Kinetic Evaluation for Hydrodesulfurization via Lumped Model in a

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Kinetic Evaluation for Hydrodesulfurization via Lumped Model in a Trickle-Bed Reactor Papop Bannatham, Sornsawan Teeraboonchaikul, Tanaree Patirupanon, Wannarat Arkardvipart, Sunun Limtrakul, Terdthai Vatanatham, and Palghat A. Ramachandran Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b00382 • Publication Date (Web): 13 Apr 2016 Downloaded from http://pubs.acs.org on April 14, 2016

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Industrial & Engineering Chemistry Research

Kinetic Evaluation for Hydrodesulfurization via Lumped Model in a Trickle-Bed Reactor

Papop Bannatham1, 2, 3, Sornsawan Teeraboonchaikul1, 2, 3, Tanaree Patirupanon1, 2, 3, Wannarat Arkardvipart1, 2, 3, Sunun Limtrakul1, 2, 3,*, Terdthai Vatanatham1, 2, 3 and Palghat A. Ramachandran4

1

Department of Chemical Engineering, Faculty of Engineering, Kasetsart University, Bangkok 10900, Thailand 2

Center of Excellence on Petrochemical and Materials Technology, Department of Chemical Engineering, Faculty of Engineering, Kasetsart University, Bangkok 10900, Thailand. 3

Center for Advanced Studies in Industrial Technology, Faculty of Engineering, Kasetsart University, Bangkok 10900, Thailand

4

Department of Energy, Environmental & Chemical Engineering, Washington University in St. Louis, Missouri 63130, USA.

KEYWORDS: Deep Hydrodesulfurization, Kinetics, Lump Model, Clean Fuels, Catalyst Deactivation, Diesel

ACS Paragon Plus Environment

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ABSTRACT

Deep hydrodesulfurization is an important process due to increasing environmental regulations. Reasonably accurate kinetics and deactivation models are important to predict the catalyst life and reactor operational adjustments. Gas oil contains various sulfur compounds known by its boiling point, with different reaction rates. Therefore, single-lumped kinetics is not accurate for the entire sulfur constituents. Hence, four- to six-lump models, grouping sulfur compounds according to their boiling points, are proposed and coupled with a catalyst deactivation model to predict the time-on-stream reactor performance. The multi-lump kinetic rate constants were obtained from fitting of operating data. The multi-lump models show more accurate prediction than the single-lump model, and the six-lump model gives the most accuracy. The obtained deactivation parameter was applied to present the long term operational adjustment curve for the operating temperature as a function of time-on-stream to achieve the specified sulfur removal. Such curves are useful in hydrodesulfurization operational planning.

1. INTRODUCTION Hydrodesulfurization (HDS) is a catalytic chemical process of reaction of hydrogen and sulfur compounds on solid catalyst and is widely used to remove sulfur from refined petroleum oil such as gasoline or petrol, jet fuel, kerosene, diesel fuel, and fuel oils.1 Deep HDS is an important process due to increasingly stringent environmental regulations for clean fuels. Here, the sulfur content in diesel has been reduced from 500 ppm2 20 years ago down to under 50 ppm or even 10 ppm3 for ultra deep HDS in Europe. In the process of desulfurizing straight-run gas oil to an ultra-low sulfur content diesel, the hydrodesulfurization step has been identified as causing the largest cost and greatest environmental burden.2 It has been reported that HDS of significant


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higher-molecular-weight refractory sulfur compounds to achieve the low sulfur level of diesel fuel required is essential.4 However, due to the presence of various types of sulfur compounds in the petroleum products, with their wide range of boiling points, deep HDS process for reducing the sulfur compounds from 1–2 % to 50 ppm or below is complicated.5 Sulfur compounds with higher boiling points, although they remain sparsely, are hardly removed due to their large, complex structure. Thus the operation requires a higher reactor temperature in order to obtain the target sulfur conversion. A trickle bed is commonly used for HDS.6 It is a packed bed of catalyst particles in which gas and liquid co-currently flow downwards.7 The catalyst particles are covered with a liquid phase as a film. Gas and liquid reactants transfer to the porous-particle catalyst, and the reaction takes place there.

In a HDS process for diesel, diesel oil and almost-pure hydrogen gas flow

downwards in a reactor in which a diesel oil film covers catalyst particles and excess hydrogen gas diffuses into the oil film. Reaction of hydrogen and sulfur compounds in the oil occurs on the catalyst pore surface. Catalyst particles used for a packed bed of a trickle bed cannot be small due to the need for pressure drop reduction. On the other hand, large catalyst particles lead to intra-particle diffusion, limitation especially in any system with catalyst deactivation resulting from pore plugging. HDS catalyst can be deactivated by catalyst pore plugging of metal and coking. Petroleum oil usually contains metals, e.g., nickel and vanadium, as impurities. Catalyst deactivation due to materials deposited in the catalyst pores significantly affects the catalyst life.8 Pore plugging leads to lower diffusion in the catalyst, resulting in a reduced rate.9 Increasing the operating reactor temperature progressively with time can increase the rate to compensate the loss from catalyst deactivation.10 However, the catalyst pores are eventually filled, leading to the need for


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catalyst bed replacement.

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Therefore, appropriate reactor operation, accessing the desired

performance and prolonging of catalyst life, is important in HDS operation planning. Appropriate mathematical models are needed to forecast the catalyst life and the best operating conditions. Mathematical models used for predicting the catalyst life and the reactor performance require a reasonably accurate lumped kinetics for the complex reacting mixture.

