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Fuel xxx (2014) xxx–xxx

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Fuel

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Vapor–liquid equilibrium of hydrogen–hydrocarbon systemsand its effects on hydroprocessing reactors

http://dx.doi.org/10.1016/j.fuel.2014.03.0620016-2361/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +5255 91758443.E-mail address: [email protected] (J. Ancheyta).

Please cite this article in press as: Chávez LM et al. Vapor–liquid equilibrium of hydrogen–hydrocarbon systems and its effects on hydroprocessintors. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.03.062

Luz M. Chávez, Fernando Alonso, Jorge Ancheyta ⇑Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas Norte 152, Col. San Bartolo Atepehuacan, C.P. 07730 México, D.F., Mexico

h i g h l i g h t s

� Literature review of VLE of H2–petroleum fractions for hydroprocessing was done.� The state-of-art was established and then an analysis of data were provided.� It was showed the importance of accounting VLE in hydroprocessing reactors.

a r t i c l e i n f o

Article history:Received 5 December 2013Received in revised form 21 March 2014Accepted 26 March 2014Available online xxxx

Keywords:Vapor–liquid equilibriumHydroprocessingH2-pseudocomponents interaction

a b s t r a c t

An exhaustive review of the literature about the vapor–liquid equilibrium (VLE) of hydrogen–hydrocar-bon (H2–HC) systems is reported in this work, including studies where reactor modeling is considered ornot. Hydrocarbons can be pure compounds or petroleum fractions. Reported petroleum fractions are fromgasoline to vacuum residue. The analyzed information was: type of device or cell used to obtain exper-imental data, model used to predict the VLE behavior, and different options to adjust the EOS by interac-tion parameters of H2–HC. Comparisons of the ranges of operating conditions (pressure and temperature)of VLE studies with or without reaction were done. The variations of the distribution coefficients of H2 onHC were compared with respect to the pressure. Several of the studies show a strategy used to charac-terize the oil fraction. It is recognized the importance to consider VLE in the reactor modeling, becauseit affects the calculation of conversion, depending on the properties of the feedstock and operating con-ditions. For future work it is recommended to obtain VLE data for H2–heavy petroleum fractions, to devel-opment appropriate experimental methods to determine the physical properties of pseudocomponentsfrom heavy petroleum fraction, or mathematical techniques to overcome this deficiency. In addition,the use of analysis of phases’ stability in the VLE is suggested to be sure about the number of phases pres-ent in the system to obtain more reliable H2-pseudocomponents interaction parameters.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

One of the most widely used reactors in petroleum refiningindustry is the trickle-bed reactor (TBR). This type of reactor is par-ticularly important for hydroprocessing operations. In a TBR theliquid trickles down over the catalyst in a thin layer and the gasphase flows continuously in between the catalyst particles.

The feeds to hydroprocessing range from naphtha to vacuumresidue. The lightest feed is hydroprocessed in two-phase (gas–solid) reactor while heavier feeds use three-phase (gas–liquid–solid) reactor. The liquid hydrocarbon feed that enters the reactoris partially vaporized in less extent as it becomes heavier. In thecase of straight-run gas oil (SRGO), it has been observed that liquid

vaporization can be as high as 90% depending on reaction condi-tions. However for heavy oils and residua the fraction of liquid thatvaporizes is expected to be lower due to the heaviness of the feed.

At the heavy oil hydroprocessing conditions a significant por-tion of the liquid phase will flash resulting in a change in effectivegas and liquid compositions as well as in the flow rates. In order todetermine the degree of flash an equation of state or data of vapor–liquid equilibrium are necessary. In other words, the reactor per-formance will depend on VLE as well as on the chemical kinetics;because the reaction rate is function of the liquid phase composi-tion which also depends on distribution coefficients’ values (Ki)and liquid densities [1].

The prediction of reactor performance under these circum-stances involves developing two types of information: (1) predic-tion of VLE for multi-component systems at elevatedtemperatures and pressures, and (2) knowledge of the intrinsic

g reac-

http://dx.doi.org/10.1016/j.fuel.2014.03.062

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Nomenclature

AAD absolute average deviation, %�API American Petroleum Institute gravityCCOR cubic chain-of-rotatorsCMG Computer Modeling Group Ltd.CSTR continuous stirred-tank reactorDBF dibenzofuraneDEB diethylbenzeneDMDBT dimethyldibenzothiopheneDMC4 dimethylbutaneEOS equations of stateHDN hydrodenitrogenationHDS hidrodesulfurizationHGO heavy gas oilHVGO heavy vacuum gas oilKi equilibrium distribution coefficientLCO light cycle oilLHSV liquid-hourly space velocityLVGO light vacuum gas oilMS methyl styreneMW molecular weightN number of stages in reactorNC number of componentsPNA paraffins, naphthenes and aromaticsPR Peng–RobinsonPVT pressure, volume, and temperature

RK Redlich–KwongSCF square cubic feetSR straight-runSRGO straight-run gas oilSRLGO straight-run light gas oilSRHGO straight-run heavy gas oilSRK Soave–Redlich–KwongSD standard deviation, %TBP true boiling pointTBR trickle-bed reactorTHN tetrahydronaphthaleneTMC5 trimethylpentaneULSD ultra low sulfur dieselVGO vacuum gas oilVLE vapor–liquid equilibriumWHSV weight hourly space velocityxH2 mole fraction of H2

Greek lettersc activity coefficientcH2 activity coefficient of H2

q density/ fugacity coefficient

0 10 20 30 40 50 60 70 80 90 1000

20

40

60

80

0

20

40

60

80

0

20

40

60

80

0

20

40

60

80

100

Mod

el

Experimental

0.06 kg/kg0.0825 kg/kg

0.105 kg/kg

0.150 kg/kg

0.1275 kg/kg

Mod

el

3 h-1

2.5 h-12 h-1

1.5 h-1

1 h-1

Mod

el

61 kg/cm2

55 kg/cm2

48 kg/cm2

42 kg/cm2

36 Kg/cm2

Mod

el

359 °C

367 °C351 °C

343 °C

375 °C(a)

(b)

(c)

(d)

Fig. 1. Parity plots of the effect of (a) temperature (P = 48 kg/cm2, H2/wax-es = 0.105 kg/kg, WHSV = 2 h�1), (b) pressure (T = 359 �C, H2/waxes = 0.105 kg/kg,WHSV = 2 h�1), (c) WHSV (T = 359 �C, P = 48 kg/cm2, H2/waxes = 0.105 kg/kg) and(d) H2/waxes ratio (T = 359 �C, P = 48 kg/cm2, WHSV = 2 h�1) on conversion (d)without VLE (N) with VLE [6].

2 L.M. Chávez et al. / Fuel xxx (2014) xxx–xxx

kinetics of the reaction. This includes information about how activ-ity and selectivity may change as the composition of the liquid isaltered and how the intrinsic kinetics may change when the cata-lyst is in contact with reactants in the liquid phase in contrast tovapor phase [2].

It is then clear that the knowledge of the experimental solubil-ity of hydrogen in hydrocarbons is quite important for accurate cal-culations of the design and simulation of hydroprocessing TBR.These calculations are usually done through equations of state,which require specific binary interaction parameters that aredetermined experimentally for each fraction [3].

Most of the VLE studies have been conducted with simulatedhydrocarbon mixtures or with light and middle distillates withhydrogen, but the use of heavy crudes or residua is limited, partic-ularly due to the difficulty to carry out the experiments, to charac-terize the oil samples and to obtain reliable data of mass balances.The state-of-the-art indicates that there is a lack of research of VLEeffect on the modeling of hydroprocessing reactors. The main rea-sons for such an absence of VLE studies are the non-easy nature ofexperimental measurements (or simulation), hydrogen handlingand injection, high pressures and temperatures, complicated anal-ysis of samples. There is little experimental data information aboutVLE of H2–oil fractions systems obtained under hydrotreating con-ditions, in particular with crudes oils and residues.

In general terms, the reported results indicate that consideringVLE in the reactor model predicts higher conversion of hydropro-cessing reactions than without taking into consideration VLE[4,5]. Pellegrini et al. [6] showed how to accounting VLE in model-ing of waxes hydrocracking could really enhance the prediction ofthe model when varying the temperature, pressure, WHSV and H2/waxes ratio, as can be seen in Fig. 1.

Akgerman et al. [5] presented simulations employing modelswith and without VLE in an isothermal reactor. The difference inconversion between the predictions of the models is significant.For first reaction order the difference ranges from 24% to 39%.

Please cite this article in press as: Chávez LM et al. Vapor–liquid equilibrium of hydrogen–hydrocarbon systems and its effects on hydroprocessing reac-tors. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.03.062


0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10

Hyd

rode

sulf

uriz

atio

n co

nver

sion

, %

Axial position, m

Too= 350 C

P = 51 kg/cm2

LHSV = 1.5/hgas/oil ratio = 800 NL/kg

Fig. 2. HDS conversion (d) without VLE, (N) with VLE [4].

L.M. Chávez et al. / Fuel xxx (2014) xxx–xxx 3

For second reaction order the difference in conversion betweenmodels varies from <6% at high conversion to >30% at low conver-sion. Chen et al. [4] showed that the total hydrodesulfurizationconversion with VLE was predicted to be higher than that withoutVLE as depicted in Fig. 2.

Only two works were found that take into account the VLE inhydroprocessing of heavy oils, one of them for a vacuum residuein a two-stage ebullated-bed reactor and the other one for anatmospheric residue with a disperse catalyst in a batch reactor.In the former the vaporized fraction was estimated as a functionof conversion, so that it was possible to assess the benefits ofinter-stage separator [7], and in the latter the VLE was determinedby performing an adiabatic flash with PROII software [8].

The absence of VLE data and their use for TBR modeling hasincreased the interest on this type of research in recent years, mostprobably because of the need for having reliable data for properreactor modeling and simulation in order to design hydroprocess-ing reactors for unconventional feeds.

The aim of this work is to review the literature reports about theVLE of hydrogen–petroleum fraction systems, particularly for thecase of heavy oil hydroprocessing. The information is organizedin the following items: (a) low temperature and pressure equilib-rium H2–hydrocarbon systems, (b) moderate to high temperatureand pressure equilibrium H2–hydrocarbon systems, and (c) reactormodeling for accounting VLE.

2. VLE of H2 with hydrocarbons at low and moderate severityconditions

2.1. Literature review

The reports of experimental data of VLE of hydrogen with purehydrocarbons, simulated mixtures and petroleum fractions atmoderate operating conditions were found at temperatures from20 to 400 �C and pressures from atmospheric to 260 kg/cm2. Allof the works make calculations with EOS, except two of them.One proposed a thermodynamic model based on Henry’s lawand Pierotti method to determine the hydrogen solubility inhydrocarbons [9], and the other one was used the methods ofGrayson–Streed, and Chao–Seader [10]. The petroleum fractioncharacterization is performed with pseudocomponents or usingthe PNA (paraffins, naphthenes and aromatics) method withcorrelations of Firoozabadi [11], Lee–Kesler [12] and Two [13,14].

