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Coupling non-isothermal trickle-bed reactor with catalyst pellet models to understand the reaction and diffusion in gas oil Hydrodesulfurization
Journal Pre-proof Coupling non-isothermal trickle-bed reactor with catalyst pellet models to understand the reaction and diffusion in gas oil Hydrodesulfurization
Xingqiang Zhao, Changfeng Yang, Mengke Lu, Yao Shi, Gang Qian, Xinggui Zhou, Xuezhi Duan PII:
S1004-9541(20)30076-8
DOI:
https://doi.org/10.1016/j.cjche.2020.02.013
Reference:
CJCHE 1652
To appear in:
Chinese Journal of Chemical Engineering
Received date:
9 August 2019
Revised date:
9 November 2019
Accepted date:
7 February 2020
Please cite this article as: X. Zhao, C. Yang, M. Lu, et al., Coupling non-isothermal tricklebed reactor with catalyst pellet models to understand the reaction and diffusion in gas oil Hydrodesulfurization, Chinese Journal of Chemical Engineering(2020), https://doi.org/ 10.1016/j.cjche.2020.02.013
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© 2020 Published by Elsevier.
Journal Pre-proof Coupling Non-Isothermal Trickle-Bed Reactor with Catalyst Pellet Models to Understand the Reaction and Diffusion in Gas Oil Hydrodesulfurization Xingqiang Zhao#, Changfeng Yang#, Mengke Lu, Yao Shi, Gang Qian, Xinggui Zhou, Xuezhi Duan* State Key Laboratory of Chemical Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China *Corresponding Author: [email protected]
These authors contributed equally to this article.
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Journal Pre-proof Abstract: In this work, a trickle-bed reactor coupled with catalyst pellet model is employed to understand the effects of the temperature and catalyst pellet structures on the reaction-diffusion
behaviors
in
gas
oil
hydrodesulfurization
(HDS).
The
non-isothermal reactor model is determined to be reasonable due to non-negligible temperature variation caused by the reaction heat. The reaction rate along the reactor is mainly dominated by the temperature, and the sulfur concentration gradient in the catalyst pellet decreases gradually along the reactor, leading to the increased internal effectiveness factor. For the fixed catalyst bed volume, there exists a compromise
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between the catalyst reaction rate and effectiveness factor. Under commonly studied catalyst pellet size of 0.8-3 mm and porosity of 0.4-0.8, an optimization of the
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temperature and catalyst pellet structures is carried out, and the optimized outlet sulfur content decreases to 7.6 wppm better than the commercial level at 0.96 mm of
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the catalyst pellet size and 0.40 of the catalyst porosity.
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Graphical abstract
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Keywords: Hydrodesulfurization; catalyst pellet; trickle-bed reactor; coupling model; reaction-diffusion behavior
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Journal Pre-proof 1. Introduction Refining of gas oil, one of the distillates of heavy crude oil, is of crucial importance to produce transportation fuels like gasoline and diesel fuel [1,2]. Due to the increasingly severe regulations for air quality over the world, the impurities in the gas oil especially for the sulfur compounds need to be removed before the refining operations to reduce SO2 emission [1,3-6]. Currently, hydrodesulfurization (HDS) is a widely used and efficient technology for the deep desulfurization [3,7]. It is usually performed in a single reactor over the Co-Mo or Ni-Mo/Al2O3 catalysts under the temperature over 300 oC and pressure between 2.0-10.0 MPa, where the outlet sulfur
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content of 500 wppm is regarded to be efficient [3,8-11].
There are two main types of commercial HDS reactors, i.e., the slurry reactor and
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trickle-bed reactor (TBR) [12]. Although the slurry reactor has simple construction, low pressure drop, large capacity and operational flexibility, its large-scale
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commercialization is still limited by some disadvantages, i.e., high cost of catalysts,
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complicated separation of catalysts and liquid products, and difficult understanding of reaction kinetics [12-16]. For the trickle-bed reactor, it has some advantages for the reaction, such as higher catalytic performance, less catalyst cost per operation run,
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safer operation at high temperature and pressure and lower operation cost [12,17-20].
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Tremendous TBR modelling and simulation studies were performed toward enhanced HDS performance [1,17-30]. However, in these studies, the isothermal reactor models
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were usually used for the TBR simulation regardless of the exothermic HDS reaction, and a constant catalyst pellet effectiveness factor was assumed without considering the variation in the catalyst pellets [7,21,24,26,29,30]. To achieve the improved HDS performance
and
catalyst
utilization,
fundamental
understanding
of
the
reaction-diffusion behaviors along the catalyst pellets and reactor is highly desirable under non-isothermal conditions. In this work, a non-isothermal trickle-bed reactor coupled with catalyst pellet model was established and then employed to understand the reaction-diffusion behaviors in gas oil HDS, where the varied effectiveness factor was considered along the catalyst pellets and reactor. Firstly, effects of the inlet temperature and wall temperature were investigated and then discussed in detail by analyzing the reaction rate as well as the reaction temperature and concentration distributions along the reactor and/or catalyst pellets. Subsequently, under commonly studied catalyst pellet 3
Journal Pre-proof size of 0.8-3 mm and porosity of 0.4-0.8, effects of the catalyst pellet size and porosity were also clarified. Finally, an optimization of the temperature and catalyst pellet structures with the outlet sulfur content as the objective was carried out. 2. Mathematical model 2.1. Trickle-Bed Reactor-Catalyst Pellet Coupling Model In this work, a trickle-bed reactor-catalyst pellet coupling model is chosen to simulate the HDS of gas oil. The HDS catalyst types and properties are listed in Table
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1.
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Table 1. Catalyst types and properties
Value 3.47 14.7 81.83 0.9943 0.9200 Extrudate trilobe
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Co content Mo content γ-Al2O3 content Bulk density (grinding) Bulk density (shaping) Shape
Unit wt% wt% wt% g/cm3 g/cm3 /
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The reactor model is based on the two-film theory and the catalyst pellet model is
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based on the reaction-diffusion equation [21,30].
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For reactor model, the mass balance equation for H2 and H2S in the gas phase is [21] ug dpiG pG kiL aL i CiL 0 RT dz Hi
(1)
The mass balance equation for H2 and H2S in the liquid phase is [21] uL
pG dCiL kiL aL i CiL kiS aS CiL CiS 0 dz H i
(2)
The mass balance equation for sulfur compound in the liquid phase is [21] uL
(3)
dCiL kiS aS CiL CiS 0 dz
The mass balance equation for H2, H2S and Sulfur Compound in the liquid phase is [21] (4)
rp
3 k aS C C 3 B i RHDS r 2 dr rp 0 S i
L i
S i
The energy balance equation is [31]
4
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rp
dTL 3 4 u c 3 B ( r H m ) RHDS r 2 dr + (Tw TL ) dz rp dR 0 L L L p
For catalyst pellet, the mass and energy equations can be expressed as follows [31,32]: De,i Ke
1 d 2 dCi (r ) p RHDS (i=H2, H2S and sulfur) dr r 2 dr
(6)
1 d 2 dT (r ) p ( r H m ) RHDS dr r 2 dr
(7)
To solve the set of differential equations, boundary conditions are required for reactor and catalyst pellet as follows:
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For reactor scale:
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CiL (CiL )in i=H2, H2S and sulfur
at z=0, pHG ( pHG )in , pHG S 0 2
2
2
dCi 0 i=H2, H2S and sulfur dr
T TL
(9)
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at r=rp, Ci CiS i=H2, H2S and sulfur
dT 0 dr
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at r=0,
(8)
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For catalyst pellet scale:
TL Tin
The inlet molar concentration for H2, H2S and sulfur can be calculated by the
( pHG2 )in
(CHL2S )in
H H2
( pHG2S )in H H 2S
(CSL )in
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(CHL2 )in
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following expressions:
( L wS )in 32
(10)
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The HDS reaction of gas oil was expressed by the following stoichiometric equation [1]:
Ar-S+2H2 Ar-H+H2S
(11)
where Ar-S is the sulfur compound and Ar-H is the generated aromatic compound free of sulfur. The intrinsic kinetics of the reaction are formulated by Langmuir-Hinshelwood relation as follows [1]: RHDS k HDS
C C 1 K C S 1.8 sul
H2S
kHDS k0 exp(
S H2
S H2S
0.96
(12)
2
Ea ) RT
(13)
34020 K H 2 S 5.166888exp RT
(14)
The internal effectiveness factor of the catalyst can be calculated by the Eq. (15) [33]:
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ηin =
AR = SR
3 i RHDS r 2 dr rp 3 0 RHDS
(15)
S
where the internal effectiveness factor is the average reaction rate in the catalyst pellet (AR) divided by the reaction rate at the external surface of the catalyst pellet (SR). The external diffusion effectiveness factor can be can be calculated by the Eq. (16): ηex =
RHDS S RHDS L
(16)
where RHDS S is the reaction rate at the external surface of the catalyst pellet and RHDS L is
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the reaction rate based on the concentration of the liquid phase. The correlations and parameters of relevant variables in the above models and kinetics are listed Table S1
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[21,34-37] and Table S2 [1].
