- Email: [email protected]
Ballast gas for heat transfer control in fixed-bed reactors
Chemical Engineering Science 54 (1999) 3683}3689
Ballast gas for heat transfer control in "xed-bed reactors Vasilis Papavassiliou*, Matthew L. Wagner Praxair, Inc., Application Research and Development, 765 Old Saw Mill River Rd., Tarrytown, NY 10591, USA
Abstract Controlled oxidation reactions of hydrocarbons are practiced today in "xed-bed, #uid bed or transport bed reactors with oxygen or air as the oxidant. In "xed-bed reactors, due to the exothermicity of the oxidation reactions, heat removal and temperature control are critical in achieving safe and optimum reaction conditions that maximize conversion and selectivity. Industrial reactors often control hot spot formation by using an appropriate diluent (ballast) gas. Steam, nitrogen, methane and carbon dioxide are the most commonly used ballast gases. The scope of this paper is to elucidate the bene"ts of ballast gas use as a tool to optimize heat transfer and reduce the hot spot e!ect in controlled oxidations with "xed-bed reactors. Ballast gas does not participate in the reaction, but it is used to control heat removal and #ammability. A homogeneous one-dimensional reactor model was used to study and compare two oxidation processes: (1) ethylene oxidation to ethylene oxide and (2) o-xylene oxidation to phthalic anhydride. For both processes hot spot temperature and conversion decreased as methane replaced nitrogen in the process ballast gas. Selectivity increased in the ethylene oxide case but decreased in the phthalic anhydride case, indicating that ballast gas e!ect on selectivity depends on the reaction mechanism. Thus, there is an optimum ballast gas composition that will optimize hot spot temperature and reactor yield. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Ballast gas; Fixed bed; Vapor-phase oxidation; Ethylene oxide; Phthalic anhydride
1. Introduction The "xed-bed multitubular reactor is today the most commonly used reactor for practicing vapor-phase catalytic oxidations of hydrocarbons. The reactor consists of a multitude of tubes arranged similar to a shell and tube heat exchanger. The tubes are "lled with a catalyst. A coolant is circulated around the tubes to dissipate heat that is released from the exothermic controlled oxidation reaction. The hydrocarbon and oxidant are pre-mixed and fed to the reactor. Proper handling is required to ensure that the hydrocarbon-oxidant feed mixture stays outside the #ammability envelope or, if a #ammable mixture is used, the reactor is appropriately designed to prevent and/or relieve a de#agration. The exothermic oxidation reaction causes a hot spot to form near the reactor entrance, due to slow heat removal from the reactor tubes to the coolant #uid. Hot spot formation is
* Corresponding author. Tel.: 001 914 345 6424; fax: 001 914 345 6405; e-mail: vasilis}[email protected].
undesirable, because it can create safety problems, reduce catalyst life, reduce reactor performance, and lead to reactor runaway if not properly controlled. Harold et al., 1995, summarize the options available to reduce the severity of hot spots in multi-tubular "xed-bed reactors by (1) (2) (3) (4) (5)
reduce coolant temperature; increase carrier (ballast) gas #ow rate; increase bed thermal conductivity; reduce tube diameter; and dilute the catalyst bed (activity pro"ling).
In addition to these options in industrial reactors, however, an inert diluent (ballast gas) is often used to facilitate hot spot control. 1.1. Ballast gas use In air-based oxidations the ballast gas is usually nitrogen, but in oxygen-based oxidations the ballast gas selection is more complex. A signi"cant amount of patent literature (Kingsley and Cleland, 1964; Severs, 1974; Ramachaadran et al., 1991; Palmer and Holzhauer, 1982;
0009-2509/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 4 9 2 - 8
3684
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
Etzkorn and Harkreader, 1988; Etzkorn and Harkreader, 1990) describes the use of ballast gas in various hydrocarbon controlled oxidation processes. We discuss next a few examples of ballast gas use. Our intent is not to be exhaustive on the matter, but rather to present the diversity of catalytic oxidation processes that advocate the use of ballast gases. Ethylene oxide production in "xed-bed reactors is currently the largest oxygen-based hydrocarbon oxidation process. Ethylene oxide production was converted from air-based to oxygen-based process in the early 1960s. Methane (Kingsley and Cleland, 1964) was selected as the most appropriate ballast gas on the base of its inertness under the reaction conditions, good thermal conductivity and heat capacity properties, and its positive e!ect on #ammability. It has been reported (Kingsley and Cleland, 1964) that a maximum ethylene oxide yield achieved as methane replaced nitrogen in the process ballast gas. The optimum yield depended on the ballast gas composition and the ethylene concentration in the reactor feed. The reason for the yield increase was the improved heat transfer properties of the methane ballast gas, which reduced the hot spot e!ect and increase selectivity. Vinyl acetate manufacture is also oxygen-based and alternative ballast gases have been proposed (Severs, 1974) for this process as well. The current technology uses an excess of ethylene in the reactor feed instead of a non-reacting alternate ballast gas. The unreacted ethylene is recycled and the excess ethylene concentration in the reactor feed does not adversely a!ect the reaction kinetics for this particular reaction. The same solution is also preferred (Yen et al., 1982) in the oxygen-based chlorination of ethylene to vinyl chloride. Oxygen-based vinyl chloride production is an improvement over the air-based production in part, due to better heat transfer properties of the reaction mixture. In most air-based oxidation processes, nitrogen is the ballast gas. Acrylic and methacrylic acid production are air-based processes that utilize steam as a component of the ballast gas (Farhad, 1987). It has been reported in recent patents (Etzkorn and Harkreader, 1988, 1990) that the use of an anhydrous ballast gas improves production. The heat capacity of the ballast gas was correlated (Etzkorn and Harkreader, 1988, 1990) with improved reactor performance. Hydrocarbons with higher heat capacity than steam were found to improve performance. Additional bene"ts included reduction of the maximum hot spot temperature and increased catalyst life. In order to increase the hydrocarbon concentration in the reactor feed for maleic anhydride production without the adverse hot spot e!ects, Ramachaadran et al. (1991) proposed to use a mixture of methane, nitrogen and CO as a ballast gas in the feed together with oxygen and the hydrocarbon. The particular mixture of methane}nitrogen}CO acts as a #ame suppressor allowing higher butane concentration to be used in the feed and facilitates
heat removal. Oxygen or oxygen-enriched air can be used as the oxidant. When enriched air was used, nitrogen was partially replaced by methane and CO . When oxygen was used, nitrogen was completely replaced by methane and CO . Both ballast gas and unreacted butane can be recycled. An oxygen-based process with recycle was also described (Marshall, 1975; Palmer and Holzhauer, 1982) for the production of maleic anhydride by butane selective oxidation. The oxygen-based process was compared (Palmer and Holzhauer, 1982) to an air-based process with a recycle and to the conventional air-based process using the same catalyst. When pure oxygen was used the ballast gas was comprised of carbon oxides (CO and CO ), whereas, when air was used, the ballast gas was comprised of nitrogen and carbon oxides. In order to prevent build-up of inerts (CO , CO and N ) in the recycle a purge stream was withdrawn from the recycle stream at a rate equal to the rate of the build-up of inerts. The air-based process with recycle did not o!er signi"cant advantages. However, Palmer and Holzhauer (1982), report that the per gram production of catalyst was increased by 50% for an oxygen-based process using a ballast gas (CO and CO ) compared to the air-based process. 1.2. Heat and mass transfer modeling To our knowledge, limited attempts have been reported (Runhong and Yuen, 1993) to elucidate the e!ect of alternate ballast gases with reactor modeling techniques. This is surprising given the industrial signi"cance of ballast gas applications. Runhong and Yuen (1993), report simulations with one- and two-dimensional homogeneous models of an ethylene oxide reactor when nitrogen or methane are used as ballast gases. In reactor simulations, methane performed better than nitrogen by lowering the hot spot temperature maximum without a selectivity penalty. Runhong and Yuen (1993), used either nitrogen or methane as a ballast gas with di!erent operating conditions in each case. Thus, the e!ect on reactor performance of gradually substituting nitrogen with methane under identical process conditions was not obvious. In recent years increasingly sophisticated models have been developed (Finlayson and Rosendal, 1995; Froment and Papageorgiou, 1995; Bey and Eigenberger, 1997a) for heat and mass transfer modeling of "xed-bed reactors. Selection of the appropriate reaction kinetic and heat transfer parameters, to be used with a theoretical model, is critical. It still remains di$cult to estimate heat transfer coe$cients (Froment and De Wachs, 1972; Li and Finlayson, 1977; Bauer and Schlunder, 1978a,b; Dixon and Cresswell, 1979; Cresswell et al., 1982; Wakao and Kaguei, 1982; Dixon, 1985; Borkink and Westerterp, 1992; Bey and Eigenberger, 1997b) in a universally accepted fashion. The problem becomes even more complicated
3685
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
if one attempts to alter the ballast gas composition. Reaction kinetics are also di$cult to obtain for industrially relevant conditions. In our simulations we used reaction and heat transfer data for ethylene oxide and phthalic anhydride reactions available in the open literature (Runhong and Yuen, 1993; Calderbank et al., 1977; Li and Finlayson, 1977; Wakao and Kaguei, 1982). It is critical that the reactor model uses identical heat transfer parameters as the model that was used to estimate the kinetic parameters. The goal of our simulations was to elucidate the ballast gas e!ect on reactor performance in oxygen or air-based hydrocarbon oxidations and for di!erent reaction mechanisms. Only the e!ect on heat transfer of a single ballast gas was examined although it is obvious that mixtures of gases are used industrially. In particular, the partial oxidation of ethylene to ethylene oxide was used as an example of a parallel reaction mechanism where the partial oxidation of o-xylene to phthalic anhydride was used as an example of a more complicated mechanism with several intermediate species. In our simulation of ethylene oxidation we assumed the following reaction equations (kinetics by Runhong and Yuen, 1993): C H #0.5 O "C H O, (I) C H #3O "2CO #2H O. (II) For the xylene oxidation simulation we used kinetic parameters estimated by Calderbank et al. (1977), who assumed the following reaction network:
Table 1 Parameters for simulations of the ethylene oxide and phthalic anhydride cases Parameter
Ethylene oxide
Phthalic anhydride
¸ (m) R (m) R d (m) N e G (kg/m s) Reaction kinetics
7.7 0.0127 0.004 0.52 18 Runhong and Yuen (1993) Li and Finlayson (1977) 22 atm
0.85 0.0127 0.003 0.56 1.318 Calderbank et al. (1977) Wakao and Kaguei (1982) 1 atm
a ,j U CP P
a multiple reaction system take the form Gy dX G"r (X , ¹ ), ! (1) G G P M dz j 8a d¹ P"! CP #(!H) r (X , ¹ ), (2) Gc G G P N dz r A R where ¹ is the reaction-averaged temperature and a is P calculated from the following equation:
4a B ln(1!a) A(¹ !¹ )" !ln(1!a)# . P U Bi 3A
(3)
The parameters A and B for multiple reaction systems at ¹"¹ are given from: P * * A" ln(H) and B" ln(H), (4) *¹ *¹ where
(III) where CO represents carbon oxides (CO and CO ). V 2. Model development Detailed two-dimensional heterogeneous models that account for radial and axial heat and mass transfer have been presented (Finlayson and Rosendal, 1995; Froment and Papageorgiou, 1995; Bey and Eigenberger, 1997). Since this was an introductory study and only the qualitative e!ect of ballast gas use was investigated, we selected to use a one-dimensional model (a model) based on asymptotic analysis (Herskowitz and Hagan, 1988; Herskowitz, et al., 1988) of the radial temperature pro"le. The details of the model are given elsewhere (Herskowitz, et al., 1988). The "nal mass and energy balances for
L H" (!DH ) r . (5) G G G The parameters used to solve the above equations for the ethylene oxide and phthalic anhydride processes are given in Table 1. The estimation of the e!ective radial conductivity (j ) and the wall heat transfer coe$cient CP (a ) are further discussed in the next section. U 3. Results and discussion The two physical parameters signi"cantly a!ected by the reaction mixture composition and closely related to heat transfer are the gas thermal conductivity and heat capacity. Heat capacity and thermal conductivity of gas mixtures were calculated according to methods presented in Perry's Handbook (1984). In a homogeneous "xed-bed reactor simulation heat transfer is characterized by two parameters: (a) the wall heat transfer coe$cient (a ) U and (b) the bed radial conductivity (j ). The e!ect of CP
3686
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
increased heat capacity and thermal conductivity on a and j was investigated using empirical or semiemU CP pirical correlations (Froment and De Wachs, 1972; Bey and Eigenberger, 1997; Westerterp, 1997; Wakao and Kaguei, 1982; Bauer and Schlunder, 1978a, b; Cresswell et al., 1982; Li and Finlason, 1977). It was found that di!erent correlations predict di!erent values for j and CP a , when ballast gas composition changes. Correlations U based on the Re number (Froment and De Wachs, 1972; Froment and Bischo!, 1990), though more accurate for the gas mixture they were derived for, are not suitable to predict j and a when the gas mixture composition CP U changes. Table 2 summarizes results of several correlations (Bey and Eigenberger, 1997; Westerterp, 1997; Wakao and Kaguei, 1982; Bauer and Schlunder, 1978a, b; Cresswell et al., 1982; Li and Finlason, 1977), incorporating the Pr number. Heat transfer parameters j and CP a were predicted for a mixture containing initially 18% U molar oxygen, 1% xylene and balance nitrogen. The ballast gas molar composition was varied by replacing nitrogen with methane in 10% increments and monitoring the change in the j and a values. The parameters CP U for the phthalic anhydride reactor reported in Table 1 were used in the calculation of j and a . The last line in CP U Table 2 represents the average % increase of j and CP a for a 1% increase of the methane concentration. U Although there is disagreement among di!erent correlations (Table 2) they all predict a signi"cant improvement in j and a equal to about 0.14}1.28 and 0.9}1.27%, CP U respectively, for every 1% methane concentration increase. Heat capacity and thermal conductivity of the gas mixture increase linearly as nitrogen concentration decreases and as a result j and a increase. The Bey and CP U Eigenberger (1997) correlation, which has a week (Pr ) dependence to the Pr number, predicted the smallest a increase. More work is needed to incorporate the U ballast gas e!ect in j and a correlations. For the CP U ethylene oxide simulations reported in this work we used correlations for j and a reported by Li and Finlayson CP U
(1977), because that correlation was also used in the derivation of kinetic parameters (Runhong and Yuen, 1993). For the phthalic anhydride simulation we used correlations by Wakao and Kaguei (1982), because it was found that when they were used in simulations the results agree with results reported by Calderbank et al. (1977). The correlations by Wakao and Kaguei can also predict j and a when the composition of the ballast gas CP U changes. 3.1. Ethylene oxide reactor simulations With the aid of the model we tested how ethylene oxide yield can be a!ected by the ballast gas composition. Fig. 1 illustrates the model results for ethylene oxide selectivity, ethylene conversion and hot spot temperature as a function of increasing methane concentration. The reactor feed consisted of 15% ethylene, 7% oxygen, 10.55% carbon dioxide with nitrogen or nitrogen}methane mixtures make up the rest. The reactor feed temperature was at 5133K and the coolant temperature was 5263K. It becomes evident (Fig. 1 left) that the selectivity (per pass) increases as methane substitutes for nitrogen until it exponentially reaches a limiting value. The simulations predict that ethylene conversion per pass decreases (Fig. 1 left). In the industrial process most of the unreacted ethylene is recycled, thus, a selectivity increase will lead to an overall yield increase for the process. Fig. 1 (right) also depicts the hot spot temperature evolution as methane replaces nitrogen. We observe that the maximum temperature decreases as methane concentration in the reaction mixture increases. Reduction of the hot spot temperature results in a selectivity increase because higher temperatures favor the undesirable reaction to carbon dioxide. These results agree qualitatively with experimental results presented elsewhere (Kingsley and Cleland, 1964) for the ethylene oxide process yield as methane replaces nitrogen in the ballast gas. The experimentally observed yield maximum (Kingsley and Cleland,
Table 2 Prediction of the wall heat transfer coe$cient (a ) and the e!ective radial conductivity (j ) from various correlations as methane substitutes nitrogen U CP in a mixture containing initially 18% oxygen, 1% o-xylene and balance nitrogen Westertep (1997)
0% CH 10% CH 20% CH 30% CH 40% CH % increase per 1% CH
Bey and Eigenberger (1997)
a U
j CP
a U
275 300 324 349 374 0.90
0.74 0.83 0.92 1.00 1.12 1.28
248 251 254 258 262 0.14
j CP
Wakao and Kaguei (1982) a U
j CP
205 229 254 280 309 1.27
0.53 0.58 0.64 0.70 0.77 1.13
Bauer and Schlunder (1978a, b) a U
Cresswell et al. (1982)
Li and Finlayson (1977)
j CP
a U
j CP
a U
j CP
0.97 1.10 1.20 1.30 1.42 1.16
408 439 471 504 539 0.8
1.10 1.20 1.30 1.40 1.54 1.00
120 134 148 163 179 1.23
1.70 1.90 2.10 2.30 2.53 1.22
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
3687
Fig. 1. Model results for ethylene oxide selectivity, ethylene conversion (left) and hot spot temperature (right) as a function of increasing methane concentration.
1964) is a function of several process parameters (per pass yield, separation system, recycle, purge rate, reactants purity), therefore, a direct quantitative comparison with experimental results is not possible without knowing of all the process details. Also kinetic parameters used in this work (Runhong and Yuen, 1993) are not representative of the catalyst used in the experimental studies (Kingsley and Cleland, 1964). The results (Fig. 1), however, demonstrate a positive e!ect on selectivity and hot spot temperature for the methane ballast gas. 3.2. Phthalic anhydride reactor simulations Production of phthalic anhydride (PA) via controlled oxidation of o-xylene with air is a well studied oxidation process. In phthalic anhydride production process proper care must be taken to ensure that the hydrocarbon-air feed mixture is outside the #ammability envelope or an elaborate safety system must be employed to prevent and/or relieve a de#agration. Operating within the #ammability envelope is possible (Lurgi, 1994) by carefully designing the reactor feed system, by using proper rupture disks to relieve pressure and by using redundant interlocks. The lower #ammability limit of o-xylene in air is 1 mol%. The model was used to predict behavior of "xed-bed reactors in the air-based controlled oxidation of o-xylene to phthalic anhydride, in which the properties of the feed gas mixture were altered by introduction of a methane ballast gas. We employed this example for the purpose of illustrating the ballast gas e!ect on heat transfer, however, several other factors (e.g. #ammability, catalyst performance, process economics) need to be evaluated before one can actually utilize a ballast gas for heat
transfer control in an industrial controlled oxidation process. Fig. 2 presents calculations for o-xylene partial oxidation to PA as a function of the methane concentration in the ballast gas. A feed molar concentration 1.5% in o-xylene, 18% in O , and balance N and CH mixtures was assumed. A total gas feed rate of 1.318 kg/m s was assumed. The reactor wall temperature and the feed temperature were 6933K. We observe from Fig. 2 (left) that xylene conversion and phthalic anhydride selectivity decrease as methane concentration in the ballast gas increases. The hot spot temperature (Fig. 2 right) also decreases as methane concentration in the ballast gas increases. The conversion and the hot spot temperature trends are similar to those observed in the ethylene case. The product selectivity trend (Fig. 2 left), however, is opposite to the one observed in the ethylene oxidation case. This di!erence is explained if one considers the more complicated reaction mechanism that we used for the xylene oxidation (reaction (III)). In this case not only the undesirable reaction rates, that form carbon oxides, are depressed by the lower temperatures encountered along the reactor but the reaction rates of the intermediate species, are depressed as well. The di!erence in the temperature pro"les along the reactor is depicted in Fig. 3 for nitrogen ballast gas (left) and for nitrogen with 10% methane ballast gas (right). We observe that the temperature maximum is lower when the ballast gas contains methane. The temperature maximum that is observed (9003K) when nitrogen only is used, would result in fast catalyst deactivation during actual reactor operation (Calderbank et al., 1977). Catalyst dilution was proposed as a solution for hot spot temperature control, and was proved e!ective in
3688
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
Fig. 2. Model results for phthalic anhydride selectivity, o-xylene conversion (left) and hot spot temperature (right) as a function of increasing methane concentration.
Fig. 3. Temperature pro"les along the reactor length for phthalic anhydride when nitrogen is used as a ballast gas (left) and when a nitrogen with 10% methane mixture is used as ballast gas (right).
theoretical simulations (Calderbank et al., 1977). The hot spot temperature maximum is reduced from 9003K (Fig. 3 left) to 8503K (Fig. 3 right) when a ballast gas containing 10% methane is used. Although conversion and selectivity are somewhat lower the catalyst life will be preserved. Further increase of the methane concentration in the ballast gas will further reduce the hot spot temperature but also reduce product yield. Thus, for a given set of process conditions, there is a methane/nitrogen ballast gas composition, that will optimize both hot spot temperature and phthalic anhydride production.
4. Conclusions Theoretical results from ethylene oxide and phthalic anhydride reactor simulations indicate that ballast gas use is an e!ective tool for improving heat removal and
hot spot temperature control in "xed-bed reactor processes. Di!erent reaction mechanisms may be a!ected di!erently by changes in the ballast gas composition as it is evident from the comparison of the ethylene oxidation and the o-xylene oxidation cases. In this work the e!ect of a single ballast gas was examined, although, the ballast gas composition is a critical parameter that requires optimization. In an industrial reactor the ballast gas selection will be guided by reactor performance evaluation, process parameters (recycle, purge, #ammability) and economic optimization. Therefore, it may not always be economical to use the best ballast gas available. Future work should focus on the development of reliable heat transfer correlations that account for composition changes, and also on the study of the ballast gas e!ect with heterogeneous models, in order to provide accurate design guidelines for reaction and process engineers.
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
Notation a U Bi c N d N G H ¸ M P r r R Re ¹ X y e j CP
wall heat transfer coe$cient Biot number heat capacity catalyst particle diameter mass velocity heat of reaction reactor length average molecular weight total pressure reaction rate reactor tube radius Reynolds number temperature conversion feed mole fraction of hydrocarbon catalytic bed porosity e!ective radial conductivity
Subscripts i w r t
species wall reaction averaged tube
References Bauer, R., & Schlunder, E.U. (1978a). Int. Chem. Engng, 18, 181}188. Bauer, R., & Schlunder, E.U. (1978b). Int. Chem. Engng, 18, 189}204. Bey, O., & Eigenberger, G. (1997a). Chem. Engng Sci., 52, 1365}1376. Bey, O., & Eigenberger, G. (1997b). Vortrag, ECCE-1, May 4}7.
3689
Borkink, J.G., & Westerterp, K.R. (1992). Chem. Engng Sci., 47, 2337}2342. Calderbank, P.H., Chandrasekharan, K., & Fumagalli, C. (1977). Chem. Engng Sci., 32, 1435}1443. Cresswell, D.L., Newson, E.J., & Wellauer, T. (1982). Chemical reaction engineering, ACS Symp. Ser. No. 196, (pp. 527}542). Dixon, A.G., & Cresswell, D.L. (1979). A.I.Ch.E. Jr., 25, 663}676. Dixon, A.G. (1985). A.I.Ch.E. Jr., 31, 826}834. Etzkorn, W.G., & Harkreader, G.G. (1988). European Patent, 293224A1. Etzkorn, W.G., & Harkreader, G.G. (1990). European Patent, 361372A1. Farhad, N. (1987). Acrylic acids and acrylic esters. SRI report 6C. Finlayson, B.A., & Rosendal, B. (1995). Comput. Chem. Engng, 19, 1207}1218. Froment, G.F., & De Wachs, (1972). Chem. Engng Sci., 27, 567}576. Froment, G.F., & Bischo!, K.B. (1990). Chemical reactor analysis and design. New York: Wiley. Froment, G.F., & Papageorgiou, J.N. (1995). Chem. Engng Sci., 50, 3043}3056. Harold, M.P., & Lerou, J.J., & Mills, P.L. (1995). Catalytic