A Novel Radial-Flow, Spherical Packed Bed Reactor for the

23 Jan 2015 - this work is to consider a radial-flow spherical packed bed reactor as an alternative for the tubular packed bed reactor in the HC proce...
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A Novel Radial-Flow, Spherical Packed Bed Reactor for the Hydrocracking Process D. Iranshahi* and A. Bakhshi Ani Department of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Avenue, Tehran 15914, Iran ABSTRACT: Hydrocracking (HC) is becoming a more important process in refineries owing to increasing demand for gasoline and jet fuel in comparison with diesel and home heating oils. In a commercial hydrocracking unit, tubular fixed bed reactors (TR) are commonly used. Some disadvantages of these reactors are pressure drop across the tube, high manufacturing costs, and low production capacity. These drawbacks can be solved by using a novel radial-flow, spherical packed bed reactor (SR). The aim of this work is to consider a radial-flow spherical packed bed reactor as an alternative for the tubular packed bed reactor in the HC process and compare the packed beds through important parameters such as pressure drop, yield of products, and temperature profile. The calculations showed that the pressure drop in the spherical reactor is negligible in comparison to that of the conventional tubular reactor. It is shown that by using more catalyst in the SR, the yield of more economical products could be well increased, but doing the same is impossible for TR because of the high pressure drop, which damages the catalyst and their structure in the reactor. Furthermore, the simultaneous effect of catalyst and feed flow rate scale-up ratio on yield of products in the spherical reactor was investigated.

1. INTRODUCTION 1.1. Hydrocracking. In recent decades hydrocracking (HC) is becoming a more important process in refineries due to the following reasons; (1) the demand for petroleum products has shifted to gasoline and jet fuel derivatives in comparison with diesel and home heating oils, (2) byproduct hydrogen at low-cost and in large amounts has become available from catalytic reforming operations, and (3) environmental regulations for limiting sulfur and aromatic compound concentrations in fuels has become more strict.1 In fact, HC is a catalytic hydrogenation process in which high molecular weight feedstock such as vacuum gas oil (VGO) and atmospheric residue (AR) are converted and hydrogenated to lower molecular weight products.2 Operating at high hydrogen pressure is the main feature of the process that would reduce catalyst deactivation and produce more stable gasoline. The catalyst used in hydrocracking is a bifunctional one. It is composed of a metallic part, which promotes hydrogenation, and an acid part, which promotes cracking. Hydrogenation removes impurities in the feed such as sulfur, nitrogen, and metals. Cracking will break bonds, and the resulting unsaturated products are consequently, hydrogenated into stable compounds.2 1.2. Kinetic Model of Hydrocracking. The feedstock of the HC unit is a complex mixture of different hydrocarbons, and there are hundreds of simultaneous chemical reactions occurring in hydrocracking including various complex reactions such as, alkane hydrocracking, hydrodealkylation, ring opening, and hydroisomerization.2 Therefore, it is difficult to identify the molecules involved in petroleum oil and study reaction kinetics of the hydrocracking process based on the real compositions of the feed oil. For this reason, a pseudocomponent approach is used to model the hydrocracker reactor. In this technique, hydrocarbons are partitioned into multiple lumps (or model compounds) based on the molecular structure or boiling point, © XXXX American Chemical Society

and the hydrocarbons of each lump are assumed to have an identical reactivity to build the reaction kinetics of hydrocracking.3 Qader and Hill4 were the first scientists who presented a kinetic model for HC. At first, they studied the process experimentally and then modeled the HC process by a twolump approach. In 1974 Stangeland et al.5 proposed a simple kinetic model for describing hydrocracking yields that represents a wide spectrum of compounds as a series of 50 °F boiling range cuts, each compound undergoing a first-order reaction to produce a spectrum of lighter products. Their model predicts product distillation curves as a function of conversion level with acceptable error. Mohanty et al.6 developed a three parameter model for a two-stage vacuum gas oil hydrocracker unit. In their model, feed and the products were lumped into 23 pseudocomponents which had been characterized by their boiling point and specific gravity. In their work, the product distribution was predicted by empirical correlations. The model predicted concentration and temperature profiles well. Their calculations show that the reactor temperature significantly affects the product yields. Laxminarasimhan and Verma7 studied HC kinetics on the basis of continuum theory of lumping. Their model has a novel skewed Gaussian distribution function to determine product yield distribution. Sanchez et al.8 proposed a five-lump kinetic model for the moderate HC. They suggested that HC can be carried out at moderate operating conditions in order to avoid sludge and sediment formation. Bhutani et al.9 studied the Received: October 22, 2014 Revised: December 28, 2014 Accepted: January 23, 2015

