Modeling of Slurry-Phase Reactors for Hydrocracking of Heavy Oils

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Modeling of Slurry-Phase Reactors for Hydrocracking of Heavy Oils Cristian J Calderon, and Jorge Ancheyta Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.5b02807 • Publication Date (Web): 28 Jan 2016 Downloaded from http://pubs.acs.org on January 30, 2016

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Energy & Fuels

Modeling of Slurry-Phase Reactors for Hydrocracking of Heavy Oils †

Cristian J. Calderón , Jorge Ancheyta * †

Facultad de Química, UNAM, Ciudad Universitaria, México D.F. 04510, México.

*Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas Norte 152, Col. San Bartolo Atepehuacan, México D.F. 07730, México. Hydrocracking, Modeling, Slurry-Phase Reactors. 1

The modeling of slurry-phase reactors for petroleum hydrocracking has been reviewed and

2

analyzed. A general description of the flow regime was proposed, and it is anticipated that due to

3

the operating conditions usually implemented in hydrocracking of heavy oils, the homogeneous

4

bubble flow is usually considered. It was also found in the literature that most of the models are

5

only able to describe the liquid phase behavior, omitting the dynamic behavior of the gas phase,

6

the dispersion and deactivation of catalysts, as well as coke formation. Computational fluid

7

dynamics formulations are preferred despite the computational effort involved in the

8

calculations. Also in the majority of those models, simple pseudo-component kinetic rate

9

expressions have been applied, without enough experimental information referring to kinetic

10

parameters. Finally a generalized reactor model, which considers all mass and heat transfer

11

phenomena, is proposed based on the literature, and details are provided to estimate all the model

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parameters. For slurry-phase hydrocracking systems it becomes evident the lack of experimental

13

information needed for validation and the necessity of exploring different types of models, as

14

axial dispersion models under different bubble flow regimes as well as a deeply study of the

15

transitory state.

16

Introduction

17

Three phase catalytic reactors have gained great importance due to its various applications in

18

different reacting systems, especially in the petroleum industry where the hydrocracking (HCR)

19

of heavy oils is one of the main processes for converting a heavy carbonaceous feedstock to

20

lower-boiling point products. There are different types of reactors commonly used in this

21

operation; fixed-bed reactors (FBR) which are simpler and result in a stable and reliable

22

performance despite the strong limitations in feedstocks properties and the inefficiency due to

23

fast deactivation of the catalyst (1, 2), ebullated-bed reactors (EBR) which are more flexible with

24

respect to the feedstock and can handle greater amounts of metals and coke, but they are limited

25

by overall conversions less than 80% due to high sediment formation developed when processing

26

problematic heavy oils, and slurry-phase reactors (SPR) which are more reliable to achieve high

27

conversions and have shown superiority especially in the treatment of hydrocarbons containing

28

sulfurous compounds in exceedingly large quantities as well as large amounts of metals, carbon

29

and asphaltenes (3).

30

SPR involved mixing the feed oil with dispersed catalysts and hydrogen, whose purpose is the

31

inhibition of coke formation by hydrogenating the coke precursor and removing heteroatoms (4).

32

Also, the catalyst acts as a supporter of coke, which reduces coking of the reactor wall. At

33

present there are several technologies for slurry-phase hydrocracking processes in pilot scale and

34

even in industrial application, which were reviewed by several authors (3-5) and are summarized


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in Table 1. Although SPRs have been used in different applications, in the particular case of

36

HCR, detailed modeling and other aspects of the reactors are scarce because they are owned by

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manufacturers (6). The present review covers basic concepts related to slurry-phase reactors such

38

as design, catalyst characteristics and fluid regime dynamics, as well as a detailed analysis of

39

proposed models reported in the literature for different reacting systems, along with a summary

40

of the correlations most commonly used in the modeling of SPR.

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Characteristics of slurry-phase reactors for hydrocracking

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Type of reactors

43

Slurry-phase reactors are three phase reactors that consist of a solid phase catalyst (known as

44

additive) suspended in a liquid in batch mode or it may move co-currently or counter-currently to

45

the gas flow (Figure 1a). Generally, heterogeneous catalysts, typically transition metals (such as

46

Mo, W, Fe or other elements), are used in the process. The purpose of catalyst and hydrogen is

47

the inhibition of coke formation by hydrogenating the coke precursor and removing heteroatoms.

48

A catalyst with high activity will result in high yield of light fuel oil and low yield of coke. In

49

SPR the catalyst is added to the heavy oil and then the slurry is mixed with hydrogen in the

50

reactor, typically operating at high temperature and pressure. Finally the products leaving the

51

reactor are separated before they are fractionated (7).

52

Another configuration of SPR very common in industry is the slurry bubble column. Slurry

53

bubble column reactors (SBCR) are multiphase systems in which the gas feed stream is

54

continuously bubbled into the slurry phase (Figure 1b). In the simplest mode of operation the

55

liquid phase is stationary while gas is sparged through the vessel. Generally the reactor is an

56

empty vessel placed vertically, optimally dimensioned with a relationship between length-to-

57

diameter-ratio of at least 5 due to large ratios promote higher conversions but also high pressure


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drop and low ratios favor a higher gas throughputs. There are different internal configurations

59

with devices to promote the mass transfer (8). SPR operating as stirred tank reactor (STR) is

60

shown in Figure 1c. This vessel in batch or semi-batch configurations is typically used to

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perform experiments at laboratory scale due to the low amount of reactants, small equipment and

62

easy operation characteristics. Most of these reactors serve for exploring catalyst properties and

63

to obtain kinetic parameters for a given kinetic model, therefore there is not evaluation of mass

64

transfer limitations, internal configuration of the reactor or details of operating characteristics

65

(9).