Simnick et al. [15] reported experimental data of VLE in H2/tol-uene mixtures at temperatures of 190–300 �C and pressures of

Please cite this article in press as: Chávez LM et al. Vapor–liquid equilibrium otors. Fuel (2014), http://dx.doi.org/10.1016/j.fuel.2014.03.062

21–258 kg/cm2 in continuous flow apparatus, reducing the resi-dence time, which is beneficial at high temperatures. The datawere used to verify the reliability of the information reported inthe experimental system of Chen et al. [16].

Laugier et al. [17] designed an equilibrium cell based on a staticmethod and developed a sampling mechanism, aiming at testingthe reliability of the experimental setup, specially the samplingsystem. The experimental error was 0.015 in mol fraction and lessdispersion is obtained compared with the work of Simnick et al.[15]. The analyzed mixtures were: H2/2,2,4-trimethylpentane(2,2,4-TMC5) and H2/toluene. They generated isotherms (226 and250 �C; 269 and 295 �C respectively) in both cases, and good agree-ment of the experimental data compared with literature data wasfound, whereby the experimental device was validated. They usedfour different correlations to model their systems: the perturbedhard-chain equation of Gmehling using three different mixingrules, the Soave EOS and two of its modifications by Graboskiand Daubert, and El Twaty and Prausnitz. The better results weregiven by the Gmehling equation, followed by El Twaty and Praus-nitz equation.

Ramanujam et al. [18] presented VLE data for a multicompo-nent system containing hydrogen and simulated coal-derivedliquid mixtures for a temperature range of 154.7–268 �C and apressure range of 21–114 kg/cm2. The simulated liquid mixtureconsists predominantly of light aromatics but also contains signif-icant amounts of heavy aromatics. The recirculation type equilib-rium apparatus was used to perform the experiments. Thedifference between the compositions of the main components inthe two phases (defined like those with mol fractions greater than1%) was in the range of 1–5%. The authors identified that in multi-component systems the H2 solubility is affected when comparedwith their respective binary systems.

Connolly and Kandalic [19] measured gas solubilities for hydro-gen in n-pentane, 2,3-dimethylbutane (2,3-DMC4), cyclohexane,n-decane, m-xylene, 1,4-diethylbenzene (1,4-DEB), and 1-methyl-naphthalene. Also, VLE ratios were measured for some of these sys-tems. The partial molar volume of hydrogen dissolved in the liquidhydrocarbons for all of the systems except 1-methyl-naphthalenewere determined as well. Temperatures and pressures fell in therange of 35–320 �C and 14–169 kg/cm2. To calculate the molarvolume an empirical correlation was used. The experimentalsystem is a static cell with sampling by capillaries. They proposeda correlation for H2 solubility as a function of bubble pressure andhydrocarbon vapor pressure. They fitted the parameters of thecorrelations with experimental information. The mathematicalexpression reported in the work does not reproduce theinformation.

Wiegand et al. [20] modified the SRK cubic EOS in such a waythat prediction of PVT data from 40 model compounds, typicallyof coal oil, becomes possible with an absolute mean deviation ofless than 2% for saturated liquid volumes and vapor pressureshigher than 1 kg/cm2. Additional correlations for binary interactionparameters are obtained by an optimization procedure usingvapor liquid equilibrium data from known heavy hydrocarbonliquid/light gas systems. Experimental VLE data were determinedusing a continuous flow equilibrium cell for the H2/liquid coalsystem in temperature and pressure ranges of 180–340 �C and51–306 kg/cm2 respectively. To characterize the liquid coal(51–459 �C cut, q = 0.914 g/cm3 at 20 �C) a pseudocomponentmodel is used. Six pseudocomponents were formulated.

Luo et al. [9] measured the H2 solubility in model compounds ofcoal liquid such as hexadecane, methylbenzene, 1,2,3,4-tetrahy-dronaphthalene (1,2,3,4-THN), naphthalene, quinoline and1-naphthol at temperatures between 180 and 400 �C and pressuresbetween 3 and 99 kg/cm2. A mathematical model based on Pierottymethod and Henry Law is proposed to calculate hydrogen

f hydrogen–hydrocarbon systems and its effects on hydroprocessing reac-



solubility in the hydrocarbons. The calculated values and experi-mental data showed a maximum average absolute deviation of 6%.

Lin et al. [21] determined H2 and methane solubility in coal liq-uids (204–232 �C cut and q = 0.932 g/cm3; 260–316 �C cut andq = 0.9844 g/cm3, 260–276 �C cut and q = 0.9826 g/cm3, 316–333 �C cut and q = 1.0306 g/cm3, 371–399 �C cut and q = 1.091 g/cm3 at 16 �C) at 190 and 270 �C and pressures up to 258 kg/cm2.The experiments were reported to be different in that bubble pointconditions, rather than equilibrium flashes, are determinedbecause there is not an appreciable vaporization. The temperatureis limited by apparatus restriction.

Lal et al. [22] measured H2 solubility in Athabasca bitumen(205–558 �C cut and q = 1.009 g/cm3 at 16 �C) using a batch auto-clave. The experiments were conducted at temperatures in therange of 50–300 �C and partial pressure of H2 up to 253 kg/cm2.The PR and SRK EOS and the Grayson–Streed method were usedto predict and correlate the solubility data. The calculation of theconstant b (repulsive term) in each EOS was modified. The vaporphase almost was composed by pure H2 at the considered temper-atures. The best result was obtained with the use of either a mod-ified PR or SRK EOS.

Ronze et al. [10] measured the H2 solubility in a SRGO (240–371 �C cut and q = 0.8636 g/cm3 at 20 �C) using a chromatographicmethod. The method was validated with cyclohexane. The experi-mental conditions were: pressure up to 41 kg/cm2 and tempera-tures from 25 to 402 �C. The experimental results are describedby five thermodynamic models: Chao–Seader and Grayson–Streedmethods and PRSV (Peng–Robinson–Stryjec–Vera), ZJ (Zudkevitch–Joffe), and SRK EOS. For the gas oil, the Henry’s law constants werecalculated at four temperatures (298, 393, 524 and 645 �C). Theexperimental measurements were developed in a high pressureautoclave and to identify the equilibrium the pressure and temper-ature were monitored until both were constants for 1.5 h. The cal-culations were developed using the Hysys_Plant 2.1.1 of Hyprotecsoftware. The gas oil was characterized using 15 pseudocompo-nents from the ASTM-D86 distillation curve. Thermo physicalproperties of each pseudocomponent are then calculated as a func-tion of the operating conditions using published relationships: spe-cific gravity [11], specific heat, ideal enthalpy and vapor pressure[12], molecular weight [13] and viscosity [14].

2.2. Highlights of the literature reports

Experimentally, the static method seems to be more reliablethan the dynamic one (continuous flow or with recycle) to obtainthe equilibrium data. The static method presents less dispersionin the experimental data than the dynamic method [15,17]. Thesampling of liquid and vapor phases in the static method can bedone with valves [10,17,18] or capillaries [19], by taking smallsamples to avoid perturbation of the pressure inside the equilib-rium cell. The continuous flow cells are used for heavy hydrocar-bons feeds (carbon liquid) reducing the residence time in thehigh temperature zone, minimizing the thermal decomposition[20,21]. Conolly and Kandalic [19] determined VLE through bubbleand dew pressure measurements for binary systems, while Linet al. [21] measured the bubble point conditions to determine H2

solubilities.The cubic EOS gave good results when the binary interaction

parameter affects the repulsive term [20,22]. On the contrary Lau-gier et al. [17] and Ronze et al. [10] used different state equationsto the traditional cubic state equations and reported acceptableresults. The Grayson–Streed model is often considered as a refer-ence model to simulate H2/hydrocarbons equilibrium. It did notgive good results as the cubic EOS (PR and SRK) properly condi-tioned for H2/hydrocarbons or liquid carbon systems [22]. This


can be due to of the limited pressure range and to its poor perfor-mance with mixtures involving heavy hydrocarbons.

With exception to Laugier et al. [17], who used maximum like-hood, the other works do not mention the optimization methodused to fit the binary interaction parameters.

Wiegand et al. [20] presented a methodology to use equationsof state with petroleum fractions. It consisted first of fitting theparameters of the equation of state with experimental informationof vapor pressure and VLE of pure compounds. Then the binaryinteraction parameter of H2–hydrocarbons is optimized withexperimental data of VLE from binary systems. These steps arerepeated for various binary systems with different hydrocarbons.Finally, a correlation is proposed with these binary interactionparameters and some properties of the hydrocarbons. This correla-tion is extended to multicomponent systems. To do this, it wasnecessary to fractionate the liquid carbon by distillation and exper-imentally determine the boiling temperature and the density ofeach fraction. These data were used to calculate molecular weightsand critical properties with correlations reported in literature.

2.3. Analysis of data

Table 1 summarizes the reports of the literature about VLE atmoderate and low severity conditions. The information includesthe range of temperature and pressure as well as the setup underwhich the experiments were conducted, the EOS employed for pre-dicting hydrogen solubility data, the method to obtain H2/hydro-carbon interaction coefficients, some properties of the feed andinvolved hydrocarbon, and the deviation between experimentaland predicted data. Some of the studies present identifiable hydro-carbons, while others indicate the number of cuts used for charac-terization. The studied systems range from H2/n-pentane up toheavy coal liquid. For all of the cases the H2 solubility is deter-mined experimentally in different experimental setups, mainlycontinuous flow units. As is known, the solubility of hydrogen isinversely proportional to the equilibrium ratio or distribution coef-ficient (KH2). For the prediction of KH2 various EOS are used andonly Luo et al. [9] employed the method of Pierotti together withHenry’s law. The reported average absolute deviation varies from1.75% to 6.7% for xH2 and 13.9% for KH2.

The variation of hydrogen equilibrium constant as function ofpressure at constant temperature for different H2–hydrocarbonsystems is presented in Figs. 3–5. Only those results with similartemperatures were selected to make a comparison.

In Fig. 3, it is shown that at pressure in the range of 20–120 kg/cm2 the differences between KH2 values of the various systems aremore significant than at higher pressures. This can be attributed tothe fact that high pressure favors the dissolution of hydrogen in thehydrocarbon liquid and inherently reduces the effects of the natureof hydrocarbon and system temperature. Fig. 3 also shows that KH2

in toluene (�) is greater than KH2 in cyclohexane (N). At 250 �C sim-ilar results were observed for the KH2 in m-xylene (s) and KH2 in2,2,4-TMC5 (+), which indicate that the solubility of hydrogen islower in aromatic compounds than in alkanes and cycloalkanes.At 270 �C KH2 is slightly higher when hydrogen is in contact withm-xylene (h) than in toluene (e). Similar behavior occurs whencomparing the KH2 in 1,4-DEB (�) with KH2 in m-xylene (d) at280 �C. This demonstrates that the solubility of hydrogen increasesas the branches or the branch’s length of aromatic compoundsdiminishes.

At similar temperature Fig. 4 shows that KH2 in 2,3-DMC4 (N) islower than KH2 in cyclohexane (d), and also that KH2 in 2,2,4-TMC5(}) is lower than that in toluene (*), indicating that hydrogen sol-ubility improves by the saturation degree of hydrocarbons(increased number of hydrogen atoms). This is confirmed by thedata of KH2 in cyclohexane at 200 �C (+), which are lower than that



Table 1Literature reports of VLE at low and moderate severity conditions.