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2.2. Numerical Method
A trickle-bed reactor-catalyst pellet coupling model was represented by partial
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differential algebraic equations (PDAE) coupled with the reaction kinetics described by Langmuir-Hinshelwood relation. The model was solved in gPROMS Model
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Builder 4.0.0. The partial differential equations were solved by the finite difference method method.2nd order backward finite differences were applied to the axial
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domain in the reactor with 200 intervals and 4th order centered finite differences were
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applied to the radial domain in the catalyst pellet with 20 intervals. 3. Results and discussion
3.1. Effect of Temperature Distribution For the HDS of gas oil, the reactor models with constant catalyst effectiveness factor were usually used in spite of its variation along the reactor, which could reduce the accuracy of simulation results [7,21]. Herein, a trickle-bed reactor-catalyst pellet coupling model was developed based on the two-film theory with varying effectiveness factor along the reactor direction, which was verified to be reliable by comparing estimated outlet sulfur concentration to experimental one, as shown in Fig. S1. Though the HDS of gas oil shows the exothermic characteristics [1,7,38], the isothermal reactor models were commonly applied to estimate the HDS behaviors, 6
Journal Pre-proof which is in principle unreasonable unless the reaction heat is negligible. To assess the reasonability of isothermal reactor model, the HDS performances (i.e., outlet sulfur content) between isothermal and non-isothermal reactors were carried out by using the above coupling model, and the results were shown in Fig. 1a. Clearly, the outlet sulfur content obtained from the non-isothermal reactor model is lower than that from the isothermal one, which is especially remarkable for the lower inlet temperature like 340 oC. The difference is assigned to the different temperature distributions in both reactors, as shown in Fig. 1b. Obviously, the temperature first increases along the reactor direction and then decreases. The maximum temperature difference along the
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reactor is around 10 oC for each inlet temperature, which will lead to non-negligible effect on the outlet sulfur content. This is because the high reaction temperature not only favors the reaction rate, but also reduces the effects of inhibition of hydrogen
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sulfide according to the Eqs. (13) and (14). Therefore, the non-isothermal reactor
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model is determined to be more reasonable for the HDS of gas oil.
Fig. 1. (a) Comparisons between isothermal and non-isothermal reactor models; (b) The effect of the inlet temperature on the reactor temperature distribution under the 7
Journal Pre-proof non-isothermal condition; The effect of the inlet temperature on the (c) external and (d) internal effectiveness factor of the catalyst under the non-isothermal condition. Conditions: Tw= Tin, dp=2.54 mm and θ=0.55. In addition to the outlet sulfur content, the external and internal effectiveness factors are also important for the HDS, which serves as assessment criterions of the catalyst utilization in the HDS [7,11]. Thus, the external and internal effectiveness factors were studied for the different inlet temperatures by using the non-isothermal reactor model, as shown in Fig. 1c and 1d. It can be seen that the external
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effectiveness factor increases from 0.6 to approximately 0.9, while internal
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effectiveness factor increases from 0.1 to around 0.6 along the reactor direction, indicating the existence of more serious internal diffusion limitation at the inlet of the
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reactor.
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Along this line, the concentration distributions of reactants (i.e., sulfur compound and H2), product (i.e., H2S) and the AR as well as SR along the reactor direction were
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investigated, as shown in Fig. 2. As expected, the sulfur concentration (Fig. 2a) decreases along the reactor direction and it consumes faster with higher inlet
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temperature in both liquid and solid surface. Meanwhile, the sulfur concentration in solid phase is lower than that in liquid phase owning to the mass transfer in
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liquid-solid phase. For the H2 concentration (Fig. 2b), it first decreases sharply at the inlet of the reactor since the reaction rate is dominant compared to mass transfer of H2
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from gas phase to the pellet, and then it increases and remains stable at the end part of the reactor, because the mass transfer gradually becomes dominant until the reaction rate and mass transfer rate achieve a balance. The generated H2S shows the reverse trend as shown in Fig. 2c. It is noted that the mass transfer from the liquid to pellet surface is mainly dependent on liquid properties like density, viscosity and velocity [26] and can be weakened by reducing the concentration gradients in liquid-solid phase [38,39].
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Fig. 2. The effects of the inlet temperature on the profiles of concentration of (a)
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sulfur compound, (b) H2 and (c) H2S in the liquid and solid phase along the reactor length and (d) the pellet average reaction rate and pellet surface reaction rate along the
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reactor length. Conditions: Tw= Tin, dp=2.54 mm and θ=0.55. (L denotes liquid phase; S denotes solid catalyst surface; AR denotes average pellet reaction rates; SR denotes pellet surface reaction rate)
Moreover, Fig. 2d shows the effects of the inlet temperature on the real reaction rate (AR) and the pellet surface reaction rate (SR) along the reactor length. Under the higher inlet temperature, the SR is higher before 7.5 cm due to the higher temperature (Fig. 1b), but lower after 7.5 cm, which seems to disagree with the higher of H 2 concentration after 7.5 cm (Fig. 2b). This is because the sulfur concentration decreases significantly before 7.5 cm and less is left, and the reaction rate is more sensitive to the sulfur concentration due to its higher reaction order (1.80) than that of H2 concentration (0.96). Meanwhile, the SR is much higher than the AR at the inlet,
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Journal Pre-proof but decreases more significantly along the reactor length, giving an explanation to the increased internal effectiveness factor. The difference of the SR and AR is mainly assigned to the internal diffusion limitation, and thus the concentration gradients in the pellet was presented as shown in Fig. 3. Clearly, at the inlet, sulfur concentrations of the pellet surface (r/rp=1) under higher inlet temperature are smaller than that under lower inlet temperature due to the higher reaction rate. Similarly, the concentrations of H2 and H2S under the higher inlet temperature change more considerably and thus the lower internal effectiveness factor in the reactor inlet (Fig. 1d). However, at the end part of the reactor, the declined
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reaction rate leads to the decreased the concentration gradients under the higher inlet
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temperature, giving the higher internal effectiveness factor (Fig. 1d).
Fig. 3. The effects of the inlet temperature (Tin) on the profiles of concentration in the reactor and catalyst pell et. Conditions: Tw= Tin, dp=2.54 mm and θ=0.55.
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Journal Pre-proof 3.2. Understanding of the Reaction and Diffusion As can be seen from last paragraph that the inlet temperature has effects on the reaction and diffusion along both the reactor and pellet directions. Thus, an understanding of the reaction and diffusion in both the reactor and pellet is important for achievement of both the high HDS performance and catalyst utilization. Considering that the reaction and diffusion can be significantly influenced by temperature distributions and concentration related to internal diffusion environment, the wall temperature and pellet size as well as porosity were systematically studied by
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concentration distribution, and the effectiveness factors.
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analyzing their effects on the reaction rates, the temperature distribution,
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3.2.1. Effects of the Wall Temperature
For non-isothermal and exothermic reaction, wall temperature is an important
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operation condition to control temperature inside the reactor. Thus, effects of the wall temperature of the trickle-bed reactor were studied, and the results are shown in Fig. 4.
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Fig. 4a shows that as the wall temperature increases from 300 to 340 oC, the surface reaction rate (SR) increases due to the difference of reaction temperatures, as shown
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in Fig. 4b. Meanwhile, at the outlet of the reactor, the surface reaction rate (SR) shows similar values for different wall temperatures because more than 60 % of the
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sulfur has been consumed before 10 cm (Fig. 4c), and the low sulfur as well as H2
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concentration (Fig. 4d) after 10 cm limit the reaction rate.