66

Due to the particular operating conditions of heavy oil hydrocracking, the typical configuration

67

is in the SPR form where the feed oil is mixed with the gas. Some of the general advantages and

68

disadvantages of SPR for hydrocracking of heavy oil are given below.

69

Advantages:

70

•

Nearly isothermal operation.

71

•

Easy temperature control.

72

•

Good interphase contacting.

73

•

Large catalyst area.

74

•

Large liquid holdup.

75

•

High conversion rates.

76

•

Operational flexibility.

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•

Low pressure drop.

78

•

Low construction and operational costs.

79

•

Easy addition of catalyst.

80

•

Uniform catalyst distribution inside the reactor.


4

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Energy & Fuels

•

82 83

The catalyst can promote cracking and restrain deposition during the catalytic reactions.

Disadvantages:

84

•

Difficult separation of solids and liquid.

85

•

Uncertain scale-up.

86

•

Plugging

87

•

Catalyst sedimentation and agglomeration.

88

•

Formation of coke during reactions.

89

As can be seen, this type of reactor offers a great number of advantages, however, special

90

attention should be taken for problems such as plugging. Plugging could be generated by

91

catalyst agglomeration as well as for catalyst sedimentation at the bottom of the reactor. This

92

problem could be avoided if the flow conditions as well as process lines and the equipment

93

assure that the catalyst is completely suspended. Also, using catalyst of small particle size with

94

similar density to the liquid phase would cause that the particles follow the motion of the liquid

95

avoiding catalyst sedimentation. Another problem that causes plugging in hydrocracking systems

96

is the coke formation during the reactions. While it is indubitable that hydrogen plays an

97

important role during the reaction inhibiting coke formation during the thermal cracking process,

98

the catalyst is also responsible for avoiding the coke formation and prolonging the coke

99

induction period. Therefore in order to avoid this problem, improved catalyst properties are of

100

significant importance.

101

Catalyst characteristics

102

Highly dispersed catalyst particles have different advantages over the supported catalysts

103

commonly used in hydroconversion and hydrotreating of crude oils, for example there are less


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susceptible to deactivation during heavy oil upgrading allowing for the elimination of catalyst

105

pore plugging issues, increase the accessibility of highly dispersed active sites by large size

106

reactant molecules and minimize diffusion control process during the reaction (9, 10). Also it

107

was recently found that the catalyst deactivation in slurry-phase hydroconversion, in which

108

unsupported catalysts are used, is likely different from the deactivation observed on supported

109

catalysts (11).

110

There are two types of catalysts for slurry-phase hydrocracking, heterogeneous solid powder

111

catalysts and homogeneously dispersed catalysts classified as water-soluble catalysts and oil-

112

soluble catalysts (9, 12). In heterogeneous solid powder catalyst, the active catalytic phase is a

113

solid mixed with the feed at the beginning of hydroprocessing. The homogeneously dispersed

114

precursors consist of catalyst added to the feed in the form of a precursor (water soluble or oil

115

soluble non-catalytic compound) that transforms into the catalytic active phase after an

116

intermediate step of activation in situ or during reaction conditions. Catalytic precursors have the

117

advantage that prior being added to the reaction mixture, a dissolution can be made (in water or

118

in oil according to the water soluble or oil soluble nature of the precursor). Then, the dissolution

119

is mixed with the feed to form a dispersion where the precursor gets well distributed all over the

120

reaction mixture. The former is no longer used because of the difficulty of separation and

121

equipment wear caused by the high dosage (13). On the other hand the water-soluble catalysts

122

are preferred over the oil-soluble catalyst due to its lower cost (14). Homogeneous dispersed

123

catalysts use transition metal compounds typically molybdenum, cobalt, iron and nickel as

124

naphthenates or multi-carbonyl compounds. Molybdenum compounds are preferred to be used as

125

homogeneously dispersed catalysts due to their high hydrogenation activity (15-19).


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Panariti et al. (20) studied the effect of operating conditions over a wide range of catalyst

127

loads, 0-5000 ppm. It was observed that at any level of reaction severity the coke formation

128

increased at high catalyst concentrations, and to avoid this situation it is recommended a low

129

catalyst load, around 50-250 ppm. Ortiz-Moreno et al. (21) studied the effect of loads from 330-

130

1000 ppm in hydrocracking of Maya crude oil at mild conditions in a slurry batch reactor. It was

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first observed that catalyst load makes no difference in the thermal process, however the product

132

distribution during the hydrocracking of heavy crude can be directed by changing the amount of

133

catalyst and the operating temperature. On the other hand with variation of catalyst loads, it was

134

also possible to analyze the thermal and catalytic hydrocracking on the liquid fractions, and the

135

different products obtained as shown by Ortiz-Moreno et al. (21). It was concluded that the

136

catalytic hydrocracking could be divided in two general stages according to the conversion of

137

vacuum residue (VR): below 50% VR conversion that is dominated by the catalytic reactions and

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the catalyst is able to inhibit the formation of both coke and asphaltenes; and above 50% VR

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conversion dominated by thermal reactions. In this stage the oil phase becomes incompatible to

140

asphaltenes due to the decrease of resins and the increase of light ends, promoting the

141

aggregation of the most dealkylated asphaltenes and its subsequent transformation to coke. The

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duration of the first stage is expected to be determined by the catalyst load, temperature of

143

operation, and the initial ratio of light/heavy fractions in the feed. These results show that the

144

optimal catalyst concentration of catalyst would depend on different variables such as operating

145

conditions, as well as external factors; use of recycle, catalyst separation, economic balance,

146

pitch specification and even environmental issues.

147

Modeling


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In the modeling of slurry-phase reactors due to the small diameter of the catalyst particles

149

( ≤ 150 μm), it is assumed a very good homogeneity between the solid and liquid phase so it

150

is considered that the catalyst is part of the liquid forming a pseudo-homogeneous phase (slurry

151

phase) and it is necessary to consider the profile of solid concentration as well as the settling

152

velocity of the particles (6, 22). The slurry column hydrodynamics is very complex to model,

153

however, if experimental or phenomenological correlations for the hydrodynamic variables are

154

available, the analysis could be simpler. The dispersion and interfacial heat and mass transfer

155

fluxes, which often limit the overall chemical reaction rates, are closely related to the fluid

156

dynamic of the system through the liquid-gas contact area and the turbulence properties of the

157

flow.

158

The development of mathematical models describing the behavior of catalytic processes

159

involving three phases is complicated since it is necessary to consider various aspects, from the

160

dispersion and interfacial gas-liquid and liquid-solid heat and mass transfer fluxes, which are

161

closely related to the fluid dynamic and turbulence properties of the flow, to pore diffusion and

162

reaction kinetics (22). However the knowledge of the system behavior in steady-state or dynamic

163

operation is essential in determining proper reactor design and scale-up, and in correctly

164

interpreting data in research and pilot-plant work as well as for the trial and start-up period and

165

optimizing the operating conditions in manufacturing.

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Classification

167

Froment et al. (23) proposed a general classification for adiabatic and non-adiabatic fixed-bed

168

reactors, this classification goes from the simplest model, which considers plug-flow, to the most

169

complicated, which involved axial and radial dispersion as well as interfacial and intrafacial

170

gradients. In this classification, the catalyst is big enough to be considered as one phase. It also


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takes into account the bulk gas phase temperature and concentration. These variables could be

172

the same at the solid surface (pseudo-homogeneous models) or different (heterogeneous models)

173

as shown in Figure 2.

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For two phase bubble columns and slurry bubble column reactors, the most popular

175

classification is based on the N+1 model proposed by Tomiyama (24) and Tomiyama and

176

Shimada (25), which considers N+1 phases, one phase corresponds to the slurry phase, and the N

177

phases correspond to gas bubbles of different size. While this classification is similar to that one

178

proposed by Froment et al. (23), its based on the system hydrodynamics and not on the state

179

variables T and C. Therefore the classification presented in Figure 3 involves both

180

classifications, in which it is first necessary to define the flow rate of the gas phase, either a

181

simple model with one gas phase or with N gas phases. Once the flow of the gas phase is

182

established, the following is to determine if the reaction is carried out in the liquid phase

183

(pseudo-homogeneous) or on the surface and inside of the catalyst (heterogeneous). This would

184

depend on the structure and size of the catalyst, for example with non-porous catalysts with very

185

small particle diameter the reaction takes place practically in the liquid phase. However for large

186

particle size and porous catalysts the reaction is carried out in the solid.

187

The flow regimes in bubble and slurry bubble columns are classified according to the

188

superficial gas velocity. Two types of flow regimes are commonly observed in slurry and bubble

189

reactors; homogeneous (bubbly flow) regime and heterogeneous (churn turbulent flow) regime.

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Another regime is called slug flow regime, which has only been observed in small diameter

191

laboratory columns at high gas flow rates.

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The homogeneous flow regime is assumed when the high pressure of the system and low gas

193

velocities prevent bubble coalescence. Then the single-phase model can be used. The


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homogeneous flow is established when the difference between density of solids and liquid is

195

small or if the liquid viscosity is high. Also operating at low gas flow rates where small bubbles

196

of gas (1-10 mm) are uniformly distributed into the slurry phase (L+S). The bubble size and

197

uniformity depend on the properties of the liquid, the design of the gas distributor and the

198

column diameter, which are defined for a uniform bubble size distribution in the axial and radial

199

direction of the vessel.

200

N gas phase models are used when the churn turbulent flow regime is found inside the reactor.

201

This flow is presented when there is a large gas fraction in a system with a high gas and low

202

liquid velocity, is frequently observed in large diameter columns at industrial scale. Typically at

203

the beginning of this regime the number of bubbles is low, which is called as ideally-separated

204

bubble flow. In this type of flow the bubbles do not interact each other directly or indirectly but

205

as the number of bubbles increases they started colliding each other and their size get reduced.

206

Suddenly a situation comes when they tend to coalesce to form cap bubbles, and the new flow

207

pattern formed is called churn turbulent flow, which in reality has a broad size distribution. This

208

model considers N bubble types plus the slurry phase, therefore each bubble type would have

209

their respective mass, heat and momentum equations in order to describe the system dynamics.

210

Nevertheless, previous studies based on the extend of the two-phase (“dilute” and “dense”

211

phases) model proposed by van Deemter (26), have shown that in a slurry bubble column

212

operating in the churn turbulent flow regime the gas phase can be split up in a “large” bubble

213

population and a “small” bubble population (27-29). In this heterogeneous system, small bubbles

214

combine in clusters to form large bubbles (20-70 mm). These large bubbles travel up through the

215

column at high velocities (1-2 m/s), in a more or less plug-flow manner. Though this is still a


10

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very complicated model, it would lead to a considerably simplification to the fluid dynamic

217

equations of the system (30-31).

218

Due to the high temperature and pressure conditions in heavy oil hydrocracking, large amount

219

of hydrogen, as well as oil and catalyst properties, the typical operating regime is the

220

homogeneous flow. Therefore when modeling these systems, one of the main considerations is

221

establishing the homogeneous gas flow inside the reactor. Hence in this review only models

222

concerning to homogeneous gas flow would be discuss.

223

Model complexity

224

There is not a general rule to select the level of sophistication of a reactor model. The

225

complexity of a model is closely related to the purpose of the investigation. In most of the cases

226

selecting the simplest model and adding complexity as the error between experimental and

227

calculated data is reduced, is a typical strategy. The simplest models are built under ideal

228

considerations neglecting gradients in concentration in all spatial directions (perfect mixing), or

229

recognizing them only in the principal flow direction (plug-flow), also a common assumption is

230

a uniform concentration of the solids throughout the reactor. These models can be used in SPR

231

operated as STR. On the other hand, while slurry and bubble column performance often can be

232

fitted with axial dispersion models (ADM), decades of research have failed to produce a

233

predictive correlation for the axial dispersion coefficient. The so-called computational fluid

234

dynamics (CFD) models solve the fluid dynamics with a numerical solution of the Navier-Stokes

235

equations and a set of partial differential equations (PDE). These are the most sophisticated

236

models but also the most difficult to solve due to their high non linearity, even two phase

237

transient simulations require high computational cost (32). Most of CFD models applied to slurry

238

and bubble columns are focused on the hydrodynamics of the system, neglecting mass and heat


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transfer effects in some cases, which clearly represents a limitation to reactive systems. From the

240

point of view of reaction engineering, a complex model for the field of velocity inside the reactor

241

would not offer advantages if the profile of concentrations of substances involved is described

242

poorly.

243 244

The reliability of a model either ideal, ADM or CFD, is function of the validation method such as testing it with independent data and thermodynamic properties at the reaction conditions.

245

Models for slurry reactors

246

Homogeneous bubble flow regime models

247

Reactor models that feature a practical way to design two/three-phase reactors and that provide

248

a basic understanding of the chemical process on the semi-industrial or even industrial scale,

249

have been published only rarely in the usual scientific literature (33), and slurry-phase reactors

250

are not the exception. Unfortunately only CFD models are often implemented in as much detail

251

as possible for the simulation of slurry hydrocracking reactors, no matter that the complex

252

modeling and computational effort required are extremely time-consuming and costly. However,

253

it has been found for simple reaction systems such as hydrogenation, that a three-phase slurry

254

reactor dynamics can be well represented by axial dispersion models where deviation from plug-

255

flow is described using an axial dispersion coefficient. For example, Toledo et al. (34) proposed

256

two dynamic non-isothermal axial dispersion models applied to describe the dynamic behavior of

257

the reactor during the hydrogenation of O-cresol on / catalyst. The authors conclude that

258

the most complete model which includes internal mass transfer, reproduces in a better way the

259

dynamic behavior of the reactor, however it is possible to use the simplified model if there is not

260

enough experimental information about catalyst properties, in fact this model is the most

261

frequently used in different reactions involving different types of catalyst particles. Both models


12

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Energy & Fuels

have been used in different applications of control and optimization (35-40). Shahrzad et al. (41)

263

presented a dynamical axial dispersion model that depicts hydrate formation in a slurry

264

bioreactor. The model considers mass transfer phenomena between gas and liquid as well as

265

liquid to solid phases. Also the particle velocity is considered along with the term of reaction,

266

Chen et al. (42) proposed a steady-state axial dispersion model for the direct dimethyl ether

267

(DME) synthesis process from syngas in which the dispersion and velocity of solid particles

268

were introduced and mass transfer resistance was ignored in liquid-solid phase. The authors

269

concluded that the particle and reactor diameters are the two main factors influencing

270

concentration distribution uniformity. On the other hand for hydrocracking reactions, it has been

271

tested that the field of velocity does not influence on a great way the conversion along the reactor

272

(43). Therefore it is expected that an axial dispersion model with adequate kinetic and

273

hydrodynamic parameters would be enough to describe slurry-phase hydrocracking reactors.

274

The work by Parulekar and Shah (44) attends in a practical way the hydrocracking in slurry-

275

phase reactors. This model consists of gas, liquid and solid mass balance equations formulated

276

under the following considerations:

277

•

Isothermal operation.

278

•

Gas phase is assumed to behave according to the ideal gas law.

279

•

All reactions are purely catalytic under the conditions of operation considered.

280

•

The axial dispersion model is assumed to be applicable in the case of non-volatile

281

liquid components.

282

•

The gas phase is assumed to move as plug-flow.

283

•

The reactor is of concurrent up-flow type.


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284

•

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All the global reaction rates are expressed in terms of the gas-phase concentration of

285

hydrogen since it is difficult to measure the liquid-phase (oil in the case of

286

hydrocracking) concentration of hydrogen.

287

They proposed a kinetic model based on three components: (AL, heavy oil; BL, light oil; and

288

CG, volatile product), and a hydrocracking reaction, all represented by a simple power-law

289

approach Eq. (1-4). Unfortunately the authors don’t give information about catalyst

290

characteristics.

291 292 293 294 295 296 297 298 299 300

→ =

(1)

→ =

(2)

→ =

+" →

(3)

" # = #

(4)

The model equations are as follows: $%& 'ℎ%&)

:

+,-. /0 1 +2

"56 'ℎ%&) : +2 789 +

"56 'ℎ%&) : +2 789 +

= −# 4

;− +2

+

+/:

;− +2

+/@

AB &CD6CAE : +2 789 +

+2

+ +2

− 4 − 4 ??/ = 0

+ 4 − 4 ??/ = 0

; − +2 GH − ,HI 1 J = 0 +2

+/F

+

(5) (6) (7) (8)

The major complication to solve these equations is that all hydrodynamic parameters (4 , 4 ,

301

4 , 89 , 89 ) as well as superficial velocities (H , H , H ) vary axially. Therefore, dynamic

302

equations for axial velocities are needed. Thus it was assumed that superficial velocities vary as

303

function of the reactive absorption rate into the catalyst and products desorption rate (Eq. 9-10).

304

K

305

L

+-. +2

+-= +2

= 4

= 4 ,# ?? − ??/ 1

(9) (10)


14

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306

Energy & Fuels

Though this model is limited by particle sizes between 75 and 250 MN with low solid loading

307

(4 ≤ 0.15) and a simple kinetic model, is possible to observe the behavior in steady-state for

308

the different variables like pressure, temperature and dimensions of the reactor, and how they

309

give an increase in products yield, whereas a maximum in products yield can be found by

310

incrementing the rest of analyzed variables. Thus the optimum operating conditions in the slurry-

311

phase hydrocracking reactor can be established. Other quantitative results show the behavior of

312

solid concentration along the reactor. In this manner, it is observed that for low particle

313

diameters, the solids distribution along the reactor remains practically constant for a given liquid

314

velocity, on the contrary when particle diameter is increased, it is noted an accumulation of

315

particles at the bottom of the reactor. Although the profile of solids concentration could vary as a

316

function of liquid velocity and column diameter, these variables have no great influence in the

317

particle distribution. Certainly this is a simple model, however it could be used as a reference for

318

future works in slurry-phase hydrocracking considering more detail kinetic models as well as

319

transitory state, gas-liquid mass transfer or even more complete axial dispersion models.

320

Carbonell and Guirardello (45) studied an isothermal reactor based on the continuity and

321

momentum balance equations using an Eulerian approach applied in the hydrocracking of heavy

322

oils in a slurry phase reactor operating at severe conditions of temperature (350-500 ºC) and

323

pressure (7-25 MPa). They considered that the thermal cracking reactions do not interfere in the

324

hydrodynamics of the system due to the high mixing of the liquid phase and the low gas

325

absorption rate. Under these conditions a single bubble class model could be assumed. Their

326

simulations were performed in two steps, first fluid dynamic variables were determined as a

327

function of radial position and then oil cracking conversion was obtained. The power-law

328

kinetics was based on experimental evidence. Feed and products are divided into several boiling


15

Energy & Fuels

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Page 16 of 72

329

range lumps, where each lump is considered a single chemical species with a single cracking rate

330

constant. The model consists of the following assumptions:

331

•

Steady-state operation.

332

•

A symmetric turbulent axial flow.

333

•

Single bubble model.

334

•

A zero model turbulence in the mixing bed.

335

•

A parabolic radial distribution for gas holdup.

336

•

Dominant convection in the axial dispersion.

337

•

Dominant dispersion in the radial dispersion.

338

•

First-order irreversible reactions.

339 340 341 342 343 344 345

The hydrodynamic equations for the slurry and the gas phases are:

B6P 'ℎ%&): Q +Q 74 M +

RSS +TF= ; +Q

$%& 'ℎ%&): Q +Q 74 M +

RSS +T. ; +Q

− 4 +2 − VL + W = 0 +U

− 4 +2 − V4 − W = 0 +U

(11) (12)

Where F is the interfacial drag force ( / N reactor) proposed by Torvik and Svendsen (46), X

axial velocity (N/&), radial position, 4 holdup (dimensionless), M RSS effective viscosity (Y% ∙

&), [/ radius of the reactor. The mass balance is: 4 L 6

+/\ +2

= ]^ L ^ + ∑ `a,^ L ^

(13)

346

Despite of isolating the hydrodynamic behavior of the system from the chemical reactions,

347

concordance with experimental data was obtained, although a more detailed model, with a more

348

complex study of the kinetics is required for scaling up and improvements in the operation.

349

Matos and Guirardello (47) presented an isothermal CFD model which includes momentum

350

equations, based on the kinetic network of six lumps presented by Krishna and Saxena (48) for

351

thermal hydrocracking reactions. The lumps are heavy and light aromatics, naphtenes and


16

Page 17 of 72

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Energy & Fuels

352

paraffins. The hydrocracking is assumed to be thermal and the catalyst is only used to avoided

353

coke formation and for the removal of heteroatoms. The main assumptions are a pseudo-

354

homogeneous system (SL+G) where the solid distribution is not taking into account due to the

355

very small diameter and the small terminal velocity of the particles, gas phase is composed

356

mainly by hydrogen, and oil completely saturated with dissolved hydrogen. Due to hydrogen is

357

found in excess inside the reactor, the reaction is independent of the hydrogen consumption.

358

Because of the lack of experimental information on hydrocracking systems, this model was

359

validated by comparing different experimental data available in the literature for the air-water

360

system. Thought this model can describe in a good manner the behavior of a SPR, it is quite

361

complicated to solve because it includes the velocity distribution for gas and slurry phases along

362

the reactor.

363

Matos and Nunhez (43) presented a fluid dynamic model based on the same considerations as

364

in Matos and Guirardello (47) using the same kinetic model of Krishna and Saxena (48), but in

365

this case the work is focused on how the feed input affects the flow fields and the reactor

366

conversion. Although unsupported of experimental data, their theoretical results show that the

367

fluid dynamic fields inside the bubble column reactor do not affect considerably the reactor

368

conversion.

369

Recently Matos et al. (49) presented a CFD model to estimate operating conditions that

370

minimize sulfur and organometallics concentrations before the petroleum is processed. In the

371

modeling it is considered the difference in density between the catalyst and the slurry-phase is

372

small thus the catalyst does not settle and a fluid dynamic model is able to suspend the catalyst

373

was considered to be enough. The model considers the petroleum to be composed of pseudo-

374

components and HDS and HDM reaction have a first-order kinetics decomposition controlled by


17

Energy & Fuels

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Page 18 of 72

375

diffusion and occurring on the catalyst pores. The chemical components in the crude mixture

376

present very low reaction rates, as a consequence there is low gas consumption and the mass

377

transfer between the phases is negligible. But the main contribution in this work is that the model

378

includes a kinetic expression for the activity reduction of the catalyst as a function of the catalyst

379

pore characteristics.

380

Heterogeneous bubble flow regime models

381

Operation at low gas velocities in homogeneous bubbly flow regime was considered to be

382

preferred in industrial slurry-phase reactors. Furthermore, most of the literature models have

383

been focused on operation at relative low superficial gas velocities (below 0.10 m/s). However

384

the growth of industrial demand generated plants to operate at higher production rates, which

385

causes the processes involved increasing operating conditions such as gas and liquid flows. As a

386

consequence this generates heterogeneous flow conditions inside the reactor. In industrial scale

387

slurry reactors are commonly used for F-T and chemical synthesis, therefore most of the

388

modeling find in literature refer to these systems (50-60). On the other hand, the latest study of

389

SBCR modeling, is presented by Khadem-Hamedani et al. (61). They showed a comparison

390

between models in homogeneous and heterogeneous flow regimes for the hydrodesulfurization

391

of diesel fuel. The mass and energy balances, as well as the model parameters are based on the

392

considerations proposed by Mills et al. (53) and de Swart and Krishna (29). Both models

393

reproduce in a good way the reactor behavior, however as it was expected, the more detailed

394

model (heterogeneous model) shows better results in the validation with experimental data.

395

These results are of great importance because they demonstrate that the parameters proposed by

396

Mills et al. and de Swart and Krishna generated for F-T synthesis for heterogeneous regime, can

397

be used in HDS of diesel, which have similar conditions of pressure and temperature to HCR.


18

Page 19 of 72

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Energy & Fuels

398

Proposed generalized model

399

Equations for the generalized model

400

Most mass balance equations as well as motion equations are derived from the general

401

equation of continuity and motion, and slurry bubble columns are not the exception. While there

402

are different ways of representing these equations, good approximations of the behavior of this

403

type of reactors have been obtained using an Eulerian approach. The fundamental form of the

404

multi-fluid continuity equation for phase c has been presented by several authors (25, 32, 62,

405

63). In this review the equations are presented for each component in the c phase, thus the

406

reaction rate and convective mass transfer are also considered. The equations are:

407

d7ef /\ ;

408

d,ef of /f Kf 1

409 410

dI

f

+ ∇ ∙ ,4S ^ hS 1 = ∇ ∙ ,4S 8S ∇^ 1 + ∑kl Sm ^ S

dI

5,pS , pvwx 1

S

,Si ,Sfji 1

+ ^n

+ ∇ ∙ ,4S LS 'S pS hS 1 = ∇ ∙ ,4S qS ∇pS 1 + MΦ + Δ

Q

(36) + 5,pS , pt 1 + 5,pS , pu 1 +

(37)

This governing set of partial differential equations consists of the continuity equations for the

411

+ 1 phases for components, and the energy and the momentum equations for + 1 phases.

412

It holds that:

413

d,ef of 1

414 415 416 417

dI

+ ∇ ∙ ,4S LS hS 1 = 0

(38)

∑kS 4S = 1

(39)

4S 6S = HS

(40)

Equation (36) shows the classical terms of transitory state, convective and molecular fluxes, as

well as the terms ∑kl Sm ^

,Si ,Sfji 1

which is related to the convective fluxes between phase

418

resistances for each component, and the reaction rate ^n . In energy equations (37), appear the

419

terms related to the transient state temperature, heat exchange caused by convective flow,

420

conduction, viscous dissipation energy (usually negligible, except in systems with large velocity


19

Energy & Fuels

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Page 20 of 72

421

gradients (64)), the generation term due to the chemical reaction, the heat fluxes, function of the

422

temperature of each phase, the temperature of fluid exchange, interfaces and solid temperatures.

423

Being strict this set of equations consists of three general equations, for the gas, liquid and solid

424

phases, but for slurry-phase reactors it is commonly considered to simplify the gas and liquid

425

phases as a continuous phase in which the temperature is the same due to the large area of

426

contact and favorable transfer coefficients (34).

427

As mentioned before, this is a very complex PDE system and particularly for hydrocracking of

428

heavy petroleum where various reactions occur simultaneously, e.g. Hydrodesulfurization

429

(HDS), Hydrodemetallization (HDM), Hydrodenitrogenation (HDN), Hydrodeasphaltenization

430

(HDA), etc. However, some considerations can be done in order to simplify this model. Taking

431

into account that the model of slurry-phase reactors is similar to EBR (22), and the reacting

432

system is the same as that presented by Mederos et al. (65), some of their general criteria can be

433

adapted. For example, though the values of mass and heat transfer coefficients are distinct, the

434

expressions for mass and heat transfer resistances between phases are expected to be the same.

435

Also due to the chemical reactions are merely catalytic, the conversion will be directly associated

436

with the concentration of catalyst particles inside the reactor. However, unlike EBR in SPR the

437

solid catalyst is found in the wake of the liquid forming a L-S suspension. This unique

438

characteristic generates a greater degree of difficulty in the approach of the mathematical model,

439

since system hydrodynamics becomes more complicated. For the bubble column slurry

440

operation, two suspension states may exist: namely, complete suspension in which all particles

441

are in suspension, commonly described by the axial sedimentation-dispersion model, and

442

homogeneous suspension, in which the particle concentration is uniform throughout the reactor


20

Page 21 of 72

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Energy & Fuels

443

(66). In the proposed generalized model the sedimentation-dispersion model is taking into

444

account. Other considerations are:

445

•

Heterogeneous bubble flow, composed by small bubbles (SB) and large bubbles (LB).

446

•

The Liquid-Solid (L+S) suspension behaves as a homogeneous phase due to the small

447 448

catalyst particle size, whereas the gas phase bubbles up through the suspension. •

449 450

Liquid and gas properties (mass and heat dispersion coefficients, specific heats, densities, viscosities) constant along the whole catalytic bed.

•

451

Catalyst properties (porosity, size, activity, effectiveness, etc.) are constant along the whole catalytic bed.

452

•

Due to the small particle size, wetting efficiency is considered to be the unity.