A

DOI: 10.1021/ie5041786 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research industrial HC unit. They used Mohanty’s model6 to simulate the unit. They noted that this kinetic model had been widely used in the fuel processing industry. They characterized feed and product into 58 pseudocomponents and their mass fractions were predicted. Valavarasu et al.10 suggested a four lump discrete lumping approach for the simulation of a HC process. Their model prediction was found to agree well with the experimental data. They also considered effects of temperature and reaction time on the process. They found that the yield of middle distillates increases with increasing temperature and also by time on reaction. Martinez and Ancheyta11 investigated the HC of heavy oil in a continuous stirred tank reactor (CSTR) involving catalyst deactivation. Their model had 10 reaction rates and discriminated different hydrocarbon groups based on boiling ranges and includes unconverted vacuum residue, vacuum gas oil, middle distillates, and naphtha. Puron et al.12 analyzed the kinetics of vacuum residue in HC. They observed that the HC of a vacuum residue is well described with first-order kinetics and proposed a four-lump kinetic model for the system. 1.3. Tubular and Spherical Reactor for Hydrocracking. In the commercial hydrocracking unit, tubular packed bed reactors (TR) are commonly used. Some disadvantages of these reactors are pressure drop across the tubes, high manufacturing costs, and low production capacity.13 These drawbacks can be solved by using a radial-flow spherical packed bed reactor (SR). In this configuration, flow enters the vessel across the external surface of the vessel and moves radially inward through the bed and finally outward via a pipe collector. The advantages of spherical reactor are mentioned below: 1. noticeable lower pressure drop in comparison to fixed bed reactors 2. spherical reactors are the most economical shape for high pressure processes14 3. lower pressure drop permits the possibility of using smaller catalyst particles, which eliminates the internal mass transfer restriction 4. the possibility of using higher feed flow rate and increasing the plant productivity 5. the spherical reactors are cheaper due to a reduction in the wall reactor thickness15 Hartig et al.16 studied the methanol production in a spherical reactor and demonstrated by using spherical reactors, it is possible to construct single train plants with a very high production capacity and less pressure drop. Guillermo et al.17 have studied spherical reverse flow reactors. They found for reversible reactions that SR presents a significant increase in conversion due to the lower temperature achieved at the center of the reactor. Furthermore, the spherical geometry prevents the formation of a hot zone. Balakotaiah et al.18 studied the effect of flow direction in radial flow fixed-bed reactors. Their research showed that when the reaction does not involve a change in the number of moles, the outward flow direction is the preferred one for any reaction with a convex rate expression, and the inward flow direction is a better choice for any reaction with a concave rate expression. Rahimpour et al.19 suggested a radial flow spherical bed reactor for methanol synthesis. They concluded that this configuration can improve reactor performance with lower pressure drop. F. Samimi et al.20 studied DME synthesis in two spherical reactors

connected in series. They found the pressure drop in a spherical reactor is significantly less than that in a tubular one, and it could be possible to increase inlet flow rate of a spherical configuration without any severe pressure drop. In our previous work,21 naphtha reforming was studied by means of a radial-flow spherical bed reactor. It was found that the pressure drop in the spherical reactor is much less, as much as it could be considered negligible in comparison with that of a tubular reactor. Furthermore, our calculation showed that hydrogen production in a spherical bed is higher than that of the conventional tubular bed. The aim of this work is to consider a radial-flow spherical packed bed reactor as an alternative for a tubular packed bed reactor in the HC process and compare the reactors through important parameters such as pressure drop, yield of products, and temperature profile. In this study, the hydrocracking reactor is modeled on the basis of Mohanty’s model6 because, as previously mentioned, this kinetic model is able to predict product yields satisfactorily and has been widely used in the fuel processing industry.