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Fig. 4. The effects of the wall temperature (Tw) on (a) the pellet average reaction rate and pellet surface reaction rate along the reactor length; (b)liquid temperature
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distribution; profiles of concentrations of (c) sulfur compound and (d) H2 in liquid phase and solid phase along the reactor length. Conditions: Tin=340 oC, dp=2.54 mm
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and θ=0.55. (L denotes liquid phase; S denotes solid catalyst surface; AR denotes average pellet reaction rates; SR denotes pellet surface reaction rate) The concentration gradients of the sulfur, H2 and H2S along the reactor and the pellet were further investigated to understand the reaction and diffusion behavior within the pellet, as shown in Fig. 5. It can be found that the sulfur and H2 exhibit similar concentration gradients within the pellet, respectively. In other words, the wall temperature has little influence on the concentration distributions at the pellet scale, leading the small difference to the AR values in Fig. 4a. Therefore, it is expected that the higher wall temperature can lead to the enhanced HDS performance (Fig. 6a), but the reduced internal effectiveness factor (Fig. 6b).
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Fig. 5. The effects of the wall temperature (Tw) on the profiles of concentration in the
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reactor and catalyst pellet. Conditions: Tin=340 oC, dp=2.54 mm and θ=0.55.
Fig. 6. The effects of the wall temperature (Tw) on the (a) outlet sulfur content in the liquid; (b) external effectiveness factor along the reactor length; (b) internal effectiveness factor along the reactor length. Conditions: Tin=340 oC, dp=2.54 mm and θ=0.55.
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Journal Pre-proof 3.2.2. Effects of the Pellet Size Considering that the pellet size can significantly influence the reaction-diffusion behavior of the HDS catalyst pellet [11,40,41], the pellet size effect was further investigated as shown in Fig. 7. It is found in Fig. 7a that at the inlet of the reactor, the smaller pellet size leads to the higher surface reaction rate (SR) due to the higher temperature shown in Fig. 7b, but SR declines more sharply during the initial 0.5 cm
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mainly because of the decreased sulfur and H2 concentration shown in Fig. 7c and 7d.
Fig. 7. The effects of the pellet size (dp) on (a) the pellet average reaction rate and pellet surface reaction rate along the reactor length; (b)liquid temperature distribution; profiles of concentrations of (c) sulfur compound and (d) H2 in liquid phase and solid phase along the reactor length. Conditions: Tin=340 oC, Tw=330 oC and θ=0.55. (L denotes liquid phase; S denotes solid catalyst surface; AR denotes average pellet reaction rates; SR denotes pellet surface reaction rate) It can also be found in Fig. 7a that the smaller pellet size gives rise to the enhanced average pellet reaction rate (AR) before 6 cm, but the declined AR after 6 cm, which 14
Journal Pre-proof can be explained by the concentration distributions in both the reactor and pellet scale as shown in Fig. 8. Clearly, compared with the HDS catalyst with larger pellet size, the sulfur and H2 concentration gradients in the smaller pellet is shallower, indicating the better diffusion performance due to the short diffusion path and thus the higher
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reaction rate as well as catalyst utilization.
Fig. 8. The effects of the pellet size (dp) on the profiles of concentration in the reactor and catalyst pellet. Conditions: Tin=340 oC, Tw=330 oC and θ=0.55. Though the catalyst with smaller pellet size will alleviate the diffusion limitation, the smaller pellets may cause larger pressure drops in fixed beds. As shown in Fig. 9a, when the pellet size is smaller than 0.8 mm, the outlet sulfur concentration keeps almost unchanged. This may result from the similar internal and external diffusivities. It can be seen from Fig. 9b and 9c that when the pellet size decreased to the 0.8 mm, the external and internal effectiveness factors range from 0.85 to 1.00 and from 0.6 to 1.00, respectively, indicating the little influence of the external and/or internal 15
Journal Pre-proof diffusion. Therefore, the suitable pellet size may range from 0.8 to 1.0 mm due to the
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compromise between the catalyst utilization and pressure drops.
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Fig. 9. The effects of pellet size (dp) on (a) outlet sulfur content in the liquid; (b) external and (c) internal effectiveness factor along the reactor length. Conditions:
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3.2.3. Effects of the Pellet Porosity
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Tin=340 oC, Tw=330 oC and θ=0.55.
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In addition to pellet size, pellet porosity is also a vital factor for reaction-diffusion behavior within the pellet[11], and its effects on both the rates, temperature and concentration distribution along the reactor length were also studied, as shown in Fig.
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10. It can be seen in Fig. 10a that the smaller porosity leads to the higher surface
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reaction rate (SR) before 12 cm due to the higher bulk density according to Eq. (S22) and (S23). The porosity has little influence on the temperature distributions in
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comparison with pellet size, as illustrated in Fig. 10b. The SR under different porosities maintains constant after 12 cm mainly due to the low reactants concentrations (Fig. 10c and 10d).
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Fig. 10. The effects of the porosity (θ) on (a) the pellet average reaction rate and pellet surface reaction rate along the reactor length; (b) liquid temperature distribution;
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profiles of concentrations of (c) sulfur compound and (d) H2 in liquid phase and solid phase along the reactor length. Conditions: Tin=340 oC, Tw=330 oC, dp=2.54 mm. (L
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denotes liquid phase; S denotes solid catalyst surface; AR denotes average pellet reaction rates; SR denotes pellet surface reaction rate) The sulfur, H2 and H2S concentration distributions along the reactor and pellet directions were also evaluated to investigate reaction-diffusion interplay within the pellet as shown in Fig. 11. Obviously, the smaller pellet porosity leads to deeper concentration gradients along the pellet direction, indicating more serious diffusion limitation. This also can be confirmed by Fig. 12b in which the internal effectiveness factor increases with the increased porosity. Though the pellet with smaller porosity has low catalyst utilization, it can also result in more active sites leading to higher HDS performance as shown in Fig. 12a. Thus, there exists a compromise between the HDS performance and catalyst utilization under different porosities.
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Fig. 11. The effects of the porosity(θ) on the profiles of concentration in the reactor
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and catalyst pellet. Conditions: Tin=340 oC, Tw=330 oC, dp=2.54 mm.
Fig. 12. The effects of the porosity(θ) on (a) outlet sulfur content in the liquid; (b) internal effectiveness factor along the reactor length. Conditions: Tin=340 oC, Tw=330 o
C, dp=2.54 mm. 18
Journal Pre-proof 3.3. General Discussion and Optimization Based on the above analyses, it is found that the inlet temperature and wall temperature can significantly influence the convection-diffusion behavior at the reactor scale, and the pellet size and porosity also play an important role in the reaction-diffusion behavior at the pellet scale. Besides, the pressure and superficial velocity of liquid phase are also the important factors in the process of HDS. As a consecutive effort, an optimization was carried to enhance the HDS performance and the catalyst utilization. The objective of optimization is to minimize the sulfur concentration at the outlet of reactor with the internal effectiveness factor along the
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reactor length kept in or even better than the commercial level (i.e., 0.4-0.6) [40,42]. Meanwhile, the control variables were the above mentioned inlet temperature, wall
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temperature, pressure, superficial velocity of liquid phase, pellet size and porosity, and their lower and upper boundaries are listed as following, which are commonly
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used values in industry:
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4 MPa P 7 MPa
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300 o C Tw 370 oC
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0.8mm dp 3mm
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0.00875 cm s uL 0.02 cm s
0 . 4 0 .8
The optimization results in the outlet sulfur content of 7.6 wppm with the average effectiveness factor of 0.86, where the initial temperature, wall temperature, pressure, superficial velocity of liquid phase, pellet size and porosity are 380 oC, 367 oC, 6.3MPa, 0.00875 cm/s, 0.96 mm and 0.40. 4. Conclusions In summary, we have clarified the effects of the temperature and catalyst pellet structures on the reaction-diffusion behaviors in gas oil HDS via our developed non-isothermal trickle-bed reactor coupled with catalyst pellet model. It has shown that the reaction rate along the reactor is mainly dominated by the temperature, and 19
Journal Pre-proof the sulfur concentration gradient in the catalyst pellet decreases gradually along the reactor, leading to the increased effectiveness factor. For the fixed catalyst bed volume, the existed compromise between the catalyst reaction rate and effectiveness factor and the constrained temperature rising have yielded an optimized temperature and catalyst pellet structures. The optimized catalyst pellet size of 0.96 mm and catalyst porosity of 0.40 have been determined, and the resultant outlet sulfur content can decrease to 7.6 wppm, which is better than the commercial level. The insights demonstrated here could guide the selection of temperature as well as the rational
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design and optimization of the HDS catalyst pellet.