In addition, a

deactivation parameter is significant for a pore-plugging deactivation model. Such a poreplugging model indicates pore diameter change, leading to a change of diffusion in the catalyst pores. This work focuses on hydrodesulfurization of a straight-run fuel oil which contains sulfur compounds ranging from benzothiophene to dibenzothiophene and higher-molecular-weight of sulfur compounds, corresponding to a range of diesel fuel boiling points from 170 oC to 380 oC.11 The difference in boiling points of diesel fuel shows differences in sulfur compound content. Diesel with higher boiling points contains higher-molecular-weight sulfur compounds which have higher boiling points.12, 13 Torrisi and coworker14 show various sulfur compounds and their relative reaction rates as a function of boiling point. The study shows that the sulfur compounds with higher boiling points have lower reaction rates. In addition, Sie15 shows the reactivity distribution of gas chromatographically determined sulfur compounds with their boiling points in a diesel fuel. Sulfur compounds with lower boiling points have higher reactivity. Typically, kinetic evaluation is based on a single rate constant parameter.16 This cannot be used for representing the rate of the entirety of sulfur constituents. Thus the sulfur compounds in diesel oil have been grouped for accurate kinetic evaluation. The resulting lumped method has been used to evaluate pseudo-first-order kinetic parameters for two-lump to six-lump models for residual oil with a simple plug-flow model of liquid transport.17 In addition, a lump kinetic


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method has been used to evaluate pseudo-first-order kinetic parameters for two-lump to model for vacuum gas oil with a simple plug flow pseudo-homogeneous model.16 However, the model did not include the effects of the operating conditions, e.g., hydrogen pressure, weight residence time, and catalyst deactivation. The model of Ma and Weng lumped the effect of hydrogen pressure into the kinetic parameter. In addition, their model did not include a deactivation effect. An intrinsic kinetic model excluding the operating effects can be more useful for reactor analysis, design, and scaling up. The deactivation of catalyst is usually caused by the plugging of catalyst pores. This results in intra-particle mass transfer changing with time of reactor operation. The pore plugging leads to slower diffusion in the pores of the catalyst. A diffusion–reaction model for a catalyst particle with changing diffusion should be proposed for predicting the reaction rate with deactivation phenomena.

In addition, the developed model should use functions of flow, pressure and

hydrogen concentration along with the performance data of a reactor operation in order to provide the intrinsic kinetics. Given the concerns and possibilities listed above, in this intrinsic-kinetic study, sulfur compounds are grouped into four, five, and six lumps for multi-lump kinetic modeling. Catalyst deactivations due to the pore plugging of the deposit materials are used for predicting the catalyst life. This work focuses on intrinsic kinetic evaluation for HDS via multi-lump models. The effects of hydrogen pressure, weight residence time, temperature, and catalyst deactivation are also included.

Combining the kinetic and deactivation model, the long term operational

adjustment curve for the operating temperature is presented as a function of time-on-stream to achieve the specified sulfur removal. Such results are useful in operational planning.


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2. MATHEMATICAL MODEL Hydrodesulfurization is a reaction to remove sulfur compounds from refined petroleum by the use of hydrogen7 as shown in eq 1: R-S + H2

R-H + H2S

(1)

The mathematical models used to capture the workings of this process consist of a reactor model, a kinetic model of a catalyst particle, and a catalyst deactivation model at the scale of a pore. The reactor model, which is a function of a reaction rate, is developed to predict the reactor performance. Available performance data from reactor operations for evaluating the kinetic model is usually obtained in terms of reactor conversion. The rate of reaction on the catalyst cannot be measured directly, and so the reactor model is necessary for the reaction rate estimation. The reactor model is developed from a mass balance of sulfur compounds in the reactor, while the kinetic model is based on the mass balance of sulfur compounds in a porous catalyst particle. Diffusion and reaction terms are involved. The evaluations of rate constants for the intrinsic kinetics in this work were carried out by two methods. In the first method, the kinetics is based on only a single rate constant. In the second method, various rate constants for hydrodesulfurization are evaluated based on multi-lump sulfur compounds. Finally, the catalyst deactivation model is developed from a mass balance of the materials deposited in a catalyst pore, leading to updating sulfur diffusion in a porous catalyst particle. 2.1 Reactor model A trickle-bed reactor is used for HDS in this work in which liquid diesel and hydrogen gas flow concurrently downwards through a fixed bed of catalyst particles in which the reaction takes place. The multi-phase reactor consists of three phases: solid catalyst, hydrogen gas, and


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liquid diesel. The mathematical model for the reactor performance prediction is based on a mass balance of sulfur compounds. The system is in a pseudo-steady state, for which the sulfur concentration profile is an instantaneous snapshot.

The system is assumed to be isothermal.

There is no sulfur

concentration gradient in the radial direction of the packed-bed reactor, and the sulfur compound concentration in the liquid oil changes with reactor height only. No mass transfer resistance in the liquid film surrounding the catalyst particles is considered. The catalyst particles are fully covered by the liquid oil. The hydrodesulfurization reaction orders with respect to hydrogen18 and sulfur19 compound mass fractions are proposed to be 0.47 and 1.7, respectively. In solving the model, the developed steady state diffusion reaction equation is first solved for each iteration time with the current diffusion coefficient. The current diffusion coefficient is updated by a catalyst deactivation model discussed in a later section. Meanwhile, the reactor model with its given operating conditions — e.g., flow rate, hydrogen pressure, WHSV — combined with the catalyst deactivation model can be applied to predict a kinetic parameter and deactivation parameter when the reactor performance is known.


