institute, T is the temperature (°C), 𝑑15.6 is the specific gravity of oil at 15.6 °C. Strictly speaking, equations (7)–(12) for calculating liq- uid characteristics are valid for petroleum distillates, espe- cially for the ones containing DBT. Considering all arguments, the given expressions were used for calculating properties of liquid phase. It should be emphasized that these calculations are approximate. 3.2. Mass balance equations HDS of oil fractions can be considered as a bimolecular ir- reversible reaction between the oil (A) and hydrogen (B) reactants [25, 36]: νAA + νBB → νPProd, (13) where νA,νB,νP are stoichiometric coefficients of A, B and product, respectively. This simplified equation of the reac- tion is assumed to be valid for the case presented with DBT. Mass balance equations for the liquid and solid phases are given below. Equation for the liquid phase (14): uL d𝐶sulL d𝑧 + 𝑘s𝑎𝑡 (𝐶sulL − 𝐶sulS) = 0 (14) where 𝑘s – the liquid–solid mass transfer coefficient, uL – the superficial velocity of the liquid in the reactor, cm s–1, at – surface area of the particles per unit volume of the bed, cm–1, 𝐶sulL – concentration of sulfur compound in the liquid phase, mol cm–3, 𝐶sulS – molar liquid phase of sulfur inside the solid, mol cm–3, z – coordinate of reactor bed length. Equation for the solid phase (15): 𝑘s𝑎t(𝐶sulL − 𝐶sulS) νA + (εB − 1)ρPη𝑘𝐶sulS 𝑛 = 0, (15) where η is the effectiveness factor, εB – void fraction of the catalyst bed, k – reaction rate coefficient. The value n = 1 was used in the presented work. According to the literature data [3], HDS of DBT follows pseudo first reaction order. HDS kinetic constant (k) was estimated only by the original approaches described in [18, 37–39]. The procedure of estima- tion of the kinetic parameters (k0 and EA) is presented in Sup- plementary materials. The inhibiting effect of H2S was not taken into account, since its concentration is not high enough. Therefore, the influence of H2S on the HDS reaction rate is not significant. Since the catalyst particles had a complex shape, the equivalent diameter of the catalyst particle was used to cal- culate the parameters below. An equivalent size 𝑑e of a cat- alyst particle can be calculated as (16): 𝑑e = 2𝑉P 𝑆P , (16) where 𝑉P – volume of the catalyst particle, cm 3, 𝑆P – area of the catalyst particle, cm2. The surface area (𝑎t) of the particles per unit volume of the bed was calculated by equation (17): 𝑎t = 6(1 − εB) 𝑑e , (17) The molecular diffusivity of sulfur in the liquid (DLsul, cm2 s–1) is calculated by equation (18) [40]: https://doi.org/10.15826/chimtech.2023.10.2.08 https://doi.org/10.15826/chimtech.2023.10.2.08 Chimica Techno Acta 2023, vol. 10(2), No. 202310208 ARTICLE 5 of 9 DOI: 10.15826/chimtech.2023.10.2.08 𝐷sul 𝐿 = 8.93 ∙ 10−8 νL 0.267𝑇 νsul 0.433μL , (18) where νLand νsul are molar volume of solute and liquid sol- vent, respectively, which are estimated with the following equations (19)–(20) [18]: νi = 0.285(νci 𝑚 )1.048 (19) νc m = 7.5214 ∙ 10−3 𝑇MeABP 0.2896 𝑑15.6 −0.7666 (20) where νi – molar volume, cm3 mol–1, νmc – critical specific vol- ume, ft3 mol–1, νmci – critical specific volume of the liquid or gas, ft3 mol–1, 𝑇MeABP – the mean average boiling point (°R). Internal diffusion limitations are usually expressed in terms of the catalyst effectiveness factor [41]. The effective- ness factor reported in [42, 43] has to be in the range of 0.0057–1. Because the particle size of the catalyst is small, the effectiveness factor can be estimated as function of Thiele modulus (ϕ) [16, 44]. For the different catalyst shapes (sphere, cylinder, 2-lobe, 4-lobe, etc.), the effectiveness factor can be calculated using expressions which has been proposed for other authors [42, 45, 46]. The generalized modulus (ϕsul) for nth-order