2. PROCESS DESCRIPTION 2.1. Conventional Process. The HC process may require either one or two stages, depending upon the process and the feed-stocks used.1 A simple diagram of a one-stage industrial HC unit is shown in Figure 1. The fresh feed is mixed with

Figure 1. A simple diagram of one-stage industrial hydrocracking unit.

makeup hydrogen and passed through a heater to reach the required temperature and then moves to the reactor. The hydrocracking reactions are done in the reactor, and temperature rises through the bed. To control reactor temperature, the feed is quenched several times through the reactor by hydrogen-rich gas. The effluent from the reactor goes to the high pressure separator where the hydrogen-rich gases are separated. The liquid product from the separator is sent to the distillation unit. 2.2. Spherical Reactor. A schematic diagram of the spherical reactor is shown in Figure 2. The feed enters the reactor across the exterior surface and passes through the catalyst that is situated between the external and internal surfaces to get to the inner sphere. The fluid collects in the inner sphere and exits from the reactor by use of a pipe which is connected to the inner sphere. B

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Industrial & Engineering Chemistry Research ⎛ −21100 ⎞ ⎟ k = 1.5 × 107 exp⎜ ⎝ RT ⎠

(6)

Then the relative rate function for the pseduocomponent (K′i ) could be calculated as follows: K i′ = 0.494 + 0.52 × 10−2tbi − 2.185 × 10−5tbi2 + 0.312 × 10−7tbi3

(7)

Finally, the rate constant (ki) is calculated from the following expression: ki = kK i′

Figure 2. A schematic of radial-flow spherical packed bed reactor.

3.1.2. Energy Balance Equation.6 The energy balance equation is calculated as follows:

3. REACTOR MODEL 3.1. Tubular Reactor. 3.1.1. Material Balance Equation. The mass balances for axial geometry are expressed in the following equation:6 dCi Mt = −kiCi + dW

dT = dW

∑ kjPijCj

i

here T is temperature, mi is the mass flow rate of the ith pseudocomponent, W is the weight of catalyst, (−ΔHR)j is the heat of reaction for hydrocracking of the jth pseudocomponent, Cpi is the heat capacity of component i, the (N + 1)th component is hydrogen and p is the lightest component undergoing cracking. 3.1.3. Pressure Drop. The pressure drop across the reactor is calculated on the basis of the Ergun equation. The equation based on the weight of catalyst for a tubular reactor is derived as follows:14

(1)

j=r

P1j = C exp( −0.00693(1.8tbj − 229.5))

AcρB

Pij = Pij′ − Pi′− 1, j

(2)

(3)

where Pij′ is the cumulative yield until the ith pseudocomponent from hydrocracking of the jth pseudocomponent, which is evaluated by the following expression:

M t dCi = −kiCi + AcρB dr

2

Pij′ = (yij + B(yij − yij ))(1 − P1j)

⎧ i = 2, ..., j − 2 ⎨ ⎩ j = 6, ..., N ⎪

⎪

(10)

N

∑ kjPijCj (11)

j=r

Other parameters are similar to eq 1 that was previously discussed. The inner diameter of the spherical reactor is 1 m, and the outer diameter of the reactor is 4.93 m. 3.2.2. Energy Balance Equation. The parameters of the following equation are similar to those in eq 9 which was previously discussed.

(4)

Here yij is the normalized temperature for the ith product formed from jth pseudocomponent: (tbi − 2.5) ((tbj − 50) − 2.5)

150μ(1 − ε)2 Q 1.75ρ(1 − ε)Q 2 dP = + Ac dW ϕs 2d p2ε 3 ϕsd pε 3Ac 2

where dP is the pressure gradient, W is the weight of catalyst, Ac is the cross-sectional area, ρB is the bulk density of catalyst, Q is the volumetric flow rate, dp is the particle diameter, ϕs is the sphericity, and μ and ρ are the fluid viscosity and density. 3.2. Spherical Reactor. The material and energy balance are modified for the spherical reactor as follows: 3.2.1. Material Balance Equation. In the following equation r represents the radius of reactor, Ac is the cross-sectional area and ρB is the bulk density of catalyst.

where tbj is the boiling point of pseudocomponent j (°C) and C is a constant. (2) Then, the actual yield of the pseudocomponent “i” from component “j” was calculated using the below expression:

yij =

j

⎧ r = 1, ..., N + 1 ⎨ ⎩ j = p , ..., N (9)

where Mt is mass flow rate of feed, Ci is mass fraction of pseudocomponent “i” in the mixture, W is the weight of catalyst, i,j are the component numbers, ki, kj, are the first-order rate constants for cracking of the ith and jth pseudocomponent, and Pij is the probability of the ith pseudocomponent being formed from the jth pseudocomponent. Pij can be calculated from the following procedure:6 (1) First, the mass fraction of butanes and lighter components (P1j) should be calculated as follows:

3

∑ (−ΔHR )kjCj/∑ miCPi

N

for i = 1, 2, ..., N ⎧ r = i + 2 for i ≥ 5 ⎨ ⎩ r = 6 for i < 5

2

(8)

(5)

1 dT = AcρB dr

The parameters C and B are 0.7 and 0.37, respectively. For prediction ki, the method of relative rate function was used.6 First we should calculate a first-order rate expression for hydrocracking of vacuum gas oil having an average boiling point of 638 K as follows:

∑ (−ΔHR )j kjCj/∑ miCPi j

i

(12)

3.2.3. Pressure Drop. The pressure drop for spherical reactor is derived as follows:21 C

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Industrial & Engineering Chemistry Research ⎛ 150μ(1 − ε)2 Q ⎞ dP ⎟1 = ⎜⎜ ⎟ r2 2 2 3 π dr 4 ϕ ε d ⎝ ⎠ s p

On the basis of plant data, the feed introduced to the reactor contains pseudocomponents A13 to A21.

⎛ 1.75ρ(1 − ε) Q 2 ⎞ ⎟1 + ⎜⎜ 3 2⎟ 4 ϕ ε (4 π ) d ⎝ ⎠r s p

7. MODEL VALIDATION A Domestic hydrocracking unit named Isomax is used to validate the proposed model.25 Typical feed and product properties, catalyst data, reactor dimensions, and process operating details are given in Table 2.

(13)

Parameters of this equation are same as those in eq 10 which was previously discussed.

Table 2. Plant Data for Hydrocracking Unit

4. FEED AND PRODUCT CHARACTERIZATIONS The feed and product of the HC unit are divided into 21 pseudocomponents with 25 K intervals and are shown in Table 1.

Feed and Reactor Specification: gravity (°API) specific gravity at 288.6 (K)/288.6 (K) total sulfur (wt %) nitrogen (ppm) characterization factor D1160 Distillation (°C): IBP 5% 10% 30% 50% 70% 90% 95% 100% boiling range of feed (K) total feed rate (m3/hr) total catalyst volume (m3) total catalyst weight (kg) bulk density of catalyst (kg/m3) reactor length (m) reactor diameter (m) reactor inlet pressure (bar) reactor outlet pressure (bar) reactor inlet temperature (K) reactor outlet temperature (K) Product Specifications: light naphtha (wt %)a heavy naphtha (wt %)a kerosene (wt %)a

Table 1. Characterization of Feed and Product of Hydrocracking Into Pseudocomponents composition no.

boiling range (K)

°API

SG 288/288 K

Vol. % in feed

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

263−288 288−313 313−338 338−363 363−388 388−413 413−438 438−463 463−488 488−513 513−538 538−563 563−588 588−613 613−638 638−663 663−688 688−713 713−738 738−763 763−788

110.8 99.7 81.8 68.4 60.1 54.7 49.1 46.6 44.7 41.5 38.4 35.2 32.1 29.8 27.6 25.6 23.6 21.7 19.9 18.3 16.6

0.58 0.61 0.66 0.71 0.74 0.76 0.78 0.79 0.8 0.82 0.83 0.85 0.86 0.88 0.89 0.90 0.91 0.92 0.93 0.94 0.95

0 0 0 0 0 0 0 0 0 0 0 0 0.28 5.95 7.04 8.69 11.51 16.58 21.24 16.94 11.72 a

5. PROPERTY PREDICTION In the pseudocomponent method, each pseudocomponent acts as a pure component which is introduced by its average boiling point and specific gravity. To calculate enthalpies and heat capacities, a method given by Mohanty et al.6 was used. In his approach, the Peng−Robinson EOS was used to calculate the above-mentioned properties. The standard heat of reaction was calculated on the basis of the stoichiometric hydrogen requirement. Briefly, the authors assumed 42 MJ of heat is released for each kmol of hydrogen consumed. Molecular weight, critical pressure, ciritical temperature, and acentric factor were calculated by Lee and Kesler correlations.22 Viscosity was predicted according to the corresponding correlations in the literature.23

22 0.922 1.88 977 11.7 317 363 375 404 422 444 473 487 502 563.15−788.15 31.78 62.2 34210 550 14 2.4 187.2 182 643.15 691 10.6 10.8 32

On the basis of total liquid product.

