Comparison of Lumping Approaches to Predict the Product Yield in a Dual Bed VGO Hydrocracker

INTERNATIONAL JOURNAL OF CHEMICAL

REACTOR ENGINEERING

Volume 9 2011 Article A4

Comparison of Lumping Approaches toPredict the Product Yield in a Dual Bed

VGO Hydrocracker

Sepehr Sadighi∗ Arshad Ahmad†

Mansoor Shirvani‡

∗Universiti Teknologi Malaysia, sadighi [email protected]†Universiti Teknologi Malaysia, [email protected]‡Iran University of Science & Technology, [email protected]

ISSN 1542-6580Copyright c©2011 The Berkeley Electronic Press. All rights reserved.

Comparison of Lumping Approaches to Predict theProduct Yield in a Dual Bed VGO Hydrocracker

Sepehr Sadighi, Arshad Ahmad, and Mansoor Shirvani

Abstract

In this research, to predict the product yields of a pilot scale VGO hydroc-racking reactor charged with mono functional hydrotreating and hydrocrackingcatalysts, two different four-lump models are developed. The first one, calledcombined bed model, is a simplex in which there is no boundary between hy-drotreating and hydrocracking reactions through the reactor. The second one,called dual bed model, is a rigorous model in which hydrogen consumption andhydrotreating reactions are included. In this way, the reactor is subdivided intotwo different layers, so the effect of hydrotreating reactions on the hydrocrack-ing section can be considered. Results show that the absolute average deviation(AAD%) of the yield prediction for the combined bed and the dual bed models are8.23 percent and 5.87 percent, respectively. The main reason for the lower averagedeviation of the dual bed model is its higher accuracy to predict the yield of gaswhich is also the major advantage of this approach. However, the simplicity of thecombined bed model can make it more applicable and attractive, especially whenhydrogen consumption as well as sulfur, nitrogen and aromatic specifications ofthe feed and products are not accessible.

KEYWORDS: hydrotreating, hydrocracking, lump kinetic model, hydrogen con-sumption, dual bed hydrocracking reactor

1. Introduction

Processing of heavy feedstock into high value products has interested refiners worldwide due to increasing demand of light oil fractions and decreasing reserves of low sulfur crude oils. With the consideration of profit margins, hydrocracking has gained interest because of being an appropriate option for upgrading of heavy feedstock into various products. Moreover, it is a process in a refinery which improves the quality and quantity of the refined petroleum products.

Among all the commercially proven technologies for hydrocracking, those using fixed-bed reactors in series charged with different functionalities are very favorable. But, the main disadvantage of fixed-bed reactors is the loss of catalyst activity over time as a result of catalyst deactivation which reduces drastically the length of run (Alvarez et al., 2008). Typical reactions which occur in hydrocracking are (i) hydrogenation of polyaromatics, sulfur and nitrogen containing compounds, and (ii) cracking of higher carbon number (cyclo)-alkanes to lighter fractions (Balasubramanian & Pushpavanam, 2008). During the hydrotrating process (HDT) a portion of the hydrogen, dependent to hydrodesulfurization (HDS) and hydrodenitrogenation (HDN) reactions, is consumed and most of heavy sulfur and nitrogen compounds are converted to the light products.

Kinetic modeling of the reactions occurring in a hydrocracker and estimation of the rate coefficients is a crucial step in its design. An accurate estimation of the rate coefficients will enable us to optimize and control the product yield distribution in a hydrocracker. Ideally, the kinetic model should take into account all elementary reactions which the different components in the feedstock undergo. However, the complexity of hydrocracking feed makes it extremely difficult to characterize and describe its kinetic at a molecular level (Ancheyta et al., 1999).