irreversible reaction is calculated according to (21) [44]. Effective diffusivity of sulfur in the pores of the cata- lyst (Desul, cm 2 s–1) was determined with the equation (20) [44]. ϕsul = 𝑉p 𝑆p [( 𝑛 + 1 2 ) ( 𝑘СsulS 𝑛−1 ρP Desul )] 0.5 , (21) Desul = θ τ ( 1 1 𝐷sul L⁄ + 1 𝐷K ⁄ ), (22) where ρp – catalyst particle density, g cm–3, θ – particle po- rosity, τ – tortuosity factor, DK – Knudsen diffusivity, cm2 s–1. The tortuosity factor (τ) generally has a value of 2–7 [41]. Usually, tortuosity factor is assumed to be 4 [16, 25, 41]. Knudsen diffusivity factor (𝐷K) is evaluated as fol- lows (23)–(25) [44, 47]: 𝐷K = 9700rg( 𝑇 𝑀w )0.5, (23) 𝑟g = 2θ 𝑆gρP , (24) θ = ρP𝑉g, (25) where 𝑀w – the molecular weight, 𝑟g – the pore radius, cm, 𝑆g – specific surface area of a catalyst particle, cm 2 g–1, 𝑉g – pore volume per unit mass of catalyst, cm 3 g–1. In present report, the following equation is employed for determining the values of η (26) [40, 44, 45]: η = 3(ϕsulcoth(ϕsul) − 1) ϕsul 2 . (26) Since the shape of the catalyst fractions mostly resem- bles a spherical shape, we used the effectiveness factor for- mula for spherical particles in the present calculation. 4. Results and Discussion 4.1. Description of the catalyst According to atomic emission spectroscopy data, the CoMo/Al2O3 catalyst used for catalytic tests contains 12.4 wt.% Mo, 2.7 wt.% Co and 1.4 wt.% P. The industrial γ- Al2O3 (produced by “NPK “Syntez”) was used as the support. Textural characteristics of the support and the catalyst are given in Table 1. The support has the specific surface area of 223 m2/g, the pore volume of 0.5 cm3/g and the av- erage pore diameter of 9 nm. According to the classification described in [48], the shape of nitrogen adsorption-desorp- tion isotherm of the support corresponds to IV(a) type, while the type of hysteresis loop relates to H2(a) (Figure S2). Such characteristics are typical for mesoporous mate- rials with cylindrical shape of pores [48]. The shapes of ni- trogen adsorption-desorption isotherm and hysteresis loop of the catalyst are the same as those of the support, con- firming that no plugging of significant pore volume by ac- tive metals during impregnation occurs. Pore size distribu- tion curves of the catalyst and the support have similar shape, also indicating no plugging of the pores in the cata- lyst (Figure S2). After supporting of active metals, the spe- cific surface area of the catalyst decreased to 147 m2/g, while pore volume and average pore diameter were similar to those of the support (Table 1). The catalyst sulfided in H2S flow was studied by X-ray pho- toelectron spectroscopy (XPS) method. The resulting Mo3d and Co2p XPS spectra were deconvoluted into several Mo and Co states (Figure 1). It was established that active metals are preferentially presented in the catalysts in the sulfur sur- rounding (more than 55%). The portion of Mo in the 4+ state (Mo in the MoS2 composition [49]) is about 72%. The rest of molybdenum is associated to 5+ (13%) and 6+ (13%) which is characteristic of Mo in oxysulfide and oxide states [49]. The fraction of cobalt in the composition of CoMoS phase [50] is about 58%. Cobalt in the catalyst is also present in the compo- sition of individual sulfide – CoxSy (12%) and Co2+ (29%) [49]. The obtained values of the CoMoS phase content in the catalyst are typical for highly active CoMo/Al2O3 catalysts [51]. Table 1 Textural characteristics of γ-Al2O3 support and CoMo/Al2O3 catalyst. Parameter Specific surface area, m2/g Pore volume, cm3/g Average pore diameter, nm Average slab length, nm Stacking number Al2O3 223 0.5 9 – – CoMo/Al2O3 147 0.4 10 3.7 2.2 https://doi.org/10.15826/chimtech.2023.10.2.08 https://doi.org/10.15826/chimtech.2023.10.2.08 Chimica Techno Acta 2023, vol. 10(2), No. 202310208 ARTICLE 6 of 9 DOI: 10.15826/chimtech.2023.10.2.08 The sulfide catalyst was also studied by HRTEM method. The examples of HRTEM images are given in Figure S3. The average slab length and stacking number of active compo- nent particles, which were calculated by analysing of sev- eral images with more than 500 particles, are 3.7 nm and 2.2, respectively (Table 1). The resulting values are typical of CoMo/Al2O3 hydrotreating catalysts [51]. 4.2. Experimental data on the effect of external and internal diffusion The data obtained in the HDS experiments to determine the impact of external diffusion are given in Table 2. The con- ditions of catalytic experiments are described in section 2. These experiments allowed us to determine the tempera- ture, at which the DBT conversion or residual sulfur content remained unchanged while the linear feedstock velocity and the catalyst’s loading changed simultaneously at constant WHSV. The residual sulfur content and DBT conversion are sim- ilar at 240 °C and at 260 °C for ϑfeed = 54.0 and 43.2 ml h–1 and mc = 0.5 g and 0.4 g, respectively (Table 2). DBT con- version is changing in the range of 59–69% at 280 °C. The residual sulfur content at the highest process temperature (280 °C) varies significantly for all catalyst loadings. The greatest difference in residual sulfur content at 280 °C is 252 ppm (Table 2). So, we cannot draw an unequivocal con- clusion about the effect of external diffusion at 280 °C from the data obtained. However, we can conclude that the influ- ence of external diffusion is the lowest at 240 °C and at 260 °C (ϑfeed = 54.0 and 43.2 ml h–1). The next step was to define conditions when the impact of internal diffusion was the smallest. The hydrotreating process was carried out at 240 °C and 260 °C. These tem- peratures were chosen because of the earlier established minimal influence of external diffusion. Table 3 shows the data of the HDS experiments to deter- mine the impact of internal diffusion. Experimental condi- tions are given in section 2. It was found that the influence of internal diffusion is more pronounced for the catalyst frac- tions 0.25–0.5 mm and 0.5–1.0 mm for both temperatures, since the DBT conversion changed in these cases. Thus, to decrease the contribution of internal diffusion, it is prefera- ble to use the catalyst fraction of 0.1–0.25 mm. Also, we calculated the value of Ea from the plot of ln(k) from 1000/T. We used this approach for additional confirmation. For the catalytic experiment, we used the cat- alyst fraction of 0.1–0.25 mm, according to the results given above (Table 3). The testing temperature varied from 225 to 280 °C. Detailed experimental conditions are given in section 2. The plot is shown in Figure 2. The Ea value was 128.0 kJ/mol. This value is close to that given in [52] for the kinetic region of reaction. So, we can conclude that diffusion influence is minimal in this region. These results partially agree with the results obtained for 240 and 260 °C (Table 2). Figure 1 Mo3d and Co2p XPS spectra. Table 3 DBT conversion for catalyst fractions 0.1–0.25 mm, 0.25–0.5 mm and 0.5–1.0 mm at 240 °C and 260 °C. Catalyst fraction, mm 0.1–0.25 0.25–0.5 0.5–1.0 Temperature process, °C XDBT, % 240 11 10 7 260 37 35 27 Table 2 Influence of temperature on the residual sulfur content and DBT conversion for the catalyst fraction 0.1–0.25 mm. mc, g ϑfeed, ml h–1 Temperature process, °C 240 260 280 Residual S content, ppm* DBT conversion, %** Residual S content, ppm* DBT conversion, %** Residual S content, ppm* DBT conversion, %** 0.5 54.0 2224 11 1745 30 923 63 0.4 43.2 2225 11 1751 30 773 69 0.3 32.4 2251 10 1850 26 1025 59 *Inaccuracy of the method for determination of residual sulfur content on TE Instruments XPLORER is 5%. ** According to PerkinElmer Gas chromatograph Clarus 580 analysis. https://doi.org/10.15826/chimtech.2023.10.2.08 https://doi.org/10.15826/chimtech.2023.10.2.08 Chimica Techno Acta 2023, vol. 10(2), No. 202310208 ARTICLE 7 of 9 DOI: 10.15826/chimtech.2023.10.2.08 Figure 2 Arrhenius plots of HDS of DBT. It can be concluded that to minimize the effects of inter- nal and external diffusion it is necessary to test the CoMo/Al2O3 catalyst in HDS of DBT at a temperature less than 260 °C using the catalyst fraction 0.1–0.25 mm. 4.3. Calculated data related to the impact of external and of internal diffusion Indirect influence of the external diffusion can be estimated by the mass transfer coefficient ks. It should be noted that calculation of this coefficient does not allow us to define the effect of external diffusion. However, effective diffusion in equation (3.16) is used in mass balance equations (3.8) and (3.9). Therefore, it is possible to find the dependence of mass balance coefficient from external diffusion at the neg- ligible effect of internal diffusion. In the present report, small catalyst fractions (0.1–0.25 and 0.25–0.5 mm) were used. Therefore, the generally ac- cepted equations for calculating ks cannot be applied [32]. In addition, well-known expressions for ks cannot be used because some of the parameters, such as phase velocities, do not satisfy the range of acceptable values. Therefore, we used experimental data given in Tables 2 and 3 in the cal- culations (3.8–3.9). The data in Table 4 shows that the ks value for the cata- lyst fraction 0.1–0.25 mm is lower than that for the catalyst fraction 0.25–0.5 mm at all temperatures. So, the effect of external diffusion will be greater for the larger catalyst (0.25–0.5 mm). The lowest ks value was obtained at 240 °C. Given the above, the 0.1–0.25 mm catalyst fraction will be less affected by external diffusion at 240 °C. Then, the effectiveness factor η will be proportional to the impact of internal diffusion because it relates to the ra- tio of the diffusion reaction rate to the total reaction rate. Therefore, the lower η, the greater the influence of internal diffusion. It allows us to calculate the η value from the equation (3.20). The data in Table 5 demonstrate the effect of the particle size on the effectiveness factor. It should be noted that the value of the effectiveness factor is much closer to 1 for the catalyst fraction 0.1–0.25 mm. In addition, the performed calculations are used in pre- sent work to confirm the behavior of diffusion effects in HDS experiments. The hydrogen flow is in large excess at the reactor inlet in present experimental conditions. Be- cause of the hydrogen-rich atmosphere, the residence time distribution of the gas phase is negligible. Therefore, only the liquid phase hydrodynamic aspects and the mass transport phenomena were analyzed in this report. The results of the calculations confirm the impact of in- ternal diffusion. The effectiveness factor for the lowest cat- alyst fraction 0.1–0.25 mm (Table 5) is lower than that for the catalyst fraction 0.25–0.5 mm. Thus, it follows from the observed correlation of the experimental and the calcula- tion data that the influence of internal diffusion is greater, when a larger catalyst fraction was used. 5. Limitations During the improvement and research of hydrotreating catalysts, it is desirable to test catalysts under conditions under which the influence of internal and external diffu- sion on catalyst activity is minimal. In this case it is pos- sible to establish more reliable correlations between prop- erties of active component particles and catalyst activity. The purpose of this study is to determine such test condi- tions for hydrotreating catalysts in plug flow regime, un- der which the influence of internal and external