The product plant data consist of three fractions: light naphtha (LN), heavy naphtha (HN), and kerosene. A comparison between plant product data and corresponding model values is shown in Table 3. According to Table 3, the model results show a good agreement with plant data and confirm the ability of the model for prediction the hydrocracking unit.

8. RESULTS AND DISCUSSION 8.1. Pressure Drop. Figure 3 shows changes in pressure for both TR and SR. It is obvious that the pressure drop in the spherical reactor is negligible in comparison to the conventional tubular reactor. The figure explains that the pressure drop in TR is about 5.4 bar more than that in SR. The reason is that the spherical reactor has more cross-sectional area than the tubular reactor. Therefore, it could be possible for SR to operate with much higher feed flow rate, more catalyst loading, and small catalyst particles. A small catalyst has a higher effectiveness factor in comparison to a larger one. Higher effectiveness factor

6. NUMERICAL SOLUTION The set of 23 ODEs including mass balances, energy balance, and pressure drop equations were solved by using the Runge− Kutta method.24 The initial condition was achieved from the plant data25 which are described in Table 1. D

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Industrial & Engineering Chemistry Research Table 3. Comparison between Calculated Results and Hydrocracking Plant Data product

IBP−FBP (°C)

light naphtha (wt %)a heavy naphtha (wt %)a kerosene (wt %)a reactor outlet temperature (K) reactor outlet pressure (bar)

43−93 93−143 143−273

a

plant data

calculated result

error %

10.6 10.8 32 691

10.55 11.05 32.2 689.46

0.47 2.31 0.62 0.22

182

181.95

0.027

On the basis of total liquid product.

Figure 5. Mass fraction profiles in the tubular reactor and spherical reactor for LN, HN, and kerosene.

Figure 3. A comparison between pressure profiles in the tubular reactor and the spherical reactor.

Figure 4. Temperature profiles in the tubular reactor and spherical reactor. Figure 6. Effect of catalyst scale up ratio on yield of products: (a) kerosene and heavy naphtha; (b) light naphtha and LPG.

means higher yields and conversion of products and reactants, respectively. In Figure 3 the curve for the tubular reactor is a straight line because of the weak dependence of density and viscosity to the temperature. 8.2. Temperature Profile. Hydrocracking reactions are exothermic, so the temperature increases throughout the reactor. To control reactor temperature, the feed is quenched several times through the reactor by hydrogen-rich gas. Figure 4 displays the temperature profile along the weight of catalyst for both of the reactors’ configurations. The temperature profiles are almost similar, but the profile of the SR is slightly lower because of reducing residence time in this reactor.

8.3. Mass Fraction Profiles for Light Naphtha (LN), Heavy Naphtha (HN), and Kerosene. The mass fraction profiles of LN, HN, and kerosene through the bed for both reactors are presented in Figure 5. However, these figures show a slight decrease in the yield of the products which is attributed to lower residence time. The slight decrease in yields could be compensated by usage of higher catalyst in the spherical reactor. Accordingly, the addition in catalyst loading improves production of more economical products such as LN and LPG, but doing the same is impossible for the tubular reactor due to E

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8.3.1. Effect of Catalyst Scale up Ratio and Feed Flow Rate Scale-up Ratio on LN, HN, Kerosene and LPG Profiles in Spherical Reactor. The effect of catalyst scale-up ratio on product yields in the spherical and tubular reactors is shown in Figure 6. In these figures, the scale up ratio for tubular reactor is limited because of a pressure drop limitation in this reactor, but the spherical reactor can operate at higher catalyst scale up ratios. For example, by using 30% more catalyst in SR, the yield of LN, HN, and LPG increases 2.91%, 0.29%, and 1.61%, respectively, which makes producing these products more economical. In fact, using high catalyst loading increases the residence time, therefore the hydrocracking reactions can proceed further, and the reactor shifts to produce light products. Figure 7 illustrates the simultaneous effect of catalyst and feed flow rate scale-up ratio on product yields in the spherical reactor. For LN (Figure 7a) and LPG (Figure 7d) in each catalyst scale-up ratio, if the feed flow rate increases, the yield would be decreased. The reason is that increasing flow rate causes residence time to reduce and the reactions do not proceed enough, so the reactor shifts to produce heavy product. For HN (Figure 7b) and kerosene (Figure 7c), the yield initially increases and then decreases due to very low residence time. In each feed flow rate scale-up ratio, increasing the catalyst improves the yield for LN and LPG. For heavy naphtha and kerosene in a low flow rate, by increasing the catalyst the yield initially increases and then decreases, but in a high-flow rate, the yield only increases similar to that of LN and LPG.