One way of simplifying the problem is to consider the partition of the species into a few equivalent classes, the so-called lumps or lumping technique, and then assume each class is an independent entity (Krambeck, 1991). The major lumping methods interested in hydrocracking are continuum theory of lumping and discrete lumping approaches. In the first method, the reactive mixture is considered to form a continuum mixture with respect to its properties such as boiling point, molecular weight, carbon number or chemical species (Basak et al., 2004; Elizalde et al., 2009). But, in the discrete lumping approach, the reaction network is reduced to the limited number of reactions among the lumped components. The lumps, based on compound types present in feedstock and products (e.g., lumps of diesel, kerosene, gasoline, etc.), are often defined by boiling point ranges. This approach is attractive for kinetic modeling of complex mixtures because of its simplicity (Ancheyta et al., 2005).

1Sadighi et al.: Lumping Model for a Dual Bed VGO Hydrocracker

Published by The Berkeley Electronic Press, 2011

However, it should be mentioned that lumped kinetics have the following major disadvantages: (1) they are strongly dependant to feedstock and catalyst; (2) they are only valid for the range of studied operating conditions, and also (3) if bench-scale trickle-bed reactors are used for the experimentation, reaction kinetics will be affected by hydrodynamics and mass transfer processes. If any of those parameters is to be changed, then the model must be refitted on the basis of a new experimental program.

To make the lumped models more accurate, it is possible to choose as many lumps as possible. However, this may lead to a large number of model parameters (e.g., rate constants). So, less number of species, especially in the case of limited number of experiments, can make the model more acceptable.

According to discrete lumping approach, there are many researches in which hydrocracking models with three-lump (Yui & Sanford, 1989; Callejas & Martinez, 1999; Aoyagi et al., 2003), four-lump (Aboul-Gheit, 1989; Valavarasu et al., 2005; Sadighi et al., 2010d), five-lump (Ancheyta et al., 1999; Almeida & Guirardello, 2005; Singh et al., 2005; Sadighi et al., 2010c) and six-lump (Sadighi et al., 2010a; Sadighi et al., 2010b) partitions have been developed. Moreover, for the other processes such as catalytic pyrolysis of heavy oil (Meng et al., 2006) and fluid catalytic cracking (Chen et al., 2007), eight-lump kinetic models were presented.

In the present study, two kinds of discrete lumping models for a dual bed pilot scale hydrocracking plant have been compared together. The first approach is a simplified model which considers only hydrocracking reactions. So, it is assumed that the catalytic bed operates like a bi-functional catalyst; hydrocracking reactions can be occurred uniformly through the bed. The second one is a rigorous approach which needs complementary data from the hydrogen consumption as well as sulfur, aromatic and nitrogen contents of the feed and products. This strategy is according to the previous study (Sadighi et al., 2010d). But its equations are formulated here in detail to make it more applicable for being used in a mathematical model. To have a more realistic model and closer to the industrial scenario, the measured yields for estimating the required parameters are calculated on the basis of mass flow rate of fresh VGO feed.

2. Experimental

The device, catalyst, feed and operating conditions were described completely in the previous work (Sadighi et al., 2010d). The reactor was composed of four sections. The first part, having a length of 100 mm, was packed with inert SiC particles. This section was used to provide a uniform distribution of gas and liquid. The two following sections with a length of 355mm and 865 mm were

2 International Journal of Chemical Reactor Engineering Vol. 9 [2011], Article A4

http://www.bepress.com/ijcre/vol9/A4

loaded with 63.5cm3 hydrotrating and 152 cm3 hydrocracking catalysts, respectively. The last section was also contained with 50mm of inert (Figure 1). Because in the under study process, two mono functional zeolite based hydrotreating and hydrocracking catalysts were used, the reactor can be called a dual bed VGO hydrocracker.

Figure 1. Sections of catalytic reactor bed

In this study, two types of commercial hydrotreating and hydrocracking (zeolite-based) catalysts with the same size of industrial application were applied. The characteristics of HDT and HDC catalysts are presented in Table 1. Before charging the feed, both catalysts were heated up to 1300C, and also they were held at this temperature about 6 hr for drying. Then, it is sulfided with an appropriate agent according to the manual of the catalyst vendor.