Authors System Temperature(�C)

Pressure(kg/cm2)

Setup EOS (VLE) Interactioncoefficients

Character-ization

ADD (SD) Feed’s properties(petroleumfractions)

q (g/cm3)at 16 �C

Cut (�C)

Simnicket al. [15]

H2/toluene 189–302 21–258 Continuousflowequilibriumcell

– – Identifiablecompounds

– – –

Laugier et al.[17]

H2/toluene;H2/2,2,4-TMC5

226–295 Static cell – – Identifiablecompounds

– – –

Ramanujamet al. [18]

H2/a simulated coal-derived liquidmixture

155–268 21–114 Continuousflowequilibriumcell


– – –

ConnollyandKandalic[19]

H2/n-pentane;H2/2,3-DMC4;H2/cyclohexane; H2/n-decane;H2/m-xylene;H2/1,4-DEB andH2/1-methyl-naphthalene

35–320 14–169 Staticsystem


– – –

Wiegandet al. [20]

H2/coal liquid 179–339 51–308 Continuousflowequilibriumcell

Modified SRK Correlations 6 TBP cuts xH2 1.75 0.9168 51–459KH2 13.89

Luo et al. [9] H2/modelcomponentsof coal liquid,such as hexadecane,methylbenzene,1,2,3,4-THN,naphthalene,quinoline and1-naphthol

180–400 3–99 Continuousflow flashpot

Henry’s coefficientsexpression of Pierottimethod and Henry’s law

Solubilityparameters

Identifiablecompounds

xH2 3.7–5.9

– –

Lin et al.[21]

H2/coal liquids (four) 190–270 Up to 264 Continuousflowequilibriumcell

– – – – 0.9320 204–2320.9844 260–3160.9826 260–2761.0360 316–3331.0910 371–399

Lal et al. [22] H2-deasphaltenedbitumen Athabasca

50–300 Up to 253 Batchautoclave

PR and SRK EOS withmodified constant b

Adjustedconstant b

FromSeluckyet al.[66,67]

– 1.0090 205 –558

Ronze et al.[10]

H2-straight run gas oil 25–402 Up to 41 Highpressureautoclave

Chao–Seader; Grayson–Streed; Zudkevitch–Joffe;Peng-Robinson-Stryjec-Vera; API method

Dependent onthermodynamicmodel

15 TBP cuts xH2 (0.12–6.7)

0.8665 240–371


of toluene (*) and higher than that of 2,2,4-TMC5 (e) at similartemperatures.

The values of KH2 in cyclohexane at 160 and 200 �C show thatthe higher the temperature the better the hydrogen solubility.The same is observed in Fig. 3 for toluene at 189 and 269 �C.

Fig. 5 depicts the profiles of KH2 in toluene (}), 1,4-DEB (—) andcoal liquid (j). A possible aromatic nature of the coal liquid maycause increased number of branches with respect to toluene and1,4-DEB. This may explain the tendency in KH2 values: KH2-CL > KH2-1,4-DEB > KH2-Tol, and that hydrogen solubility is less inthe coal liquid than in the other two hydrocarbons.

3. VLE of H2 with hydrocarbons at high severity conditions

3.1. Literature review

Experiments of VLE of H2 at high pressures and temperatureswere found for hydrogen– petroleum fraction or coal liquid sys-tems, which were carried out in continuous and batch setups. Most


of the calculations are done with EOS. The petroleum fractions arecharacterized by pseudocomponents. The Radosz correlation isused to determine binary interaction parameters.

Hwang et al. [23] determined experimentally the volatility ofWyoming coal liquids (five feeds with similar distillation range,204–399 �C, and different densities: 0.965, 0.970, 0.972, 0.987,and 1.055 g/cm3 at 16 �C) at high temperature (371–454 �C) andpressure (137 kg/cm2) using a flow apparatus to minimize thermaldecomposition effects. The experimental volatilities are comparedwith the predictions of a modified Chao–Seader correlation andmodified Redlich–Kwong EOS (by Joffe–Zudkevitch). Both modelsusing the vapor pressure method proposed by Wilson et al. [24]are reported to be equivalent in the prediction of the volatility ofcoal liquids.

Lin et al. [25] experimentally determined the VLE for a coalliquid (q = 0.9793 g/cm3 and MW of 214), including mixtures withH2 at temperature up to 437 �C and pressure up to 255 kg/cm2. Theboiling point, molecular weight and specific gravity of vacuum dis-tillation fractions of the coal liquid and of vapor and liquid frac-tions are obtained experimentally. The critical properties were



0

10

20

30

40

50

60

70

0 30 60 90 120 150 180 210 240 270

Dis

trib

utio

n co

effi

cien

t of

hyd

roge

n, K

H2

Pressure, kg/cm2

T189 C_toluene [15]

T190 C_cyclohexane [19]

T250 C_2,2,4-TMC5 [17]

T250 C_m-xylene [19]

T269 C_toluene [15 and 17]



T280 C_1,4-DEB [19]

o

o

o

o

o

o

o

o

Fig. 3. Comparison of equilibrium distribution coefficients of H2 in several systemsat similar temperatures.

0

10

20

30

40

50

60

70

0 30 60 90 120 150 180 210 240 270Dis

trib

utio

n co

effi

cien

t o

f hy

drog

en, K

H2

Pressure, kg/cm2

T150 C_2,3-DMC4 [19]



T226 C_2,2,4-TMC5 [17]

T229 C_toluene [15]

o

o

o

o

o

Fig. 4. Comparison of equilibrium distribution coefficients between H2/n-alkanessystems.

0

5

10

15

20

25

30

35

40

45

50

0 50 100 150 200 250 300 350Dis

trib

utio

n co

effi

cien

t of

hyd

roge

n, K

H2

Pressure, kg/cm2

T290 C 1,4-DEB [19]

T295 C_toluene [17]

T299 C coal liquid [20]

o

o

o

Fig. 5. Variation of KH2 versus pressure at similar temperature for petroleumfractions.


calculated with the Lin–Chao correlation [26]. The VLE data werecorrelated with the Cubic Chain-of-Rotators (CCOR – the perturba-tion type), Soave and Soave modified by Radosz EOS, and the Gray-son–Streed correlation. A flow apparatus was used to measure VLEwhile minimizing thermal decomposition of the coal liquid. Thecoal liquid is characterized by 14 or 28 pseudocomponents. Better


agreement between the calculated and experimental data wasobserved when the coal liquid characterization is more detailed.For CCOR and Soave modified by Radosz EOS, the H2–hydrocarbonsbinary interaction parameters were determined using the Radoszcorrelations [27].

Lin et al. [28] also determined experimental VLE of carbon liq-uids with and without hydrogen at temperature up to 437 �C andpressure up to 255 kg/cm2. Boiling point, molecular weight andspecific gravity of VLE overhead and bottoms fractions as well asthe true boiling point (TBP) fractions of the coal liquid wereinspected. In this case 20 and 35 pseudocomponents were usedto characterize the coal liquids. CCOR EOS was employed to corre-late the VLE data. The Lin and Chao [26] correlations were used tocalculate critical properties and acentric factor. The binary interac-tion parameters for H2–hydrocarbons were calculated by theRadosz et al. [27] correlations.

Wiegand and Strobel [29] measured VLE data of hydrogenatedcarbon liquid (77–501 �C cut and q = 1.0205 g/cm3 at 20 �C) usinga high pressure and temperature flow cell. The temperature andpressure ranges were 180–400 �C and 51–306 kg/cm2 respectively.The molecular weight values were calculated using the correlationof Brulé et al. [30].

Cai et al. [31] reported an indirect method based on pressurechanges at constant temperature and volume measurements todetermine gas solubility in a liquid media as heavy oil, residueoil and low volatility hydrocarbon model compounds. The applica-tion of the method depends on the cell, which can be operatedfrom ambient temperature up to 450 �C and up to 306 kg/cm2. H2

solubility in hexadecane, 1,2,3,4-tetrahydronaphthalene, SRGO(184–454 �C cut and q = 0.893 g/cm3 at 20 �C), straight-run heavygas oil (SRHGO) (274–595 �C cut and q = 0.973 g/cm3 at 20 �C),Athabasca bitumen vacuum bottoms (525 �C+ cut and q = 1.05 g/cm3 at 20 �C) and Gudao atmospheric residuum (350 �C+ cut andq = 0.922 g/cm3 at 20 �C) over a broad range of temperatures(80–380 �C) and pressures (5–122 kg/cm2) was reported. The solu-bility values differ significantly for all of the cuts at low tempera-ture, but not at high temperature. Chemical reaction interferencein solubility measurements for Athabasca bitumen vacuum resid-uum and SRHGO at temperature above 330 �C was reported.

Harrison et al. [32] measured H2 solubility in 1,2,3,4-tetrahy-dronaphthalene, four-component mixture and several coal liquidsat high pressure and temperature as well as equilibrium liquidphase densities. They used a static system with an autoclave. Thesystem can operate at 125–400 �C and 51–255 kg/cm2.

Ding et al. [33] presented experimental data of H2 solubility in ahydrogenated coal liquid (125–536 �C cut and q = 1.018 g/cm3 a25 �C) as well as partial pressure of the liquid in the system. Theranges of the operating conditions are 147–407 �C and 37–112 kg/cm2. With a sufficient H2 partial pressure there was notobserved coke formation in the experiments. Two in-situ hydrogenprobes were used to measure hydrogen partial pressure in bothphases without sampling. The experimental system is a staticone. RK EOS was employed to determine H2 compressibility factor.Hydrogen solubility and partial pressure were correlated byHenry’s law with the Henry’s constants as a function oftemperature.

In the Riazi and Roomi [34] work a method based on regularsolution theory (Scatchard–Hildebrand theory) was proposed topredict H2 solubility in hydrocarbons (n-decane, n-hexadecane,n-octacosane, n-hexatriacontane, n-hexatetracontane, ethylben-zene, and hexadecane), petroleum fractions (naphtha reformatewith q = 0.864 g/cm3, LVGO with q = 0.896 g/cm3, HVGO withq = 0.975 g/cm3, and SRGO with q = 0.868 g/cm3 at 16 �C) and coalliquids (204–260 �C cut with q = 0.932 g/cm3, 260–315 �C cut withq = 0.984 g/cm3, and 260–276 �C cut with q = 0.983 g/cm3) at var-ious pressures (1–163 kg/cm2) and temperatures (10–350 �C).




Vapor phase was assumed to behave as ideal and there are twoparameters (correction factors) that depend on the solvent. Thesolvent characterization consists of three compounds: paraffins,naphthenes and aromatics. This method does not require criticalproperties from solvent neither interaction parameters that areused in state equations. The system is represented as a binary mix-ture with H2 as the component l and the solvent (petroleum frac-tion, carbon liquid or identifiable hydrocarbons) as component 2.The method was applied to hydrocarbons with molecular weightsin the range of 70–650.

Ferrando and Ungerer [35] modeled H2–hydrocarbons VLE bytwo approaches. The hydrocarbons are considered identifiable:hexane, cyclohexane, benzene, n-hexadecane, 2,3-DMC4, 1-hex-ene, 1-octene, methylcyclohexane, toluene, ethylbenzene, naph-thalene, and phenanthrene. The pressure and temperatureconditions of the experiments range between 21–704 kg/cm2 and22–391 �C, respectively. The first approach consists of flash calcu-lations involving the improved PR EOS coupled with the H2–hydro-carbon interaction parameter correlation of Moysan et al. [36],which only depends on temperature. The Lorentz–Berthelot’ mix-ing rules were used. However, the high value of the interactionparameter at high temperatures made questionable the model.The deviation using this approximation was �7.2%, particularlyat high pressures. The authors of this study recommend for a pos-sible upgrade to incorporate a correction factor in the repulsiveterm of the equation of state. The second approach is a Monte Carlosimulation using the Anisotropic United Atom 4 (AUA4) intermo-lecular potential for hydrocarbons and an intermolecular potentialfor hydrogen (Darkrim) including the quadrupole momentum ofthe molecule. The Monte Carlo method is more predictive becauseit does not require interaction parameters and corresponds to amolecular simulation, but it needs to know the chemical structureof the hydrocarbon involved in the mixture with H2. This approxi-mation is recommended when experimental information is notavailable. They report an approximate deviation of 5.2%, especiallyat high pressures. The model does not predict accurately the H2/poliaromatics mixtures VLE. Both approaches are tested with bin-ary systems.

Sebastian et al. [37] developed a correlation for H2 solubility inhydrocarbons (identifiable) at 37–427 �C and pressure up to306 kg/cm2. The correlation is based on H2 solubility data on sol-vents of different nature, including paraffins, polynuclear aromat-ics, naphthenes and aromatics with heteroatoms. The H2 fugacitydissolved at zero pressure is correlated as a function of the solubil-ity parameter and temperature. For high pressure, the fugacity isobtained by application of the Poynting factor, requiring H2 molarvolume. Likewise this property has been correlated in terms of sol-ubility parameter and temperature. The fugacity coefficient wascalculated using the Redlich Kwong (RK) EOS modified by Praus-nitz and Chueh. Also, a correlation for the H2–hydrocarbon interac-tion parameter as a function of solvent critical volume is used.


The equilibrium cells used in the works of this section were ofcontinuous [23,25,28,29] or static [31–33] type. The static methodswere used mainly to measure partial pressures [33] and indirectmeasurement of hydrogen solubility [31]. This is because at hightemperatures and the residence time required in these systems,thermal decomposition of the heavy hydrocarbons could occur[31,32]. The static methods have the advantage of easy operation[32], however for heavy fractions the continuous flow systemsare recommended.

To model the hydrogen–petroleum fractions systems, a varietyof methods were presented, from modified Chao–Seader [23] toMonte Carlo method [35], including modifications to the


traditional cubic equations of state [25,31,35]. Some of these worksapplied the regular solution theory [34,37]. The authors stated thatthe precision of this model was as good as that of the EOS when themolecular weights of the hydrocarbons were in the range estab-lished by the authors [34].

The Monte Carlo method is limited by the necessity of thechemical structure of the hydrocarbons involved in the system,which, for petroleum fractions is a complicated task [35].

In some cases, the correlations of the binary interaction param-eters are optimized using binary systems experimental data andthe application is extended to petroleum fractions. These modelscan be considered as predictive [25].

In petroleum fractions, an important aspect for the precision ofresults is the number of pseudocomponents used in the modeling.These pseudocomponents can be the same as the number of frac-tions obtained in the distillation of petroleum fraction [25,28].The physical properties that are used in the modeling can beobtained experimentally [25,28], or with correlations from the lit-erature [33]. According to Lin et al. [25], the greatest the pseudo-components number, the better VLE prediction. It is important toconsider that there are petroleum fractions that cannot be sepa-rated in narrow boiling ranges, because the boiling point of themixture is very high and can be thermally decomposed [28].


VLE data at high severity conditions are shown in Table 2. Thefeedstock densities are higher than 0.7342 g/cm3, while the molec-ular weights range from 142.3 to 1700, indicating middle, or heavypetroleum fractions. A great variety of thermodynamic models areused, from correlations such as Chao–Seader and Grayson–Streed[23,25] to non cubic EOS, such as Chain of Rotator [25,28], evensimulations using Monte Carlo method [35]. Interaction parame-ters are determined using known correlations. Characterizationof petroleum fractions used 14 and 35 pseudocomponents[25,28], and only one work utilizes the PNA method [34]. Caiet al. [31] studied hydrogen systems with residues, but onlyexperimentally.

Fig. 6 presents KH2 values as function of temperature at quasy –constant pressure, which correspond to data reported by Lin et al.[25,28] and Wiegand and Strobel [29] for H2/coal liquid systems atpressures of 50, 100, 200, 250 and 300 kg/cm2. It is seen that at50 kg/cm2 H2 solubility improves when the coal liquid molecularweight increases, since the KH2 for molecular weight of 239 islower than that for molecular weight of 185. Similar behavioroccurs at the other pressures. Some data slightly differ from thistrend, which could indicate that the coal liquid with MW of 236is more paraffinic in nature than that with MW of 239, but no dataare available to confirm this.

Fig. 6 also shows that KH2 is greater when pressure decreases.The data at 50 kg/cm2 have two tendencies corresponding eachto two types of coal liquids: in one the decrease of KH2 with tem-perature is more pronounced than in the second one. The molecu-lar weight of the former is lower as compared with the latter. Thisimplies that in the coal liquid in [28] the paraffinic nature predom-inates, while coal liquid in [29] may be richer in aromatics.

For the series corresponding to 100 kg/cm2 there are quite welldefined behaviors that is the hydrogen solubility enhances withincreased temperature. As the pressure increases, the differencesbetween sets of data for all coal liquids at the same pressure arebecoming less significant, this indicates that at high pressure theeffect of nature of the oil fraction and temperature on the solubilityof hydrogen is not relevant as in the case of low pressure. This isparticularly observed at pressures of 250 and 300 kg/cm2. At thesevalues solubility of hydrogen in the petroleum fractions is thehighest and it slightly increases when increasing the temperature.



Table 2Literature reports of VLE at high severity conditions.


Pressure(kg/cm2)

Setup EOS (VLE) InteractionCoefficients

Characterization ADD Feed’s properties (petroleumfractions)

q (g/cm3)at 16 �C

Cut (�C) MW

Hwang et al. [23] H2/CH4/coal liquids (five) 371–454 137 Continuousflowequilibriumcell

Chao–Seader y RKJZ Wilson et al.[68]

– Volatility 6–25.4

0.970,0.987,0.972,0.965,1.055

204–399foursimilarcoalliquids.

167,169,168,169,214

KH2 13.5–30.2

Lin et al. [25] H2/coal liquid Up to 437 Up to255

Continuousflowequilibriumcell

Chain of Rotators, Soave y Soave–Radosz, Grayson–Streed

Correlations 14 TBP cuts KH2 5.41 0.9793 – 21428 TBP cuts KH2 5.75

Lin et al. [28] H2/coal liquid (two) Up to 437 Up to255

Continuousflowequilibriumcell

Chain of rotators Correlations 35 TBP cuts –Wyoming Coalliquid

KH2 4.43 0.9534 – 206

20 TBP cuts –Illinois Coalliquid

KH2 8.43 0.9938 – 239

Wiegand andStrobel [29]

H2/coal-derived liquid 180–400 51–306 Continuousflowequilibriumcell

– – – – – 1.0234 77–501 184.6

Cai et al. [31] H2/Athabasca light virgin gas oil 80–380 5–122 Static system – – – – – 0.8959 184–454 250H2/Athabasca heavy virgin gas oil 0.9758 274–595 350H2/Athabasca bitumen vacuumbottoms

1.0529 525+ 1700

H2/Gudao atmospheric residuum 0.9248 350+ 1678

Harrison et al.[32]

H2/middle distillate 125–400 51–255 Staticautoclave

– – – – – – 200–325 146H2/heavy distillate 325–425 203.8

Ding et al. [33] H2/hydrotreated coal liquid 147–407 37–112 Static system Modified RK – – – – 1.0219 125–536 221

Riazi and Roomi(more other11 studiedsystems) [34]

H2/n-Decane 10–350 1–163 Data fromdifferentsources (onlymodeling)

Regular solution theory Not necessary PNA: Paraffins,Naphthenes yAromatics

xH2 2.7 0.7342 – 142.3H2/LVGO 3.1 0.8960 – 250H2/HVGO 2.4 0.9750 – 350H2/coal liquid (two) 6.7 0.9320 204–260 154.7

10.4 0.9830 260–276 182

Ferrando andUngerer [35]

H2/different hydrocarbon families(n-alkanes, iso-alkanes, alkenes,cycloalkenes, aromatics andpolyaromatics)

22–391 21–704 Onlymodeling

Improved PR Moysan’correlation


xH2 4.9–9.5

– – –

Monte Carlo simulation Intermolecularpotential

2.8–24

Sebastian et al.[37]

H2/solvents of diverse nature(paraffins, polynuclear aromatics,naphthalenes, and hetero-atomcontaining aromatics)

37–427 Up to306

Data fromdifferentsources (onlymodeling)

Modified RK [69] by Prausnitzand Chueh [70] and regularsolution equation of Scathardand Hildebrand

Correlations Identifiablecompounds

cH2 2.3–28.2

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Fig. 6. Variation of KH2 versus temperature at similar pressures for petroleumfractions [25,28,29].


4. Accounting for VLE in reactor modeling

Some reports in the literature have considered the hydrogen/hydrocarbons VLE to simulate catalytic hydroprocessing reactor,with the justification that vaporization of the feed increases thereactants concentration in the liquid phase and this affects themodel predictions.

Most of the reported models assume the reactor to behave asTBR. Various EOS or thermodynamic correlations have been usedfor calculating VLE, such as SRK, PR and Grayson–Streed. Theranges of operating conditions of the reactors used in simulationvary from atmospheric to 207 kg/cm2 of pressure and from 80 to450 �C of temperature depending on the feed and reaction type.When petroleum fractions are used, the characterization of thefeed is done by 5 up to 29 pseudocomponents. In some studies,commercial simulators are employed such as Aspen Plus, Pro II,ProSimPlus and CMG (Computer Modeling Group Ltd.).

4.1. Literature review of modeling with single hydrocarbons or withsimulated hydrocarbon mixtures

Akgerman et al. [5] presented a reactor model that considers theeffect of feed volatility on conversion and compared it withoutvaporization of the liquid phase, both using the same reactionkinetic model. The difference in the conversion between both mod-els is significative, about 38% when a first order reaction isconsidered.

To calculate the fugacity coefficients in both phases of the VLE,the SRK EOS is used. The authors considered H2/hydrocarbonsinteraction parameters to be equal to zero, assuming that theyhave little effect on conversion. The reactor is considered isother-mal at the simulation conditions. The reaction considered is:

3Aþ B! C þ D

where A is the hydrogen (gas phase reactant), B is benzothiophene(liquid phase reactant), C is ethylbenzene (gas or liquid phase prod-uct) and D is hydrogen sulfide (gas phase product). Decahydronaph-thalene is used as inert to dissolve the liquid phase reactant.

Smith and Satterfield [2] discussed some consequences of alter-ing the gas/liquid ratio in quinoline hydrodenitrogenation (HDN)in presence of H2S. Quinoline is initially dissolved in white oil (rel-atively non volatile naphthenic liquid, C18–C36). The experimentswere conducted at 365 �C and 70 kg/cm2, using two gas/liquidratios (2500 and 9000 SCF H2/bbl of liquid) and LHSV from 2.2 to31 h�1. Under these conditions, the HDN reaction has an orderslightly greater than zero and conversion is not affected by the


gas/liquid ratio neither by the vapor phase reaction versusvapor–liquid reaction. The authors calculate VLE using the meth-ods reported by Prausnitz et al. [38]. The activity coefficients aredetermined by UNIFAC group contribution method. Non idealbehavior is considered because the reaction conditions are rela-tively severe. The equilibrium constants, however, have not signif-icant change during the HDN reaction.

LaVopa and Satterfield [39] showed the effect of H2/feed ratio,relative volatilities changing the solvent nature, and temperaturein the distribution of reactant and inert liquid (solvent) betweenthe vapor and liquid phases in a TBR used for hydrotreating. Stud-ies are reported for two reaction models: the hydrodeoxygenationof dibenzofurane (b.p. 285 �C) and the hydrogenation of n-buthyl-benzene (b.p. 183 �C) dissolved in n-hexadecane (b.p. 287 �C) ortetracosane (a C30 branched paraffin with b.p. 350 �C). The experi-mental results obtained at low conversion in a laboratory TBR arecompared with theoretical predictions generated with a reactormodel that explicitly takes into account the distribution of the spe-cies between both phases. The reactor involves N stages in seriesand each one is conformed by an VLE zone and a differential reac-tion zone, modeled as a continuous stirred-tank reactor (CSTR) asshown in Fig. 7 [39].

In the experimental work relatively low reactant concentrationsare used and the consumed H2 is maintained constant, below 5%.To estimate the VLE programs developed by Prausnitz et al. [38]were used. The fugacity coefficients are determined from the trun-cated virial EOS and the activity coefficients are predicted by theUNIFAC group contribution method. The experiments are carriedout at pressure of 71 kg/cm2 and temperature ranging from 350to 390 �C. The effect of reactant volatility on conversion is alsoinvestigated. The stronger effect on conversion changing the gas/liquid feed ratio is observed when the liquid volatility is low andthe difference between the reactive and solvent volatilities is high.

Collins et al. [40] presented the effect of the feed partial vapor-ization on benzothiophene hydrodesulfurization reaction rate andconversion, particularly the effect of solvent volatility (decahydro-naphthalene, 1-methylnaphthalene, n-hexadecane and n-eico-sane). The feed is conformed by 5% of benzothiophene and 95%of solvent. Pressure is maintained constant at 70 kg/cm2 and tem-perature ranges between 273 and 333 �C. The equilibrium calcula-tions are developed using the SRK EOS for both phases. The binaryinteraction parameters are considered to be equal to zero and thereactor was assumed to operate in isothermal or quasi isothermalmode at the studied conditions.

Tesser et al. [41] analyzed gas–liquid and gas–solid–liquid reac-tors with reactants and products distributed in both phases (liquidand vapor). Specially, when the amount of components presentedin both phases is not negligible or when the VLE does not havean ideal behavior. They introduced the mass balance equations inthe kinetic model to describe the components distribution thataffect the liquid phase concentration, and also considered thenon ideal behavior of the involved phases when it is necessary.The systems analyzed were: (1) grease alcohols etoxilation andproxilation, (2) chloroform fluorination, (3) p-cresol alkylationwith isobutene, and (4) methanol homologation with H2 and COto acetaldehyde. To avoid experimentation, the authors developeda simple method using UNIFAC to generate reliable equilibriumdata of all the binary interactions involved at pressures in whichUNIFAC works well (5–10 kg/cm2). From the generated data, theinteraction parameters were obtained using the SRK EOS by amathematical regression. Those parameters can be used, afterextrapolation, to describe the multicomponent system at highpressure.

Kulikov et al. [42] studied experimentally the combined effectof liquid phase vaporization and exothermal chemical reaction indynamic and steady-state operations of catalyst pellets. The



Stage 1

Stage 2

Stage N

Equilibrium Flash Stage 1

ReactionZone 1

L’ 1, x’1,j , C’1,j V’1, y’1,j

FHC’s+H2, P1,T1,zi,1, C1,j

FΔR-1, C1,j

FHC’s+H2, P2,T2, C2,j

FΔR-1 = L’ 1

Equilibrium Flash Stage i

ReactionZone i

L’ i, x’i,j , C’i,j V’i, y’i,j

FΔR-i, Ci,j

FHC’s+H2, Pi+1,Ti+1, Ci+1,j

FHC’s+H2, Pi, Ti, Ci,j

Stage i+1FHC’s+H2, PN,TN, CN,j

FΔR-i = L’ iStage i

i = {1, 2,…, N}j = {1, 2,…, NC}

H2 + hydrotreated oil

H2 + oil

Ci

T

Fig. 7. Representation of the reactor model considering VLE calculation [4,39,45].


alpha-methyl-styrene (a-MS) to cumene catalytic, exothermalhydrogenation is used as a reaction model. Experiments were car-ried out in a single catalytic pellet reactor with five different cata-lysts of different porous structure, thermal conductivity, apparentcatalytic activity and distribution of catalyst on the pellet. Temper-ature and a-MS concentration were varied, as well as the liquidflowrate. Two different steady states were identified (totally liquidand totally vapor) in the liquid flowrate range, and temperatureand pellet dynamics were found to depend significantly of thea-MS amount in the vapor phase and catalyst properties. Theseexperimental data are useful to determine the mechanism of for-mation of hot spots and the runaway on TBR’s. All the experimentswere performed at atmospheric pressure and hydrogen constantflowrate. Gases temperature was varied between 80 and 136 �C.It is stated that bad liquid distribution in a trickle bed reactorcan result in hot spot formation.

Khadilkar et al. [43] presented a review of the limited literatureof experiments and models for TBR systems with volatile liquids. Arigorous model to solve the reactor and the transport flow-reactionphenomena at pellet scale based on the multicomponent diffusiontheory is proposed. Comparisons of the model predictions with theresults obtained with a simplified model are shown. Also, to assurethe precision of the model, the predictions are compared withexperimental information previously published of cyclohexene tocyclohexane hydrogenation.

Akgerman et al. [1] used seven cubic equations of state to deter-mine their effects on predicting reactor performance as well asparameters estimation. To do this, the authors assume isobaricoperation, complete catalyst wetting, and no transport effects.Additionally, it is considered that VLE is presented in all reactorpoints. From the EOS the VLE and the liquid phase molar densityare calculated. The authors show that this last variable has a signif-icant effect on the reactor operation (conversion) and parameterestimation, while the VLE does not impact significantly on thereactor model results. To determine the effect of the EOS, the


benzothiophene on decahydronaphthalene hydrodesulfurizationreaction is used as reaction model.

Nalltham et al. [44] studied analytically and experimentally theeffect of the feed liquid vaporization on the reactor operation. Thereaction model system is the catalytic hydrogenation of naphtha-lene dissolved in toluene, cyclohexane, hexadecane and white oil.The effect of solvent equilibrium constant, H2 flowrate, tempera-ture, pressure and feed concentration over naphthalene conversionwas reported. The role of VLE in hydrotreating kinetics is examinedby a simulation model. To obtain experimental data they used anisothermal CSTR. Liquid vaporization was taken into account inthe model by introducing the VLE relationships of the components.Equilibrium constants only depend on temperature and pressure.The ranges of reactor operating conditions are 52–207 kg/cm2 ofpressure and 250–350 �C of temperature. The H2 solubility in theliquid medium is mainly function of pressure and temperature. Itwas found that the more volatile the solvent, the higher the naph-thalene conversion.

4.2. Literature review of modeling with light, middle and heavypetroleum fractions

In the work of Kocis and Ho [45] a model to quantify the effectsof partial liquid vaporization and the vapor phase reactants con-densation in TBR’s is presented. The reactor is represented by a ser-ies of small plug-flow reactors interconnected with vapor–liquidseparators (Fig. 7). The model reduces the LHSV using a 1 � f factorin the kinetic model, where f is the vaporizated fraction of feed-stock at reaction conditions. Parametric studies show that not con-sidering the effect of vaporization can lead to misleadingconclusions about chemical kinetics.

To illustrate the use of the model, the first order dibenzothio-phene hydrodesulfurization reaction at 325 �C and 32 kg/cm2 isconsidered. Also, the effects of liquid vaporization with two differ-ent solvents are examined: (1) n-hexadecane (n-C16H34), a more




volatile compound than dibenzothiophene, and (2) tetracosane(nC24H50) a less volatile compound than dibenzothiophene. Idealbehavior of liquid and vapor phases is assumed, where Raoult’slaw is valid. The vapor pressures of the solvents are determinedby Antoine equation for n-hexadecane and an equation developedby the authors for tetracosane. It was shown that solvent volatilityhas significant effects on chemical kinetics.

Jong [46] investigated coke deposition on catalyst during vac-uum heavy gas oil (VHGO, 370–520 �C cut) conversion in a TBRat high temperature (�450 �C) and moderate hydrogen pressure(31 kg/cm2). The amount of deposited coke on the catalyst showsmaxima as function of temperature and H2/oil ratio. Those maximaare induced by VLE in the reactor. A qualitative description of cokeprecursors in the oil is presented. To limit coke deposition underhydrocracking conditions it is essential to balance carefully: cata-lyst properties, process conditions and reactor type and configura-tion. It is considered that VHGO Ramsbottom carbon content isproportional to the amount of coke precursors in the feed. Theexperiments were carried out in an isothermal micro-reactor. Thecomplete feed vaporization leads to shorter residence times andlower cracking conversion. Conversely, if the feed is partiallyvaporized, the coke deposition increases, which depends on thevaporization degree when the concentration of coke precursorincreases in the liquid phase.

Bellos and Papayannakos [47] studied the hydrodesulfurizationkinetics of straight-run gas oil and hydrogen consumption, usingexperimental information collected from a micro reactor with adiluted bed of a commercial catalyst. Feed vaporization and VLEthrough the reactor were taken into account. Gas oil and sulfurcompounds are characterized by 5 pseudocomponents. The gasoil pseudocomponents react with H2 obtaining 5 hydrogenatedcompounds. Those reactions simulate H2 consumption. The sulfurpseudocomponents concentration in each fraction is calculatedfrom the sulfur concentration curve. Kinetic experiments were per-formed at reaction temperature in the range of 320–350 �C andWHSV between 1 and 4.5 h�1. Pressure was kept constant at55 kg/cm2 in all the experiments. Only those reactants present inthe liquid phase participate in the catalytic reaction. Using Miqueland Castells method [48] the pseudocomponents boiling points arecalculated. Molecular weight is determined by Riazi method [49]and critical properties by the Lee–Kesler correlations [12]. Thethermodynamic equilibrium, Henry’s coefficient and hydrogen sol-ubility are obtained by using the translated form of Van der WaalsEOS (t-vdW). A flash calculation in each differential catalytic bedzone is computed.

Some pilot plant data and analysis that show the effect of gas/oil ratio (175–1167 NL/kg) in VLE inside an ultra low sulfur diesel(ULSD) hydrotreating reactor at constant temperature and pressureare presented by Hoekstra [50]. The effect was modeled using theFrye–Mosby equation, which takes into consideration the feedvaporization and VLE impact on reaction rate of the individual sul-fur compounds. In this equation the Raoult’s law describes thephase equilibrium. The authors also consider that the H2/oil molarratio, temperature and vaporization percentage are constants. Theoperating conditions of the experiments are temperature of 343 �C,pressure of 57 kg/cm2 and LHSV of 2 h�1. The sulfur contained inthe product decreases from 84 ppm(w) with a gas/oil ratio of175 NL/kg to 3 ppm(w) with a ratio of 1167 NL/kg. This behavioris attributed to the effect of increased feed vaporization in thedibenzothiophene reaction rate.

Chen et al. [51] design, build and use a continuous flow unit forVLE flash experiments (H2–oil fractions) at bench scale and hydro-processing conditions (temperature of 250–400 �C and pressure of52–103 kg/cm2). This experimental unit allows for studying theVLE during catalytic hydroprocessing of petroleum fractions. Theunit has an equilibrium cell and a micro reactor. Both sections


are well defined within the unit of continuous flow such that theyare independent.

The authors present a gross sulfur speciation, that is they reportonly three components and their respective values of equilibriumrelationships at ten different temperatures when using light cycleoil (LCO) as feedstock (q = 0.936 g/cm3 at 16 �C, 128–431 �C cut),and at nine different temperatures when employing hydrotreatedLCO (q = 0.9201 g/cm3 at 16 �C, 116–426 �C cut).

Later Chen et al. [16] obtained experimental data in H2 – hydro-treated LCO and H2 – LCO systems. They discussed in detail the dis-tribution of various sulfur compounds between both equilibriumphases (vapor–liquid) to determine the intrinsic kinetics of hydro-treating reactions free of phase equilibrium. The experimental con-ditions covered specified range for the production of ultra-lowsulfur diesel [51]. The total concentration of sulfur in both phasesat various pressures and the total concentration of 4,6-dim-ethyldibenzothiophene (4,6-DMDBT) in both phases at differenttemperatures and pressures are reported. The authors generate afinest sulfur compound speciation (27 sulfur identifiable com-pounds) than in their previous work [51]. Equilibrium relation-ships with experimental data for each sulfur compound weredetermined at four temperatures maintaining the pressure con-stant, and at four different pressures while keeping constant thetemperature.

Chen et al. [52] also compared the effect of three feedstockswith different volatilities (LCO: q = 0.936 g/cm3 at 16 �C, 128–431 �C cut; white oil: q = 0.8152 g/cm3 at 16 �C, 211–490 �C cut;and a 50/50 wt% mixture: q = 0.8714 g/cm3 at 16 �C, 148–484 �Ccut) in the vaporized fraction at hydrotreating conditions [51].Density and simulated distillation of the liquid samples weredetermined from the equilibrium and the feedstocks for furthercharacterization in 29 pseudocomponents. Each feedstock is dis-tilled and eight fractions are obtained, which molecular weight,specific gravity, and simulated distillation are measured experi-mentally. From this information correlations are generatedbetween molecular weight and boiling point, and between spe-cific gravity and boiling point. These correlations are used toobtain the molecular weight and density of the 29 pseudocompo-nents. They modified a commercial program (CMG by ComputerModeling Group Ltd.) which performed flash calculations byadjusting interaction coefficients between hydrogen–hydrocarbonpseudocomponents in the VLE modeling (Peng–Robinson EOS)until predictions match with experimental data. The interactioncoefficients are correlated with boiling point of the pseudocom-ponents and the aromatic content of the feedstock.

After that, Chen et al. [53] investigated the relative volatility oftwo types of heavy gas oil (heavy gas oil 1: q = 0.9609 g/cm3 at16 �C, 202–703 �C cut; heavy gas oil 2: q = 0.8866 g/cm3 at 16 �C,201–800 �C cut) under similar operating conditions (350–430 �Cand 71–112 kg/cm2). The heavy gas oils have different composition(aromatic content), but similar boiling ranges. They also comparethe behavior of the kinetic constant (pseudo-first order) of the hyd-rodesulfurization of 4-methyldibenzothiophene and 4,6-DMDBT,without and with VLE effect at ultra-low sulfur diesel productionconditions [51,54] with LCO. The flow dynamics in hydrotreatersat pilot plant level using two different feeds (straight-run-LGO:q = 0.8392 g/cm3 at 16 �C, 127–435 �C cut; and LCO: q = 0.936 g/cm3 at 16 �C, 128–431 �C cut) was also studied [55]. Additionally,they perform computations to provide a mapping of the operatingconditions under which the desired operating regimes (plug flow,full catalyst wetting, and absence of reactor wall effects) aremaintained.

More recently, Chen et al. [4] developed a model of a trickle-bedreactor to simulate an adiabatic, steady-state hydrotreating reac-tor, considering the VLE effects. The feed was light gas oil:q = 0.8392 g/cm3 at 16 �C and 127–435 �C cut. VLE calculations




were performed simultaneously in each step of integration of thesimulation model of reactor, as represented schematically inFig. 7. The thermo-physical properties and mass flow of each phaseare updated as function of local variables along the catalyst bed.They make a comparison of the temperature profile and conversionof hydroprocessing reactions considering and excluding the VLEeffect. They also analyze the effect of varying the input tempera-ture, the gas/oil ratio and the pressure in the reactor operation.

In the last paper of Munteanu and Chen [56] the operatingregimes of a hydrotreating reactor at pilot plant level were inves-tigated, which processes a heavy gas oil (q = 0.9609 g/cm3 at16 �C, 202–703 �C cut) under conditions of commercial operation.They performed VLE experiments and calculations to accuratelypredict flowrates and properties of liquid and vapor phases. Withthis information the operating regimes under different conditionswere established, that in turns allows for generating a map of theconditions under which desired operating regimes are maintained.

Murali et al. [57] developed a two phase reactor model thatallows for simulating bench and commercial scale diesel hydro-treating reactors considering feed vaporization effects. Using theAspen Plus commercial simulator with the SRK EOS, they esti-mated a significant feed vaporization (20–50%). The model wasvalidated with plant data of a diesel hydrotreater to obtain ULSD.The model does not consider mass transfer limitations for sulfurcompounds due to the lack of data, except for H2 and H2S. Kineticparameters estimated from the bench scale experiments were usedto simulate the commercial reactor.

Avraam and Vasalos [58] developed a steady-state model forthe hydrotreating of trickle-bed reactors with light petroleumfeedstocks with a lot of volatiles compounds. It was found thatthe liquid phase holdup varies through the reactor due to partialvaporization of the oil light fractions, which modified the phaseproperties. A software for the thermophysical properties estima-tion as function of pressure, temperature and composition wasgenerated. The same software was used for calculating VLE (withSRK EOS) taking into account the non ideal behavior of the phase.Mass transfer velocities are determined by the effective diffusiv-ity method. Estimated results show good agreement with exper-imental data of a hydrodesulfurization pilot plant. Diesel wascharacterized by an inert pseudocomponent (Cþ17 fraction) toequalize the physical properties of the feed. The reactor is mod-eled in an adiabatic mode and an increased temperature profilethrough the catalytic bed is obtained. The temperature increaseis limited by the vaporization of the lighter hydrocarbon com-pounds because they consume a considerable amount of the gen-erated heat of the hydrotreating reactions.

Henry et al. [59] proposed a methodology to study complex feedconversion (heavy gas oil, 370–520 �C) with a hydrocracking cata-lyst. The reaction is carried out in a bench scale batch reactor at400 �C and 122 kg/cm2. Two types of bifunctional catalysts wereused to study the conversion. The feedstock and products werecharacterized by two-dimension gas chromatograph with a massspectroscopy detector. Samples of vapor and liquid were taken atdifferent times-on-stream. VLE calculation was performed usingthe Pro Sim Plus software with the Grayson–Streed thermody-namic model. The convergence criteria were vaporized fractionand vapor and liquid phase compositions.

Bellos et al. [60] studied the liquid phase vaporization effectand the gas–liquid mass transfer in an up-flow micro reactor. Amodel that takes into account both effects in H2–petroleum frac-tions systems was developed. Gas oil vaporization rate and masstransfer between gas and liquid through the reactor using a glo-bal mass transfer coefficient are determined. The gas oil is repre-sented by five fractions, each one having a hydrocarbonpseudocomponent and a sulfur pseudocomponent. The estimationof the pseudocomponents properties is based on the ASTM-D86


curve distillation. VLE and Henry’s constant are estimated withthe SRK EOS.

Pellegrini et al. [6] described a method to estimate heavyhydrocarbons critical properties and a procedure for integratingVLE with a reactor model for waxes hydrocracking (Fischer–Trop-sch). The integration allows for a better concordance betweenexperimental data and model predictions. The effect of H2/waxratio on conversion and product distribution was presented.Operating conditions were 343–371 �C and 36–61 kg/cm2. TheSRK EOS for VLE with own interaction parameters is used. Abench TBR is employed for the hydrocracking. Using a secondorder factorial design the effect of operating conditions is inves-tigated. Critical properties of short chain hydrocarbons areobtained from the literature, those of medium chain are obtainedfrom a data bank (Aspen HYSYS [61]) and for hydrocarbons oflarge chain the method developed by Soave [62] is used. To esti-mate the hydrocarbon–H2 interaction parameters, the Tsonopou-los and Heidman [63] correlations are applied. It was reportedthat H2/wax affects more the VLE than temperature and pressure.The model uses the SRK EOS for the VLE calculations in each inte-gration step.

4.3. Literature review of modeling with heavy crude oil and residue

Gauthier et al. [7] used an ebullated-bed hydroconversion unitwith two reactors and a flash separator between them to processa vacuum residue (3.91 �API) and generated VLE data at reactionconditions to describe the feed vaporization. The aim of the workwas to estimate the vaporized fractions as function of conversion.To improve the reactor modeling and to evaluate the interstageseparator benefits. Due to the lack of information to support theVLE prediction at the conditions of this process (temperature of400–450 �C, and LHSV of 0.15–1.3 h�1), the authors used owninformation to determine VLE in a theoretical manner using theGrayson–Streed thermodynamic model and PR EOS to comparethe predictions with experimental data, by means of the PRO II5.5 process simulator. The results showed that Grayson–Streedmodel subestimates the vaporized fraction while PR works well.It was found that the vapor flowrate in the two stages of ebullatedbeds can be controlled by gas remotion between stages, whichreduces the gas feed to the second reactor.

Nguyen et al. [8] proposed a kinetic model to describe theatmospheric residue (Arabian light) hydroconversion using a dis-perse catalyst in a batch reactor. The model takes into accountthe gas–liquid mass transfer, including hydrogen and fivepseudocomponents: unconverted residue (>510 �C), VGO (350–510 �C), distillates (180–350 �C), naphtha (40–180 �C) and gases(CH4, C2H6, C3H8, C4H10, C5H12 and H2S). The VLE is determinedby an adiabatic flash using the PROII software. The reaction con-ditions of the experiments were 420 and 430 �C, H2 partial pres-sure of 153 kg/cm2 and different reaction times. They estimatedstoichiometric coefficients, kinetic parameters and transfer coeffi-cients by minimum square non-linear regression. They proposedto introduce the H2 in the kinetic model and its transfer intothe liquid–vapor interphase. The reactions were proposed tooccur in the liquid phase and are global reactions between thepseudocomponents, representing the simultaneous catalytic andthermal contributions. The same mass transfer coefficient for H2

and for all the pseudocomponents is assumed, thus reducingthe number of parameters to be estimated. VLE for the pseudo-components is represented by an empirical correlation, whichdepends on the equilibrium constants. The thermodynamical dataare estimated by the Provision II (PROII) software from the simu-lated distillation curve and the liquid product experimental den-sity. The behavior of the vapor phase is predicted with SRK EOSand the liquid phase with Grayson–Streed.



Table 3aLiterature reports that consider VLE in reactor modeling.


Pressure(kg/cm2)

Setup EOS (VLE) Interactioncoefficients

Characterization Software forVLEand reactor

Feed’sproperties(petroleumfractions)

q (g/cm3) at16 �C

Cut(�C)

Akgerman et al. [5] H2/benzothiophene dissolved indecalin

313–358 70 Trickle bed reactor(isothermal)

SRK To be zero (H2 andhydrocarbons)


– – –

Smith and Satterfield[2]

H2/quinoline plus H2S dissolvedin white oil (C18–C36 naphthenicliquid)

365 70 Trickle bed reactor VLE by methods ofPrausnitz and c –UNIFAC

– Identifiablecompounds

– – –

LaVopa and Satterfield[39]

H2/DBF dissolved in n-hexadecane or squalane

350–390 71 Trickle bed reactor /i – Truncated virialEOSci – UNIFAC


VLE – computerprogramsprovidedby Prausnitzet al.[38]

– –

H2/n-butylbenzene dissolved insqualane

Collins et al. [40] H2/benzothiophene dissolved indecalin, 1-methylnaphthalene,n-hexadecane or n-eicosane

273–333 70 Trickle bed reactor(isothermal)

SRK To be zero (H2 andhydrocarbons)


– – –

Tesser et al. [41] Ethoxylation and propoxylationof fatty alcohols, chloroformfluorination, p-cresol alkylationwith isobutene or methanolhomologation toacetaldehydeH2/CO2

– – – UNIFAC-SRK – – – – –

Kulikov et al. [42] H2/a-methylstyrene 80–136 Atmospheric Pellets – – – – – –Khadilkar et al. [43] H2/cyclohexene – – Only modeling – Trickle

bed reactor and pellet(data collection)

– – – – – –

Akgerman et al. [1] H2/benzothiophene dissolvedin decalin

– – Only modeling – Tricklebed reactor (isothermaland nonisothermal)

RK, modified RK byWilson, modified RK byJoffe–Zudkevitch, SRK,PR, modified SRK byGraboski–Daubert, andSRK with Moysancorrelation (IB)

– – – – –

Nalltham et al. [44] H2/naphthalene dissolved intoluene, hexadecane,cyclohexane and white oil

250–350 52–207 Continuous stirred tankreactor (isothermal) –Gas/liquid separator

Ki = f(P, T) Ki’s values – adjustableparameters by cyclohexaneand white oil


– – –

Kocis and Ho [45] H2/benzothiophene dissolvedin hexadecane or tetracosane

325 32 Reactor model with VLE Raoult’s law andAntoine equation


– – –

Jong et al. [46] H2/HVGO 450 31 Trickle bed reactor(isothermally-operatedmicroflow equipment)

– – – – 0.921 370–520

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Table 3bLiterature reports that consider VLE in reactor modeling.


Pressure(kg/cm2)

Setup EOS (VLE) InteractionCoefficients

Characterization Software forVLE and Reactor

Feed’sproperties(petroleumfractions)

q (g/cm3)at 16 �C

cut (�C)

Bellos andPapayannakos [47]

H2/SRHGO 320–350 55 Trickle bed microreactor Translatedform of the Vander Waals

Five hydrocarbon and fivesulfur pseudocomponents

– – –

Hoekstra [50] H2/SR diesel(dibenzothiophenes)

343 57 Trickle bed reactor Raoult’s law – – 0.8570 152–424

Chen et al. [51] H2/LCO 250–400 52–103 Continuous bench-scale unit (VLEplus microreactor, independentinside the unit)

– – Speciation of three sulfurcompounds(dibenzothiophenic)

– 0.9360 128–431H2/hydrotreatedLCO

0.9201 116–426

Chen et al. [16] H2/LCO 250–400 52–103 Continuous flowbench-scale unit

– – Speciation of 27 sulfurcompounds(dibenzothiophenic)

– 0.9360 128–431H2/hydrotreatedLCO

0.9201 116–426

Chen et al. [52] H2/LCO 250–400 52–103 Continuous flowbench-scale unit

PR Owncorrelation

29 Hydrocarbonpseudocomponents

Commercial flash program fromCMG and modified to perform theflash calculation

0.9360 128–431H2/white oil 0.8152 211–490H2/mixture LCO-white oil (50–50 wt.%)

0.8714 148–484

Chen et al. [55] H2/SRLGO 250–400 52–103 Continuous flowbench-scale unit

PR Owncorrelation


Modified CMG 0.8392 127–435H2/LCO 0.9360 128–431

Chen et al. [53] H2/HGO (highcontent of aromatic)

350–430 71–112 Continuous flowbench-scale unit

PR Owncorrelation


Modified CMG 0.9609 202–703

H2/HGO (highcontent of paraffins)

0.8866 201–800

Chen et al. [54] H2/LCO 242–412 Pilot plant continuous-flow trickle-bed reactor andbench-scale continuous-flow VLEcell

Not mentioned Owncorrelation

Not mentioned Not mentioned – –

Chen et al. [4] H2/SRLGO 340–380 41–71 Reactor model (adiabatic) withVLE

PR Owncorrelation



Munteanu and Chen[56]

H2/HGO 350–420 0–143 Reactor model (adiabatic) withVLE

PR Owncorrelation

29 Hydrocarbonpseudocomponents modifiedby a corrective procedurewhen T P 390 �C becausefeed undergoes thermalcracking


Murali et al. [57] H2/diesel 300–380 40–46 Fixed bed reactor(bench scale) andmodeling (isothermal)

SRK – – Aspen-Plus 0.8595 198–364

14L.M

.Chávezet

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Tabl

e3c

Lite

ratu

rere

port

sth

atco

nsid

erV

LEin

reac

tor

mod

elin

g.

Au

thor

sSy

stem

Tem

pera

ture

(�C

)Pr

essu

re(k

g/cm

2)

Setu

pEO

S(V

LE)

Inte

ract

ion

Coe

ffici

ents

Ch

arac

teri

zati

onSo

ftw

are

for

VLE

and

Rea

ctor

Feed

’spr

oper

ties

(pet

role

um

frac

tion

s)

q(g

/cm

3)

at16

�Ccu

t(�

C)

Avr

aam

and

Vas

alos

[58]

H2/l

igh

toi

lfe

edst

ock

340

31O

nly

mod

elin

gfo

rtr

ickl

e-be

dre

acto

rsSR

K–

Sulf

ur

and

nit

roge

nco

mpo

un

ds,o

lefi

ns,

mon

o,di

and

tri

arom

atic

s,an

dC

17

+

Ow

nso

ftw

are

––

Hen

ryet

al.

[59]

H2/V

GO

400

122–

143

Bat

chre

acto

rG

rays

on–

Stre

ed–

–Pr

oSim

Plu

s0.

8618

370–

520

Bel

los

etal

.[6

0]H

2/L

owsu

lfu

rga

soi

l(L

SGO

)30

0–36

0–

–SR

K–

Five

hyd

roca

rbon

and

five

sulf

ur

pseu

doco

mpo

nen

ts–

0.82

2621

6–38

0H

2/H

igh

sulf

ur

gas

oil

(HSG

O)

0.85

5021

0–39

8Pe

lleg

rin

iet

al.[

6]H

2/w

axes

343–

371

36-6

1B

ench

scal

etr

ickl

e-be

dre

acto

rSR

KR

elat

ion

sby

Tson

opou

los

and

Hei

dman

[63]

n-A

lkan

es/i

so-a

lkan

es–

––

Gau

thie

ret

al.[

7]H

2/v

acu

um

resi

due

410–

440

163

Ben

chU

nit

Gra

yson

–St

reed

,PR

–Id

enti

fiab

leco

mpo

un

dsan

dh

ydro

carb

onps

eudo

com

pon

ents

ProI

I5.

51.

0450

500–

580

Ngu

yen

etal

.[8

]H

2/a

tmos

pher

icre

sidu

e42

0an

d43

015

3A

uto

clav

e(b

atch

mod

e–

disp

erse

dca

taly

st)

/i

–SR

Kc i

–G

rays

on–

Stre

ed

–Fi

velu

mps

Prov

isio

nII

(Pro

II)

0.95

76–




When the reaction is conducted with identifiable hydrocarbons,the reactor used for most of the authors is a TBR [2,39,40], exceptone study carried out in a CSTR [44], and another one that analyzethe effect of vaporization of the liquid in a catalyst pellet [42].

In general, the effect of operating conditions, gas liquid ratioand the volatility of the feedstock (solvent and reagent) upon con-version is studied. Regarding volatility, LaVopa and Satterfield [39]indicate that the greatest effect occurs when the fluid exhibits lowvolatilization and the absolute difference in volatility betweenreagent and solvent that does not react is high. The VLE model usedin the reactor simulation consists of conventional thermodynamicequations (SRK, PR, UNIFAC, Raoult law and Antoine). Only Akger-man et al. [1] analyzed the effect of calculating VLE with seven EOS,most of them are modifications in the SRK EOS.

Except for Nalltham et al. [44], the other works with identifiablehydrocarbon reactions do not consider the binary interactionparameter, or they do not mention it.

When working with petroleum fractions, most of the experi-mental equipment is bench or pilot scale, mainly trickle-bed reac-tors [4,6,7,16,46,47,50–56], fixed-bed reactor [57] and two batchesreactors [8,59].

The feedstocks are mainly middle distillates (LGO, HGO andLCO), and only two studies used residue [7,8].

Two approaches to determine properties of the pseudocompo-nents generated from the distillation curve of petroleum fractionsare presented. The first one is by generating correlations from ownexperimental data from the system [52–54,58], and the second oneis by using correlations reported in the literature [6,7,47,60]. Theexperimentation includes the feedstock fractionation by boilingpoints and determination of specific gravity and molecular weightfor each petroleum fraction. Finally, with these data correlations asa function of average boiling point of the cut can be developed.Chen et al. [52] obtained experimental data for 8 petroleum frac-tions and the correlations that they generated were used to calcu-late properties of 28 pseudocomponents.

The VLE model used for simulating the reactor consists of con-ventional thermodynamic equations such as SRK, PR, Grayson–Streed, and Raoult. Only two authors mention the binary interac-tion parameters: Pelligrini [6] calculated the parameters usingthe relations by Tsonopoulos and Heidman [63], while Chen et al.[52] developed their own correlation to calculate binary interac-tion parameters as a function of the average boiling temperatureof the pseudocomponents and the aromatic content of thefeedstock.

As the system becomes complex, the model to predict VLE issimplified, as can be seen progressively from Tables 1–3. Whenconsidering reaction and VLE in petroleum fractions systems, theauthors used conventional equations (Tables 3b and 3c). If identi-fiable compounds in solvent are used as reactive instead of petro-leum fractions, some authors employed UNIFAC to calculateactivity coefficients as shown in Table 3a. When the reaction isnot taken into account, more complex thermodynamic modelsare used (Tables 1 and 2), especially when using petroleum frac-tions or coal liquids.

4.5. Comparison of operating conditions for VLE, with and withoutconsidering reactor modeling

Figs. 8–10 summarize the ranges of operating conditions (pres-sure and temperature) and the type of feed used during experi-ments of the literature reports.

Fig. 8, shows that the majority of the research works indicatecompounds as an interval of the number of carbon atoms (e.g.C6–C16), belonging to families of alkanes, alkenes, aromatics, and



0

40

80

120

160

200

240

280

320

360

400

440

480

520

560

600

640

680

720

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460

Pre

ssur

e, k

g/cm

2

Temperature, C

C6-C16

Toluene

[35]

[37]

[19]

[18]

[15]

[9]

C3-C13

C5-C11

C6-C18 mixtureC7-C16 and coal

liquids

o

Fig. 8. Operating conditions for VLE of H2-pure hydrocarbons systems, without reactor modeling.

0

40

80

120

160

200

240

280

320

360

400

440

480

520

560

600

640

680

720

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460

2

Temperature, C

Coal liquids[25, 28]

Coal-derivedliquid[29]

Coal liquids[21]

Middleand heavy distillate. [32]

n-Decane, LVGO, HVGO and coalliquids[34]

Deasphaltenedbitumen Athabasca [22]

SRGO [10]

Hydrotreatedcoalliquid. [33]

SRLGO, SRHGO, atmosphericand vacuumresiduum[31]

Coal liquids[23]

Coal liquid[20]

Pre

ssur

e, k

g/cm

o

Fig. 9. Operating conditions for VLE of H2-petroleum fractions systems, without reactor modeling.


compounds containing heteroatoms of nitrogen or sulfur, whichare common compounds in coal liquids.

It is seen that H2-pure components systems have wide range ofpressure and temperature, which allows for obtaining more reli-able and accurate equations from proper treatment of the experi-mental data.


For H2–petroleum fractions systems, the pressure range isdecreased. The values of pressure are more practical for hydropro-cessing since there are not commercial processes that operate atsuch high pressures (300 kg/cm2 or more). The temperature rangeremains high as in the previous case (Fig. 9).




For studies that include reaction apart from VLE, due to the nat-ure of the hydrotreating process, it is not important to analyze thephase equilibrium at low temperatures, since there is no reactionto these conditions. The pressure that has been used for hydro-treating processes does not exceed 200 kg/cm2, which is reflectedin the range of pressures that explores the VLE of petroleum frac-tions that take into account the hydrotreating reactor model. Thehigh temperature is limited by the formation of coke (Figs. 10aand 10b).


Table 3 summarizes the main features of the literature reportsincluding the effects of VLE on the reactor performance study.The first work was published in 1985 and was VLE developed foridentifiable compounds. Most of the researches have conductedexperiments or theoretical calculations at high severity operatingconditions of pressure and temperature. The preferred thermody-namic models are the EOS’s of PR, SRK and modifications of them.Some authors use the correlation of Grayson–Streed, and othersthe Raoult’s law [45] or Ki values [44]. This is most probably dueto the ease simultaneous integration of the thermodynamic modelwith the reactor model. The vast majority of experimental andmodeling works used trickled-bed reactors. Collins et al. [40] andAkgermann [5] exclude interaction coefficients in the calculationof VLE due to excess hydrogen during experiments. Chen et al.[52] highlighted the need to generate correlations for H2-pseudo-components interaction coefficients as well as correlations todetermine molecular weight and density of the pseudocompo-nents. Most of the reports do not mention information about theinteraction coefficients. Heavy petroleum fractions are not com-mon in this type of studies most probably because at typical hydro-treating conditions the fraction of the feed that vaporizes is small,and VLE calculations are not necessary. The reported densities

0

40

80

120

160

200

240

280

320

360

400

440

480

520

560

600

640

680

720

0 20 40 60 80 100 120 140 160 180 200 22

Nallthamet al. [44]

Munteanu& Chen[56]

Chenet al. [4]

Pellegrini et al. [6]

Chenet al. [16, 51, 53, 55]

Muraliet al. [57]

Chenet al. [53]

Tempera

Pre

ssur

e, k

g/cm

2

Fig. 10a. Operating conditions for VLE of H2-petrol


(>0.8152 g/cm3) indicate that heavy petroleum fractions are used.Only two studies using residue (atmospheric or vacuum) as feedwere found [7,8], in which VLE is not described with detail.

5. General comments

In experimental works where solubility of H2 in hydrocarbons,petroleum fractions and carbon liquid was measured, there werefindings that establish that the solubility of H2 in solvent increaseswith a rise in temperature and pressure.

During experiments to measure VLE, either in batch or continu-ous systems, particular care needs to be put on the selection ofoperating conditions, e.g. residence time and temperature, to avoidor minimize thermal cracking of the feed due to the high severityof hydroprocessing.

As for petroleum fraction characterization (feed and products),it has been demonstrated that the more detailed pseudocompo-nents the better the agreement of the VLE prediction with experi-mental data.

Better determination of molecular weight and specific gravity ofthe pseudocomponents requires the development of correlationsbetween molecular weight and boiling point, and specific gravityand boiling point from enough experimental measurements.

The thermodynamic models commonly used for VLE predictionat hydroprocessing conditions are PR and SRK EOS’s. These equa-tions require the H2-pseudocomponents interaction parametersto be fitted with VLE experimental data.

The Grayson–Streed model [64] is often considered as a ‘‘refer-ence’’ model to simulate hydrogen/hydrocarbon equilibrium. How-ever, its pressure validity range is limited (up to 204 kg/cm2), andits performance is poor for mixtures involving heavy hydrocarbons[65]. Hence it is not the most adequate to predict phase equilib-rium data at operating conditions of hydrotreaters.

0 240 260 280 300 320 340 360 380 400 420 440 460

ture, Co

eum fractions systems, with reactor modeling.



50

70

90

110

130

150

170

270 290 310 330 350 370 390 410 430 450

Pre

ssu

re, k

g/cm

2

Temperature, C

Benzothiophene dissolved in decalin [5]

Sulfur compounds in some solvents [39]

Benzothiophene in several solventes. [40]

SRHGO [47]

VGO [59]

Vacuum Residue [7]

o

Fig. 10b. Operating conditions for VLE of H2–petroleum fractions systems, with reactor modeling.


The H2 solubility in hydrocarbons increases with pressure andtemperature. At pressure higher than 120 kg/cm2, the differencein hydrogen distribution coefficients does not depend strongly onthe nature of hydrocarbon neither on the temperature. At pressurebetween 20 and 120 kg/cm2, the differences are significantbetween the various systems reported in the literature.

The hydrogen solubility depends on the hydrocarbon type. Thearomatic hydrocarbons have the lowest value and the paraffinichydrocarbons the greatest.

Considering VLE in the reactor model predicts higher conver-sion of hydroprocessing reactions as compared with predictionswhere the VLE is not considered, due to the increment in concen-tration of the reactive species in liquid phase.

The experimental findings suggest that increasing the tempera-ture and the hydrogen flowrate and decreasing pressure, the oilvaporizated fraction is enhanced.

References about VLE for hydrogen with crude oil or residues athydrotreating conditions are scarce in the literature, i.e. only tworeports were found that consider the VLE in reactor modeling,which in principle is due to the difficulty to carry out the experi-ments and feed and product characterization.

Commercial softwares (Apen Tech, PRO-II, and CMG) are com-monly used to perform flash calculations when modeling VLE ofH2/hydrocarbons at hydroprocessing conditions.

To obtain good agreement between VLE predictions and exper-imental measurements, it is required to estimate the interactioncoefficients for the H2-pseudocomponents.

6. Concluding remarks

From the literature review, the following conclusions can bepointed out:

� When VLE is not considered in the simulation of hydrotreatingreactors for heavy petroleum fractions, the prediction of conver-sion may be affected depending on the feed properties andoperating conditions.


� Obtaining equilibrium data of H2/heavy petroleum fraction sys-tems requires to have a continuous flow equilibrium cell toreduce thermal cracking produced at severe hydroprocessingconditions. Due to the need to accurately measure gas andliquid flowrates and take liquid and gas samples for furtheranalysis, it is necessary to link the cell with an atmosphericflash unit.� The feed and product liquid streams are recommended to be

characterized by at least 30 pseudocomponents, to allow for abetter agreement between VLE prediction and experimentaldata. Higher number of pseudocomponents does not affect thecalculations.� Calculation of physical properties (e.g. molecular weight,

specific gravity, etc.) of feed and liquid product streamspseudocomponents requires to be done by means ofcorrelations, either taken from the literature or developedfrom experimental data. It is convenient to generate thecorrelations from own experimental data, because most of thetimes literature correlations are limited due to the range ofapplication.� The most used thermodynamic models to predict VLE at hydro-

treating conditions are PR and SRK EOS. To obtain good resultswith these equations, it is necessary to determine the H2-pseudocomponents interaction parameters with experimentalinformation.

7. Suggestions for future work

The following are some recommendations that were identifiedfrom the analysis of the state-of-the-art that need attention toproperly model feed vaporization during hydrotreating of oilfractions:

� To include the phases’ stability analysis in the VLE prediction todetermine the number of phases present in the system at thespecified temperature and pressure, which ensure its state of




the minimum Gibbs energy. Also, this analysis generates goodinitial values of the equilibrium constants to begin the phaseequilibrium calculations.� To develop or identify useful laboratory methods for finely frac-

tionation (by distillation or some other separation process) ofthe feedstock, mainly when it contains heavy material. If it werepossible, to obtain between 20 and 30 cuts with a uniform dis-tribution without thermal decomposition. Also, to developaccurate methods to experimentally determine average boilingtemperature, molecular weight and specific gravity of thesecuts. Instead, to propose or improve mathematical techniquesthat allow for substituting the lack of experimental data withgood results, such as molecular simulation.� To design, construct and operate the experimental device for

obtaining data of VLE of the systems: H2/crude or H2/atmo-spheric or vacuum residues. This information is useful for moreaccurately prediction of conversion of the reactions occurringduring hydrotreating of crude or residues, because it allowsfor properly selection of state equations for estimating the VLE.� To apply methodologies to define the number and appropriate

operating condition experimental runs to obtain sufficientexperimental data in the shortest possible time and reducingcosts.� To develop correlations to calculate binary interaction parame-

ters from enough experimental information of binary systemsH2-identifiable hydrocarbons to predict the H2-pseudocompo-nents binary interaction parameter. The correlations must befunction of some hydrocarbon property, such as boiling pointtemperature, molecular weight or others.� To identify a robust optimization method to fit the H2-pseudo-

components interaction parameters when the phase stabilityanalysis is included.

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