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Associated Content Supporting Information The following files are available free of charge. (Figure S1) Comparison between the calculated sulfur concentration and the previously reported experimental value in the liquid phase at the exit of the reactor under the isothermal condition; (Table S1) The correlations of variables in the model;
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(Table S2) The values of parameter and variables used in the model. (PDF)
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Author Information Corresponding Author
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E-mail address: [email protected]
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Author Contributions
These authors contributed equally to this article. (X.Q. Zhao and C.F. Yang)
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Acknowledgments
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#
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*Tel.: +86-21-64250937, Fax.: +86-21-64253528,
This work was supported by the National Key R&D Program of China (2018YFB0604500), the Natural Science Foundation of China (21776077), the Shanghai Natural Science Foundation (17ZR1407300 and 17ZR1407500), the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, the Shanghai Rising-Star Program (17QA1401200), the Open Project of SKLOCE (SKL-Che-15C03) and the 111 Project of the Ministry of Education of China (B08021). Conflict of Interest Statement: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Journal Pre-proof Nomenclature gas–liquid interfacial area, cm-1
as
liquid–solid interfacial area, cm-1
c Lp
liquid capacity, J/g/K
Ci
molar concentration of compound i, mol/cm3
dR
reactor diameter, cm
dp
catalyst pellet diameter, cm
DiL
molecular diffusivity coefficient of compound i in liquid, cm2/s
De,i
effective diffusivity coefficient of compound i in catalyst pellet, cm2/s
DK,i
Knudsen diffusion coefficient, cm2/s
Ea
activation energy for reaction of HDS, J/mol
GL
liquid superficial mass velocity, g/cm2/s
Hi
Henry’s law coefficient, MPa/cm3/mol
k
liquid conductivity coefficient, J/K /m/s
kiL
gas–liquid mass-transfer coefficient of compound i, cm/s
kiS
liquid–solid mass-transfer coefficient of compound i, cm/s
k0
frequency factor for reaction of HDS, (cm3)m+n/mol(m+n-1) /g/ s
kHDS
reaction rate constant, (cm3)m+n/mol(m+n-1)/ g/ s
K H 2S
adsorption equilibrium constant for H2S,
Ke
effective conductivity coefficient, J/ K /cm/s
Mw
molecular weight of liquid phase, g/mol
piG
P
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Pr
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aL
partial pressure of component i in the bulk gas phase, MPa total pressure, MPa
22
Journal Pre-proof mean pore radius, cm
rp
catalyst pellet radius, cm
R
universal gas constant, J/mol/K
RHDS
reaction rate of HDS, mol/g/s
TL
temperature of liquid phase, K
TMeABP
mean average boiling point, oR
T
temperature in the catalyst pellet, K
Tw
cooling temperature of the reactor, K
uL
superficial velocity of liquid phase, cm/s
uG
superficial velocity of gas phase, cm/s
vi
molar volume of component i, cm3/mol
vic
critical specific volume of component i, cm3/mol
vNi
molar gas volume of component i, Nl/mol
wi
weight fraction of compound i in the liquid phase, wt%
zR
reactor length, cm
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Greek Symbols
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f
rg
r H m
heat of reaction, J/mol
α
heat transfer coefficient from wall to catalyst bed, W/cm3/K
ρB
bulk density, g/cm3
ρL
liquid density at process conditions, g/cm3
ρp
pellet density, g/cm3
ρs
solid density, g/cm3
ρ0
liquid density at standard conditions (15.6 °C and 101.3 kPa), lb/ ft -3
23
Journal Pre-proof liquid density at 20 °C, g/cm3
L
liquid viscosity, mPa‧s
H 2 , H2 S
solubility coefficient of H2 and H2S, Nl/kg/MPa
η
catalyst effectiveness factor
ε
bed void fraction
θ
catalyst pellet porosity
τ
tortuosity factor for catalyst pellet
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f
ρ20
Abbreviations liquid phase
S
solid catalyst surface
AR
average pellet reaction rates
SR
pellet surface reaction rate
Jo u
rn
al
Pr
e-
pr
L
24
Journal Pre-proof References: [1] F. S. Mederos, J. Ancheyta, I. Elizalde, Dynamic modeling and simulation of hydrotreating of gas oil obtained from heavy crude oil, Appl. Catal. A 425 (2012) 13-27. [2] G. Marroquı́n-Sánchez, J. Ancheyta-Juárez, Catalytic hydrotreating of middle distillates blends in a fixed-bed pilot reactor, Appl. Catal. A 207 (2001) 407-420. [3] F. S. Mjalli, O. U. Ahmed, T. Al-Wahaibi, Y. Al-Wahaibi, I. M. Alnashef, Deep oxidative desulfurization of liquid fuels, Rev. Chem. Eng. 30 (2014) 337-378. [4] L. C. Green, S. R. Armstrong, Particulate matter in ambient air and mortality: Toxicologic
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[5] R. F. Sawyer, R. A. Harley, S. H. Cadle, J. M. Norbeck, R. Slott, H. A. Bravo, Mobile sources critical review: 1998 NARSTO assessment, Atmos. Environ. 34 (2000) 2161-2181.
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[7] I. Elizalde, F. S. Mederos, C. Monterrubio, N. Casillas, H. Díaz, F. Trejo, Mathematical modeling and simulation of an industrial adiabatic trickle-bed reactor for upgrading heavy crude oil by hydrotreatment process, React. Kinet., Mech. Cat. 126 (2018) 31-48.
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[8] K. Jeong, T. Kim, J. Kim, H. Chae, C. Kim, Y. Park, S. Jeong, Selective oxidation of refractory
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[9] I. V. Babich, J. A. Moulijn, Science and technology of novel processes for deep desulfurization of oil refinery streams: A review, Fuel 82 (2003) 607-631. [10] B. Pawelec, R. M. Navarro, J. M. Campos-Martin, J. L. Fierro, Towards near zero-sulfur liquid fuels: A perspective review, Catal. Sci. Technol. 1 (2012) 23-42. [11] M. J. Macías, J. Ancheyta, Simulation of an isothermal hydrodesulfurization small reactor with different catalyst particle shapes, Catal. Today 98 (2004) 243-252. [12] F. S. Mederos, J. Ancheyta, J. Chen, Review on criteria to ensure ideal behaviors in trickle-bed reactors, Appl. Catal. A 355 (2009) 1-19. [13] C. J. Calderón, J. Ancheyta, Dynamic modeling and simulation of a slurry-phase reactor for hydrotreating of oil fractions, Energy Fuels 31 (2017) 5691-5700. [14] A. Quitian, J. Ancheyta, Experimental methods for developing kinetic models for hydrocracking reactions with slurry-phase catalyst using batch reactors, Energy Fuels 30 (2017) 4419-4437. [15] C. J. Calderón, J. Ancheyta, Modeling of slurry-phase reactors for hydrocracking of heavy 25
Journal Pre-proof oils, Energy Fuels 30 (2016) 2525-2543. [16] C. J. Calderón, J. Ancheyta, Modeling of CSTR and SPR small-scale isothermal reactors for heavy oil hydrocracking and hydrotreating, Fuel 216 (2018) 852-860. [17] M. Bhaskar, G. Valavarasu, B. Sairam, K. S. Balaraman, K. Balu, Three-phase reactor model to simulate the performance of pilot-plant and industrial trickle-bed reactors sustaining hydrotreating reactions, Ind. Eng. Chem. Res. 43 (2004) 6654-6669. [18] R. Lopez, C. G. Dassori, Mathematical modeling of a VGO hydrotreating reactor, Proceedings of SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, 2001.
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[19] A. Heidari, S. H. Hashemabadi, CFD simulation of isothermal diesel oil hydrodesulfurization and hydrodearomatization in trickle bed reactor, J. Taiwan Inst. Chem. Eng. 45 (2014) 1389-1402. [20] S. Uribe, M. E. Cordero, E. P. Reyes, A. Regalado-méndez, L. G. Zárate, Multiscale CFD
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modelling and analysis of TBR behavior for an HDS process: Deviations from ideal behaviors,
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[21] H. Korsten, U. Hoffmann, Three-phase reactor model for hydrotreating in pilot trickle-bed
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reactors, AIChE J. 42 (1996) 1350-1360.
[22] Z. M. Cheng, X. C. Fang, R. H. Zeng, B. P. Han, L. Huang, W. K. Yuan, Deep removal of sulfur and aromatics from diesel through two-stage concurrently and countercurrently operated
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A.
Rodríguez,
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hydrodesulfurization
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fixed-bed reactors, Chem. Eng. Sci. 59 (2004) 5465-5472.
hydrodenitrogenation (HDN), and the hydrogenation of aromatics (HDA) in a vacuum gas oil
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hydrotreater, Energy Fuels 18 (2004) 789-794. [24] F. Jiménez, V. Kafarov, M. Nuñez, Modeling of industrial reactor for hydrotreating of vacuum gas oils. simultaneous hydrodesulfurization, hydrodenitrogenation and hydrodearomatization reactions, Chem. Eng. J. 134 (2007) 200-208. [25] J. Ancheyta, Modeling and Simulation of Catalytic Reactors for Petroleum Refining, John Wiley & Sons, New York, 2011. [26] A. T. Jarullah, I. M. Mujtaba, A. S. Wood, Kinetic parameter estimation and simulation of trickle-bed reactor for hydrodesulfurization of crude oil, Chem. Eng. Sci. 66 (2011) 859-871. [27] F. S. Mederos, I. Elizalde, J. Ancheyta, Steady-state and dynamic reactor models for hydrotreatment of oil fractions: A review, Catal. Rev. 51 (2009) 485-607. [28] F. S. Mederos, M. A. Rodríguez, J. Ancheyta, E. Arce, Dynamic modeling and simulation of catalytic hydrotreating reactors, Energy Fuels 20 (2006) 936-945. [29] L. da Rocha Novaes, N. S. de Resende, V. M. M. Salim, A. R. Secchi, Modeling, simulation
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Journal Pre-proof and kinetic parameter estimation for diesel hydrotreating, Fuel 209 (2017) 184-193. [30] A. Bakhshi Ani, H. Ale Ebrahim, M. J. Azarhoosh, Simulation and multi-objective optimization of a trickle-bed reactor for diesel hydrotreating by a heterogeneous model using non-dominated sorting genetic algorithm II, Energy Fuels 29 (2015) 3041-3051. [31] Y. N. Wang, Y. Y. Xu, Y. W. Li, Y. L. Zhao, B. J. Zhang, Heterogeneous modeling for fixed-bed Fischer-Tropsch Synthesis: Reactor model and its applications, Chem. Eng. Sci. 58 (2003) 867-875. [32] G. F. Froment, K. B. Bischoff, J. De Wilde, Chemical Reactor Analysis and Design, Wiley, New York, 1990.
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[33] G. W. Roberts, Chemical Reactions and Chemical Reactors, Wiley, New York, 2008. [34] M. E. Cordero, S. Uribe, L. G. Zárate, R. N. Rangel, A. Regalado-Méndez, E. P. Reyes, CFD Modelling of Coupled Multiphysics-Multiscale Engineering Cases. Computational Fluid
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Dynamics-Basic Instruments and Applications in Science. IntechOpen, 2017.
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[35] G. E. Mueller, Prediction of radial porosity distributions in randomly packed fixed beds of uniformly sized spheres in cylindrical containers, Chem. Eng. Sci. 46 (1991) 706-708.
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[36] M. R. Riazi, A. Faghri, Thermal conductivity of liquid and vapor hydrocarbon systems: Pentanes and heavier at low pressures, Ind. Eng. Chem. Pro. Des. Dev. 24 (1985) 398-401. [37] N. J. Mariani, G. D. Mazza, O. M. Martínez, L. Ana, G. F. Barreto, On the influence of liquid
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[38] A. Alvarez, J. Ancheyta, Modeling residue hydroprocessing in a multi-fixed-bed reactor
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system, Appl. Catal. A 351 (2008) 148-158. [39] M. Bhaskar, G. Valavarasu, A. Meenakshisundaram, K. S. Balaraman, Application of a three phase heterogeneous model to analyse the performance of a pilot plant trickle bed reactor, Petrol. Sci. Technol. 20 (2002) 251-268.
[40] J. Ancheyta, C. Esteban, A batch reactor study to determine effectiveness factors of commercial HDS catalyst, Catal. Today 104 (2005) 70-75. [41] K. M. Brunner, H. D. Perez, R. P. Peguin, J. C. Duncan, L. D. Harrison, C. H. Bartholomew, W. C. Hecker, Effects of particle size and shape on the performance of a trickle fixed-bed recycle reactor for Fischer-Tropsch Synthesis, Ind. Eng. Chem. Res. 54 (2015) 2902-2909. [42] M. P. Dudukovic, Catalyst effectiveness factor and contacting efficiency in trickle-bed reactors, AIChE J. 23 (1977) 940-944.
27
Xingqiang Zhao, Changfeng Yang, Mengke Lu, Yao Shi, Gang Qian, Xinggui Zhou, Xuezhi Duan PII:
S1004-9541(20)30076-8
DOI:
https://doi.org/10.1016/j.cjche.2020.02.013
Reference:
CJCHE 1652
To appear in:
Chinese Journal of Chemical Engineering
Received date:
9 August 2019
Revised date:
9 November 2019
Accepted date:
7 February 2020
Please cite this article as: X. Zhao, C. Yang, M. Lu, et al., Coupling non-isothermal tricklebed reactor with catalyst pellet models to understand the reaction and diffusion in gas oil Hydrodesulfurization, Chinese Journal of Chemical Engineering(2020), https://doi.org/ 10.1016/j.cjche.2020.02.013
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© 2020 Published by Elsevier.
Journal Pre-proof Coupling Non-Isothermal Trickle-Bed Reactor with Catalyst Pellet Models to Understand the Reaction and Diffusion in Gas Oil Hydrodesulfurization Xingqiang Zhao#, Changfeng Yang#, Mengke Lu, Yao Shi, Gang Qian, Xinggui Zhou, Xuezhi Duan* State Key Laboratory of Chemical Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China *Corresponding Author: [email protected]
These authors contributed equally to this article.
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#
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Tel.: +86-21-64250937; Fax.: +86-21-64253528
1
Journal Pre-proof Abstract: In this work, a trickle-bed reactor coupled with catalyst pellet model is employed to understand the effects of the temperature and catalyst pellet structures on the reaction-diffusion
behaviors
in
gas
oil
hydrodesulfurization
(HDS).
The
non-isothermal reactor model is determined to be reasonable due to non-negligible temperature variation caused by the reaction heat. The reaction rate along the reactor is mainly dominated by the temperature, and the sulfur concentration gradient in the catalyst pellet decreases gradually along the reactor, leading to the increased internal effectiveness factor. For the fixed catalyst bed volume, there exists a compromise
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between the catalyst reaction rate and effectiveness factor. Under commonly studied catalyst pellet size of 0.8-3 mm and porosity of 0.4-0.8, an optimization of the
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temperature and catalyst pellet structures is carried out, and the optimized outlet sulfur content decreases to 7.6 wppm better than the commercial level at 0.96 mm of
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the catalyst pellet size and 0.40 of the catalyst porosity.
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Graphical abstract
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Keywords: Hydrodesulfurization; catalyst pellet; trickle-bed reactor; coupling model; reaction-diffusion behavior
2
Journal Pre-proof 1. Introduction Refining of gas oil, one of the distillates of heavy crude oil, is of crucial importance to produce transportation fuels like gasoline and diesel fuel [1,2]. Due to the increasingly severe regulations for air quality over the world, the impurities in the gas oil especially for the sulfur compounds need to be removed before the refining operations to reduce SO2 emission [1,3-6]. Currently, hydrodesulfurization (HDS) is a widely used and efficient technology for the deep desulfurization [3,7]. It is usually performed in a single reactor over the Co-Mo or Ni-Mo/Al2O3 catalysts under the temperature over 300 oC and pressure between 2.0-10.0 MPa, where the outlet sulfur
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content of 500 wppm is regarded to be efficient [3,8-11].
There are two main types of commercial HDS reactors, i.e., the slurry reactor and
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trickle-bed reactor (TBR) [12]. Although the slurry reactor has simple construction, low pressure drop, large capacity and operational flexibility, its large-scale
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commercialization is still limited by some disadvantages, i.e., high cost of catalysts,
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complicated separation of catalysts and liquid products, and difficult understanding of reaction kinetics [12-16]. For the trickle-bed reactor, it has some advantages for the reaction, such as higher catalytic performance, less catalyst cost per operation run,
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safer operation at high temperature and pressure and lower operation cost [12,17-20].