9. CONCLUSION A novel radial-flow spherical packed bed reactor was suggested for the hydrocracking process as an appropriate alternative for a tubular reactor. A profound comparison in the pressure drop, the yield of products, and temperature profile was carried out. The pressure drop in the spherical reactor is negligible in comparison to that in the conventional tubular reactor. For the same amount of catalyst, the yield of products in the spherical reactor are slightly fewer than that in the tubular reactor, but it is shown that by using 30% more catalyst in the spherical reactor, the yield of more economical products increases well, but doing the same is impossible for the tubular reactor due to high pressure drop, which damages the catalysts and their structure in the reactor. Also the spherical reactor can operate with a much higher feed flow rate and smaller catalyst particle. Furthermore, the simultaneous effect of catalyst and feed flow rate scale-up ratio on the yield of products in the spherical reactor was investigated.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +98 21 64543189. Fax: +98 21 66405847. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Figure 7. 3D Figure which shows the effect of feed flow rate scale-up ratio and catalyst scale-up ratio on the yield of (a) light naphtha, (b) heavy naphtha, (c) kerosene, and (d) LPG.

high pressure drop (above 5.2 bar) which damages the catalyst and its structure in the reactor.25 F

NOMENCLATURE MT = mass flow rate of feed, kg h−1 Ci = mass fraction of pseudocomponent i W = weight of catalyst, kg ki,kj = first order rate constant for cracking of the ith and jth pseudocomponent, kg reactant kg catalyst−1 h−1 DOI: 10.1021/ie5041786 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

(9) Bhutani, N.; Ray, A. K.; Rangaiah, G. P. Modeling, simulation, and multi-objective optimization of an industrial hydrocracking unit. Ind. Eng. Chem. Res. 2006, 45, 1354. (10) Valavarasu, G.; Bhaskar, M.; Sairam, B.; Balaraman, K. S.; Balu, K. A Four Lump Kinetic Model for the Simulation of the Hydrocracking Process. Pet. Sci. Technol. 2005, 23, 1323. (11) Martinez, J.; Ancheyta, J. Kinetic model for hydrocracking of heavy oil in a CSTR involving short term catalyst deactivation. Fuel 2012, 100, 193. (12) Puron, H.; Arcelus-Arrillaga, P.; Chin, K. K.; Pinilla, J. L.; Fidalgo, B.; Millan, M. Kinetic analysis of vacuum residue hydrocracking in early reaction stages. Fuel 2014, 117, 408. (13) Rahimpour, M. R.; Pourazadi, E.; Iranshahi, D.; Bahmanpour, A. M. Methanol synthesis in a novel axial-flow, spherical packed bed reactor in the presence of catalyst deactivation. Chem. Eng. Res. Des. 2011, 89, 2457. (14) Fogler, H. S. Elements of Chemical Reaction Engineering, 2nd ed.; Prentice-Hall: Englewood Cliffs NJ, 1992. (15) Rahimpor, M. R.; Iranshahi, D.; Pourzadi, E.; Paymooni, K.; Bahmanpour, A. M. The aromatic enhancement in the axial-flow spherical packed-bed membrane naphta reformers in the presence of catalyst deactivation. AIChE J. 2011, 57, 3182. (16) Hartig, F.; Keil, F. J. Large-scale spherical fixed bed reactors: Modeling and optimization. Ind. Eng. Chem. Res. 1993, 32, 424. (17) Guillermo, A. V.; Caram, H. S. The spherical reverse flow reactor. Chem. Eng. Sci. 2002, 57, 4005. (18) Balakotaiah, M.; Luss, D. Effect of flow direction on conversion in isothermal radial flow fixed-bed reactors. AIChE J. 1981, 27, 442. (19) Rahimpor, M. R.; Abbasloo, A.; Amin, J. S. A novel radial-flow, spherical-bed reactor concept for methanol synthesis in the presence of catalyst deactivation. Chem. Eng. Technol. 2008, 31, 1615. (20) Samimi, F.; Bayat, M.; Rahimpour, M. R.; Keshavarz, P. Mathematical modeling and optimization of DME synthesis in two spherical reactors connected in series. J. Nat. Gas Sci. Eng. 2014, 17, 33. (21) Iranshahi, D.; Rahimpour, M. R.; Asgari, A. A novel dynamic radial-flow, spherical-bed reactor concept for naphtha reforming in the presence of catalyst deactivation. Int. J. Hydrogen Energy 2010, 35, 6261. (22) Riazi, M. R. Characterization and Properties of Petroleum Fractions; ASTM: West Conshohocken, PA, 2005. (23) Korsten, H.; Hoffmann, U. Three-phase reactor model for pilot trickle-bed hydrotreating in reactors. AIChE J. 1996, 42, 1350. (24) Suli, E.; Mayers, D. An introduction to Numerical Analysis; Cambridge University Press: U.K., 2003. (25) Operating Data and Manual of Domestic Isomax Unit; Chevron: San Ramon, CA,2007.