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Liquid Xs in,

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Gas PH2 in, 0

W ∆l

L

Xs out

PH2 out

Figure 1. Trickle-bed reactor. The shell mass balance of sulfur compounds according to Figure 1 can be written as:

dxs η A kxH0.47 x1.7 1  s  =−   dl L  WHSV 

(2)

where is the mass fraction of sulfur in the oil ( / ), the mass fraction of hydrogen in the oil ( / ), the effectiveness factor, the specific surface of the porous catalyst ( /), the axial position in the reactor ( ), the reactor height ( ), the rate constant, and the weight hourly space velocity as a ratio of the oil flow rate and catalyst weight ( = / , ℎ ). A high partial pressure of hydrogen and high solubility of hydrogen in petroleum oil lead to excess hydrogen in the liquid oil. Thus hydrogen mass fraction can be considered to be uniform


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throughout the catalyst particle. Due to small hydrogen consumption along the reactor height, the axial hydrogen mass fraction is also constant and is treated as such. The effectiveness factor ( ) is the ratio of the actual mean reaction rate within a porous catalyst particle to the reaction rate without diffusion resistance. This factor indicates the degree to which reaction rate has decreased due to the pore-diffusion resistance. With this factor, the actual rate based on the catalyst surface area can be expressed as a function of the catalyst particle outer surface concentration. The reaction rate can be further written as a function of the liquid bulk concentration, because there is no mass-transfer resistance in the liquid film surrounding the catalyst particles. 2.2 Kinetic models The reaction rate is calculated based on the reaction taking place on the surface of the catalyst porous particle, with the intrinsic rate being written as a function of the hydrogen and sulfur mass fractions, as shown in eq 3: rs = − kxH0.47 x1.7 s

(3)

2.2.1The effectiveness factor As indicated above, the effectiveness factor ( ) is defined as the ratio of the actual mean reaction rate within the catalyst pores to the reaction rate without diffusion resistance, with the actual reaction rate within catalyst pores being obtained from solving a diffusion–reaction model. The diffusion–reaction model here is the mass balance of sulfur compound on a porous catalyst written as a function of sulfur diffusing through the porous particle and the reaction term on the catalyst surface inside a pore. The steady-state mass balance is shown in eq 4:

ρ 1 d  2 dxs  r De = A cat kxH0.47 x1.7 s   2 r dr  dr  ρoil

(4)


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where is the radial position in the catalyst particle ( ), the effective diffusivity ( /ℎ),

! the catalyst particle density ( / ), and

! the diesel oil density ( / ).

Solving the diffusion–reaction equation, the actual rate can be obtained. The effectiveness factor20 is expressed as:

η=

1 tanh M T MT

(5)

where "# is the generalized Thiele modulus defined as: MT =

Rp 3

2.7 A 0 ρcat kxH0.47 xs0.7 2 ρoil De

(6)

where $% is the catalyst particle radius. The effective diffusivity is defined as a function of molecular diffusivity as: De =

Dε

τ

(7)

where is the molecular diffusivity (& /'), ( the catalyst porosity, and ) the tortuosity. The molecular diffusivity of sulfur in oil can be expressed as: D=

7.4 × 10−8 (ΦΒ Μ Β )1 2Τ

(8)

υ A0.6 µ B

where *+ is the dimensionless association factor, "+ the normal molar weight of oil (/ ,), -. the molar volume of sulfur at the boiling point (& ! / ,), /+ the viscosity of oil (&01234,3'0'), and 5 the temperature (6). Although the above equation is based on a steady-state condition, the time dependence can be evaluated by updating diffusivity, , which can be obtained from the catalyst-pore-plugging model shown in Section 2.3. 2.2.2 Rate-constant parameters


10

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Kinetic models were developed based on two main concepts: a single lumped rate constant based on the weighted average boiling point and multi-lump rate constant parameters based on the boiling point cuts as described below. (a) Single rate constant In this case, the kinetic behavior is based on only a single rate constant, although the rate constant, k, depends on the boiling point of the sulfur compounds, which is referred by the boiling points of petroleum oil. In this work the boiling point effect was included by expressing the rate constant as a function of weight-averaged boiling point of the petroleum oil. Sie15 showed that the activity of hydrodesulfurization exponentially decreases as the boiling point increases. In addition, the rate constant also depends on the reaction temperature according to the Arrhenius law. Thus the rate constant can be written as a function of a weight-averaged boiling point and an operating reactor temperature as:  E  k = k 0 exp ( − kbTBPa ) exp  − a   RT 

(9)

where 7 is the frequency factor, 8 the constant parameter for a boiling point effect, 5+9 the weight-averaged boiling point of the feed (5+9 = ∑ the activation energy, and 5 the reaction temperature. The parameters, 7 , 8 , and > can be evaluated from fitting the data sets. In addition, the catalyst deactivation effect is included in the effective diffusion coefficient term in this work. (b) Lumped-rate-constant model Since the kinetic evaluation based on a single rate constant parameter cannot represent well the reaction rate of the whole range of sulfur constituents, the sulfur compounds can be lumped in


