yang 2006 chinese journal of chemical engineering

7/29/2019 YANG 2006 Chinese Journal of Chemical Engineering

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Chinese J . Chem. Eng., 14(3) 301-308 (2006)

Multiplicity Analysis in Reactive Distillation Column Using ASPENPLUS*YANG Bolun(#2 $lf'k)**,WU Jiang(% iI), ZHAO Guosheng(&@ E),WANG H uaj un( qq)and LU Shiqing( f m)State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, ChinaAbstract Reactive distillation processes for synthesis of ethylene glycol (EG) and ethyl tert-butyl ether (ETBE)were modeled with the simulation package ASPEN PLUS. The input multiplicity and output multiplicity were dis-cussed with the method of sensitivity analysis for both cases. In EG production process, steady state multiplicitieswere studied in terms of effective liquid holdup volume and boil-up ratio. In ETBE synthesis process, the user ki-netic subroutine was supplied into ASPEN PLUS firstly, and then the composition, temperature and reaction-rateprofiles within the reactive distillation column were presented in detail. A set of stable solution branches based ondistinct initial guesses for a range of boil-up ratio were found in EG synthesis. Input multiplicities were observedfor a range of reboiler duty at several values of reflux ratio for ETBE synthesis process. These results can be used toavoid excessive energy consumption and achieve optimum design of reactive distillation column.Keywords reactive distillation, ASPEN PLUS, multiplicity, ethyl tea-butyl ether, ethylene glycol

1 INTRODUCTIONReactive distillation is a multifunction reactor

concept combining chemical reaction and distilla-t i ~ n " - ~ ' .The integration of reaction and distillation inone unit may yield seve ral advantages: (1) Selectivityand conversion can be improved by continuous re-moval of produ cts from reaction zone; (2) The directheat integration decreases the heat dema nd especiallyfor strong exothermic reaction, so that hot spot istherefore avo ided; (3) Com bination of the reaction andseparation into one unit leads to significant capitalsaving; (4) When the feed point is located below thereaction zone, poisoning of the catalyst can be avoided,resulting in a longer catalyst life than in the conven-tional systems.

Due to the interaction between chem ical reactionand d istillation, reactive distillation can exhibit intri-cate nonlinear phenomena and m~ltiplicity[~-~].wotypes of multiplicities such as input multiplicity andoutput multiplicity have been confirmed in reactivedistillation processe s.

Input multiplicity refers to the case when thefmed output states correspond to a multiple set of in-put variables. It depends on the choice of output ormeasured variables, and always associated with the

so-called zero dynamics of the system, which can beobserved by an unexpected inverse response of theoutput. On the other hand, output multiplicity indi-cates the case when the fixed input states correspondto a multiple set of output states which possibly con-tain both stable and un stable states. Only stable stateshave practical significance, some of the stable statesare desirable, and the rest states are trivial for practicalapplication.

To design a reactive distillation process, it is im-portant to discover all m ultiple steady states within thepractical domain of operating variables, to knowwhether they are desirable, and to understand how thecolumn response to changes in ope ration variables.

For the production of ethylene glycol (EG), Chicand Miao"' used an equilibrium model with thehomotopy continuation method to show the existenceof m ultiple steady states. However, only one operationparameter, the overall effective liquid holdup was in-vestigated, other important operating variables such asreflux ratio and reboiler duty were not considered inpractical operation.

Sneesby et aZ.[9s'01escribed the input multiplic-ity for the synthesis of ethyl tert-butyl ether (ETBE)and ind icated the significance of input m ultiplicity for

Received 2005-04-04, accepted 2006-01-31.Scicnce Foundation of China (No.20176044, No.20476084).