453

•

Inside the catalyst particle, mass and heat effective diffusivity coefficients may also be

454 455 456 457 458

assumed constant. •

The liquid phase is assumed to be in thermal equilibrium with the gas phases. Then the energy equation can be formulated for the continuous phase f defined as (SB+LB+L).

A detailed description of each term of Tables 4 and 5 is shown by Mederos et al. (65), except for the solid dispersion terms, which are presented below.

459

Solids concentration

460

Equation (E) in Table 4 describes the dynamic behavior of solid concentration in a solid-liquid

461

mixture along the reactor through the Sedimentation-Dispersion Model (SDM). This model

462

considers a solids axial dispersion flux and a solids sedimentation flux superimposed on the

463

average slurry convection flux. One of the main variables in this equation is the particle settling

464

velocity, which is the result between the liquid and particles terminal settling velocities as shown

465

in Figure 4. Terminal settling velocity 6I is defined as the highest velocity reach for particles


21

Energy & Fuels

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Page 22 of 72

466

immersed in a fluid, it occurs when the drag and gravity forces are equal. For spherical shapes it

467

typically has the form:

468

6I =

y+z

{|=

(41)

469

By definition, the terminal settling velocity could be positive or negative depending on the

470

density difference between solid and liquid phases and on the coordinate system adopted. On the

471

other hand, the prediction of the particles settling velocity is found in the literature given by

472

different correlations, for example Parulekar and Shah (44) and Kojima et al. (67) consider the

473

settling velocity to be the same as the terminal settling velocity. Recently, Sehabiague et al. (57)

474

applied the correlation proposed by Kato et al. (68), where the particle settling velocity is

475

proportional to the superficial gas velocity and to the liquid fraction in the slurry phase:

476

6 = 1.336I 7T . ; -

~F

.

.

(42)

477

Most of the models that use the sedimentation dispersion model consider a constant average

478

value of the liquid and gas superficial velocities, then an analytical solution of this equation is

479

possible as a function of the Peclet particle number. The mass balance on the external surface of

480

catalyst particles is given in Equations (F) and (G) in Table 4. The gradients are the product of an

481

effective diffusion of liquid and gas phases through the catalyst surface. It also has the generation

482

terms, which include the catalyst effectiveness factor associated to reaction in the surface and at

483

the inner of catalyst particle, however for slurry-phase reactors, the catalyst commonly used in

484

fixed-bed reactors is crashed to generate small catalyst diameters, which are know to have a high

485

catalyst effectiveness (69), then it could be assumed to be the unity.

486

Initial and boundary conditions

487

All transitory mass and energy balance equations presented in Tables 4 and 5 have initial

488

(C = 0) and boundary conditions (C > 0), which relate the surface properties to the bulk ACS Paragon Plus Environment

22

Page 23 of 72

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Energy & Fuels

489

properties of the reacting system. Considering a symmetric reactor of radius R in which gas,

490

liquid and solid phases of radius = R /2 enter at the bottom of the reactor at = 0 and that

491

the reactor outlet is located at =

492

for the transitory state are typically set to the inlet properties of the system

493

^ = ^ , = , S^vwx = S^vwx , S^\ = S^\ , pS = pS

494

S

S

, all coordinate system has been fixed. The initial conditions

(43)

These conditions could vary depending on the considerations made for the system under study,

495

for example in some cases it is considered that the liquid is saturated with the gaseous

496

compound, while in others there is not initial concentration of gas in the liquid phase. Also the

497

initial catalyst concentration could vary in case that recirculation is used as well as the catalyst

498

activity. Moreover since the system is described by a set of PDE, four boundary conditions are

499

needed in order to describe the longitudinal and radial variation of the system properties ( = 0,

500

0 ≤ ≤ [, =

501

form of Danckwerts’s conditions:

502

%C = 0,

503

%C = ",

+ +2

+ +2

, 0 ≤ ≤ [, 0 ≤ ≤

, = 0, 0 ≤ ≤

, = [), which typically have the

=

(44)

=0

(45)

504

For the case of the reactor bottom at = 0, 0 ≤ ≤ [, there are different ways of setting the

505

inlet conditions, for example some authors consider that the axial dispersion of mass and

506

temperature is too small compared with the convective term, therefore the gradients at the inlet

507

could be omitted and the conditions are the same as in Equation (43). In order to describe the

508

dynamics of solid concentration, two conditions are needed due to it is a second-order partial

509

differential equation, first at z = 0, 0 ≤ r ≤ R Danckwerts s conditions are the most commonly

510

used. In this case the inlet concentration of catalyst is obtained as a function of the weight

511

fraction of solid in the feed slurry through:


23

Energy & Fuels

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

512 513

=

Page 24 of 72

(46)

Instead of this equation, simple average concentrations could be also used (57). At =

,

514

0 ≤ ≤ [ the condition is given by a simple balance where the flux of solid entering the reactor

515

must equal that leaving the reactor:

516

H =

517

(47)

On the other hand, considering internal and external particle diffusion effects in the modeling

518

could lead to a more realistic representation of real reactors, when modeling catalytic slurry

519

phase reactors, due to reduced dimensions typically found in practice, these effects are

520

commonly neglected and it is assumed that the reaction takes place on the liquid phase. However

521

the conditions proposed in Table 4 for the concentration of component i component at the solid

522

phase would be ignored.