Pij = probability of the ith pseudocomponent being formed from the jth pseudocomponent P1j = mass fraction of butanes and lighter components formed P′ij = cumulative yield until the ith pseudocomponent from hydrocracking of the jth pseudocomponent tbj = boiling point of pseudocomponent j, °C yij = normalized temperature for the ith product formed from jth pseudocomponent B, C = product distribution parameters R = ideal gas constant, 8.314 Pa m3 mol−1 K−1 T = temperature, K k = rate constant for hydrocracking of vacuum gas oil having an average boiling point of 638 K Ki′ = relative rate function mi = mass flow rate of pseudocomponent i, kg h−1 Cpi = specific heat capacity of component i, kj kg−1 °C−1 Ac = cross sectional area, m2 Q = volumetric flow rate, m3 s−1 dp = particle diameter of catalyst, m r = radius of spherical reactor, m P = pressure, kPa Greek Letters

ε = void fraction of catalyst bed μ = viscosity of fluid, kg m−1 s−1 ρ = density of fluid, kg m−3 ρB = catalyst bulk density, kg m−3 ϕs = sphericity (−ΔH R ) j = heat of reaction for hydrocracking of pseudocomponent j per unit mass of hydrocarbon reactant, kJ kg−1

Subscript

i,j = pseudocomponent number Definitions

HC = hydrocracking VGO = vacuum gas oil AR = atmospheric residue TR = tubular packed bed reactor SR = radial-flow spherical packed bed reactor EOS = equation of state DME = dimethyl ether LN = light naphtha HN = heavy naphtha IBP = initial boiling point FBP = final boiling point

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REFERENCES

(1) Gary, J. H.; Handwerk, G. E. Petroleum Refining; Marcel Dekker: New York, 2001. (2) Fahim, M. A.; Al-Sahhaf, T. A.; Elkilani, A. S. Fundamentals of Petroleum Refining; Elsevier: Oxford, 2010. (3) Chang, A. F.; Pashikanti, K.; Liu, A. F. Refinery Engineering; WileyVCH: Weinheim, Germany, 2012. (4) Qader, S. A.; Hill, G. R. Hydrocracking of Gas Oil. IEC Process Des. Dev. 1969, 8, 98. (5) Stangeland, B. A. A Kinetic Model for the Prediction of Hydrocracker Yields. Ind. Eng. Chem., Process Des. Dev. 1974, 13, 71. (6) Mohanty, S.; Saraf, D. N.; Kumzru, D. Modeling of hydrocracking reactor. Fuel Process. Technol. 1991, 29, 1. (7) Laxminarasimhan, C. S.; Verma, R. P. Continuous lumping model for simulation of hydrocracking. AIChE J. 1996, 42, 2645. (8) Sanchez, S.; Rodriguez, M. A.; Ancheyta, J. Kinetic model for moderate hydrocracking of heavy oils. Ind. Eng. Chem. Res. 2005, 44, 9409. G

DOI: 10.1021/ie5041786 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX