Le Wu ,Xiaoqiang Liang ,Lixia Kang ,Yongzhong Liu ,2,*

1 Department of Chemical Engineering,Xi'an Jiaotong University,Xi'an 710049,China

2 Key Laboratory of Thermo-Fluid Science and Engineering,Ministry of Education,Xi'an 710049,China

1.Introduction

Hydrogen is commonly used in hydrotreating(HDT)units in refineries to produce clean products.HDT units are key devices to improve the quality of fuel products by removing impurities in crude oil,such as sulfur,nitrogen,aromatics and olefins.The hydrogen demand of refinery is becoming even larger with processing inferior and heavy crude oiland increasing demand ofclean fuels.Itis imperative to reduce huge hydrogen consumption while satisfying the stringent regulations of clean fuels.

At present,the pinch analysis methods[1,2]and mathematical programming methods[3,4]are often used for the integration of hydrogen network.To couple the HDT processes with the hydrogen network,Wanget al.[5]extended the concentration potential concepts from water-using networks to the synthesis of hydrogen networks with multiple contaminants.Zhouet al.[6]presented a mixed integer nonlinearprogramming(MINLP)modelforhydrogen network with consideration of H2S removal by proposing an optimal desulfurization ratio in the absorber.The hydrogen network was effectively optimized with removing H2S in the recycle network.Based on this work,Jia and Liu[7]extended the desulfurization ratio to the removal of H2S,NH3and CH4in the recycle hydrogen,which enhanced the practicability of optimal hydrogen network.However,in the abovementioned work,the optimization of hydrogen network was usually conducted under the assumption that the hydrogen demand of each sink is fixed.In other words,the hydrogenation reactions in HDT processes are often ignored,which determine the hydrogen demands in the HDT units.To resolve this problem,Maoet al.[8]proposed a method for the optimization of hydrogen network,in which the hydrogen consumption of vacuum gas oil hydro-cracking reactor was considered,and the quantitative relationship between the hydrogen utility consumption and the sulfur concentration of the feed oil was proposed.In Umanaet al.'s work[9],the hydrodesulfurization(HDS)reaction was incorporated into the optimization of the hydrogen network,and the effect of hydro-cracking reaction was also analyzed[10].Nevertheless,the hydrogen consumption are underestimated because the hydrodenitrogenation(HDN),hydrodearomatization(HDA),hydrodeoxygenation and demetalation[11]are not taken into consideration.This is to say that all these reactions associated with hydrogen consumption in the HDT units in refineries should be considered if much more rigorous hydrogen consumption is involved,especially for the hydrogen consumed by HDS,HDN and HDA reactions[12].

In this work,to resolve the problem mentioned above,we proposed an integration strategy of hydrogen network optimization coupled with an operational optimization for hydrogen sinks,which features that before the optimization of all HDT units,an operational optimization modelofthe HDT units is established to optimize the operational conditions of HDT units and to determine the parameters of hydrogen sinks base on the characteristics of reaction kinetics of HDS,HDN and HDA processes.An example of a refinery with annual process capacity of eight million tons is adopted to demonstrate the feasibility of the proposed strategy and the related optimization models.

2.Integration Strategy of Hydrogen Network Based on the Operational Optimization of HDT Units

The hydrogen network in a refinery consists of hydrogen sources and hydrogen sinks.The demand of hydrogen sink depends on the hydrogenation reactions.In the HDT processes,hydrogen is mainly consumed to remove sulfur,nitrogen,aromatics and other impuritieset al.Therefore,the operational conditions of HDT units should be optimized before the hydrogen consumption of the hydrogen network is minimized.

In this work,an integration strategy of hydrogen network and an operational optimization model of HDT units are proposed.The relationship between these two models is shown in Fig.1.In general,the hydrogen network optimization model is a MINLP model.When the hydrogen network optimization model is coupled with the HDS,HDN and HDA reaction kinetics,it is extremely difficult to obtain the optimal solution because a large amount of non-linear terms are included in the reaction kinetics[13,14].To overcome this difficulty,the proposed integration strategy in this work is to segregate the hydrogenation kinetics from the hydrogen network optimization model.To this end,there are two steps ofthis strategy.Thefirststep is thata nonlinearprogramming(NLP)modelis established to optimize the operationalconditions ofthe HDT units in the refinery,in which the HDS,HDN and HDA reaction kinetics are included.Hence,the hydrogen consumption for each HDT unit is optimized.Thereafter,the parameters of hydrogen sinks of the hydrogen network are determined for the hydrogen network optimization.The second step is that the MINLP model for hydrogen network optimization is solved to achieve the optimal structure and operational conditions of the hydrogen network,in which the parameters of hydrogen sinks are obtained by the previous step.And the cost of the hydrogen network is minimized.

Fig.1.Diagram of a hydrogen network and HDT units.

3.Mathematics Models for the Proposed Strategy

3.1.Optimization ofoperational conditions ofHDT units and determination of the parameters of hydrogen sinks

3.1.1.Hydrogen consumption of HDT units

In a HDT unit,hydrogen and the impurities in the distillate or fuel oil react at high temperature and high pressure to remove sulfur,nitrogen and aromatics.Acertain amountofhydrogen is also dissolved in the distillate and involved in some fast reactions,olefin saturation and demetalation,for examples.Therefore,the hydrogen consumption of a certain HDT unit or hydrogen sink(SK),denoted byi,can be calculated by[15]

whereFdenotes the flowrate of hydrogen consumption in a HDT unit(or hydrogen sink),in Nm3·h-1;i∈SK;The superscripts S,N,A,D and O stand for the processes of desulfuration,denitrification,aromatic hydrogenation,dissolution and other processes that consume hydrogen.

For a certain HDT unit,the hydrogen consumption of HDS can be calculated by[16]

wherevfieedis the volumetric flowrate of feed in the HDT unit,in m3·h-1;SfeedandSprodare sulfur concentration in feed and product,in μg·g-1.

The hydrogen consumption of HDN can be represented by[16]

whereNdenotes nitrogen concentration in stream,in μg·g-1.

The hydrogen consumption of HDA can be calculated by[16]

whereAdenotes aromatic concentration in stream,in%.

The dissolved hydrogen can be calculated by[16]

wheredidenotes dissolution coefficient in the HDT unit.

In a HDT unit,apart from the hydrogen consumption mentioned above,the remaining hydrogen consumption mainly attributes to the processes of olefin saturation and demetalation.Because the process of olefin saturation is a fast reaction and the metal concentrations in streams are much less than other impurities,we assumed that the termFiOin Eq.(1)is constantalthough the reactions occurunder differentoperational conditions[17,18].Therefore,in practice,if the total hydrogen consumption of a certain HDT unit in the original hydrogen network is known,the termFiOcan be calculated by subtracting the hydrogen consumption of the processes of desulfuration,denitrification,aromatic hydrogenation and dissolution from the total hydrogen consumption.

3.1.2.Characteristics of hydrogenation reaction kinetics

In this paper,the processes ofHDS,HDNand HDAare mainly considered,their kinetics characteristics are listed in Table 1.

Table 1Kinetics of HDS,HDN and HDA

In Table 1,kdenotes the kinetic constant;K1,K2andK3are the inhibition coefficient of three-ring aromatics,nitrogen and sulfur concentration in feed on HDS reaction;3+R,N and S are the concentrations of threering aromatics,nitrogen and sulfur in feed,in μg·g-1;pH2is the partial pressure of hydrogen,in MPa;α denotes the coefficient of pressure;LHSV is liquid hourly space velocity,in h-1;Xis the conversion of aromatics,in%;The superscripts fand rare the forward and reverse reactions of HDA.

whereAis the pre-exponential factor;Edenotes the activation energy,in kJ·kmol-1;Trepresents the reaction temperature,in K.

3.1.3.Minimization ofhydrogen consumption ofHDTunitsand optimization of hydrogen sinks

In this work,we assume the hydrogen purities of inlet streams of HDT units are kept constant.Then,the total hydrogen consumption of HDT units in a refinery can be minimized by optimizing the operational conditions of each HDT unit coupled with the reactions kinetics of hydrogenation process.For the HDT units in a refinery,the objective is to minimize the hydrogen consumption of the entire HDT system,i.e.

When the operational conditions and the removal rates of impurities are optimized,the specifications on feedsand products should be satis fied.

1.The concentrations of sulfur,nitrogen and aromatic in products

When the hydrogen consumption ofthe HDT units is minimized,the operational conditions would be changed according to the characteristics of reaction kinetics.To make these changes feasible,we can adjust the temperatures and pressures of the hydrogenation reactions within the allowable ranges.

These above equations(Eqs.(1)–(14))are a NLP model.It can be solved to obtain the hydrogen flowrate of each HDT unit,the parameters of hydrogen sinks and operational temperatures and pressures.

3.2.The integration of hydrogen network based on optimal parameters of hydrogen sinks

3.2.1.Objective function

The cost of the hydrogen utility and the benefit of fuel gas are taken as the objective function.

whereCH2denotes the cost of hydrogen utility,in CNY·a-1;Cfuelis the revenue of fuel gas,in CNY·a-1.

The cost of the hydrogen utility can be calculated by

3.2.2.Constraints

The constraints in this model are mass balance,hydrogen balance,hydrogen purity and demand constraints.

Mass balance

wherezi,jdenotes the connection betweenith hydrogen sink andjth hydrogen source,0 or1;Fi,jisthe hydrogenflow rate fromjth hydrogen source toith hydrogen sink,in mol·s-1.

The optimal structure and operational conditions of the hydrogen network can be obtained by solving the model mentioned above that is a MINLP model.

4.Case Study

4.1.Fundamental data of a refi nery

For a typical refinery with annual process capacity of 8 million tons,the optimization of the hydrogen network in the refinery is conducted based on the actual running data with the proposed strategies in the previous sections.

In this refinery,the crude oil is distilled to separate kerosene(K),straight-run diesel(SD)and vacuum gas oil(VGO)in the atmospherevacuum distillation unit.VGO are refined in the VGO HDT unit with annual process capacity of 2.6 Mt,and the refined VGO enters into a fluid catalytic cracker to obtain the cracked diesel(CD)and the cracked gasoline(CG),which are refined in the CD HDT unit with annual process capacity of 0.8 Mt.and the CG HDT unit with the annual process capacity 1.4 Mt.And the kerosene(K)and the straight-run diesel(SD)enter the K HDT unit with 0.8 Mt annual process capacity and SD HDT unit with 2.6 Mt annual process capacity to obtain the qualified products.In short,there are 5 hydrogen sinks of the hydrogen network in this refinery.The hydrogen utility of the hydrogen network is provided by the continuous catalytic reformer(CCR).The properties of streams and the operational conditions are listed in Table 2.In addition,the ranges of operational conditions and specifications are listed in Table 3.

The hydrogen sinks and hydrogen sources are listed in Table 4.In the original hydrogen network,the hydrogen stream from CCR is used to satisfy all the demand of hydrogen sinks,which is 599.5 mol·s-1.And the off gas streams from VGO,CD and SD HDT units discharge to the fuel system.The original structure of hydrogen network is shown in Fig.2.

Table 4Original parameters of hydrogen sources and sinks

Fig.2.Original hydrogen network of the refinery.

Table 2Properties and operation conditions

Table 3Ranges of operational conditions and specifications

4.2.Comparisons of three integration strategies for hydrogen network

In this work,three strategies are proposed to study the effects of hydrogenation reactions on the hydrogen network.These strategies are as follows.

Strategy A:Optimization of the hydrogen network is performed on the basis of the original data of the hydrogen network in refinery.This means that based on original data we directly solve the MINLP model for the hydrogen network,as shown in Section 3.2;

Strategy B:Minimization of hydrogen consumption of the refinery is based on the reactions kinetics of HDS,HDN and HDA processes in the HDT units.This implies that the NLP model shown in Section 3.1 is solely solved to minimize of entire hydrogen consumption of the refinery;

Strategy C:Optimization of the hydrogen network based on the optimal parameters of hydrogen sinks based on Strategy B.In this strategy,the MINLP model shown in Section 3.2 is solved based on the optimal parameters of hydrogen sinks obtained by solving the NLP model shown in Section 3.1.

The comparisons of the three strategies on the hydrogen consumption of each HDT unit are shown in Fig.3.

Fig.3.Comparison of the hydrogen consumption of HDT units.

As shown in the figure,the hydrogen consumption of each HDT unit is remarkably reduced when Strategy A is applied.The hydrogen consumption in the VGO HDT unit accounts for 90.3%of the hydrogen consumption in the originalhydrogen network.The hydrogen consumption of the CD,SD and K HDT units reduce approximately 25%of the original hydrogen consumption,and the hydrogen consumption in the CG HDT unit is only 66.1%of the original consumption.

When Strategy B is applied,the hydrogen consumption is also decreased.Results show that the hydrogen consumptions in the VGO and CG HDT units are 93.4%and 76.8%of the original ones.It implies that the hydrogen consumption of each HDT unit can be reduced by merely optimizing its operational conditions.

Strategy C can be considered a combination of Strategy A and Strategy B.When Strategy C is used,the hydrogen network is optimized with the operational optimization of the HDT units in the entire system.The results show that the hydrogen consumption of the VGO and CG HDT units are only 84.3%and 50.6%of the original ones,respectively.This indicates that the hydrogen consumption of a refinery can be effectively reduced when the hydrogen network is integrated with the operational optimization of the system of the HDT units.

In this context,these results also reveal that the operational optimization ofthe HDT units in refineries should be imposed to determine the parameters of hydrogen sinks base on the characteristics of reaction kinetics ofthe hydrogenation processes before the optimization ofthe hydrogen network is performed through the source-sink matching methods.In the next section,the effects of the optimization by Strategy B will be further analyzed and discussed to clarify the hydrogen consumptions of the HDS,HDN and HDA processes in the HDT units.

4.3.Analysis of the operational optimization of HDT units

According to Strategy B,the NLP model proposed in Section 3.1 is solved on GAMS software package with the solver KNITRO under thefixed impurities concentrations in feed oil of each HDT unit to optimize operational conditions and determine the parameters of hydrogen sinks.

The optimal parameters of hydrogen sinks and the operational conditions are listed in Tables 5 and 6.And the hydrogen consumption for the removal of different impurities in each HDT unit is shown in Fig.4.The results from Tables 4 and 5 show that the hydrogen flowrate from the CCR unit reduces from 599.5 mol·s-1to 527.3 mol·s-1with 72.2 mol·s-1reduction,which accounts for 12%of the original hydrogen consumption,when Strategy B is applied.

Table 5Optimal hydrogen flowrates of hydrogen sinks

Table 6Optimal operation conditions of HDT units

From Fig.4 we can see that Tables 4 and 5 show the hydrogen consumed to remove sulfur,nitrogen and aromatics takes 90%proportion of the total hydrogen consumption of the VGO and SD HDT units,for instance,in the original data the hydrogen consumed in HDS,HDN and HDA reactions in VGO HDT unit is 222.1 mol·s-1and the total consumption is 246.6 mol·s-1,whereas the proportion in the K,CD and CG HDT units is over 50%.This indicates that the hydrogen consumption would be underestimated if the hydrogen consumption of the HDS process is only considered.In other words,the hydrogen consumption of HDS,HDN and HDA reactions in the VGO and SD HDT units must be taken into consideration,and these three reactions,the olefins saturation,and dissolved hydrogen should be also considered when calculating the hydrogen consumptions of the K,CD and CG HDT units.

From Fig.4 and Table 6 we can see that the hydrogen consumed in the HDS and HDA processes can be reducedviathe optimization of operationalconditions ofthe HDT units.The reason is thatthe HDAprocess is a reversible reaction of which the conversion is higher under higher temperatures.Therefore,as long as the specifications are satis fied in the refinery,the aromatics in products should be increased by lowering the reaction temperature to obtain a low conversion,which can decrease the hydrogen consumption in the HDA process.In this context,low temperature may lead to the increase of sulfur concentration in product,but the process can be enhanced by increasing the reaction pressure.Despite thatthese adjustments may increase the degree ofdenitrification and lead to the increase of hydrogen consumption in the HDN process,the total hydrogen consumption is reduced.This point can be verified by the data in Fig.5,which presents the comparisons of sulfur,nitrogen and aromatics concentrations of products in HDT units with the original data.

Itcan be seen from Fig.5 thatthe sulfurand aromatic concentrations ofproducts in allHDT units increase by a certain amountcompared with the originaldata.In the VGOHDT unit,the nitrogen concentration ofthe refined VGO increases.Thus its hydrogen consumption reduces.On the other hand,in other HDT units,the hydrogen consumption for denitri fication increases due to the decrease of nitrogen concentration in their products.However,the total hydrogen consumption of each HDT unit reduces accordingly.

Fig.4.Comparison of hydrogen consumptions of HDS,HDN and HDA reactions in HDT units.

4.4.Analysis of the integration of hydrogen network with operational optimization of HDT units

In this section,the effects of Strategy C is further analyzed and discussed.

According to Strategy C,the MINLP model proposed in Section 3.2 is solved on GAMS software package with the solver SCIP by using the optimal parameters of hydrogen sinks in Table 5 to optimize the hydrogen network of the refinery.The optimal structure of the hydrogen network is shown in Fig.6,and comparisons between the results obtained by Strategy C and those in the original network are listed in Table 7.

It can be seen from Fig.6 and Table 7 that when Strategy C is employed,the hydrogen consumption of CCR is further reduced from 527.3 mol·s-1to 429.9 mol·s-1with 97.4 mol·s-1reduction,the annual hydrogen cost reduction is 5.73×107CNY from 3.173×108CNY to 2.600×108CNY.Compared with the original hydrogen network,and the reduction proportion reaches 28.2%.Furthermore,although the benefit of fuel gas reduces to 2.260 × 107CNY·a-1by the VGO off gas recovery,it leads to the decrease of the total annual cost by 3.21 × 107CNY·a-1,reduced by 11.9%.Consequently,the hydrogen consumption of the refinery could be effectively reduced by using Strategy C in this work.

Fig.5.Comparisons of sulfur(a),nitrogen(b)and aromatics(c)concentration of product in HDT units.

Fig.6.Optimal structure of the hydrogen network.

Table 7Comparisons between the results of Strategy C and the original network

5.Conclusions

An integration strategy of hydrogen network and an operational optimization modelofHDT unitsare proposed based on the characteristics of reaction kinetics of HDT units.Three strategies are proposed to analyze the effects of hydrogenation reactions in HDT units on the hydrogen network integration.For Strategy A,the hydrogen network is integrated by the conventional method;For Strategy B,a NLP model is established to minimize of the hydrogen consumption of the HDT units in the refinery;For Strategy C,the hydrogen network is integrated by the combination ofStrategy Aand Strategy B,in which a MINLP modelcoupling with the hydrogenation reactions kinetics is used.

A practical refinery with annual processing capacity of eight million tons is taken as an example to demonstrate the feasibility and effectiveness of the proposed strategies and the model.The results show that the HDS,HDN and HDA reactions are major sources of the hydrogen consumption in the HDTunits.The hydrogen consumption is underestimated if the HDN and HDA reactions are neglected during the integration of hydrogen network.The total hydrogen consumption is reduced by 18.9%by applying the conventional hydrogen network optimization.When the hydrogen network is optimized after the operational optimization ofHDT units is performed,the hydrogen consumption is reduced by 28.2%.When the benefit of the fuel gas recovery is further considered,the total annual cost of hydrogen network can be reduced by 3.21× 107CNY·a-1,decreased by 11.9%.

In conclusion,the proposed strategy and the related model could effectively reduce the hydrogen consumption of a refinery.And the operational optimization of the HDT units in refineries should be performed prior to the conventional optimization of hydrogen network during when the entire hydrogen network is optimized.

Nomenclature

Aaromatic concentration,μg·g-1

Ccost,CNY·a-1

ddissolve

Eactivation energy,kJ·kmol-1

Fhydrogen flowrate,mol·s-1

ΔHcalorific value,kJ·mol-1

HSinternal hydrogen sources

HU hydrogen utilities

Kinhibition coefficient to HDS reaction

kkinetic constant

LHSV liquid hourly space velocity,h-1

Mratio between non-aromatics and aromatics

Nnitrogen concentration,μg·g-1

Putilities prices,CNY·mol-1or CNY·kJ-1

preaction pressure,MPa

Ssulfur concentration,μg·g-1

SK hydrogen sinks

SR hydrogen sources

Treaction temperature,°C

vvolume flowrate of feed,m3·h-1

Xconvert ratio of aromatic,%

yhydrogen mole purity,%

zexistence of matches between hydrogen sources and hydrogen sinks,0 or 1

3+R concentration of three-ring aromatics,μg·g-1

α pressure dependence term

Superscripts

A aromatic

CH cycle hydrogen

D dissolution

f forward reaction of HDA

L lower bound

N nitrogen

O other

r reverse reaction of HAD

S Sulfur

U upper bound

Subscripts

fuel fuel gas

ieach HDT unit or hydrogen sink

jeach hydrogen source

[1]G.P.Towler,R.Mann,A.J.L.Serriere,C.M.D.Gabaude,Refinery hydrogen management:Cost analysis of chemically-integrated facilities,Ind.Eng.Chem.Res.35(7)(1996)2378–2388.

[2]G.Liu,H.Li,X.Feng,C.Deng,Pinch location of the hydrogen network with purification reuse,Chin.J.Chem.Eng.21(12)(2013)1332–1340.

[3]S.Wu,Y.Wang,X.Feng,Unified model of purification units in hydrogen networks,Chin.J.Chem.Eng.22(6)(2014)730–733.

[4]X.Liang,L.Kang,Y.Liu,The flexible design for optimization and debottlenecking of multiperiod hydrogen networks,Ind.Eng.Chem.Res.55(9)(2016)2574–2583.

[5]X.Wang,Z.Wang,H.Zhao,Z.Liu,A procedure for design ofhydrogen networks with multiple contaminants,Chin.J.Chem.Eng.23(9)(2015)1536–1541.

[6]L.Zhou,Z.Liao,J.Wang,B.Jiang,Y.Yang,Hydrogen sul fide removal process embedded optimization of hydrogen network,Int.J.Hydrog.Energy37(23)(2012)18163–18174.

[7]X.Jia,G.Liu,Optimization of hydrogen networks with multiple impurities and impurity removal,Chin.J.Chem.Eng.24(9)(2016)1236–1242.

[8]J.Mao,G.Liu,Y.Wang,D.Zhang,Integration ofa hydrogen network with the vacuum gas oil hydrocracking reaction,Chem.Eng.Trans.45(2015)85–91.

[9]B.Umana,A.Shoaib,N.Zhang,R.Smith,Integrating hydroprocessors in refinery hydrogen network optimisation,Appl.Energy133(0)(2014)169–182.

[10]B.Umana,N.Zhang,R.Smith,Developmentofvacuumresidue hydrodesulphurization—hydrocracking models and their integration with refinery hydrogen networks,Ind.Eng.Chem.Res.55(8)(2016)2391–2406.

[11]H.Korsten,U.Hoffmann,Three-phase reactor model for hydrotreating in pilot trickle-bed reactors,AIChE J.42(5)(1996)1350–1360.

[12]M.A.Rodríguez,J.Ancheyta,Modeling of hydrodesulfurization (HDS),hydrodenitrogenation(HDN),and the hydrogenation of aromatics(HDA)in a vacuum gas oil Hydrotreater,Energy Fuel18(3)(2004)789–794.

[13]S.K.Bej,A.K.Dalai,J.Adjaye,Comparison of hydrodenitrogenation of basic and nonbasic nitrogen compounds present in Oil Sands derived heavy gas oil,Energy Fuel15(2)(2001)377–383.

[14]F.Jiménez,V.Kafarov,M.Nu?ez,Modeling of industrial reactor for hydrotreating of vacuum gas oils:simultaneous hydrodesulfurization,hydrodenitrogenation and hydrodearomatization reactions,Chem.Eng.J.134(3)(2007)200–208.

[15]L.C.Casta?eda,J.A.D.Mu?oz,J.Ancheyta,Comparison of approaches to determine hydrogen consumption during catalytic hydrotreating of oil fractions,Fuel90(12)(2011)3593–3601.

[16]D.Li,Hydrotreating Technology and Engineering,China Petrochemical Press,Beijing,2004(In Chinese).

[17]X.Liang,Y.Liu,Simulation of a wax oil hydrotreating unit and calculations of hydrogen consumption at off-design conditions,J.ECUST.38(6)(2012)718–723(In Chinese).

[18]L.Wu,Y.Liu,Environmental impacts of hydrotreating processes for the production of clean fuels based on life cycle assessment,Fuel164(2016)352–360.

[19]T.V.Choudhary,S.Parrott,B.Johnson,Unraveling heavy oildesulfurization chemistry:Targeting clean fuels,Environ.Sci.Technol.42(6)(2008)1944–1947.

[20]R.M.Cotta,M.R.Wolf-Maciel,R.M.Filho,A cape of HDT industrial reactor for middle distillates,Comput.Chem.Eng.24(2)(2000)1731–1735.

[21]S.M.Yui,E.C.Sanford,Kinetics of aromatics hydrogenation of bitumen-derived gas oils,Can.J.Chem.Eng.69(5)(1991)1087–1095.