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Tremendous TBR modelling and simulation studies were performed toward enhanced HDS performance [1,17-30]. However, in these studies, the isothermal reactor models
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were usually used for the TBR simulation regardless of the exothermic HDS reaction, and a constant catalyst pellet effectiveness factor was assumed without considering the variation in the catalyst pellets [7,21,24,26,29,30]. To achieve the improved HDS performance
and
catalyst
utilization,
fundamental
understanding
of
the
reaction-diffusion behaviors along the catalyst pellets and reactor is highly desirable under non-isothermal conditions. In this work, a non-isothermal trickle-bed reactor coupled with catalyst pellet model was established and then employed to understand the reaction-diffusion behaviors in gas oil HDS, where the varied effectiveness factor was considered along the catalyst pellets and reactor. Firstly, effects of the inlet temperature and wall temperature were investigated and then discussed in detail by analyzing the reaction rate as well as the reaction temperature and concentration distributions along the reactor and/or catalyst pellets. Subsequently, under commonly studied catalyst pellet 3
Journal Pre-proof size of 0.8-3 mm and porosity of 0.4-0.8, effects of the catalyst pellet size and porosity were also clarified. Finally, an optimization of the temperature and catalyst pellet structures with the outlet sulfur content as the objective was carried out. 2. Mathematical model 2.1. Trickle-Bed Reactor-Catalyst Pellet Coupling Model In this work, a trickle-bed reactor-catalyst pellet coupling model is chosen to simulate the HDS of gas oil. The HDS catalyst types and properties are listed in Table
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1.
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Table 1. Catalyst types and properties
Value 3.47 14.7 81.83 0.9943 0.9200 Extrudate trilobe
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Co content Mo content γ-Al2O3 content Bulk density (grinding) Bulk density (shaping) Shape
Unit wt% wt% wt% g/cm3 g/cm3 /
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The reactor model is based on the two-film theory and the catalyst pellet model is
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based on the reaction-diffusion equation [21,30].
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For reactor model, the mass balance equation for H2 and H2S in the gas phase is [21] ug dpiG pG kiL aL i CiL 0 RT dz Hi
(1)
The mass balance equation for H2 and H2S in the liquid phase is [21] uL
pG dCiL kiL aL i CiL kiS aS CiL CiS 0 dz H i
(2)
The mass balance equation for sulfur compound in the liquid phase is [21] uL
(3)
dCiL kiS aS CiL CiS 0 dz
The mass balance equation for H2, H2S and Sulfur Compound in the liquid phase is [21] (4)
rp
3 k aS C C 3 B i RHDS r 2 dr rp 0 S i
L i
S i
The energy balance equation is [31]
4
Journal Pre-proof (5)
rp
dTL 3 4 u c 3 B ( r H m ) RHDS r 2 dr + (Tw TL ) dz rp dR 0 L L L p
For catalyst pellet, the mass and energy equations can be expressed as follows [31,32]: De,i Ke
1 d 2 dCi (r ) p RHDS (i=H2, H2S and sulfur) dr r 2 dr
(6)
1 d 2 dT (r ) p ( r H m ) RHDS dr r 2 dr
(7)
To solve the set of differential equations, boundary conditions are required for reactor and catalyst pellet as follows:
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For reactor scale:
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CiL (CiL )in i=H2, H2S and sulfur
at z=0, pHG ( pHG )in , pHG S 0 2
2
2
dCi 0 i=H2, H2S and sulfur dr
T TL
(9)
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at r=rp, Ci CiS i=H2, H2S and sulfur
dT 0 dr
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at r=0,
(8)
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For catalyst pellet scale:
TL Tin
The inlet molar concentration for H2, H2S and sulfur can be calculated by the
( pHG2 )in
(CHL2S )in
H H2
( pHG2S )in H H 2S
(CSL )in
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(CHL2 )in
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following expressions:
( L wS )in 32
(10)
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The HDS reaction of gas oil was expressed by the following stoichiometric equation [1]:
Ar-S+2H2 Ar-H+H2S
(11)
where Ar-S is the sulfur compound and Ar-H is the generated aromatic compound free of sulfur. The intrinsic kinetics of the reaction are formulated by Langmuir-Hinshelwood relation as follows [1]: RHDS k HDS
C C 1 K C S 1.8 sul
H2S
kHDS k0 exp(
S H2
S H2S
0.96
(12)
2
Ea ) RT
(13)
34020 K H 2 S 5.166888exp RT
(14)
The internal effectiveness factor of the catalyst can be calculated by the Eq. (15) [33]:
5
Journal Pre-proof rp
ηin =
AR = SR
3 i RHDS r 2 dr rp 3 0 RHDS
(15)
S
where the internal effectiveness factor is the average reaction rate in the catalyst pellet (AR) divided by the reaction rate at the external surface of the catalyst pellet (SR). The external diffusion effectiveness factor can be can be calculated by the Eq. (16): ηex =
RHDS S RHDS L
(16)
where RHDS S is the reaction rate at the external surface of the catalyst pellet and RHDS L is
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the reaction rate based on the concentration of the liquid phase. The correlations and parameters of relevant variables in the above models and kinetics are listed Table S1
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[21,34-37] and Table S2 [1].
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2.2. Numerical Method
A trickle-bed reactor-catalyst pellet coupling model was represented by partial
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differential algebraic equations (PDAE) coupled with the reaction kinetics described by Langmuir-Hinshelwood relation. The model was solved in gPROMS Model
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Builder 4.0.0. The partial differential equations were solved by the finite difference method method.2nd order backward finite differences were applied to the axial
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domain in the reactor with 200 intervals and 4th order centered finite differences were
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applied to the radial domain in the catalyst pellet with 20 intervals. 3. Results and discussion
3.1. Effect of Temperature Distribution For the HDS of gas oil, the reactor models with constant catalyst effectiveness factor were usually used in spite of its variation along the reactor, which could reduce the accuracy of simulation results [7,21]. Herein, a trickle-bed reactor-catalyst pellet coupling model was developed based on the two-film theory with varying effectiveness factor along the reactor direction, which was verified to be reliable by comparing estimated outlet sulfur concentration to experimental one, as shown in Fig. S1. Though the HDS of gas oil shows the exothermic characteristics [1,7,38], the isothermal reactor models were commonly applied to estimate the HDS behaviors, 6
Journal Pre-proof which is in principle unreasonable unless the reaction heat is negligible. To assess the reasonability of isothermal reactor model, the HDS performances (i.e., outlet sulfur content) between isothermal and non-isothermal reactors were carried out by using the above coupling model, and the results were shown in Fig. 1a. Clearly, the outlet sulfur content obtained from the non-isothermal reactor model is lower than that from the isothermal one, which is especially remarkable for the lower inlet temperature like 340 oC. The difference is assigned to the different temperature distributions in both reactors, as shown in Fig. 1b. Obviously, the temperature first increases along the reactor direction and then decreases. The maximum temperature difference along the
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reactor is around 10 oC for each inlet temperature, which will lead to non-negligible effect on the outlet sulfur content. This is because the high reaction temperature not only favors the reaction rate, but also reduces the effects of inhibition of hydrogen
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sulfide according to the Eqs. (13) and (14). Therefore, the non-isothermal reactor
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model is determined to be more reasonable for the HDS of gas oil.
Fig. 1. (a) Comparisons between isothermal and non-isothermal reactor models; (b) The effect of the inlet temperature on the reactor temperature distribution under the 7
Journal Pre-proof non-isothermal condition; The effect of the inlet temperature on the (c) external and (d) internal effectiveness factor of the catalyst under the non-isothermal condition. Conditions: Tw= Tin, dp=2.54 mm and θ=0.55. In addition to the outlet sulfur content, the external and internal effectiveness factors are also important for the HDS, which serves as assessment criterions of the catalyst utilization in the HDS [7,11]. Thus, the external and internal effectiveness factors were studied for the different inlet temperatures by using the non-isothermal reactor model, as shown in Fig. 1c and 1d. It can be seen that the external
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effectiveness factor increases from 0.6 to approximately 0.9, while internal
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effectiveness factor increases from 0.1 to around 0.6 along the reactor direction, indicating the existence of more serious internal diffusion limitation at the inlet of the
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reactor.
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Along this line, the concentration distributions of reactants (i.e., sulfur compound and H2), product (i.e., H2S) and the AR as well as SR along the reactor direction were
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investigated, as shown in Fig. 2. As expected, the sulfur concentration (Fig. 2a) decreases along the reactor direction and it consumes faster with higher inlet
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temperature in both liquid and solid surface. Meanwhile, the sulfur concentration in solid phase is lower than that in liquid phase owning to the mass transfer in
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liquid-solid phase. For the H2 concentration (Fig. 2b), it first decreases sharply at the inlet of the reactor since the reaction rate is dominant compared to mass transfer of H2
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from gas phase to the pellet, and then it increases and remains stable at the end part of the reactor, because the mass transfer gradually becomes dominant until the reaction rate and mass transfer rate achieve a balance. The generated H2S shows the reverse trend as shown in Fig. 2c. It is noted that the mass transfer from the liquid to pellet surface is mainly dependent on liquid properties like density, viscosity and velocity [26] and can be weakened by reducing the concentration gradients in liquid-solid phase [38,39].
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Fig. 2. The effects of the inlet temperature on the profiles of concentration of (a)
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sulfur compound, (b) H2 and (c) H2S in the liquid and solid phase along the reactor length and (d) the pellet average reaction rate and pellet surface reaction rate along the
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reactor length. Conditions: Tw= Tin, dp=2.54 mm and θ=0.55. (L denotes liquid phase; S denotes solid catalyst surface; AR denotes average pellet reaction rates; SR denotes pellet surface reaction rate)
Moreover, Fig. 2d shows the effects of the inlet temperature on the real reaction rate (AR) and the pellet surface reaction rate (SR) along the reactor length. Under the higher inlet temperature, the SR is higher before 7.5 cm due to the higher temperature (Fig. 1b), but lower after 7.5 cm, which seems to disagree with the higher of H 2 concentration after 7.5 cm (Fig. 2b). This is because the sulfur concentration decreases significantly before 7.5 cm and less is left, and the reaction rate is more sensitive to the sulfur concentration due to its higher reaction order (1.80) than that of H2 concentration (0.96). Meanwhile, the SR is much higher than the AR at the inlet,
9
Journal Pre-proof but decreases more significantly along the reactor length, giving an explanation to the increased internal effectiveness factor. The difference of the SR and AR is mainly assigned to the internal diffusion limitation, and thus the concentration gradients in the pellet was presented as shown in Fig. 3. Clearly, at the inlet, sulfur concentrations of the pellet surface (r/rp=1) under higher inlet temperature are smaller than that under lower inlet temperature due to the higher reaction rate. Similarly, the concentrations of H2 and H2S under the higher inlet temperature change more considerably and thus the lower internal effectiveness factor in the reactor inlet (Fig. 1d). However, at the end part of the reactor, the declined
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reaction rate leads to the decreased the concentration gradients under the higher inlet
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temperature, giving the higher internal effectiveness factor (Fig. 1d).
Fig. 3. The effects of the inlet temperature (Tin) on the profiles of concentration in the reactor and catalyst pell et. Conditions: Tw= Tin, dp=2.54 mm and θ=0.55.
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Journal Pre-proof 3.2. Understanding of the Reaction and Diffusion As can be seen from last paragraph that the inlet temperature has effects on the reaction and diffusion along both the reactor and pellet directions. Thus, an understanding of the reaction and diffusion in both the reactor and pellet is important for achievement of both the high HDS performance and catalyst utilization. Considering that the reaction and diffusion can be significantly influenced by temperature distributions and concentration related to internal diffusion environment, the wall temperature and pellet size as well as porosity were systematically studied by
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concentration distribution, and the effectiveness factors.
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analyzing their effects on the reaction rates, the temperature distribution,
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3.2.1. Effects of the Wall Temperature
For non-isothermal and exothermic reaction, wall temperature is an important
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operation condition to control temperature inside the reactor. Thus, effects of the wall temperature of the trickle-bed reactor were studied, and the results are shown in Fig. 4.
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Fig. 4a shows that as the wall temperature increases from 300 to 340 oC, the surface reaction rate (SR) increases due to the difference of reaction temperatures, as shown
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in Fig. 4b. Meanwhile, at the outlet of the reactor, the surface reaction rate (SR) shows similar values for different wall temperatures because more than 60 % of the
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sulfur has been consumed before 10 cm (Fig. 4c), and the low sulfur as well as H2
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concentration (Fig. 4d) after 10 cm limit the reaction rate.
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Fig. 4. The effects of the wall temperature (Tw) on (a) the pellet average reaction rate and pellet surface reaction rate along the reactor length; (b)liquid temperature
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distribution; profiles of concentrations of (c) sulfur compound and (d) H2 in liquid phase and solid phase along the reactor length. Conditions: Tin=340 oC, dp=2.54 mm
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and θ=0.55. (L denotes liquid phase; S denotes solid catalyst surface; AR denotes average pellet reaction rates; SR denotes pellet surface reaction rate) The concentration gradients of the sulfur, H2 and H2S along the reactor and the pellet were further investigated to understand the reaction and diffusion behavior within the pellet, as shown in Fig. 5. It can be found that the sulfur and H2 exhibit similar concentration gradients within the pellet, respectively. In other words, the wall temperature has little influence on the concentration distributions at the pellet scale, leading the small difference to the AR values in Fig. 4a. Therefore, it is expected that the higher wall temperature can lead to the enhanced HDS performance (Fig. 6a), but the reduced internal effectiveness factor (Fig. 6b).
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Fig. 5. The effects of the wall temperature (Tw) on the profiles of concentration in the
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reactor and catalyst pellet. Conditions: Tin=340 oC, dp=2.54 mm and θ=0.55.
Fig. 6. The effects of the wall temperature (Tw) on the (a) outlet sulfur content in the liquid; (b) external effectiveness factor along the reactor length; (b) internal effectiveness factor along the reactor length. Conditions: Tin=340 oC, dp=2.54 mm and θ=0.55.
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Journal Pre-proof 3.2.2. Effects of the Pellet Size Considering that the pellet size can significantly influence the reaction-diffusion behavior of the HDS catalyst pellet [11,40,41], the pellet size effect was further investigated as shown in Fig. 7. It is found in Fig. 7a that at the inlet of the reactor, the smaller pellet size leads to the higher surface reaction rate (SR) due to the higher temperature shown in Fig. 7b, but SR declines more sharply during the initial 0.5 cm
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mainly because of the decreased sulfur and H2 concentration shown in Fig. 7c and 7d.
Fig. 7. The effects of the pellet size (dp) on (a) the pellet average reaction rate and pellet surface reaction rate along the reactor length; (b)liquid temperature distribution; profiles of concentrations of (c) sulfur compound and (d) H2 in liquid phase and solid phase along the reactor length. Conditions: Tin=340 oC, Tw=330 oC and θ=0.55. (L denotes liquid phase; S denotes solid catalyst surface; AR denotes average pellet reaction rates; SR denotes pellet surface reaction rate) It can also be found in Fig. 7a that the smaller pellet size gives rise to the enhanced average pellet reaction rate (AR) before 6 cm, but the declined AR after 6 cm, which 14
Journal Pre-proof can be explained by the concentration distributions in both the reactor and pellet scale as shown in Fig. 8. Clearly, compared with the HDS catalyst with larger pellet size, the sulfur and H2 concentration gradients in the smaller pellet is shallower, indicating the better diffusion performance due to the short diffusion path and thus the higher
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reaction rate as well as catalyst utilization.
Fig. 8. The effects of the pellet size (dp) on the profiles of concentration in the reactor and catalyst pellet. Conditions: Tin=340 oC, Tw=330 oC and θ=0.55. Though the catalyst with smaller pellet size will alleviate the diffusion limitation, the smaller pellets may cause larger pressure drops in fixed beds. As shown in Fig. 9a, when the pellet size is smaller than 0.8 mm, the outlet sulfur concentration keeps almost unchanged. This may result from the similar internal and external diffusivities. It can be seen from Fig. 9b and 9c that when the pellet size decreased to the 0.8 mm, the external and internal effectiveness factors range from 0.85 to 1.00 and from 0.6 to 1.00, respectively, indicating the little influence of the external and/or internal 15
Journal Pre-proof diffusion. Therefore, the suitable pellet size may range from 0.8 to 1.0 mm due to the
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compromise between the catalyst utilization and pressure drops.
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Fig. 9. The effects of pellet size (dp) on (a) outlet sulfur content in the liquid; (b) external and (c) internal effectiveness factor along the reactor length. Conditions:
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3.2.3. Effects of the Pellet Porosity
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Tin=340 oC, Tw=330 oC and θ=0.55.