* Supported by the Key Project of National Natural Science Foundation of China (No.20436040) and the National Natural**To whom correspondence should be addressed. E-mail: [email protected]


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302 Chinese J. Ch. E. (Vol. 14,No.3)process control problems. Bisowarno and Tad&"]evaluated the importance of input multiplicity duringstartup by dynamic sim ulation. Although several au-thors simulated the reactive distillation process ofETBE synthesis, output multiplicity was seldom men-tioned and the effects of operating parameters oncolumn performance were not discu ssed thoroughly.The o bjective of this paper is to analyze and dis-cuss steady-state multiplicity more thoroughly andcomprehensively by considering more operation pa-rameters in reactive distillation column. Tlvo cases,EG production and synthesis of ETBE, a re chosen asthe model system using the simulation packageASPEN PLUS, which is w idely used for the flowsheetsimu lation in the process industries"2-'s1. The multi-ple solutions may be found by pe rformin g a sen sitivityanalysis on one or more parameters, or varying initialguess, the input and output multiplicity thus can beconfirmed.2 BASIC PROCEDURE FOR MULTIPLICITYANALYSIS

In order to analyze the multiplicity in reactivedistillation column using ASPEN PLUS, two basicsteps are required.

Firstly, the reactive distillation column is simu-lated by the module, RadFrac. For this purpose,ASPEN PLUS requires the specification of compo-nents, property method, feed conditions (flow rate,composition and thermal state), operating pressure,column configuration (number of stages, feed location,reaction stage, types of condenser and reboiler), twooperating parameters, and reaction type. The two op-erating parameters can be chosen from a set of pa-rameters such as reflux ratio, distillate rate, bottomsrate, reboiler duty, condenser duty, etc. The reactiontype can be chosen from kinetic, equilibrium andconversion.

Secondly, sensitivity analysis is carried out toinvestigate the effects of operating parameters oncolumn performance. As one of model analysis tools,sensitivity analysis provides a feasible method to findmultiplicity in reactive distillation column. In the fol-lowing studies, the option is selected that current re-sults are used as initial estimates for the next step. Inthis case, only one operating parameter and the initialestimates are variable. Simulations are trivially con-verged to extreme (very low and very high) values ofcertain parameter at first, and then the param eter var-June, 2006

ies continuously with a small step towards the otherextreme. If divergence occurs, the step size is reducedby half until the step size is sma ll enough. The abovesimulation procedure is repeated for all possible oper-ating parameters until all interesting cases are con-verged. After the solution curves are observed andanalyzed, the multiplicity existence in the operatingregion can be determined. It is of interest to discusswhy multiple steady states can be found by perform-ing a sensitivity analysis.

A typical solution behavior is shown in Fig.1 forthe system which is in the region of output multiplicity.When the value of parameter 1 s in the range betweena an d b, the system has three states, A, B and C withdifferent value of y. In this case, initial guess leads towhether a simulation converges towards the high orlow steady state or if divergence occurs. In order totrace steady-state solution paths, the simulations arerun outside the region of multiplicity. Once the simu-lation converges, current results are used a s the initialguess, and then a small step is given to parameter 1.According to local convergence of the algorithm, thesolution will trace one steady-state solution path andwill not deviate it until a turning point such as point cand d is encountered yhen the step is small enough.When the solution approaches to the turning point, i twill jump from one solution branch to another or di-vergence will occur. From the behavior of the solutioncurve, multiplicity and turning points can be deter-mined.

Ia h L

Figure 1 'Qpical behaviorof target parameter in theregion of output multiplicity

3 RESULTS AND D ISCUSSION3.1 Multiplicity analysis for EG synthesis

The hydration of ethylene oxide (EO) is irre-versible and proceeds in the presence of a catalyst:


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Multiplicity Analysis in Reactive Distillation Column Using ASPEN PLUS 303C,H,O +H,O --+ C,H,O, ( 1 )

Simultaneously, a side reaction in which EG re-acts with ethylene oxide to yield diethylene glycol(DEG) ill take place:

CzH4O+CzH60,+4HloO3 (2 )Baur et a1.[3' ndicated there are two main disad-vantages for EG production in a conventional reactor.

Firstly, the reaction rate constant of the side reaction isabout three times that of the main reaction, therefore aconsiderable amount of DEG s produced. Secondly,the two reactions are both highly exothermic and re-quire better temperature con trol. A reactive distillationcolumn offers both the ad vantages of heat integrationand timely removal of the desirable product, EG, oprevent further reaction to DEG Thus, reactive d istil-lation process enh ances selectivity, attains better tem-perature control and avoids hot spot formation.

The rate equation and the reaction rate constantwe re taken from Ciric and Miao'']:rEG=exp( 7.0-- "ya7)Eox, ( k m d .m-3 .h-I)

(3)rDEG=exp( 7.3-- xEoxEG (kmol .m-3 .h-' )

(4)where T is given in K.Figure 2 shows a column configuration used forEG production. This column contains 10 trays includ-ing a total condenser and a partial reboiIer. A distillateto feed ratio of 0.01 is maintained. Water feed entersonto the top tray of the colum n, while the EO eed isdistributed along the top section of the column. The

Total cond enserStage 1

Pressure=l0 .3kPa

Partial reboilerProducts EG, DEG

Figure 2 EG system: Column configurationandspecificationfor simulation by ASPEN PLUS

reactions are assumed to occur only in the liquid phaseof trays 2-6 because of the presence of a cataly st.The total effective liquid holdu p, 2.5m3, is ev enly dis-tributed among the reaction trays. All the feed stream senter at boiling point. The WILSON vapor-liquidequilibrium model was used to predict componentactivities due to the strong non-ideality of the reactivemixture. The ope rating parame ters and their values forthe base case are shown in Table 1.

Table 1 The input for the simulation of EG columnFeed 1 water 7.31mol.s-'

- . Feed2EO 2.24mol.s-'EO 1.39mol-s-'Feed Feed 3 EO 1.32mol-s-'

Feed 4Feed 5

EO 1.34mol.s-'EO 1.36mol.s-'

column pressure, Wadistillate to f eed ratioboil-up ratiototal stageseffective liquid holdupper stage, m3

Columnspecifica tion reaction stages

101.30.0 115Stages 2 - 6100.5

~

To locate the steady states, the effective liquidholdup and boil-up ratio are chosen as the continua-tion parameters. Fig.3 shows that three steady statesare present in a range of holdup volum e. The low so-lution branch can be obtained when the effective liq-uid holdup is increased from zero. It is of interest tonote that there is a sud den increase in EG purity whenthe effective liquid holdup is increased to 3.9m3. Then,there is an overlap of low branch and intermediatebranch when the effective liquid holdup is between

total holdup volume, m3Figure3 Output multiplidties for a variationof

effective liquid holdupChinese J. Ch. E. 14(3) 301 (2006)


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304 Chinese J. Ch. E. (Vol. 14,No.3)3.9m3 and 4.9m3. After the e ffective liquid holdup isincreased to 4.9m 3, the divergence occurs . However, ifthe effective liquid holdup is decreased from 4.9m3,the solution does not trace the same path, and the in-termediate branch as shown by the dashed line inFig.3 is found. When the effective liquid holdup isdecreased from very large values, the high solutionbranch is found. Of course, there are many othermethods to find three solution branches. Which solu-tion branch can be found depends on the initial guessfed into ASPEN PLUS.

EG mole fraction profiles of the three steadystates in the base case are shown in Fig.4 while dis-tribution of other key operation parameters of threesteady states in the case of effective liquid holdupreaches 3.8m3 are listed in Table 2.

The solid lines in Fig.4 represent the high solu-tion branch and low solution branch, respectively. Thedashed line represents the intermediate solutionbranch. EG system is a good case to study multiplesteady states in reactive distillation process. In thissystem three multiple states exist in a wide range andthe difference between low steady state and highsteady state is very interesting. In the base case, EGpurity of low steady state is near to zero and almost noEG i s produced. However, in the high steady state EGpurity is about 93.5% and a large amount of EO reactwith water to produce EG

Output multiplicities are also found when otheroperating variables such as boil-up ratio are chosen a scontinuation parameters. Fig.5 show s the output mul-tiplicity for a range of boil-up ratio, and the stablesolution branches found here are different from

0 1 2 3 4 5 6 7 8 9 10stage number from the top

Flgure 4 EG mole fraction profiles of thethree steady stateshigh steady state; 0 intermediate steady state;

A low steady state

I .", I

\ . 40.2-

I I I

0 10 20 30 40boil-up rationFigure 5 Output m ultiplicity for a wide range of

boil-up ratio(initial guess: 1-4.0001; 2- 0. 1; 3 -0 .7 ; 4-1.0)

Table 2 Distribution of key operationparameters on three steady states i a reactive distillation columnLow steady state Intermediate steady state High steady state

XEO xw T, XEO x w T, K XEO X W T, KStage number1 0.9995 0.0005 283.50 0.9996 0.0004 283.50 0.0003 0.9994 373.062 0.9587 0.0351 284.55 0.9648 0.0306 284.38 0 0.9854 373.563 0.9575 0.0305 284.58 0.9642 0.0270 284.40 0 0.9763 373.814 0.9562 0.0263 284.61 0.9634 0.0238 284.42 0 0.9674 374.075 0.9550 0.0226 284.65 0.9622 0.0214 284.46 0 0.9572 374.366 0.9537 0.0194 284.68 0.9185 0.0524 285.63 0 0.9059 375.897 0.9537 0.0194 284.68 0.3519 0.6084 311.71 0 0.3969 399.798 0.9493 0.0235 284.80 0.0346 0.9227 362.66 0 0.0420 454.159 0.7488 0.2158 290.90 0.0026 0.9124 374.65 0 0.0032 469.3310 0.0844 0.3801 356.71 0.0001 0.3092 408.09 0 0.0002 471.91

Note: xm--EO mole fraction; x,-water mole fraction.June, 2006


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Multiplicity Analysis in Reactive Distillation Column Using ASPEN PLU S 305

.Feed 2 d

previous paper^"^"^'. Here, four distinct stable solu-tion branches based on four different initial guesses ofboil-up ratio are compared as example, which are0.0001, 0.1, 0.7 and 1.0. The simulation results sug-gest that the initial guess affects strongly the separa-tion capability of a reactive distillation column, andwith the increase of the initial boil-up ratio, the separa-tion ability becomes worse. Once the state is deter-mined in one solution branch, it will maintain therestably even at very large or s m d value of boil-up ratio.

Stages 4-12XIStage 19

3.2 Multiplicity analysis for ETBE synthesisETBE has emerged more recently as a potential

fuel oxygenate since it can be obtained from renew-able bi~-ethanol"~-'~].n addition, ETBE has superiorqualities such as lower blending Reid vapor pressurecompared to MTBE. The reactive mixture consideredis isobutene (IB) reacting with ethanol (EtOH) toproduce the desired product ETBE, in the presence oftwo inert components (1-butene and cis-Zbutene):

IB+EtOHHTBE ( 5 )In this reaction, a heterogeneous catalyst, e.g. a

strong acidic macro porous ion exchange resin, can beused. An activity-based rate expression has been usedto describe the kinetics of ETBE synthesis catalyzedby Amberlyst 15. The reaction rate expression is listedas follows[91:

(6)KETBE 10.387+4060.59/T -2.89055hT -

0.019151MT +5 .2858 6xm5T2- (7)5.32977X 10-*T3

lnK, =-1.0707+1323.1/T (8)k,, (mol .kg-' . - ' ) =7.418x10" x (9),exp(40.4 x lo3 R T)

where T is given in K. A user kinetic subroutine pro-grammed by FORTRAN was incorporated into theASPEN PLUS simulation.

In this simulation, the vapor-liquid equilibrium isdescribed by the UNIFAC model. The column chosenfor ETBE synthesis was basically taken from the pa-per on dynamic simulation"]. This column has 20stages, a partial reboiler and a total condenser, Stages

4-12 for reaction section, Stages 1-3 for rectifyingsection and Stages 13-20 for stripping section. Fig.6shows the column configuration for the base case indetail.

1

Feed 1

Stage 1Total condenser

Partial reboilerFigure6 ETBE system: Column configuration andspecification forsimulation by ASPEN PLUS

(pressure=700kPa;Feed 1: EtOH-O.312mol~s-';Feed 2: IB-0.3Omol.s-', l-butene--4.35mol~s-',cis-2-butene-O.35mol~s-';liquid at boiling point; reflux ratio=5; reboiler duty=76000W,

catalyst loading 2kg per stage)

The composition profiles within the column areshown in Fig.7, where the liquid phase is dominatedby 1-butene and cis-2-butene from the condenserdown to Stage 16.Below Stage 16, the liquid quicklybecomes rich in ETBE because of the temperatureincreasing. This is reflected in the temperature profileshown in Fig.8. The temperature almost keeps con-stant from the top stage to Stage 16, but below Stage16, the temperature increases drastically to 405Kwhen the temperature of reboiler is close to the boilingpoint of ETBE. These changes are mainly because thelarge difference between the K-values for ETBE andthose for the other four components. The reaction-rateprofile shown in Fig.9 indicates that the forward reac-tion dominates every stage of the reaction section. Thelargest amount of reaction occurs on Stage 4, whereEtOH feed enters, and then it decreases rapidly alongthe reaction section. However, it increases a little atthe end of the reaction section because the IB,1-butene and cis-2-butene feed enters on Stage 13.

Chioese J. Ch. E. 14(3) 301 Zooa)


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306 Chinese J. Ch. E. (Vol.14, No3)

- - - - - - ____- - - - - - - _ _ _ _ _ _ _ _

i! 0.4-!- 0.2-ti2 ;

.. .2 4 6 8 10 12 14 16 18 20stage number from th e top

Figure7 Liquid-phase mass fraction profile in the columnW IB; 0 1-butene; A cis-2-butene; EtOH; +ETBE

I 1 I I I I I I 1 I I2 4 6 8 10 12 14 16 18 20stage number from the top

Figure8 Temperature profile in the column

0.10-v)-$ 0.08E$ 0.06Q?w 0.04CI2 0.02

0stage number from the top

Figure9 Reactionrate profileInput multiplicity as show n in Figs.10 and 11 was

found in this ETBE reactive distillation column. In theconventional distillation column, the purity in bottomincreases monotonically with the increase of reboilerduty. However, in ETBE reactive distillation processthere is a distinct maximum of the desired ETBEproduct concentration in bottom dependent upon re-

boiler duty as shown in Fig.10. Actually, the ETBE re-active distillation is not a special case, for the phe-nomenon of input multiplicity exists in most reactivedistillation columns. Bisowarno and Tad d"] divided theinput m ultiplicity region into separation-controlled andreaction-controlled ones. Below the reboiler duty forthe maximum ETBE concentration, the system is con-trolled by separation process, thus increasing the re-boiler duty leads to the improved ETBE purity due tothe improved separation. Similarly, increasing the re-boiler duty leads to the increase of temperature andETBE concentration in the reaction zone, and it has anegative effect on the ETBE purity. It is reflected in thereaction-controlled region on the right-hand side of themaximumthat the ETBE purity decreases with the in-creasing reboiler duty. Fig.11 shows that it exhibits thesame phenomena when the reflux ratio is chosen asoperating variable with other variables kept con stant.

I I I I20 40 60 80 100 120 140reboiler duty, kW

Figure10 Input multiplicities for a variation of reboilerduty in the flxed reflux ratios R=2,7(other conditions remained the same as those in Fig.6)

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307Multiplicity Analysis in Reactive Distillation Column UsingASPEN PLUSIt can be known from Fig.12, in the case of R=5,

the output multiplicity exists near the optimum re-boiler duty although the region is very narrow and thegap between high state and low state is small. Thesolid line was obtained as the reboiler duty increasedstep by step; while the dashed line was obtained asreboiler duty changed in the inverse direction.

I nn

0.70 I I 4 I60 65 70 75 80 85 90reboiler duty, kW

Figure 12 Output multiplicity for a variation of reboilerduty and fured reflux ratio R=5(other conditions remained the same as those in Fig.6)

------decreasing reboiler duty;- ncreasing reboiler dutyTo our best knowledge, the output multiplicity

stated above was seldom reported in ETBE synthesissystems, the desirable operating region is very narrowfor the reason that the mass fraction of ETBE in thebottom is extremely high. It means that this processhas to be operated with a strict control system.4 CONCLUSIONS

Multiple steady states were found in reactive dis-tillation for both EG production and ETBE synthesisprocesses by the method of sensitivity analysis withdifferent initial guess of the solution.

For EG synthesis, output multiplicity was pro-duced with variation of operation parameters such aseffective liquid holdup and reflux ratio. A set of stablesolution branches which are based on distinct initialguesses are found for a range of boil-up ratio. Theseresults show that a strictly controlled start up is nec-essary for the EG system.

For ETBE synthesis, output multiplicity wasfound at reflux ratio of 5 over a n m w range of re-boiler duty. The input multiplicities were also con-f m e d for a variation of reboiler duty at several valuesof reflux ratio. The multiplicity regions are near to theoptimum operation parameters, therefore, it should be

noted when an optimum design of reactive distillationcolumn is achieved.REFERENCES

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