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multiple groups according to their boiling points for more accurate kinetic evaluation.12, 13 In this method, various kinetic rate constants for hydrodesulfurization were evaluated based of multi-lump sulfur compound groups. In this work, four-lump to six-lump models are considered and compared. Table 1 shows the boiling points of various types of sulfur compounds in petroleum oil.21, 22 The boiling point distributions of this work are in the range of 163–382 °C. The first boiling point cut in this work is below 260 °C and the last boiling point cut is above 375 °C. Table 2 shows the boiling point cuts for each group for four-lump, five-lump, and six-lump kinetic models. The boiling point cut for the four-lump model naturally covers a larger range than that of the six-lump model. Table 1. Boiling points of several sulfur compounds in petroleum oil (R-S) Sulfur compounds

Boiling Point (°C)

Thiophene

84

Benzothiophene

221

Dibenzothiophene

260

4-methyl-dibenzothiophene

327

4,6-dimethyl-dibenzothiophene

343

2,4,6-trimethyl-dibenzothiophene

364

Naphthobenzothiophene

>364

Table 2. The boiling-point cuts of each group for four-lump to six-lump models

Lump model

Cut 1 (°C)

Cut 2 (°C)

Cut 3 (°C)

Cut 4 (°C)

Cut 5 (°C)

Cut 6 (°C)

Number of Total number kinetic parameters of unknown (k) parameter


12

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(K0, Ea) Four-lump

< 260

260-327

327-364

>364

-

-

4

8

Five-lump

< 260

260-327

327-343

343-364

>364

-

5

10

Six-lump

< 260

260-327

327-343

343-364

364-375

>375

6

12

Each sulfur compound group in the boiling point cut has its own reaction rate constant. The rate constant of the sulfur compound group with higher boiling points is low and vice versa for lower boiling points. The effect of reaction temperature on each rate constant is also considered so that the sets of frequency factor and activation energy have to be evaluated and that, in addition, in the lump model the deactivation parameter can be evaluated. 2.3 Catalyst deactivation model The catalyst deactivation for hydrodesulfurization is caused by pore plugging of oil contaminants. The petroleum oil used usually contains metals as contaminants (i.e. vanadium, nickel). Demetallization results in metal deposits in the pores of the catalyst. In addition, pore plugging can be caused by coking. Eventually, when the catalyst pores are filled up, the catalyst has to be replaced. The pore plugging causes slower effective diffusion in the porous catalyst particle. It thus becomes useful to use the effective diffusivity as the parameter indicating the deactivation in the porous catalyst and which is changed as the catalyst deactivation proceeds. The diffusion–reaction model with changing effective diffusivity is thus the proposed model for prediction of the reaction rate. In itself, the catalyst pore plugging can be estimated from a mass balance on the deposit materials in a pore. The deactivation reaction consists of the removal (reaction) of the contaminant, ML, and production of the material, MD, which is deposited and clogged in the pores: ML (in oil)

MD (deposit material)

(10)


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Figure 2. Catalyst pore. The mass balance of deposit materials in a pore of the catalyst (see Figure 2 for an illustration) is written as a function of the reaction rate of the contaminant removal and is shown in eq 11:

ρM M d N p

rp

drp dt

=−

dVM = − AM l kM xH xM2 dt A Lp M l 2πρ M M d N p

(11)

k M xH xM2 (12)

where ? is the volume of deposit material in the catalyst pore ( ! ),

?

the deposit material

! density (? / ? ), "= molar molecular weight of deposited metal (=% / ,=% ), " molar

molecular weight of contaminant in the feed ( / , ), ? the mass fraction of contaminant in the oil (? / ), ? the rate constant of contaminant removal, @% the number of catalyst pores per catalyst weight, % the pore radius ( ) at any time, %7 the pore radius of fresh catalyst ( ), and 2 the time (;AB). The orders are first- and second-order with respect to hydrogen and metal mass fractions, respectively, in the demetallization reaction.9 Integrating eq 12 with the initial condition, 2 = 0, % = %7 yields:

rp rp 0

= 1−

Ao Ml 1 kM xH xM2 l t 2π LP N p ρ M M d rp 0

(13)


14

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where ̅ ?F is the spatially averaged mass fraction of contaminant in the pore, and 9 is catalyst pore length ( ). The catalyst pore radius decrease with time as eq 13 can be written in a simple form as: rp rp 0

= 1 − k pt (14)

where % =

.

?F

GHI JI KL ?M NIO

? ̅? is a lumped parameter describing the deactivation effect F

which is fitted from the data of reactor operations for a given period of time. This pore radius change affects the effective catalyst diffusivity change23, written in the form:

 rp  De = De 0    rp 0   

2

(15)

where 7 is the effective diffusivity at 2 = 0 and 2 is the time dependent in a term of operation days. Thus the effective diffusivity can be updated with time and written in the form: De = De 0 (1 − k p t )

(16)

Pore plugging leads to slower diffusion in the pores of the catalyst. The intra-particle mass transfer changes with the time of the reactor in operation. 2.4

Operating data

2.4.1 Catalyst characterization The catalyst used for the HDS reactor in this work was a commercial catalyst. The properties of the catalyst are listed in Table 3.

Table 3. Properties of Catalyst


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Type

Co-Mo/Al2O3

Form

Trilobe

Equivalent diameter (mm)

1.5

Surface area (m2/g)

220

2.4.2

Page 16 of 35

Operating data

The operating data in the trickle bed reactor for HDS are summarized in Table 4.