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In addition to pellet size, pellet porosity is also a vital factor for reaction-diffusion behavior within the pellet[11], and its effects on both the rates, temperature and concentration distribution along the reactor length were also studied, as shown in Fig.
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10. It can be seen in Fig. 10a that the smaller porosity leads to the higher surface
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reaction rate (SR) before 12 cm due to the higher bulk density according to Eq. (S22) and (S23). The porosity has little influence on the temperature distributions in
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comparison with pellet size, as illustrated in Fig. 10b. The SR under different porosities maintains constant after 12 cm mainly due to the low reactants concentrations (Fig. 10c and 10d).
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Fig. 10. The effects of the porosity (θ) on (a) the pellet average reaction rate and pellet surface reaction rate along the reactor length; (b) liquid temperature distribution;
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profiles of concentrations of (c) sulfur compound and (d) H2 in liquid phase and solid phase along the reactor length. Conditions: Tin=340 oC, Tw=330 oC, dp=2.54 mm. (L
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denotes liquid phase; S denotes solid catalyst surface; AR denotes average pellet reaction rates; SR denotes pellet surface reaction rate) The sulfur, H2 and H2S concentration distributions along the reactor and pellet directions were also evaluated to investigate reaction-diffusion interplay within the pellet as shown in Fig. 11. Obviously, the smaller pellet porosity leads to deeper concentration gradients along the pellet direction, indicating more serious diffusion limitation. This also can be confirmed by Fig. 12b in which the internal effectiveness factor increases with the increased porosity. Though the pellet with smaller porosity has low catalyst utilization, it can also result in more active sites leading to higher HDS performance as shown in Fig. 12a. Thus, there exists a compromise between the HDS performance and catalyst utilization under different porosities.
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Fig. 11. The effects of the porosity(θ) on the profiles of concentration in the reactor
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and catalyst pellet. Conditions: Tin=340 oC, Tw=330 oC, dp=2.54 mm.
Fig. 12. The effects of the porosity(θ) on (a) outlet sulfur content in the liquid; (b) internal effectiveness factor along the reactor length. Conditions: Tin=340 oC, Tw=330 o
C, dp=2.54 mm. 18
Journal Pre-proof 3.3. General Discussion and Optimization Based on the above analyses, it is found that the inlet temperature and wall temperature can significantly influence the convection-diffusion behavior at the reactor scale, and the pellet size and porosity also play an important role in the reaction-diffusion behavior at the pellet scale. Besides, the pressure and superficial velocity of liquid phase are also the important factors in the process of HDS. As a consecutive effort, an optimization was carried to enhance the HDS performance and the catalyst utilization. The objective of optimization is to minimize the sulfur concentration at the outlet of reactor with the internal effectiveness factor along the
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reactor length kept in or even better than the commercial level (i.e., 0.4-0.6) [40,42]. Meanwhile, the control variables were the above mentioned inlet temperature, wall
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temperature, pressure, superficial velocity of liquid phase, pellet size and porosity, and their lower and upper boundaries are listed as following, which are commonly
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used values in industry:
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340 o C Tin 380 oC
4 MPa P 7 MPa
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300 o C Tw 370 oC
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0.8mm dp 3mm
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0.00875 cm s uL 0.02 cm s
0 . 4 0 .8
The optimization results in the outlet sulfur content of 7.6 wppm with the average effectiveness factor of 0.86, where the initial temperature, wall temperature, pressure, superficial velocity of liquid phase, pellet size and porosity are 380 oC, 367 oC, 6.3MPa, 0.00875 cm/s, 0.96 mm and 0.40. 4. Conclusions In summary, we have clarified the effects of the temperature and catalyst pellet structures on the reaction-diffusion behaviors in gas oil HDS via our developed non-isothermal trickle-bed reactor coupled with catalyst pellet model. It has shown that the reaction rate along the reactor is mainly dominated by the temperature, and 19
Journal Pre-proof the sulfur concentration gradient in the catalyst pellet decreases gradually along the reactor, leading to the increased effectiveness factor. For the fixed catalyst bed volume, the existed compromise between the catalyst reaction rate and effectiveness factor and the constrained temperature rising have yielded an optimized temperature and catalyst pellet structures. The optimized catalyst pellet size of 0.96 mm and catalyst porosity of 0.40 have been determined, and the resultant outlet sulfur content can decrease to 7.6 wppm, which is better than the commercial level. The insights demonstrated here could guide the selection of temperature as well as the rational
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design and optimization of the HDS catalyst pellet.
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Associated Content Supporting Information The following files are available free of charge. (Figure S1) Comparison between the calculated sulfur concentration and the previously reported experimental value in the liquid phase at the exit of the reactor under the isothermal condition; (Table S1) The correlations of variables in the model;
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(Table S2) The values of parameter and variables used in the model. (PDF)
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Author Information Corresponding Author
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E-mail address: [email protected]
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Author Contributions
These authors contributed equally to this article. (X.Q. Zhao and C.F. Yang)
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Acknowledgments
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#
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*Tel.: +86-21-64250937, Fax.: +86-21-64253528,
This work was supported by the National Key R&D Program of China (2018YFB0604500), the Natural Science Foundation of China (21776077), the Shanghai Natural Science Foundation (17ZR1407300 and 17ZR1407500), the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, the Shanghai Rising-Star Program (17QA1401200), the Open Project of SKLOCE (SKL-Che-15C03) and the 111 Project of the Ministry of Education of China (B08021). Conflict of Interest Statement: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Journal Pre-proof Nomenclature gas–liquid interfacial area, cm-1
as
liquid–solid interfacial area, cm-1
c Lp
liquid capacity, J/g/K
Ci
molar concentration of compound i, mol/cm3
dR
reactor diameter, cm
dp
catalyst pellet diameter, cm
DiL
molecular diffusivity coefficient of compound i in liquid, cm2/s
De,i
effective diffusivity coefficient of compound i in catalyst pellet, cm2/s
DK,i
Knudsen diffusion coefficient, cm2/s
Ea
activation energy for reaction of HDS, J/mol
GL
liquid superficial mass velocity, g/cm2/s
Hi
Henry’s law coefficient, MPa/cm3/mol
k
liquid conductivity coefficient, J/K /m/s
kiL
gas–liquid mass-transfer coefficient of compound i, cm/s
kiS
liquid–solid mass-transfer coefficient of compound i, cm/s
k0
frequency factor for reaction of HDS, (cm3)m+n/mol(m+n-1) /g/ s
kHDS
reaction rate constant, (cm3)m+n/mol(m+n-1)/ g/ s
K H 2S
adsorption equilibrium constant for H2S,
Ke
effective conductivity coefficient, J/ K /cm/s
Mw
molecular weight of liquid phase, g/mol
piG
P
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aL
partial pressure of component i in the bulk gas phase, MPa total pressure, MPa
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Journal Pre-proof mean pore radius, cm
rp
catalyst pellet radius, cm
R
universal gas constant, J/mol/K
RHDS
reaction rate of HDS, mol/g/s
TL
temperature of liquid phase, K
TMeABP
mean average boiling point, oR
T
temperature in the catalyst pellet, K
Tw
cooling temperature of the reactor, K
uL
superficial velocity of liquid phase, cm/s
uG
superficial velocity of gas phase, cm/s
vi
molar volume of component i, cm3/mol
vic
critical specific volume of component i, cm3/mol
vNi
molar gas volume of component i, Nl/mol
wi
weight fraction of compound i in the liquid phase, wt%
zR
reactor length, cm
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Greek Symbols
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Pr
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rg
r H m
heat of reaction, J/mol
α
heat transfer coefficient from wall to catalyst bed, W/cm3/K
ρB
bulk density, g/cm3
ρL
liquid density at process conditions, g/cm3
ρp
pellet density, g/cm3
ρs
solid density, g/cm3
ρ0
liquid density at standard conditions (15.6 °C and 101.3 kPa), lb/ ft -3
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Journal Pre-proof liquid density at 20 °C, g/cm3
L
liquid viscosity, mPa‧s
H 2 , H2 S
solubility coefficient of H2 and H2S, Nl/kg/MPa
η
catalyst effectiveness factor
ε
bed void fraction
θ
catalyst pellet porosity
τ
tortuosity factor for catalyst pellet
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ρ20
Abbreviations liquid phase
S
solid catalyst surface
AR
average pellet reaction rates
SR
pellet surface reaction rate
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L
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