kinetics of front-end acetylene hydrogenation in ethylene production
TRANSCRIPT
Kinetics of Front-End Acetylene Hydrogenation in EthyleneProduction
Noemı S. Schbib, Miguel A. Garcıa, Carlos E. Gıgola, and Alberto F. Errazu*
Planta Piloto de Ingenierıa Quımica, UNS-CONICET, 12 de octubre 1842, 8000 Bahıa Blanca, Argentina
The kinetics of acetylene hydrogenation in the presence of a large excess of ethylene was studiedin a laboratory flow reactor. Experiments were carried out using a Pd/R-Al2O3 commercialcatalyst and a simulated cracker gas mixture (H2/C2H2 ) 50; 60% C2H4; 30% H2, and traces ofCO), at varying temperature (293-393 K) and pressure (2-35 atm). Competing mechanismsfor acetylene and ethylene hydrogenation were formulated and the corresponding kineticequations derived by rate-determining step methods. A criterion based upon statistical analysiswas used to discriminate between rival kinetic models. The selected equations are consistentwith the adsorption of C2H2 and C2H4 in the same active sites followed by reaction with adsorbedhydrogen atoms to form C2H4 and C2H6 in a one-step process. Good agreement between computedand experimental results was obtained using a nonisothermal reactor model that takes intoaccount the existence of external temperature and concentration gradients. The derived kineticequations together with a pseudohomogeneous model of an integral adiabatic flow reactor wereemployed to simulate the conversion and the temperature profiles for a commercial hydrogenationunit.
Introduction
The selective hydrogenation of acetylene in the pres-ence of large amounts of ethylene is a process ofconsiderable importance in the manufacture of polymer-grade ethylene. Small amounts of alkyne, in the partsper million range, affect the polymerization catalyst.Thus the acetylene concentration in the product streammust be reduced to 5 ppm or less.This hydrogenation process could be located at dif-
ferent points in the purification section of an ethyleneplant (Lam and Lloyd, 1972; Derrien, 1986). In onescheme the converter is placed after the conversionsection, following a caustic scrubbing treatment toeliminate CO2. Another alternative involves the hy-drogenation of C2H2 in the C2H4-rich stream taken fromthe top of the de-ethanizer. The first alternative isknown as front-end hydrogenation and the second oneas tail-end hydrogenation.Quite different operating conditions are used in each
case. The front-end configuration involves the hydro-genation of C2H2 in the raw cracked-gas mixture so thatthe stream has a high H2/C2H2 (≈100) ratio and severalacetylenic, olefinic, and diolefinic components. Carbonmonoxide also appears in the feed due to the inversewater-gas shift reaction in the cracking furnaces. Theyall act as inhibitors of C2H4 hydrogenation. Pure C2H2in the tail-end converter is dosed with H2 to obtain astoichiometric H2/C2H2 ratio.Supported palladium catalysts with lowmetal content
are used for both processes due to their exceptional highactivity and selectivity. It is important to point out thatPd is unique, among other metals, for the preferentialhydrogenation of alkynes and diolefins in the presenceof olefins. However the C2H4 f C2H6 reaction becomessignificant when the C2H2 concentration is low, that is,at high levels of conversion.Despite the commercial importance of C2H4 purifica-
tion processes, there is limited kinetic information on
the hydrogenation of C2H2 in the presence of C2H4.Most studies have been performed with pure C2H2under conditions far removed from industrial opera-tions. Some papers deal with the hydrogenation ofC2H2-C2H4 mixtures (McGown et al., 1978; Moses etal., 1984; Aduriz et al., 1990). Orders in H2 lie between1 and 1.6, and that for C2H2 has been found to be zeroor negative. Activation energy values between 9 and16 kcal/mol have been quoted. For C2H4 hydrogenationon Pd the information is more scarce. Schuit and VanReijen (1958) reported an activation energy of 8.4 kcal/mol, a H2 order of 0.6, and an C2H4 order of 0, for Pd onSiO2. Weiss et al. (1984) have investigated the effect ofCO on C2H2 and C2H4 conversion. The former wasfound to be 50-60 times lower in the presence of CO(800 ppm) than in its absence, but the effect was smallat low H2 concentration. On the other hand, thehydrogenation of C2H4 was almost suppressed by theaddition of CO.The tail-end hydrogenation process, under conditions
similar to those of industrial reactors, has been studiedin a pilot plant by Battiston et al. (1982). The experi-mental results were correlated by an empirical modelto take into account the influence of the several reactionvariables on C2H2. Increasing the H2/C2H2 ratio, atconstant CO concentration, increases the conversion ofboth C2H2 and C2H4. A more standard approach wasused by Men’shchikov et al. (1975). A commercial Pdcatalyst was tested in a flow reactor at 20 atm, in the353-430 K temperature range using a tail-end mixture.Rate equations for C2H2 and C2H4 hydrogenation, whichwere written under the assumption that the reactionsoccur on separate sites, gave good correlation of experi-mental data.Studies of this kind for front-end C2H2 hydrogenation
have not been reported. In this paper, laboratory dataobtained on a wide range of pressure, temperature, andconversion values were fitted to several kinetic equa-tions for C2H2 and C2H4 hydrogenation. The selectedmodels were used to simulate the operation of anindustrial acetylene converter. Predicted conversionand temperature profiles were compared with plantdata.
* Author to whom correspondence should be addressed.E-mail: [email protected]. FAX: 54-91-883764.