Table 4. The operating data for HDS of gas oil H2 partial Data set

WHSV

Temperature

Inlet sulfur

Outlet sulfur

IBP

FBP

(ppm)

(ppm)

(oC)

(oC)

pressure (hr-1)

(oC)

(bar)

× 10

1

2.12

353

36

93

43

187

379

2

2.11

353

36

92

45

183

375

3

2.10

353

36

97

40

186

373

4

2.12

355

37

102

48

183

373

5

2.11

354

37

98

47

183

375

6

2.11

355

37

98

46

185

376

7

2.11

354

37

98

43

183

376

8

2.12

356

38

91

41

185

374

9

2.12

356

39

105

48

190

375

10

2.12

356

38

99

48

181

373

11

2.11

354

38

97

39

178

370

12

2.13

356

37

110

49

187

379


16

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13

2.12

353

38

98

49

184

381

14

2.12

353

37

98

50

183

381

15

2.11

350

38

84

46

178

371

16

2.13

355

37

92

39

198

377

17

2.14

354

37

91

47

188

371

18

2.14

355

37

95

47

182

378

19

2.11

353

36

91

51

179

377

20

2.10

356

38

95

40

176

371

21

2.12

355

37

96

45

179

375

22

2.10

355

37

94

45

179

375

23

2.11

352

38

97

39

185

366

24

2.11

353

38

80

40

179

372

25

2.08

356

37

103

42

184

371

26

2.08

351

39

81

50

171

375

27

2.11

358

44

83

47

173

373

28

2.03

353

40

62

54

168

380

29

2.03

360

44

90

34

178

352

30

2.03

362

40

73

42

180

353

3. RESULTS AND DISCUSSION 3.1

Kinetic equations

3.1.1 Single-parameter kinetic model A total of 30 data sets of reaction operations were fitted with the single-parameter model described by eq 9. Three parameters, 7 , 8 , and > , related to the effects of boiling point12 and operating temperature were obtained. The optimization algorithm named simulated annealing


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Page 18 of 35

was used to estimate the kinetic parameters. In addition, reactor running time data was fitted to eq 16 to update the effective diffusivity. Using 30 operation data sets with different catalyst ages, the deactivation parameter, % , was obtained. The obtained parameters for the single-lump-parameter kinetic model are 8.55×1016 kg/m2hr, 0.04 oC-1, 131.91 kJ/mol, and 0.0011 day-1 for 7 , 8 , > and % , respectively. Thus the rate constant for hydrodesulfurization is written as a function of the boiling point and reaction temperature as:  131.91  k = 8.55 × 1016 exp ( −0.04TBPa ) exp  −  RT  

(17)

where 5+9 is the weight-averaged boiling point temperature (oC), $ the gas constant (R 6 , ), and 5 the reaction temperature (6 ). Catalyst deactivation causes reduction of the reactor conversion as the reactor is operated for more and more time. The effective diffusivity ( ) can be obtained from the pore-plugging model in the form of: De = De 0 (1 − 0.0011t )

(18)

where t is the operating time (;AB). Using the rate constant as written in eq 17 and the catalyst deactivation model, eq 18, with the reactor model in eq 2, the reactor performance can be predicted as shown in Figure 3.


18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Outlet sulfur mass fraction, ppm, calculation

Page 19 of 35

100 80

40%

60 40 -40%

20 0 0 20 40 60 80 100 Outlet sulfur mass fraction, ppm, operation

Figure 3. Comparison of the exit sulfur mass fractions from calculation and operation data with the single-lumped-parameter model using 30 reaction operation data sets. The parity plot comparison of the exit sulfur mass fractions of sulfur from the calculation with single-lumped-parameter model and the reactor operation is presented in Figure 3. The scatter diagram shows less agreement. It was found that the kinetic model based on a single lumped parameter could not predict the reactor performance satisfactorily. The comparison shows an error of 40 %, shown in the parity plot. Moreover, using the kinetic parameters of the single-parameter model, eq 17 with the reactor model, eq 2, and the catalyst deactivation parameter, the operating reactor temperature can be predicted as shown in Figure 4. The parity plot of the calculated temperature and the actual operating reactor temperature for the same conversion is shown in Figure 4.


19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Temperature, ̊C, calculation


Page 20 of 35

370 365

+9 ̊C

360 355 -9 ̊C

350 345

345 350 355 360 365 370 Temperature, ̊C, operation

Figure 4. Parity plots of predicted operating reactor temperature and actual reactor temperature The scatter diagram shows less agreement. It was found that the kinetic model with single lumped parameter model could not predict the temperature satisfactorily. The comparison gives a temperature error of ±9 oC, shown in the parity plot. 3.1.2 Multi-lump kinetic models The rate constants in the multi-lump kinetic models depend on the reaction temperature according to the Arrhenius law:  E  ki = k0,i exp  − a ,i   RT 

(19)

where i represents a lumped group. In a four-lump model, eight parameters including four frequency-factor and four activationenergy data sets, are unknown. Fitting 30 reaction operation data sets with the reactor model, eq 2, and the deactivation model, eq 18, the rate constants in terms of frequency factor and activation energy for four groups can be evaluated. Similarly, for five-lump and six-lump kinetic models, 10 and 12 kinetic parameters must be calculated. Table 5 shows the frequency-factor and activation-energy values evaluated for the multi-lump models. The values of activation


20

Page 21 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


energy of hydrodesulfurization are in the ranges of 56.70–158.02, 61.56–156.54, and 63.03– 162.68 kJ/mol for the four-, five-, and six-lump kinetic models, respectively. Higher activation energy was found in the group of heavy sulfur compounds, which constitute the refractory. The range of activation energy is approximately the same range as that in the literature, which was found to be 57.84 kJ/mol for thiophene24 and 80.05–120.58 kJ/mol for dibenzothiophene, 4methyl-dibenzothiophene and 4,6-dimethyl-dibenzothiophene5. In addition, it was found that the deactivation parameter, kp is 0.0011 day-1 for four-lump, five-lump, and six-lump kinetic models —which is the same as that for the single-parameter model. The number of cutting groups does

not affect the deactivation phenomena, since the deactivation phenomena occur due to pore plugging by coking and demetallization.