Table 1- characteristics of HDT&HDC catalyst

Property HDT HDC

Size & Shape 1/16” & Quadralobe 1/16” & Cylindrical

Color Green Brown

Bulk density (kg/m3) 750 850

BET Surface Area (m2/g) 186.56 199.46

Langmuir Surface Area(m2/g) 259.20 273.71

Average Pore Diam (A0) 89.09 69.14

Main Ingredients Mo, Ni, Ti Zr, W, Ni, Si, Al

The hydrocracking feed was prepared by blending of the fresh VGO and recycle feed (unconverted oil) taken from Isomax unit of a real refinery. The feed properties are shown in Table 2. Mixing ratio of fresh and recycle feeds were 83.3 vol% and 16.7 vol %, respectively.

Table 2- Properties of fresh VGO and recycle feed

Property Fresh VGO Recycle Feed

[email protected]°C 0.8777 0.8738

Distillation Range (vol%)

ASTM D1160 ºC ºC

IBP 329.7 287.8

10% 390.6 390.7

30% 423.2 430.1

50% 445.6 452.9

70% 475.1 478.3

90% 523.7 517.1

End point 567.1 561.3

Nitrogen (ppmwt) 800 200

Sulfur (wt%) 1.4 0.03

Aromatics (wt%) 34 14.5

Asphalt & Resin (wt %) <0.1 <0.1

The pilot scale experiments were carried out under the following process

conditions: (1) H2/HC=1357 Nm3/Sm3; (2) LHSV=0.8, 0.9 and 1.05 hr-1; (3) Temperature=360°C, 370°C, 380°C and 390°C, and (4) Pressure =146 bar. The pressure, the range of LHSV and H2/HC were selected according to the recommendation of the catalyst manufacturer.



3. Modeling approach for the dual bed hydrocracking reactor This work considers 4-lump mathematical model, i.e., VGO, distillate, naphtha and gas to match main products (Table 3). The kerosene and diesel, also light and heavy naphtha are lumped together as distillate and naphtha cuts, respectively. Additionally, it is assumed that only VGO (as hydrocracking feed) consumes hydrogen to be cracked to lighter cuts. So, the total consumed hydrogen in hydrocracking section can be calculated on the basis of cracked VGO. Therefore, hydrogen can be included in the mass balance equations without creating high complexity. Figure 2 illustrates the process pathways associated with the mentioned strategy. Note that if all pathways of reactions are considered, the model will include twelve kinetic parameters which should be estimated by using experimental data.

Table 3. Average properties of hydrocracking product (Sadighi et al, 2010d)

Lump Sp.g @15°C IBP-FBP (°C)

Gas 0.35 40-

Naphtha 0.75 40-160

Distillate 0.823 161-370

VGO 0.89 370+

Figure 2. The complete 4-lump kinetic model



The following assumptions are considered in the development of the present models (Mohanty et al., 1991):

1- Hydrocracking is a first order hydrocracking reaction and since hydrogen

is present in excess, the rate of hydrocracking can be taken to be independent of the hydrogen concentration.

2- The pilot reactor operates under isothermal conditions. 3- A plug flow pattern exists in the trickle bed reactor. 4- Hydrogen feed is pure. 5- The petroleum feed and the products are in the liquid phase in the reactor. 6- The pilot unit is in steady state operation. 7- Catalyst activity does not change with time; therefore simulation is only

valid for start of run conditions. For each reaction, the kinetic expression is formulated as the function of

mass concentration and kinetic parameters ( 0k , E ). Based on the mentioned

assumptions, rate constants of the proposed models are as follows:

Vacuum gas oil or Feed ( F ): )exp(0 RT

Ekk Fj

FjFj

(1)

Note that j in Eq. 1 represents distillate ( D ), naphtha ( N ) and gas (G )

Distillate ( D ): )exp( ''0' RT

Ekk Dj

DjDj

(2)

'j in Eq. 2 represents naphtha ( N ) and gas (G ).

Naphtha ( N ): )exp(0 RT

Ekk NG

NGNG

(3)

In equations 1 to 3, T and R are the bed temperature and ideal gas constant, respectively.



From Figure 2, it can be found that for converting VGO to the lighter products, hydrogen should be consumed for each path. Therefore, the reaction rates for these products can be described as follows:

Distillate ( DR ):

G

NjDDjFFDD CkCkR

'')1( (5)

Naphtha ( NR ): NGNGDDNFFNN CkCkCkR )1( (6)

Gas ( GR ): NNGDDGFFGG CkCkCkR )1( (7) In equations 5 to 7, shows the consumed unit mass of hydrogen per unit mass of converted VGO which is added to the molecular structure of products (distillate, naphtha and gas) during hydrocracking reactions.

3.1. Combined bed model

In this approach, the hydrogen consumption is neglected. It is obvious that during hydrocracking and hydrotreating reactions, hydrogen molecule is absorbed in the hydrocarbon structure, but sulfur and nitrogen are removed. According to the experimental data (Sadighi et al, 2010d), this assumption can create 1% error in the mass balance which can be considered negligible. So, the coefficient in equations 5 to 7 is assumed to be zero.

Additionally, it is assumed that hydrocracking and hydrotreating reactions are carrying out simultaneously through the reactor bed similar to a bi-functional hydrocracking catalyst. Therefore, there is no boundary between hydrotrating and hydrocracking reactions. The scheme of combined bed model is illustrated in Figure 3(A).

So, the reaction rates ( jR ) can be formulated as follows:

Vacuum gas oil reaction ( FR ): F

G

DjFjF CkR

(4)



Figure 3. Schematic representation of the developed lumping models (A) Combined bed model (B) Dual bed model

3.2. Dual bed model

In this approach, the reactor is divided into two distinguished layer. In the first one, after carrying out the hydrotrating reactions (Table 4), the product is entered to the second layer. Therefore, the second step is only involved of hydrocracking reactions. The scheme of the dual bed model is illustrated in Figure 3 (B).

Before entering the products of the hydrotrating step into the hydrocracking one, it is imagined that by using two pseudo streams, H2S and NH3 are extracted from the hydrotrating products. So, they are not involved in the mass balance equations of hydrocracking section. Because these components are stable and also their flow rates are negligible, this assumption will not create a considerable error for the mathematical model. After hydrotrating reactions, to calculate the mass flow rate of feed, naphtha and distillate, equations 8 to 10 are formulated. Because the contents of sulfur and nitrogen in the product of the reactor are less than 50 ppm, they have been neglected.

))(1( 200AfAp

VGO

HNfSfffh XX

Mw

MwXXmm (8)



)7.(.

32

0

0NHHNc

N

Nff

Nh MwMwMwMw

Xmm (9)

)2.(.

22

00

SHHScS

SffDh MwMwMw

Mw

Xmm (10)

In above equations, 0fm is the mass flow rate of the fresh VGO; 0

fhm , 0Nhm , 0

Dhm

are the mass flow rate of the purified VGO, naphtha and distillate leaving the hydrotreating section, respectively; SfX , NfX , AfX are the mass fraction of

sulfur, nitrogen and aromatics in the fresh feed, respectively;

SHNHHVGOScNcSN MWMWMWMwMwMwMwMw232

,,,,,,, are the molecular weight

of nitrogen, sulfur, nitrogen lumped component (quinoline), sulfur lumped component (4,6-DMBT), VGO feed (420), hydrogen, ammonia and hydrogen sulfide, respectively. Table 4. Major reactions in the hydrotreating of VGO (Sadighi et al., 2010d)

Reaction Lumped component Consumed hydrogen Products

Hydrodesulfurization 4,6-DMBT 2 moles per S atom Distillate & H2S Hydrodenitrogenation Quinoline 7 moles per N atom Naphtha & NH3 Hydrodearomatization di-aromatics 2 moles per arom. molecule VGO

The reactions in the hydrocracking step are according to equations 5 to 7;

but the coefficient is calculated by the following quadratic polynomial equation (Sadighi et al., 2010d).

LHSVTLHSVTLHSVT ..... 122

222

11210 (12) In this equation, T is the reaction temperature (K); LHSV is liquid hourly space velocity of the reacting stream through the bed (hr-1). Also, 0 is the intercept

coefficient, 1 and 2 are the linear terms, 11 and 22 are the squared terms and

12 is the interaction term (Table 5).

Table 5. Coefficient values for the hydrogen consumption

Variable 0 1 2 11 22 12

T.LHSV 3441.319 -10.762 -18.906 0.00854 5.452 -0.00858



3.3. Model development and parameter estimation

In order to model the reactor, a cell network is applied. All beds from the inlet to the outlet are divided into a number (Nl=200) of well-mixed cells which are grouped along the flow direction. Mixing only occurs within each cell and back mixing is not accounted for between the adjacent cells. The accuracy of this approach for the VGO hydrocracking process in trickle bed regime was confirmed in the previous work (Sadighi et al., 2010d).

To improve the accuracy of the developed model, the volumetric flow rate in the reactor ( ) is considered variable, and it is calculated according to the density of output stream of each cell. Therefore, the mass balance equation for each cell can be written as follows:

)()()()('..)1()1( iiCiViRiiC jcatjj (13)

In Eq. 13, j ranges from the fresh feed ( F ) to the gas (G ), and a negative sign indicates reactant (fresh feed or VGO).

l

bcat N

ViV )( (14)

)()(

0

i

mi

G

fjj

(15)

)().(0 iiCm jj (16)

G

Fjj

G

Fj j

j

m

m

i .)(

10

0

(17)

0

)().(

f

lljj m

NNCY

(18)

In above equations, j is density of lumps (Table 3); i is the number of cells

which ranges from 1 to 200; C is the mass concentration of lumps; is the

effectiveness factor; ' is the catalyst volume fraction; )(iVcat is the volume of

hydrocracking catalyst in each cell; bV is the volume of the bed; Nl is the number

of cells (200); 0

fm is the mass flow rate of fresh feed, and jY is the yield of each

lump in the product stream leaving the reactor. The effectiveness factor for cylindrical catalyst in trickle bed regime and the bed void fraction are 0.7 (Mills & Dudukovic) and 0.35, respectively.



For parameter estimation, sum of squared error, SQE , as given below, is minimized:

2

1)( pred

jntN

n

measjn

G

FjYYSQE

(19)

In Eq.19, tN , measjnY and pred

jnY are the number of test runs, the measured and the

predicted yields, respectively. For the combined bed model, equations 1 to 7 and 13 to 18 should be

solved simultaneously by applying the following boundary conditions:

f

fm

0

)0( ; ffC )0( ; 0)0( DC ; 0)0( NC ; 0)0( gC (20)

But, for the dual bed model, equations 1 to 7 and equations 12 to 18

should be solved simultaneously by applying the following boundary conditions:

)0()0(

0

N

fjjhm

(21)

N

fjjhN

NhN

fjjhD

DhN

fjjhf

fh

m

m

m

m

m

m0

0

0

0

0

0

1)0(

(22)

)0()0(

0

fh

f

mC ;

)0()0(

0

Dh

D

mC ;

)0()0(

0

Nh

N

mC ; 0)0( gC (23)

To develop the model, Aspen Custom Modeler (ACM) programming

environment (AspenTech, 2004) is used. Then Eq.19 is minimized by sequencing NL2Sol and Nelder-Mead algorithm which are both existed in Aspen Custom Modeler software. NL2Sol algorithm is a variation on Newton's method in which a part of the Hessian matrix is computed exactly and a part of that is approximated by a secant (quasi-Newton) updating method. To promote convergence from a poor initial point, a trust-region is used along with a choice of model Hessian. Hence, the approximate region is found with NL2Sol; then to fine tune the parameters; Nelder-Mead method is used.

To evaluate the estimated kinetic parameters, absolute average deviation of predictions ( %AAD ) is calculated by using the following expression.



100

)(

%1 2

2

t

tN

n measjn

predjn

measjnG

Fj

N

Y

YY

AAD (24)

Moreover, the goodness of fitting of developed models is checked with analysis of variance (ANOVA) using Fischer test with 99% probability.

4. Results and discussions At first for the combined bed model, twelve kinetic parameters, frequency factors and activation energies were estimated by using the experimental data. After estimating parameters and predicting yields, the AAD% of the model was 8.28% in comparison to the measured data.

In Table 6, kinetic constants and the rate order of reactions at the mean operating temperature (3750C) to the highest one (kDN or distillate to naphtha) are presented. It is found that for the combined bed model, the rate orders of converting VGO to naphtha (kFN) and distillate to gas (kDG) are significantly lower than the highest value (kDN). It means that these reactions can be ignored. After eliminating the low-reaction-rate pathways and re-estimating the parameters (Table 7), the AAD% of the reduced model was found to be 8.23%. It can be concluded that the model reduction can improve the accuracy of the yield prediction which is the similar scenario with respect to the previous works (Sadighi et al., 2010a; Sadighi et al., 2010b; Sadighi et al., 2010c).

From Table 7, it is obvious that apparent activation energies of VGO to middle distillate and gas are 14.97 kcal/mol and 7.32 kcal/mol, respectively. The reported ones by Aboul-Ghiet (1989) were about 13-17.5 kcal/mol, and 18-19 kcal/mol, respectively. It is thought that the lower estimated activation energy for hydrocracking of feed to gas in this work is due to the higher hydrocracking activity of zeolite type catalyst. Additionally, the estimated activation energy (Botchwey et al., 2004) for formation of naphtha from middle distillate in the low severity temperature regime (340 to 370 0C) was about to 8.8 kcal/mol. Moreover the reported value for hydrocracking of kerosene to heavy naphtha in an industrial hydrocracking process charged with amorphous catalyst was 7.43 kcal/mol (Sadighi et al., 2010 a). It can be concluded that the estimated activation energy of distillate to naphtha in this work (7.11 kcal/mol) is not far from the others.

The simplified reaction-path network for the four-lump combined bed model is shown in Figure 4.



Table 6. Kinetic parameters for complete network of combined bed model

Frequency Factor (m3.hr-1.m3 total cat-1)

Activation Energy (kcal/mol)

Rate order

k0FD 3.49E+05 EFD 15.80 kFD 0.61

k0FN 2.44E+07 EFN 69.30 kFN 3.79E-17

k0FG 3.34E-01 EFG 2.10 kFG 0.024

k0DN 900.84 EDN 7.49 kDN 1

k0DG 2.48E+07 EDG 34.07 kDG 2.98E-05

k0NG 1.10E+00 ENG 0 kNG 0.41

Table 7. Kinetic parameters for reduced network of combined bed model

Frequency Factor (m3.hr-1.m3 total cat-1 )


Rate order

k0FD 1.82E+05 EFD 14.97 kFD 0.62

k0FN - EFN - kFN -

k0FG 2.29E+01 EFG 7.32 kFG 0.03

k0DN 660.20 EDN 7.11 kDN 1

k0DG - EDG - kDG -

k0NG 8.33E-01 ENG - kNG 0.32

Figure 4. The reduced 4-lump kinetic network for the combined bed model After following again the described strategy for the dual bed model, it was

found that the AAD% of the complete and reduced approaches were 6.77% and 5.87%, respectively. The apparent kinetic constants of those are presented in Tables 8 and 9, respectively. Also, the reduced kinetic network of this strategy is depicted in Figure 5.



Table 8. Kinetic parameters for the complete network of the dual bed model

Frequency Factor (m3.hr-1.m3 HCR cat-1)


Rate order

k0FD 6.72E+07 EFD 23.37 kFD 0.57

k0FN 1.04E+08 EFN 24.63 kFN 0.33

k0FG 0 EFG 13.08 kFG 0

k0DN 0 EDN 2.14 kDN 0

k0DG 6.90E+03 EDG 28.15 kDG 1.43E-06

k0NG 1.55E+00 ENG 0 kNG 1

Table 9. Kinetic parameters for the reduced network of the dual bed model

Frequency Factor (m3.hr-1.m3 HCR cat-1 )


Rate order

k0FD 1.32E+07 EFD 21.25 kFD 0.59

k0FN 1.42E+10 EFN 31.02 kFN 0.32

k0FG - EFG - kFG -

k0DN - EDN - kDN -

k0DG - EDG - kDG -

k0NG 1.514 ENG - kNG 1

Figure 5. The reduced 4-lump kinetic network for the dual bed model It should be noted that the kinetic constants and the kinetic network of the

combined bed model (Table 7 and Figure 4) show the performance of hydrotreating and hydrocracking sections together. But the related ones for the



dual bed model (Table 9 and Figure 5) only demonstrate the performance of the hydrocracking catalyst.

Therefore, it can be understood that in comparison to the combined bed approach, the dual bed one can predict the yield of hydrocracking reactor with lower AAD% about 2.36%. The brilliant point in this approach which can be understood from Table 9 is its requirement to only five kinetic parameters (frequency factors and activations energies) to predict twelve sets of test runs (three levels of LHSV and four levels of temperature). But, this approach needs complete information from hydrogen consumption as well as sulfur, nitrogen and aromatic contents of the feed and product. In contrast, combined bed model needs seven parameters to predict the yield of products with AAD % of 8.23. But it is a simplex in which no hydrotrating or hydrogen consumption data is needed.

In the previous works (Sadighi et al., 2010a), it was reported that the activation energies for both light and heavy naphtha to gas were about to 9 kcal/mol for a dual-functional amorphous hydrocracking-hydrotreating catalyst. But, from Tables 7 and 9, it can be concluded that in this range of operating temperature, the activation energy for hydrocarcking of naptha to gas is independent to temperature (ENG=0). The reason for this phenomenon is supposed to be higher ability of zeolite type catalysts for hyrocracking (Shimada et al., 1997). So, gas formation from naphtha may be influenced by the nature of catalyst, and it is independent to temperature within the operating range.

The AAD percentages for all lumps are presented in Table 10. It can be concluded that the predictions of the combined and dual bed models are close together and they are acceptable for all products except to the case of gas for the combined bed model. Additionally, in the Table 11, the ANOVA of both strategies has been presented. The positive point in this table is acceptable difference between the F-critical and the F-test of the proposed models.

Table 10. The AAD% for the different dual bed lumping models

Lump Combined bed (Completed)

Combined bed (Reduced)

Dual bed (Completed)

Dual bed (Reduced)

Gas 21.04 20.7 11.00 9.26

Naphtha 4.92 5.34 8.29 7.04

Distillate 5.33 5.11 4.87 4.34

Un.VGO 1.83 1.76 2.90 2.85

Ave. 8.28 8.23 6.77 5.87



Table 11. ANOVA results of the developed models

Combined bed

(complete) Combined bed

(reduced) Dual bed

(complete) Dual bed (reduced)

DF* of regression 11 6 11 4

DF* of residual 36 41 36 43

R2-adjusted (%) 99.944 99.974 99.916 99.976

F-value 1789.69 3865.29 1189.87 4193.26

F-critical (1%) 2.79 3.28 2.79 3.79

*DF is degree of freedom

Figures 6 to 9 show comparisons between the measured yields and the predicted ones. To evaluate the accuracy of the prediction, the corresponding deviation plot is also presented. The deviation error reported in these figures was calculated as follows:

100Pr

%

yieldMeasured

yieldedictedyieldMeasuredError (25)

As it was resulted from Table 10, close mappings between the measured

and predicted yields by using both approaches can be understood. Moreover, it can be found that deviations are acceptably distributed evenly around the zero; but in the Figure 6, more deviation for the gas lump can be found for the combined bed model.

Additionally, the deviation plot for the predicted gas by the combined bed model in the Figure 6 demonstrates that in most of temperatures and LHSVs, the dual bed model predicts lower yield for the gas lump in comparison to the measured data. It is supposed that this deviation is because of disregarding the reactions which can produce gas in the hydrotreating layer. Conversely, for most of temperatures and LHSVs, the combined bed model predicts higher values for the yield of gas. It is supposed that the main reason for this deviation is the consideration of gas producing reactions in all points along the catalytic bed. Because of lower ability of hydrotreating catalyst to produce gas than that of hydrocracking one, the model predicts more gas in comparison to the measured values. Therefore the yield of gas can be laid between the values predicted by the combined and dual bed models.



Figure 6. Predicted yields (♦, ▲&●), measured yields (□, ∆ & ○) and deviation plots for the prediction of gas lump



Figure 7. Predicted yields (♦, ▲&●), measured yields (□, ∆ & ○) and deviation plots for the prediction of naphtha lump



Figure 8. Predicted yields (♦, ▲&●), measured yields (□, ∆ & ○) and

deviation plots for the prediction of distillate lump



Figure 9. Predicted yields (♦, ▲&●), measured yields (□, ∆ & ○) and deviation plots for the prediction of VGO lump

5. Conclusions It was demonstrated that the product yields of a pilot scale VGO-hydrocracker could be predicted with the AAD% of 5.87% by using a four-lump rigorous model approach, called the dual bed model. This model could predict the yield of gas, naphtha, diesel and residue with the AAD% of 9.26%, 7.04%, 4.34% and 2.85%, respectively. These deviations for 12 test runs (48 observations) in three levels of LHSV and four levels of temperature can be satisfying. But to develop such a



model, the hydrogen consumption of the process was needed. Moreover, sulfur, nitrogen and aromatic content of the feed and product should be analyzed. In contrast, there was a simpler four-lump approach, called the combined bed model which was capable of predicting the yield of products with the AAD% of 8.23%. This model could predict the yield of gas, naphtha, diesel and residue with the AAD% of 20.7%, 5.34%, 5.11% and 1.76%, respectively. The enormous deviation for the gas lump can be the disadvantage of this model. But, the advantage of this model over the dual bed model was its simplicity because it only required product yields to tune the model parameters. 6. Nomenclature

6.a Notations AAD Absolute Average Deviation, %

C Mass concentration, kg/m3

D Distillate

E Apparent activation energy, kcal/mol

G Gas

k Reaction rate constant, m3.hr-1.m3 cat-1

0k Frequency factor, m3.hr-1.m3 cat-1

LHSV Liquid Hourly Space Velocity, hr-1 0m Mass flow rate, kg/hr

Mw Molecular weight

SMw Molecular weight of sulfur (32)

NMw Molecular weight of nitrogen (14)

N Naphtha

lN Number of cells (200)

tN Number of experiments

R Ideal gas constant, 1.987 kcal.kmol-1.K-1

jR Reaction rate of lump j, kg.hr-1.m3 cat-1



T Temperature, K or R

bV Total Volume of bed, m3

catV Volume of catalyst per cell, m3

VGO Vacuum Gas Oil

X Mass fraction of lumps

Y Yield of products

6.b Greek letters

Consumed mass of hydrogen per mass of VGO

122211210 ,,,,, Coefficient values for the hydrogen consumption

' Catalyst void fraction

Effectiveness factor

Volume flow rate, m3/hr

Density, kg/m3

6.c Subscripts

Af Aromatic in feed

Ap Aromatic in product

'Dj Distillate to lighter lumps

Dh Diesel in the output stream of hydrotrating bed

fh VGO feed or residue in the output stream of hydrotrating bed

Fj Feed to lighter lumps

i Cell number j Distillate, naphtha and gas lumps

'j naphtha and gas lumps

2H Hydrogen

SH 2 Hydrogen sulfide

n Number of experiments

Nc Nitrogen lumped component



Nf Nitrogen in feed

Nh Naphtha in the output stream of hydrotrating bed

3NH Ammonia

Sc Sulfur lumped component

Sf Sulfur in feed

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Comparison of Lumping Approaches to Predict the Product Yield in a Dual Bed VGO Hydrocracker

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