1496 Ind. Eng. Chem. Res. 1996, 35, 1496-1505
S0888-5885(95)00600-2 CCC: $12 00 © 1996 American Chemical Society
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Methods
In the present study the experimental and theoreticalwork has been organized as follows:1. Several reaction schemes were written for C2H2
and C2H4 hydrogenation on Pd using information fromfundamental kinetic studies.2. The rate-determining step method was applied to
the proposed mechanisms in order to derive the corre-sponding kinetic equations.3. Conversion versus temperature curves for C2H2
and C2H4 hydrogenation were obtained in a laboratoryreactor, in the 1-30 atm pressure range, using acommercial Pd/R-Al2O3 catalyst.4. The rate equations were coupled to three reactor
models of increasing complexity. The algebraic anddifferential equations, which are not linear in the kineticparameters, define a set of regression models.5. A nonlinear regression routine that selects the
conversion as a response variable was used to estimatethe unknown parameters.6. The discrimination between rival models was
based upon the requirement of positive parameterssupplemented with a variance analysis performed onthe conversion residuals.
Kinetic Models
The first task of the present study was to derivekinetic equations that could be compared with experi-mental data for parameter estimation and discrimina-tion. Several sequences of elementary steps werewritten on the basis of information available fromprevious studies. It is well-known that H2 is dissocia-tively adsorbed on Pd to form H-Pd surface entities.On the other hand, it is accepted that C2H2 and C2H4adsorption occurs by an associative mechanism involv-ing one or two Pd surface atoms (π-bonded or σ-bondedstructures). Consequently it was considered that simi-lar or different types of sites may exist for H2 andhydrocarbon adsorption. For the interaction of CO withthe metal surface, an associative mechanism involvinghydrogen adsorption sites has been postulated.Regarding the surface reactions, three different reac-
tion paths were assumed: a stepwise addition of ad-sorbed hydrogen atoms, the simultaneous addition oftwo atoms, or the reaction of gaseous hydrogen withadsorbed hydrocarbons. It has already been shown(Aduriz et al., 1990; Sarkany et al., 1986) that C2H6formation during hydrogenation of C2H2-C2H4 mixturesis mainly due to C2H4 hydrogenation. Consequently wehave excluded the direct formation of C2H6 from C2H2.Reaction schemes 1-5, shown in Table 1, were writtenon the basis of these considerations. In principle allsteps were assumed to be reversible. If the stepwiseaddition of adsorbed hydrogen and the Eley-Ridealmechanism operate simultaneously (schemes 1 and 3,respectively), scheme 6 is obtained. On the other hand,,the combination of schemes 2 and 3 leads to scheme 7.In order to obtain the steady-state kinetic models the
rate-determining-step method was used. In principleany step can be rate limiting, but it is possible to reducethe number of equations on the basis of informationavailable from surface chemistry studies. Hydrogenadsorption is a fast, nonactivated process, and thereforethis step could be assumed to be at equilibrium. Thedesorption of ethane cannot be the rate-limiting step,for ethylene hydrogenation, because it is readily dis-placed from the surface by the strongly bound hydro- T
able
1.ReactionMechan
ism
fortheSelective
Hyd
rogenationof
C2H
2an
dC2H
4
schem
e1
schem
e2
schem
e3
schem
e4
schem
e5
schem
e6
schem
e7
(1)A
+S
fAS
(1)A
+S
fAS
(1)A
+S
fAS
(1)A
+S
fAS
(1)A
+S
fAS
(1)A
+S
fAS
(1)A
+S
fAS
(2)H
2+2S
f2H
S(2)H
2+2S
f2H
S(2)H
2(g)
+AS
fES
(2)H
2+2Z
f2H
Z(2)H
2+2Z
f2H
Z(2)H
2+2S
f2H
S(2)H
2+2S
f2H
S(3)AS
+HS
fAHS
+S
(3)AS
+2H
SfES
+2S
(3)E
+S
fES
(3)AS
+2H
ZfES
+2Z
(3)AS
+HZ
fAHS
+Z
(3)AS
+HS
fAHS
+S
(3)AS
+2H
SfES
+2S
(4)AHS
+HS
fES
+S
(4)E
+S
fES
(4)H
2(g)
+ES
fEtS
(4)E
+S
fES
(4)AHS
+HZ
fES
+Z
(4)AHS
+HS
fES
+S
(4)AS
+H
2(g)
fES
(5)E
+S
fES
(5)ES
+2H
SfEtS
+2S
(5)Et
+S
fEtS
(5)ES