diffusion is minimal. Table 5 Effectiveness factor for catalyst fractions 0.1–0.25 mm and 0.25–0.5 mm under different temperature process. Catalyst fraction, mm 0.1–0.25 0.25–0.5 Temperature process, °C Ƞ 240 0.9423 0.8933 260 0.9476 0.9025 280 0.9523 0.9106 Table 4 Mass transfer coefficient factor for catalyst fractions 0.1–0.25 mm and 0.25–0.5 mm under different temperature process. mc, g ϑfeed, ml h–1 Temperature process, °C 240 260 280 Catalyst Fraction, mmd 0.1–0.25 0.25–0.5 0.1–0.25 0.25–0.5 0.1–0.25 0.25–0.5 𝒌𝐬 ∙ 𝟏𝟎 −𝟐, cm s–1 0.5 54.0 0.7329 1.4215 0.8530 1.6743 0.9820 1.9475 0.4 43.2 0.9113 1.7690 1.0605 2.0822 1.2553 2.4910 0.3 32.4 1.1997 2.3258 1.3853 2.7165 1.6078 3.1839 https://doi.org/10.15826/chimtech.2023.10.2.08 https://doi.org/10.15826/chimtech.2023.10.2.08 Chimica Techno Acta 2023, vol. 10(2), No. 202310208 ARTICLE 8 of 9 DOI: 10.15826/chimtech.2023.10.2.08 6. Conclusions The conditions for carrying out catalytic tests of the frac- tion of CoMo/Al2O3 hydrotreating catalyst in the fixed-bed flow microreactor were established. The chosen testing conditions complied with the requirements of ideal plug flow. Simultaneous variation of a linear feedstock velocity (54.0 ml h–1, 43.2 ml h–1 and 32.4 ml h–1) and a catalyst weight (0.5 g, 0.4 g and 0.3 g) at constant WHSV (80 h–1) showed that the influence of external diffusion was the low- est at 240–260 °C. The testing of catalysts fractions with the sizes of 0.1–0.25 mm, 0.25–0.5 mm and 0.5–1.0 mm at 240°С and at 260°С allowed us to establish that the influ- ence of internal diffusion was minimal for the catalyst frac- tion of 0.1–0.25 mm. When the catalyst fraction size in- creased to 0.25–0.5 mm and 0.5–1.0 mm, the effect of the mass transfer of feedstock molecules in catalysts pores to active sites on catalytic activity was observed. The obtained results are in good agreement with the mass transfer coef- ficient and the effectiveness factor, which were calculated by the mass balance equations and mathematical expres- sions adapted to the size of the catalyst fraction. ● Supplementary materials This manuscript contains supplementary materials, which are available on the corresponding online page. ● Funding This work was carried out within the framework of the budget projects of Ministry of Education and Science of Rus- sian Federation AAAA-A21-121011390010-7 and АААА-А21- 121011890074-4 for Boreskov Institute of Catalysis. ● Acknowledgments None. ● Author contributions Conceptualization: Y.V.V., P.P.M., I.A.M. Data curation: Y.V.V., P.P.M., K.A.N. Formal Analysis: P.P.M., I.A.M., O.P.K. Funding acquisition: O.V.K., A.S.N. Investigation: P.P.M., Y.V.V., I.A.M., O.P.K. Methodology: P.P.M., I.A.M., O.P.K. Project administration: O.V.K., A.S.N. Supervision: K.A.N., O.V.K., A.S.N. Validation: M.O.K, O.V.K., A.S.N. Visualization: P.P.M., Y.V.V., I.A.M. Writing – original draft: P.P.M., Y.V.V., I.A.M. Writing – review & editing: P.P.M., Y.V.V., I.A.M., K.A.N. ● Conflict of interest The authors declare no conflict of interest. ● Additional information Author IDs: Polina P. Mukhacheva, Scopus ID 57226795240; Yuliya V. Vatutina, Scopus ID 57189731746; Ivan A. Mik, Scopus ID 55375424900; Ksenia A. Nadeina, Scopus ID 57218590135; Maksim O. Kazakov, Scopus ID 23485283300; Oleg P. Klenov, Scopus ID 6506012360; Oleg V. Klimov, Scopus ID 7003783535; Aleksandr S. Noskov, Scopus ID 7005685096. Website: Boreskov Institute of Catalysis SB RAS, https://cataly- sis.ru. References 1. Wang TE, Yang F, Song M, Han D. Recent advances in the un- supported catalysts for the hydrodesulfurization of fuel. Fuel Proc Technol.2022:235. doi:10.1016/j.fuproc.2022.107386 2. Ancheyta J. Modeling and simulation of catalytic reactors for petroleum refining. 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