The sulfur compound lumping cuts have no

contribution to the amount of coking and demetallization.

Table 5. Frequency factor and activation energy for the multi-lump kinetic models Lump Cut Group

k0 (× 10U ) (/ ℎ) Ea (R/ , )

1

0.0185

56.70

2

0.300

74.23

3

21.9

100.02

4

52,503

158.02

1

0.0186

61.56

2

0.301

80.05

3

0.902

89.56

4

130

120.58

5

52,503

156.54

1

0.0187

63.03

4

5

6


21


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2

0.261

79.06

3

0.701

85.49

4

553

128.08

5

22,374

151.75

6

151,759

162.68

Page 22 of 35

The obtained rate constants shown in Table 5 were applied in the reactor model, eq 2, to calculate the exit mass fraction of sulfur for the multi-lump models. The comparison of the exit mass fractions of sulfur from the calculation and the operation data are shown in Figure 5 (a), 5 (b), and 5 (c) for four-lump, five-lump, and six-lump kinetic models, respectively.


22

Page 23 of 35


(a)

100 80

35%

60 40

-35%



(b)

100 80 20%

60 40

-20%


(c)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


100 80

15%

60 40

-15%



23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 35

Figure 5. Comparison of the exit sulfur mass fractions from calculation and operation data with (a) four-lump, (b) five-lump, and (c) six-lump kinetic models using 30 reaction operation data sets. The parity plot comparisons of the exit sulfur mass fractions from the calculation with fourlump, five-lump and six-lump kinetic models and from the operation data are presented in Figure 5 (a) – 5 (c). The predictions, comparing to Figure 3, clearly show that the kinetic model with multi-lumped parameters can predict the reactor performance better than the single-parameter model. In the multi-lump kinetic models, lower numbers of lumped groups give more scatter in the parity plot. Four-lump, five-lump, and six-lump kinetic models can predict the reactor performance with errors of 35, 20, and 15 %, respectively, as shown in the parity plot, Figure 5 (a), 5 (b) and 5 (c), respectively. The more lumped groups, the greater the prediction accuracy obtained. As the number of cutting lumps increases, variation of sulfur compounds in each lump (that is, for a smaller range of boiling point) is reduced. Various sulfur compound types have different boiling points and thus also different reaction rates. By cutting the lumps into smaller ranges of boiling points one obtains less sulfur compound variation for a single lump, leading to better representation of sulfur grouping and providing more accuracy in modeling. However, the use of models with too many lumped groups will complicate the needed calculations and require more data for fitting. Thus, a six-lump kinetic model should be optimally chosen for more accurate prediction of the reaction rate of hydrodesulfurization of diesel.


24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Relative error, ppm

Page 25 of 35

20 15 10 5 0 -5 1 -10 -15 -20

Single Four-lump Five-lump Six-lump

6

11

16

21

26

Data set Figure 6. Comparison of the relative error for actual exit sulfur mass fractions and calculated sulfur mass fractions from the multi-lump kinetic models and that for the single-parameter model. Figure 6 shows the comparison of the relative error for the single-parameter kinetic model and the multi-lump kinetic models obtained from 30 data sets selected from a total of 780 days. It appears that the multi-lumped kinetic models provide better accuracy in prediction compared to the single-parameter model. The lumped kinetic model with many lumped groups gives a better fit to the results. Although the errors for all three types of lump kinetic models are not much different for the data set numbers 1–26, the errors are substantially different for those three types of kinetic models for the data set numbers of 27–30, that is, on the later days. The error of a sixlump kinetic model is clearly shown to be the smallest. In the later days, the catalyst is in the deactivated mode, and the required operation reactor temperature is higher. Thus, the effect of the activation energy is important. Under these circumstances, different numbers of lump cuts can perform the prediction differently.


25



(a)

370 365

+9 ̊C

360 355 -9 ̊C

350 345

345 350 355 360 365 370 Temperature, ̊C, operation


(b)

370 365

+5 ̊C

360 355 -5 ̊C

350 345 345 350 355 360 365 370 Temperature, ̊C, operation

(c)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 35

370 365

+4 ̊C

360 355

-4 ̊C

350 345 345 350 355 360 365 370 Temperature, ̊C, operation


26

Page 27 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7. Parity plots of predicted operating reactor temperature and actual reactor temperature for the same reactor performance with (a) four-lump, (b) five-lump, and (c) six-lump kinetic models. In addition, the kinetic parameters of the multi-lump kinetic models as shown in Table 5, with the reactor models and catalyst deactivation models can be applied to predict the operating temperature, as discussed in Section 3.1.1. Figure 7 (a) – 7 (c) shows the calculated operating reactor temperature for all 30 data sets. Figure 7 (a) – 7 (c) also show the comparisons of the operating reactor temperature obtained from calculation and from the actual operation for fourlump, five-lump, and six-lump kinetic models, respectively. It was found that more scatter occurs in a model with fewer lump groups. A temperature error of ±9, ±5, and ±4 oC was found for a four-lump, five-lump, and six-lump kinetic models, respectively. These findings are similar to those for the reactor performance predictions. Note that the six-lump kinetic model gives the smallest error; thus, it can be concluded that the six-lump kinetic model is the most appropriate model for reactor analysis. 3.2 Deactivation curve for prediction of catalyst life Catalyst deactivation of hydrodesulfurization is caused by plugging of catalyst pores by contaminants. This leads to decreasing of effective diffusivity of reactants into the porous catalyst particle, and, as a result, the sulfur removal efficiency is therefore reduced. In order to increase the catalyst activity so as to keep an equivalent reactor performance, increasing the operating reactor temperature should be carried out, throughout the catalyst lifetime, since catalyst activity loss due to deactivation can be compensated by increasing reactor temperature. With the kinetic parameters of the six-lump model, and the deactivation parameter, the reactor


27


model, and catalyst deactivation model, a deactivation curve can be predicted. The deactivation curve is a plot of the operating reactor temperature and operating time.

Running temperature, oC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 35

368 363 358 353 348 0

200 400 600 Running time, day

Figure 8. Deactivation curve: the plot of operating temperature and operating day obtained by prediction and actual operations for a total of 780 days. Figure 8 plots the calculated deactivation curve, in which the operating temperature and the operating day are correlated for all selected data sets. Although the operating conditions for all data are not the same, trends can be seen. The deactivation curve is in an S shape, as is commonly found.25 The actual running data of the operating temperature and operating time are also compared in Figure 8. Actual running data fluctuate due to the difference of feed conditions during operation. Even so, the trends are in a good agreement. During days 1–440, the operating temperature only increases slightly due to less significant deactivation. In the calculation, the effect of decrease of the diffusion is still not significant, due to less deactivation. Thus, in this region, the calculated required temperature does not change much with time.


28

Page 29 of 35

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On the other hand, in the later period of operation, the deactivation effect dominates. Increased pore plugging in the later period of operation causes increased deactivation. Therefore, the operating reactor temperature increases sharply in the period of days 440 to 780.

4. CONCLUSIONS A kinetic model using a single lump and including the parameter constants for feed average boiling point, reactor temperature, and deactivation effect was presented. In addition, multilump kinetic models were proposed, in which the sulfur compounds in the feed were lumped according to the boiling point into four, five, or six group cuts to obtain four-, five-, and six-lump kinetic models, respectively. Frequency factor and activation energy were obtained for each group cut. A deactivation parameter based on pore plugging in the porous catalyst was also obtained. It was found that the kinetic model with a single lump parameter model could not predict the reactor performance satisfactorily. In contrast, the multi lumped kinetic models provide better accuracy in prediction compared to the single-parameter model. In the multi-lump kinetic models, lower numbers of lumped groups give more error in prediction, especially for the later days of operation when the catalyst is in the deactivated mode and the reactor operating temperature must be higher for compensation. Thus, the effect of the activation energy is important. More lumped groups used, the greater is the prediction accuracy. However, models with too many lumped groups will complicate the calculations required and will themselves require more data to obtain a fit.

Thus, the six-lump kinetic model is put forward as an

appropriate model for the analysis of a hydrodesulfurization reactor. This mathematical model is a useful tool for optimizing the operation conditions and prolonging the catalyst life leading to the cleaner process in the petroleum refinery.


29


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Page 30 of 35

AUTHOR INFORMATION Corresponding author: *Fax: +66-2561-4621. Email: [email protected] ACKNOWLEDGMENTS This work was financially supported by the Kasetsart University Research and Development Institute (KURDI), the Faculty of Engineering of Kasetsart University, and the Center of Excellence on Petrochemical and Materials Technology (PETROMAT). REFERENCES (1) Gary, J.H.; Handwerk, G.E.; Kaiser, M.J. Petroleum refining: Technology and economics; CRC Press: New York, 1984. (2) Burgess, A.A.; Brennan, D.J.; Desulfurization of gas oil: A case study in environmental and economic assessment. J. Clean. Prod. 2001, 9, 465–472. (3) Al-Barood, A.; Stanislaus, A. Ultra-deep desulfurization of coker and straight-run gas oils: Effect of lowering feedstock 95 % boiling point. Fuel Process. Technol. 2007, 88, 309–315. (4) Sano, Y.; Ki-Hyouk, C.; Korai, Y.; Mochida, I. Effects of nitrogen and refractory sulfur species removal on the deep HDS of gas oil. Appl. Catal., B 2004, 53, 169–174. (5) Varga, Z.; Hancsók, J.; Nagy, G. Investigation of the deep hydrodesulphurization of gas oil fractions. Hungarian J. Ind. Chem. Veszpr. 2003, 31, 37–45.