+2H
ZfEtS
+2Z
(5)E
+S
fES
(5)AS
+H
2(g)
fES
(5)E
+S
fES
(6)ES
+HS
fEHS
+S
(6)Et
+S
fEtS
(6)CO
+S
fCOS
(6)Et
+S
fEtS
(6)ES
+HZ
fEHS
+Z
(6)E
+S
fES
(6)ES
+2H
SfEtS
+2S
(7)EHS
+HS
fEtS
+S
(7)CO
+S
fCOS
(7)CO
+S
fCOS
(7)EHS
+HZ
fEtS
+Z
(7)ES
+HS
fEHS
+S
(7)ES
+H
2(g)
fEtS
(8)Et
+S
fEtS
(8)Et
+S
fEtS
(8)EHS
+HS
fEtS
+S
(8)Et
+S
fEtS
(9)CO
+S
fCOS
(9)CO
+S
fCOS
(9)ES
+H
2(g)
fEtS
(9)CO
+S
fCOS
(10)Et
+S
fEtS
(11)CO
+S
fCOS
Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996 1497
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carbons (ethylene and acetylene). In addition it hasbeen shown recently (Park and Price, 1991) that COenhances the desorption of C2H4. Consequently only theadsorption of C2H2 and C2H4 and the surface interac-tions were chosen as rate-controlling steps to derive thekinetic models. To further reduce the number of equa-tions, the same determining step was selected for C2H2and C2H4 hydrogenation. By use of this approach 14kinetic models were derived, as shown in Table 2.As an example let us consider scheme 2 when the
adsorption of C2H2 and C2H4, steps 1 and 4, are rate-controlling. The corresponding kinetic equations are
where k1 and k4 are the rate constants and [S] is theconcentration of free surface sites. Considering theirreversible nature of the overall hydrogenation reac-tions, the reverse reactions of steps 1 and 4 have beenneglected. The remaining steps, 2, 3, 5, 6, and 7 areconsidered to be in a quasiequilibrium state. We useletters to identify the adsorption-desorption processesat equilibrium: KH for H2, KEt for C2H6 , KE for C2H4,and KCO for CO, while the constants KAS and KES takeinto account the surface reactions of adsorbed C2H2 andC2H4 at equilibrium. In order to simplify the rate
equations the following constants were introduced
Using these constants, [S] may be written in termsof the gas phase concentrations
where
and [St] is the concentration of free and occupied sites.Combining the previous equations, the rates of disap-
pearance of C2H2 and C2H4 are
where
Experimental Section
A laboratory scale reactor was used to obtain conver-sion vs temperature curves in the 1-30 atm pressurerange. Catalyst charges of 1-3 g were packed in a
Table 2. Kinetic Equations Derived from the Reaction Schemes Presented in Table 1a
r2,14 ) r7,15 rA ) kACA/DrE ) kECE/DD ) 1 + (KHCH)1/2 + CEt ∑i)1
2 KiCH-i + KEtCEt + KCOCCOr1,36 rA ) kACACH
1/2/D2
rE ) kECECH1/2/D2
D ) 1 + KACA + KECE + (KHCH)1/2 + (K1CE + K2CEt)CH-1/2 + KEtCEt + KCOCCO
r1,47 rA ) kACACH/D2
rE ) kECECH/D2
D ) 1 + KACA + KECE + (KH + K1CA + K2CE)CH1/2 + KEtCEt + KCOCCO
r2,35 rA ) kACACH/D3
rE ) kECECH/D3
D ) 1 + KACA + KECE + (KHCH)1/2 + KEtCEt + KCOCCOr3,13 ) r4,14 rA ) kACA/D
rE ) kECE/DD ) 1 + (KEt + K1CH
-1 + K2CH-2)CEt + KCOCCO
r3,24 rA ) kACACH/DrE ) kECECH/DD ) 1 + KACA + KECE +KEtCEt + KCOCCO
r4,35 rA ) kACACH/DrE ) kECECH/DD ) (1 + KACA + KECE +KEtCEt + KCOCCO)(1 + KH
1/2CH1/2)2
r5,15 rA ) kACA/DrE ) kECE/DD ) 1 + (KEt + K1CH
-1/2 + K2CH + K3CH-3/2 + K4CH
-2)CEt + KCOCCOr5,36 rA ) kACACH
1/2/DrE ) kECECH
1/2/DD ) (1 + KACA + KECE + (K1CE + K2CEt)CH
-1/2 + KEtCEt + KCOCCO)(1 + KH1/2CH
1/2)r5,47 rA ) kACACH/D
rE ) kECECH/DD ) (1 + KACA + KECE + (K1CA + K2CE)CH
1/2 + KEtCEt + KCOCCO)(1 + KH1/2CH
1/2)r6,16 ) r1,15 rA ) kACA/D
rE ) kECE/DD ) 1 + (KHCH)1/2 + (K1CH
-1/2 +K2CH-1 + K3CH
-3/2 + K4CH-2)CEt + KEtCEt + KCOCCO
r6,35/79b rA ) kACACH1/2/D2 + k*ACACH/D
rE ) kECECH1/2/D2 + k*ECECH/D
D ) 1 + KACA + (KHCH)1/2 + KECE + (K1CE + K2CEt)CH-1/2 + KEtCEt + KCOCCO
r6,45/89b rA ) kACACH/D2 + k*ACACH/DrE ) kECECH/D2 + k*ECECH/DD ) 1 + KACA + KECE + (KH
1/2 + K1CA + K2CE) CH-1/2 + KETCET + KCOCCO
r7,34/67b rA ) kACACH/D3 + k*ACACH/DrE ) kECECH/D3 + k*ECECH/DD ) 1 + KACA + (KHCH)1/2 + KECE + KEtCEt + KCOCCO
a The first digit identifies the sequence of steps and the others the controlling steps for C2H2 and C2H4 hydrogenation. b Simultaneousmechanisms with two different controlling steps for acetylene and ethylene hydrogenation are considered.
r2,1 ) -rA ) k1CA[S]
r2,4 ) -rE ) k4CE[S] (1)
K1 )KEt
KHKESK2 )
KEt
KH2KESKAS
(2)
[S] ) [ST]/D
D ) 1 + (KHCH)1/2 + CET ∑
i)1
2
KiCH-i +
KETCET + KCOCCO (3)
-rA ) kACA/D and -rE ) kECE/D (4)
kA ) k1[St] and kE ) k4[St]
1498 Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996
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stainless-steel tube (10 mm i.d.) immersed in a dieth-ylene glycol bath. The total pressure was adjusted bymeans of a back-pressure regulator. Experiments wereperformed in the 288-393 K temperature range whilethe gas flow rate was held constant at 100 cm3 STPmin-1 using a mass flow controller. A thermocouple incontact with the catalyst particles was located in anaxial position to monitor the reaction temperature. Inaddition the wall temperature was measured.The analysis of reactants and products was performed
by on-line gas chromatography using a Carbosieve S-IIcolumn (1/8 in. × 80 cm) held at 393 K. Fresh catalystsamples were pretreated in N2 at 433 K for 8 h beforefeeding the hydrocarbon mixture.The reaction mixture was prepared by mixing CP-
grade hydrocarbons with high-purity hydrogen and CO.Table 3 summarizes the gas composition and the mainoperating conditions.A commercial catalyst, ICI 38-1, containing 0.04%
Pd, was used in this study. The main catalyst proper-ties are shown in Table 4.The effect of increasing temperature on C2H2 and
C2H4 conversion was investigated in the presence ofvarying amounts of CO and a total pressure of 1, 9, 16,and 32 atm. In these runs the space velocity was heldconstant. When the conversion of C2H2 was almost100%, the heat of reaction produced a small temperaturedifference between the catalyst bed and the reactor wall.The maximum C2H4 conversion was about 10-15%. Alarge experimental error was present in this measure-ment as compared with C2H2 conversion, due to the highconcentration of C2H4 and C2H6 in the feed mixture. Athigh C2H4 conversion isothermal conditions could notbe maintained and a large temperature gradient wasdetected by the thermocouples. In some experimentsthe temperature was held constant and the conversionwas measured as a function of the total pressure.The effect of temperature on C2H2 and C2H4 conver-
sion, at 1 and 9 atm and 800 ppm CO, is shown inFigure 1. The initial trend is a large increase in C2H2conversion within a narrow temperature range, followedby a marked decrease in the rate of reaction above 90%conversion. In this case the conversion of ethylene wasobserved after the complete elimination of C2H2, witha temperature span of about 15 K from øA ) 100% to øE
) 1%. Consequently the Pd/R-Al2O3 catalyst, under thepresent experimental conditions, is very selective in thesense that it allows the total elimination of C2H2 withminimum C2H4 losses. Increasing the total pressureaccelerates both reactions, and therefore similar conver-sions are obtained at lower temperatures. However amore detailed testing, in the region of high C2H2conversion, indicates that the effect of pressure is moremarked on the rate of C2H4 hydrogenation. Table 5shows that the conversion of C2H2, at constant temper-ature, increases with pressure in the 1-9 atm rangebut remains constant afterward. On the other hand,the hydrogenation of C2H4 reflects a steady increase inconversion from 1 to 32 atm. Consequently the tem-perature span between complete elimination of C2H2and the onset of C2H4 hydrogenation is reduced and thecatalyst becomes less selective.The effect of CO on activity and selectivity, for
experiments performed at 16 atm, is shown in Table 6.Increasing the concentration of CO, from 150 to 1400ppm, lowered the C2H2 hydrogenation rate, and a highertemperature was needed to obtain nearly the sameconversion. Despite the large increase in temperature,18 K, the conversion of C2H4 decreased from 10.85% to6.70%. When the CO concentration was raised to 5000ppm, a further increase in temperature was requiredto maintain the same conversion of C2H2. However theconversion of C2H4 was almost the same: 6.08%. Theseresults indicate that the concentration of CO at >150ppm affects the rate of C2H2 and C2H4 hydrogenationto the same extent.
Table 3. Feed Mixture and Operating Conditions for theLaboratory Reactor
components composition (mol % ( 0.02)
CH4 6.53C2H2 0.52C2H4 43.99C2H6 26.72H2 22.1CO 150-5000 ppm
flow rate 100 cm3 (STP)/minmass of catalyst 1-3 gpressure 1-35 atmtemperature 288-393 K
Table 4. Catalyst Characterization
support R-Al2O3palladium content (wt %) 0.04BET surface area (m2/g) 21metal dispersion (H/Pd) 0.15apparent density (g/cm3) 1.61real density (g/cm3) 3.61average pore diameter (Å) 1000pore volume (cm3/g) 0.338porosity (%) 54.5
Figure 1. Acetylene and ethylene conversion as a function oftemperature. Feed mixture as given in Table 3. SV ) 33 cm3 gcat-1min-1. CCO ) 800 ppm. Pressure: 0, 1 atm; O, 9 atm.
Table 5. Effect of Pressure on C2H2 and C2H4 Conversion(CO Content ) 1400 ppm; SV ) 100 cm3 STP gcat-1 min-1)
conversion (%)
temp (K) 1 atm 8 atm 16.50 atm 32 atm
348 C2H2 85.54 95.86 95.39 94.13C2H4 0.00 0.00 0.00 0.00
359 C2H2 94.44 97.75 97.75 96.64C2H4 0.00 1.02 1.67 4.50
368 C2H2 96.13 98.16 98.02 96.97C2H4 0.00 3.12 6.07 14.50
Table 6. Effect of CO on C2H2 and C2H4 Conversion atConstant Pressure (Pressure ) 16 atm; SV ) 100 cm3 STPgcat-1 min-1)
conversion (%)
CO content (ppm) temp (K) C2H2 C2H4
150 341 98.31 10.451400 359 98.99 6.705000 393 98.62 6.08
Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996 1499
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Reactor Models
In order to process the experimental data, a suitablereactor model must be used. As a first approximation,a perfectly mixed flow reactor was considered (modelI). Although this model is not appropriate to describeour laboratory setup, it has been chosen in an attemptto evaluate a large number of kinetic equations withoutconsiderable computing effort. The basic mass balanceequations were written as
where i refers to C2H2 and C2H4. They can be readilycoupled to the rate models given in Table 2 to relatethe fractional conversion øi to the kinetic parameters.Therefore a set of nonlinear algebraic equations wasobtained. Using experimental w/Fi and T values asindependent variables and assuming tentative kineticconstants, the conversion (⟨øi⟩) was estimated andcompared with the measured values (øi).The second reactor model (model II) was assumed to
be nonisothermal, isobaric with a plug flow pattern, andpseudohomogeneous. In this case the mass and energybalance defined a set of nonlinear ordinary differentialequations coupled through the rate model ri:
The overall heat transfer coefficient U was definedas follows:
In this equation the heat transfer coefficient h takesinto account the total resistance to heat flow in theradial direction and it is given by the Crider and Fossequations (Crider and Foss, 1965).
where hw is the heat transfer coefficient at the tube wall.The radial effective thermal conductivity kref was ob-tained from the Dixon and Cresswell correlation (Dixonand Cresswell, 1979)
where krf and krs are the radial conductivities of the fluidand the solid, respectively. The effective conductivitydepends also on the fluid/wall (hwf) and the fluid/solid(hfs) heat transfer coefficients. Suitable correlations forthese coefficients are found in the previous reference.The previous equations constitute an initial value
problem that has been solved by means of a Runge-
Kutta method. In this way, the C2H2 and C2H4 conver-sions (⟨øi⟩) at the reactor outlet are obtained.A more complex reactor model (model III) emerges if
one assumes the existence of temperature and concen-tration gradients in the gas phase region adjacent tothe catalyst particles. Therefore T * Ts and Ci * Csi.This situation is likely to occur in the laboratory reactordue to the low gas velocity over the catalyst particles.Under steady-state conditions the rate of mass trans-
port of a reactant (i) through the gas phase film is equalto the observable surface reaction rate (rsi):
Introducing the external effectiveness factor ηi,
where rio is the maximum rate or reaction obtainedwhen Csi ) Ci. In addition the Damkohler number Diois defined as the ratio of the maximum surface rate tothe maximum mass transport rate:
Following the treatment of Carberry (Carberry, 1976)eqs 13 and 14 can be related to define a dimensionlessobservable quantity:
Combining eqs 12 and 15, a dimensionless concentra-tion in terms of an observable quantity may be obtained:
For C2H2,
Taking into account that ethylene is a product andalso a reactant, the concentration on the gas-solidinterphase is given by
On the other hand, the H2 concentration is related tothe consumption of both C2H2 and C2H4:
Under steady-state, nonisothermal conditions, thesurface temperature could be related to the bulk gasphase temperature through an energy balance on thecatalyst particles.
Dividing this equation by (kmHamT) and recalling thejD ) jH heat and mass transfer analogy,
rsi ) kmiam(Ci - Csi) (12)
rsi ) ηirio (13)
Dio ) rio/(kmiamCi) (14)
ηiDio ) rsi/(kmiamCi) (15)
C*i ) Csi/Ci ) 1 - ηiDio
C*A ) CsA/CA ) 1 - ηADAo (16)
C*E ) 1 - ηEDEo + ηADAokmACA/(kmECE) (17)
C*H ) 1 - ηADAokmACA/(kmHCH) -ηEDEokmECE/(kmHCH) (18)
hfsam(Ts - T) ) (-∆HA)(-rA) + (-∆HE)(-rE) (19)
Fcp(Sc/Pr)2/3(T* - 1) ) (-∆HA)(-rA)/(kmHamT) +
(-∆HE)(-rE)/(kmHamT)
T* ) 1 + [(-∆HA)(-rA)/(kmHamTFcp)](Pr/Sc)2/3 +
[(-∆HE)(-rE)/(kmHamTFcp)](Pr/Sc)2/3 (20)
wFi
)øiri
(5)
d(vCi)dz
) (-ri)Fcat (6)
cpdT
dz) Fcat ∑
i
(-∆Hi)(-ri) - 4U(T - Tw) (7)
U ) ( 1hA +ln(dto/dt)2FkwA )-1
(8)
1/h ) 1/hw + dt/6kref (9)
hw ) 3krefRe-0.25/dt (10)
kref ) krf + krs[ 1 + (8krf/hwfdt)
1 +(16/3krs)( 1
hfsdp+ 0.1
kp )(1 - ε)(dt/dp)
2 ] (11)
1500 Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996
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Using eq 15 the dimensionless temperature may bewritten
where
The temperature dependence of the rate constant ki andthe adsorption equilibrium constant Ki may also bewritten in a dimensionless form:
where:
To integrate eqs 6 and 7 for a given axial coordinate,eqs 16-22 must be solved to find the concentrations andtemperature at the catalyst surface. Consequently, asystem of coupled nonlinear differential and algebraicequations has to be solved. In this work, the ordinarydifferential equations were integrated with the Runge-Kutta-Gill method and the algebraic equations weresolved using a quasi-Newton algorithm, where the firstJacobian was numerically evaluated and then updatedby means of Broyden’s method (Paloschi and Perkins,1988) at each iteration step. Thus the overall computingtime was greatly reduced.A nonlinear regression routine based on the Mar-
quardt algorithm was used for the three reactor modelsdescribed above to adjust the kinetic parameters cor-responding to the rate models given in Table 2. Theobjective function to be minimized was defined as
In the models discussed above we have neglected thepresence of internal diffusion limitations. This simpli-fying assumption was based on the fact that the averagepore diameter of the catalyst pellets was quite large,1000 Å. However, due to the high hydrogenation rateand the homogeneous distribution of Pd in the pellet,internal concentration gradients may be present. Inorder to check for the absence of intrapellet diffusionlimitations, we selected the criterion of Weisz and Prater(Froment and Bischoff, 1990) which in turn requires ameasured value of the rate of reaction. Consequentlyapplication of this criterion was performed after ad-equate kinetic equations were available to calculate therates of C2H2 and C2H4 hydrogenation at differentconversion levels.
Results and Discussion
Determination of Kinetic Constants and ModelDiscrimination. The process parameters were con-sidered as independent or input variables to be intro-duced as data in the mathematical models. On theother hand, the measured conversion values were thedependent variables to be compared with the theoreticalpredictions. From this comparison the regression rou-tine estimates the kinetic parameters. The rate equa-tions of Table 2 were first included in model I. Thecalculation starts with an initial guess for each param-
eter, and it continues until the variance analysisindicates that a reasonable agreement between experi-mental and calculated conversions has been found. Aset of 163 experimental points was used for theseestimations.For the more complex reactor models, the procedure
described above uses a large computing time due to thefact that the calculated conversion is obtained bynumerical integration of differential equations. Inaddition each step of the regression routine requiresabout 2600-3200 simulations to evaluate the Jacobian.In order to reduce computing time, a shortcut methodwas adopted, based on sequential discrimination, so thatmany rate models were eliminated early in the processusing model I, where only one algebraic equation needsto be solved. A set of parameters was estimated for eachrate equation. The variance of the experimental andcalculated conversion values provided a convenientmethod to analyze the quality of this fitting procedure.In addition the discrimination between the different rateequations was done on the basis of negative parametersor unexpected trends in the conversion versus temper-ature curves. In this way 11 rate models were elimi-nated, as shown in Table 7.In the following stage the remaining kinetic equations
were processed with the same regression routine butusing model II. The parameters derived in the previousstage were now used as initial values. One kineticmodel was eliminated when the discrimination criterionwas applied. Finally the parameters determined withmodel II were adopted as initial values to fit theexperimental data with model III. Therefore the adoptedprocedure uses a simple reactor model when the solutionis a long way off, and the more realistic but time-consuming models were applied when few iterationswere needed.The Kinetic Equations. The best fit with the
experimental data was provided by the rate model r2,35that assumes the adsorption of C2H2, C2H4, and H2 onthe same type of sites and the simultaneous addition oftwo hydrogen atoms to the absorbed hydrocarbons asdetermining steps. Table 8 presents the selected kineticexpressions and the parameter values obtained byminimization of the sum of residual squares. Uponexamination these equations reveal some interestingfeatures. First it is observed that the hydrocarbonadsorption constants KE, KET, and KA have a negligibleeffect on the rates and consequently the kinetic equa-tions can be simplified to
It is observed that the rate of C2H4 hydrogenationdoes not depend on the concentration of C2H2 aspreviously reported by Margitfalvy et al. (1981). Theexplanation may be found in the presence of CO. Aspointed out by Bos and Westerterp (1993a), CO maysuppress the influence of C2H2 in C2H4 hydrogenation.Another surprising feature is the positive values for
the adsorption energy on the CO and H2 constantswhich indicates that they will increase with tempera-ture. It is reasonable to expect that the adsorptionterms decrease with temperature due to the exothermiccharacter of the adsorption processes. This anomalous
T* ) 1 + âAηADAo + âEηEDEo (21)
âi ) [(-∆Hi)(kmiCi)/(kmHTFcp)](Pr/Sc)2/3 i ) A, E
k*i ) ksi/ki (or K*i ) Ksi/Ki) ) exp(-E*i (1/T* - 1))(22)
E*i ) Ei/RT
φ ) ∑i
[øi - ⟨øi⟩]2 (23)
-rA )kACACH
[1 + (KHCH)1/2 + KCOCCO]
3(24)
-rE )kECECH
[1 + (KHCH)1/2 + KCOCCO]
3(25)
Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996 1501
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result may be due to data error, inadequate selectionof experimental conditions, or data analysis. Problemsof this kind are often encountered on rate modeling asdiscussed by Doraiswamy and Sharma (1984). In spiteof this difficulty the hydrogenation rates predicted byour models exhibit a normal Arrhenius behavior becausethe effect of temperature on the adsorption parametersis overcompensated by the large activation energy onthe rate constants kA and kE.Equations 24 and 25 and those of model III were used
in the simulation of an adiabatic reactor to observe thepredicted rate versus temperature profiles, as shown inFigure 2. The rate of C2H2 hydrogenation is initiallylarger than that of C2H4, as expected. As the reactionproceeds, the decrease in C2H2 concentration is com-
pensated by the increase in temperature, so the rate isnearly constant in the 325-340 K temperature range.Eventually the decrease in C2H2 becomes so importantthat the rate falls below that of C2H4, so at highconversion values there is a marked decrease in selec-tivity.It should be noted that our kinetic equations do not
predict a change in selectivity with the CO contentbecause the rA/rE ratio depends only on the concentra-tion of C2H2 and C2H4. In other words, the presence ofCO seems to affect the rate of C2H2 and C2H4 hydroge-nation to the same extent, in accordance with the resultsof Table 6. As the concentration of CO increases, ahigher temperature is required to obtain a given conver-sion of C2H2, but the conversion of C2H4 remains thesame. The effect of CO may be explained by assumingthat it limits the amount of adsorbed H2 in accordancewith kinetic models based on the adsorption of H2 andCO on the same type of sites. However it is importantto stress that the presence of a minimum level of CO isessential to avoid the uncontrolled hydrogenation ofC2H4.As mentioned by one reviewer, there is evidence of
adsorption of acetylene and ethylene on separate sites,which may suggest additional hydrogenation mecha-nisms. We are aware of several studies that postulateddifferent sites for acetylene and ethylene hydrogena-tiona (All-Ammar andWebb, 1978; McGown et al., 1978;Leviness et al., 1984). Therefore a reaction schemebased on a two-site mechanism could have been includedin Table 1. However this model would lead to morecomplex kinetic equations as shown by Gva and Kuo(1988), increasing the number of adjustable parameters.In addition, our experimental results indicate that thepresence of CO prevents the hydrogenation of ethyleneup to a very high level of acetylene conversion, asobserved in Figure 1. Consequently, a two-site mech-anism that may be relevant under different experimen-tal conditions was not used here to obtain additionalkinetic equations.Quite recently Bos et al. (1993b) used rate models
from previous studies (Men’shchikov et al., 1975; Gvaand Kuo, 1988) to correlate kinetic data obtained witha typical tail-end hydrogenation mixture. The originalequations were based on the assumption that thehydrogenation of C2H2 and C2H4 proceeds on differenttypes of sites, and they were properly modified to takeinto account the effect of CO. In this case the temper-ature dependence of the adsorption terms was accordingto expectations; that is they decrease with an increase
Table 7. Discrimination Sequence for the Kinetic Models of Table 2
model I model II model III
riiselectionprocedure variance
selectionprocedure variance
selectionprocedure variance
r2,14 ) r7,15 a 0.366E-1r1,36 b 0.481E-2 c 0.307E-2r1,47 a 0.402E-2r2,35 b 0.487E-2 b 0.270E-2 b 0.229E-2r3,13 ) r4,14 c 0.319r3,24 a 0.127E-1r4,35 a 0.426E-1r5,15 c 0.838E-2r5,36 a 0.662E-2r5,47 a 0.211E-1r6,16 ) r1,15 a 0.592E-2r6,35/79 a 0.779E-2r6,45/89 a 0.340E-2r7,34/67 b 0.273E-2 b 0.239E-2 c 0.819E-2
a Adjusted by regression. b Rejected because Eact < 0.b c Rejected because of high variance.
Table 8. Selected Rate Equation and KineticParameters for C2H2 and C2H4 Hydrogenation
kinetic parameters log Ai E (kcal/gmol)
kA (m6/(s gcat kmol)) 31.1 45.51kE (m6/(s gcat kmol)) 26.6 42.94KH (m3/kmol) 20.2 21.22KCO (m3/kmol) 13.6 9.95KE (m3/kmol) 0.26 0.005KEt (m3/kmol) -0.012 0.001KA (m3/kmol) -16 0.001
-rA )kACACH
[1 + (KHCH)1/2 + KACA + KECE + KEtCEt + KCOCCO]
3
-rE )kECECH
[1 + (KHCH)1/2 + KACA + KECE + KEtCEt + KCOCCO]
3
where kA ) k3St3KAKH and kE ) k5St3KAKH
Figure 2. Acetylene and ethylene hydrogenation rate vs tem-perature for an adiabatic reactor. Kinetic equations of Table 8.Feed mixture as given in Table 3. T0 ) 325 K, P ) 16.3 atm; CCO) 1400 ppm.
1502 Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996
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in temperature. The equations of Bos et al. predict alarger difference between acetylene and ethylene hy-drogenation rates due to the reduced partial pressureof hydrogen. They also found that the addition of COin the 0-60 ppm range does not have the same effecton C2H2 and C2H4 hydrogenation. The experimentalconditions were certainly different from those of thepresent study, and this situation precludes a bettercomparison of results. Most of the kinetic studiespublished to date are related to tail-end hydrogenationprocesses where low concentrations of CO and H2 areused.Finally we need to mention that the absence of pore
diffusion limitations in the laboratory experiments wasverified using the Weisz-Prater criterion:
where the observable rate (-rA)obs was calculated fromeq 24 at different conversion levels. Only at øA > 90%does the Φ module become greater than 1, due mainlyto the low value of CsA. For C2H4 hydrogenation thecriterion is always satisfied because -rE < -rA and theconversion is less than 10-15%.Comparison of Reactor Model III with Experi-
mental Data. Computer simulations of the laboratoryreactor, using model III and the kinetic equations ofTable 8, are presented in Figures 3 and 4 where theconversion and the axial temperature are plotted as afunction of the bed length. The predicted C2H2 andC2H4 conversions at the reactor end are in good agree-ment with the experimental results. On the other hand,the temperature profiles show the presence of a hot spot
near the reactor entrance. A sharp rise in temperatureprofiles is followed by a slow decrease along the axialcoordinate. The temperature overshoot depends on thefeed-reactor wall temperature: at 325 K, with a conver-sion of 70.7% it is about 1.5 K. Increasing the inlettemperature to 345 K, the C2H2 conversion was closeto 98% and the temperature overshoot exceeded 3 K.The simulations also indicate that a temperature gradi-ent of about 0.5 K, between the exit gas and the reactorwall, should be expected. As mentioned in the Experi-mental Section, temperature differences of this magni-tude were observed in our runs, which shows theconvenience of using a nonisothermal model to fit theexperimental data.As described above, reactor model III takes into
account the presence of temperature and concentrationdifferences between the catalyst particle and the gasphase. The calculated concentration gradients werefound to be negligible for all runs. On the other hand,the ∆T ) Ts - T values were found to depend on thegas phase temperature which in turn is related to therate of reaction. At the reactor entrance, in the hot-spot region, large temperature gradients between thegas phase and the catalyst particles were calculated. InFigure 3, at 326 K the ∆T value was about 8 K. Itincreased to nearly 20 K when the gas phase temper-ature overshot to 348 K, as was the case in Figure 4.These results confirm the suitability of reactor modelIII to treat the laboratory data in order to obtain thekinetic parameters.Industrial Reactor Simulation. In order to check
the validity of our kinetic equations to predict conver-sion and temperature profiles, an attempt was made tosimulate the operation of an industrial acetylene hy-drogenation reactor. The process scheme consists of anethane cracker followed by three adiabatic reactors inseries in a typical front-end hydrogenation configura-tion. The simulation was restricted to the first unit.The reactor has a diameter of 170 cm and a length of180 cm, with a catalyst mass of 4290 kg. A typical feedmixture consists of 4.30 wt %H2, 32.94 wt % C2H6, 51.96wt % C2H4, 0.48 wt % C2H2, 5.33 wt % CH4, 0.08 wt %C3H4, 1.37 wt % C3H6, 1.67 wt % C4H6, and 0.04 wt %CO as main components. The flow rate was about57 900 kg/h, the total pressure was 35 atm, and the inlettemperature was 342.5 K. The pressure drop was quitenegligible. These conditions allow us to simulate thereactor with a plug flow, pseudohomogeneous, isobaric,and adiabatic model. The high flow velocity eliminatesthe need for external mass transport considerations, andthe absence of internal concentration gradients wasalready demonstrated using the laboratory reactor data.Consequently the industrial reactor can be described byeq 6 and a simplified form of eq 7:
The simulation results are presented in Figures 5 and6. The predicted conversion of C2H2 is close to 100%,but the measured value in the plant reactor was around77%. In addition the actual C2H4 loss was lower thanexpected. On the other hand, an exit temperature of364.5 K was calculated, which is close to the measuredvalue of 363.2 K. The pronounced disagreement be-
Figure 3. Calculated conversion and temperature profiles for thelaboratory reactor using reactor model III and the rate equationsof Table 8. Feed mixture as given in Table 3 T0 ) 325 K; P ) 16.3atm; CCO ) 1400 ppm. 9, Experimental data.
Figure 4. Calculated conversion and temperature profile for thelaboratory reactor using reactor model III and the rate equationsof Table 8. Feed mixture as given in Table 3, T0 ) 345 K; P )16.3 atm.; CCO ) 1400 ppm. 9, Experimental data.
Φ )(-rA)obsFcatdp
2
DeACsA< 1 (26)
d(vCi)dz
) (-ri)Fcat (6)
cpdT
dz) Fcat ∑
i
(-∆Hi)(-ri) (7′)
Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996 1503
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tween the estimated and measured conversion valuesand the approximate temperature profile is due to thelarge concentration of 1,3-C4H6 in the feed mixture.Industrial practice indicates that the hydrogenation of1,3-C4H6 takes place simultaneously with C2H2 hydro-genation. The conversion of 1,3-C4H6 for the operatingconditions mentioned above was around 44%, and thisreaction limits the activity for C2H2 hydrogenation.The good agreement between the predicted and
measured temperature profiles is due to compensationof the heat of reaction of unconverted C2H2 by thatproduced in the hydrogenation of 1,3-C4H6. A certaindegree of catalyst deactivation, due to green oil forma-tion, may also have altered the results. A suitableequation for the rate of 1,3-C4H6 hydrogenation mustbe developed in order to predict the observed conversionvalues in the industrial reactor. As an alternative, wehave developed an empirical model for butadiene andpropylene + methylacetylene hydrogenation, based onindustrial data. By including these equations in themathematical model of the industrial reactor and alsoadding a deactivation parameter, a good correspondencebetween the steady state experimental data and simu-lation results was obtained (Schbib et al., 1994).
Conclusions
Rate equations for C2H2 and C2H4 hydrogenation ona commercial Pd/R-Al2O3 catalyst have been obtainedfor reaction conditions similar to those of a front-endhydrogenation process. Experimental data as a functionof temperature, pressure, and CO content were obtainedin a laboratory reactor covering a wide C2H2 conversionrange. To our knowledge, kinetic studies of this kindhave not been reported in the open literature. The rateequations reflect (i) that the rate of C2H2 hydrogenation
exceeds that of C2H4 hydrogenation up to a high levelof conversion and (ii) that the presence of CO is anecessary condition to avoid a runaway situation butthe selectivity is not dependent on the CO concentration.Computer simulation of the laboratory reactor using
a nonisothermal model that accounts for interfacialgradients provides a good correlation of experimentaldata and indicates the existence of a temperatureovershoot near the reactor entrance. We were not ableto reproduce the conversion profile of an industrialadiabatic converter due to the presence of a largeamount of 1,3-C4H6 in the cracked gas mixture.
Nomenclature
A ) heat transfer area per unit length of the reactor, m2
Ai ) preexponential factor in Arrhenius expression,moln-1/(m3(n-1) s)
am ) specific interfacial surface areaCi ) concentration of ith component in the gas phase, mol/m3
C*i ) dimensionless concentration, Csi/CiCsi ) surface concentration of component i, mol/m3
cp ) average heat capacity, J/(mol K)De ) effective diffusivityDio ) Damkohler numberdp ) pellet diameter, mdt ) inside diameter of tube, mdto ) outside diameter of tube, mEi ) activation energy of the component i, J/molFi ) molar flow rate of component i, mol/s(-∆H)i ) heat of reaction, J/molh ) heat transfer coefficient, J/(m2 K s)hw ) wall heat transfer coefficient, J/(m2 K s)hwf ) wall/fluid heat transfer coefficient, J/(m2 K s)hfs ) fluid/solid heat transfer coefficient, J/(m2 K s)ki ) Arrhenius type rate constant of component iKi ) equilibrium constant of component ikmi ) mass transfer coefficient, m/skp ) pellet conductivity, J/(m K s)kref ) radial effective conductivity, J/(m K s)krf ) radial conductivity of the fluid, J/(m K s)krs ) radial conductivity of the solid, J/(m K s)ksi ) Arrhenius type rate constant of component i at thesurface
KSi ) equilibrium constant of component i at the surfacekw ) wall conductivity, J/(m K s)Pr ) Prandt numberRe ) Reynolds numberri ) rate of reaction of component i, mol/(kgcat s)[S] ) concentration of unoccupied sitesSc ) Schmidt number[St] ) concentration of free and occupied sitiesSV ) space velocity, cm3 STP gcat-1 min-1
T ) temperature in the gas phase, KT* ) dimensionless temperature of the fluid, TS/TTs ) surface temperature, KTw ) wall temperatureU ) overall heat transfer coefficient, J/(m2 K s)v ) average velocity of the fluid through the bed, m/sw ) mass of catalyst, kgyi ) molar fraction of component iz ) reactor length coordinate, m
Greek Lettersε ) void fraction of packed bedF ) fluid density, kg/m3
Fcat ) apparent catalyst densityøi ) experimental conversion of component i⟨øi⟩ ) calculated conversion of component iηi ) effectiveness factor of component i
Figure 5. Simulation of an industrial reactor. Acetylene andethylene conversion axial profiles for a model II adiabatic reactor.9, C2H2 conversion; O, C2H4 conversion.
Figure 6. Simulation of an industrial reactor. Computed andmeasured temperature profiles. 9, Plant data.
1504 Ind. Eng. Chem. Res., Vol. 35, No. 5, 1996
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SubscriptsA ) acetyleneCO ) carbon monoxideE ) ethyleneEt ) ethaneH ) hydrogen
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Received for review September 27, 1995Accepted January 19, 1996X
IE950600K
X Abstract published in Advance ACS Abstracts,March 15,1996.
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