523

Estimation of model parameters

524

Even in the most complex models, it is necessary to evaluate several parameters and chemical

525

properties of the system. An adequate description of the system dynamics needs reliable data on

526

parameters which are specific for the slurry-phase reactors � , , �, and parameters which

527

are not specific for the type of reactor (′, 8^ ), and particle and fluids properties (M, L). Those

528

parameters can be estimated with existing correlations, whose accuracy is of great importance for

529

the whole robustness of the model. Density and viscosity of the liquid phase (heavy oil) play an

530

important rule in system hydrodynamics. For slurry systems these properties could be affected by

531

the presence of solid particles. High concentrations of particles in the feed oil could lead to

532

notorious changes in the viscosity of the liquid phase. There are correlations that estimate the

533

viscosity and density of the slurry phase as a function of the solids concentration (29, 61). In

534

general all liquid and gas phase properties at the operating conditions could be estimated through


24

Page 25 of 72

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Energy & Fuels

535

different correlations reported in the literature as reported by Mederos et al. for heavy oil

536

hydrocracking (65). On the other hand, there are a few reviews in the literature dealing with

537

slurry-phase reactors and bubble columns. Chaudhari and Ramachandran (66), Shah et al. (70)

538

and Fan (71) presented a very complete review of previous works published until the 80 decade

539

for parameters estimation for slurry and bubble column reactors. Beenackers and Swaaij (72)

540

focused only on the mass transfer phenomena in slurry-phase reactors, and more recently

541

Kantarci et al. (30) reviewed bubble column reactors with application to bioprocess. However

542

most of the parameters reported were obtained for two phase and low viscosity systems, typically

543

Air-Water or Air-Organic Liquids. In order to better reproduce the dynamics of the reactor, one

544

should select the parameters that were obtained under similar conditions to those used in the

545

modeling system of interest. Leonard et al. (73) presented a review of bubble column reactors

546

operating in high pressure and temperature. Their work is focused on overhaul the effect of

547

pressure and temperature on hydrodynamic variables such as gas holdup, as well as mass transfer

548

parameters and axial dispersion coefficients. On the other hand, Mederos et al. (65) presented a

549

summary of the typical correlations used in hydrocracking systems for diffusion coefficients,

550

viscosities and densities, which are needed in mass transfer calculations.

551

Gas holdup

552

Gas holdup is one of the most important parameters characterizing the hydrodynamics of BCR

553

and SBCR, which is defined as the percentage of gas volume in the two or three phase mixture

554

inside the reactor. The gas holdup in conjunction with the knowledge of mean bubble diameter

555

allows for the determination of interfacial area and thus leading to the mass transfer rates

556

between phases. It depends mainly on the superficial gas velocity, but it is also sensitive to the

557

physical properties of the liquid, gas and solid particles, column dimensions, operating


25

Energy & Fuels

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Page 26 of 72

558

temperature and pressure and gas distributor design. For practical simplicity it is usually

559

estimated using the pressure profile method (74), in which the gas holdup is obtained from the

560

static pressure drop as:

561

4 = 1 −

562

(48)

Where ϕ and ϕ are the volume fractions of liquid and solid particles in the slurry phase,

563

respectively:

564

ϕ =

565

U

y

=

F =

, ϕ =

F

F =

(49)

The term V∆L in Equation (48) has been approximated to the static pressure

566

difference ∆Y , when no gas is flowing in the column (75). In these equations the effect of wall

567

shear stress and liquid acceleration due to void changes are neglected. When more reliable

568

models are required, predictions of radial gas holdup profiles would lead to better understanding

569

of system hydrodynamics. There are a large number of correlations proposed for gas holdup

570

especially for two-phase bubble columns (30, 70), although there is no a general correlation

571

applicable to any system mainly due to the extreme sensitivity of the holdup to the materials

572

properties and to the trace impurities (76). It has been pointed out that for some slurry systems

573

the presence of non-catalytic solids does not affect the gas holdup significantly (70, 77).

574

However, recent experimental results focused on catalytic systems show that increasing the solid

575

concentration decreases the gas holdup to a significant extent (78).

576

There are several correlations of gas holdup for slurry-phase reactors (79-89). Unfortunately

577

most of these correlations have several limitations. On the one hand, these correlations were

578

developed for aqueous systems in small-diameter reactors operating under atmospheric pressure

579

or ambient temperature, and on the other hand the majority of solids were non-catalytic particles.

580

This leads that some authors choose solving the dynamic of the holdup along with the state


26

Page 27 of 72

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Energy & Fuels

581

variables of the system introducing turbulence equations, despite the computational effort.

582

Addressing this situation, the correlations proposed by Behkish et al. (58) predict the total holdup

583

of single bubbles and large bubbles in pseudo-homogeneous and heterogeneous flows in BCR

584

and SBCR, operating under a ranged of elevated pressures (P = 0.1-15 MPa). In their study,

585

several literature data were considered in order to obtain the correlations. Afterward, the

586

agreement between predicted and experimental values were evaluated, presenting acceptable

587

results with a standard deviation between 15-20%.

588

For hydrocracking systems, most of the literature is focused on kinetic or catalyst studies at

589

batch conditions, thus validation of hydrodynamic parameters is complicated. At pilot scale and

590

based on previous studies focused on the effect of superficial gas velocity, interfacial tension and

591

column diameter, Parulekar and Shah (44) proposed that the gas phase holdup in a slurry

592

hydrocracking system operating at 10 MPa and 350 ºC was proportional to the variables

593

according to Equation (50).

594

4 = 0.0866l. H. 8/l.{

595

(50)

While this correlation was implemented successfully in the model in order to obtain the

596

quantitative behavior of the system, the lack of experimental data does not allow to corroborate

597

its validity or even the model itself. Recently the model for diesel HDS of Khadem-Hamedani et

598

al. (61) includes hydrodynamic parameters obtained by Deckwer et al. (90), Krishna and

599

Ellenberger (52), Maretto and Krishna (51), de Swart and Krishna (29) for F-T Synthesis. It

600

should be noted that good results were obtained in the model validations using these

601

approximations.

602

Moreover in EBR

− H >

+

− H >

−

Modeling of Slurry-Phase Reactors for Hydrocracking of Heavy Oils

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