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(6) Bhaskar, M.; Valavarasu, G.; Sairam, B.; Balaraman, K.S.; Balu, K. Three-phase reactor model to simulate the performance of pilot-plant and industrial trickle-bed reactors sustaining hydrotreating reactions. Ind. Eng. Chem. Res. 2004, 43, 6654–6669. (7) De la Paz-Zavala, C.; Burgos-Vázquez, E.; Rodríguez-Rodríguez, J.E.; Ramírez-Verduzco, L.F. Ultra low sulfur diesel simulation. Application to commercial units. Fuel 2013, 110, 227– 234. (8) Kallinikos, L.E.; Bellos, G.D.; Papayannakos, N.G. Study of the catalyst deactivation in an industrial gasoil HDS reactor using a mini-scale laboratory reactor. Fuel 2008, 87, 2444–2449. (9) Elizalde, I.; Ancheyta, J. Modeling the deactivation by metal deposition of heavy oil hydrotreating catalyst. Catal. Today 2013, 220–222, 221–227. (10) Tanaka, Y.; Shimada, H.; Matsubaysshi, N.; Nishijima, A.; Nomura, M. Accelerated deactivation of hydrotreating catalysts: comparison to long-term deactivation in a commercial plant. Catal. Today 1998, 45, 319–325. (11) Mollenhauer, K.; Tschöke, H. Handbook of diesel engines; Springer-Verlag: Berlin Heidelberg, 2010. (12) Becker, P.J.; Celse, B.; Guillaume, D.; Dulot, H.; Costa, V. Hydrotreatment modeling for a variety of VGO feedstocks: A continuous lumping approach. Fuel 2015, 133–143. (13) Elizalde, I.; Ancheyta, J. Modeling the simultaneous hydrodesulfurization and hydrocracking of heavy residue oil by using the continuous kinetic lumping approach. Energy Fuel 2012, 26, 1999–2004.


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(14) Torrisi Jr., S.; Remans, T.; Swain, J. The challenging chemistry of ultra-low-sulfur diesel. Process. Technol. Catal. 2009, 1–4. (15) Sie, S.T. Reaction order and role of hydrogen sulfide in deep hydrodesulfurization of gas oils: consequences for industrial reactor configuration. Fuel Process. Technol. 1999, 61, 149– 171. (16) Rodríguez, M.A,; Elizalde, I.; Ancheyta, J. Comparison of kinetic and reactor models to simulate a trickle-bed bench-scale reactor for hydrodesulfurization of VGO. Fuel 2012, 91–99. (17) Ma, C.G.; Weng, H.X. A study on the lumping kinetic model for a residual oil hydrodesulfurization process. Energy Sources, A 2012, 34, 1933–1942. (18) Ronze, D.; Fongarland, P.; Pitault, I.; Forissier, M. Hydrogen solubility in straight run gasoil. Chem. Eng. Sci. 2002, 57, 547–553. (19) Daage, M.; Teh, C.H.; Kenneth, L.R. Stacked bed catalyst system for deep hydrodesulfurization. USA. US5474670 A. 1995. (20) Levenspiel, O. Chemical Reaction Engineering; John Wiley & Sons: New York, 1999. (21) Mishra, R.; Jha, K.K.; Kumar, S.; Tomer, I. Synthesis, properties and biological activity of thiophene: A review. Scholars Research Library Der Pharma Chemica 2011, 3(4), 38–54. (22) Valla, J.A.; Mouriki, E.; Lappas, A.A.; Vasalos, I.A. The effect of heavy aromatic sulfur compounds on sulfur in cracked naphtha. Catal. Today 2007, 127, 92–98. (23) Zeynali, M.E. Effect of catalyst pore size on styrene production rate. The Open-Access J. Basic Princ. Diffus. Theory, Exp. and Appl. 2010, 13, 1–18.


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(24) Borgna, A.; Hensen, E.J.M.; van Veen, J.A.R.; Niemantsverdriet, J.W. Intrinsic kinetics of thiophene HDS over a NiMo/SiO2 model catalyst. Prepr. Pap. -Am. Chem. Soc., Div. Fuel Chem.

2003, 48(2), 603. (25) Furimskya, E.; Massoth, F.E. Deactivation of hydroprocessing catalysts. Catal. Today

1999, 52, 381–495.

NOMENCLATURE

: specific surface of the porous catalyst, /

;

: percent of distribution, %

: molecular diffusivity, & /'

: effective diffusivity, & /'

7

: effective diffusivity at 2 = 0, & /'

>

: activation energy, R/ ,

3

: lumped group

: rate constant, / ℎ

7

: frequency factor, / ℎ

8

: constant parameter for a boiling point effect, oC-1

?

: rate constant of contaminant removal, / ℎ

%

: lumped parameter describing the deactivation effect, ;AB

: axial position in the reactor,

: reactor height,

9

: catalyst pore length,

"+

: normal molar weight of oil, / ,


33


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

"=

: molar molecular weight of deposited metal, =% / ,=%

"

: molar molecular weight of contaminant in the feed, / ,

"#

: Thiele modulus

1;

: number of sulfur compound

@%

: number of catalyst pores per catalyst weight

: radial position in the catalyst particle,

%

: pore radius at any time,

%7

: pore radius of fresh catalyst,

$

: gas constant, R 6 ,

%$: catalyst particle radius,

2

: time dependent, ;AB

5

: reaction temperature, 6

5+9

: weight-averaged boiling point temperature of the feed, oC

5+9

: boiling point temperature of each sulfur compound, oC

?

: volume of deposit material in the catalyst pore, !

: weight hourly space velocity, ℎ

: mass fraction of hydrogen in the oil, /

?

: mass fraction of contaminant in the oil, ? /

̅?F

: spatially averaged mass fraction of contaminant in the pore, ? /

: mass fraction of sulfur in the oil, /

Page 34 of 35

Greek symbols

(

: catalyst porosity

! : catalyst particle density, /


34

Page 35 of 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


?

! : deposit material density, ? / ?

! : diesel oil density, ,3/

: effectiveness factor

*+

: dimensionless association factor

)

: tortuosity

/+

: viscosity of oil, &01234,3'0'

-.

: molar volume of sulfur at the boiling point, & ! / ,

Table of Content graphic


35

Kinetic Evaluation for Hydrodesulfurization via Lumped Model in a

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