oxidations, (pp. 291}369). Herskowitz, M., & Hagan, P.S. (1988). A.I.Ch.E. Jr., 34(8). Herskowitz, M., Hagan, P.S., & Pirkle, C. (1988). SIAM Jr. Appl. Math., 48, 1083}1101. Kingsley, H.A., & Cleland, F.A. (1964). ;.S. Patent 3119837. Li, C.H., & Finlayson, B.A. (1977). Chem. Engng Sci., 32, 1055}1066. Lurgi, A.G. (1994). Lurgi brochure, Phthalic anhydride. Marshall, E.F. (1975). ;S Patent 3904652. Palmer, D., & Holzhauer, J. (1982). ;S patent 4342699. Perry, R.H., & Green, D. (1984). Perry's chemical engineering handbook. (6th ed.). New York: McGraw Hill. Ramachaadran, R., Shukla, Y., & MacLean, D.L. (1991). ;S Patent 4987239. Runhong, Q., & Yuen, T. (1993). Shiyou Huagong (Petrochemical Engineering). (vol. 22, pp. 792}798. Severs, G.M. (1974). ;S patent 3855280. Wakao, N., & Kaguei, S. (1982). Heat and mass transfer in packed beds. London: Gordon and Breach. Yen, Y., Hsu, L.C., & Chiou, C. (1982). SRI Report 5C.
Ballast gas for heat transfer control in "xed-bed reactors Vasilis Papavassiliou*, Matthew L. Wagner Praxair, Inc., Application Research and Development, 765 Old Saw Mill River Rd., Tarrytown, NY 10591, USA
Abstract Controlled oxidation reactions of hydrocarbons are practiced today in "xed-bed, #uid bed or transport bed reactors with oxygen or air as the oxidant. In "xed-bed reactors, due to the exothermicity of the oxidation reactions, heat removal and temperature control are critical in achieving safe and optimum reaction conditions that maximize conversion and selectivity. Industrial reactors often control hot spot formation by using an appropriate diluent (ballast) gas. Steam, nitrogen, methane and carbon dioxide are the most commonly used ballast gases. The scope of this paper is to elucidate the bene"ts of ballast gas use as a tool to optimize heat transfer and reduce the hot spot e!ect in controlled oxidations with "xed-bed reactors. Ballast gas does not participate in the reaction, but it is used to control heat removal and #ammability. A homogeneous one-dimensional reactor model was used to study and compare two oxidation processes: (1) ethylene oxidation to ethylene oxide and (2) o-xylene oxidation to phthalic anhydride. For both processes hot spot temperature and conversion decreased as methane replaced nitrogen in the process ballast gas. Selectivity increased in the ethylene oxide case but decreased in the phthalic anhydride case, indicating that ballast gas e!ect on selectivity depends on the reaction mechanism. Thus, there is an optimum ballast gas composition that will optimize hot spot temperature and reactor yield. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Ballast gas; Fixed bed; Vapor-phase oxidation; Ethylene oxide; Phthalic anhydride
1. Introduction The "xed-bed multitubular reactor is today the most commonly used reactor for practicing vapor-phase catalytic oxidations of hydrocarbons. The reactor consists of a multitude of tubes arranged similar to a shell and tube heat exchanger. The tubes are "lled with a catalyst. A coolant is circulated around the tubes to dissipate heat that is released from the exothermic controlled oxidation reaction. The hydrocarbon and oxidant are pre-mixed and fed to the reactor. Proper handling is required to ensure that the hydrocarbon-oxidant feed mixture stays outside the #ammability envelope or, if a #ammable mixture is used, the reactor is appropriately designed to prevent and/or relieve a de#agration. The exothermic oxidation reaction causes a hot spot to form near the reactor entrance, due to slow heat removal from the reactor tubes to the coolant #uid. Hot spot formation is
* Corresponding author. Tel.: 001 914 345 6424; fax: 001 914 345 6405; e-mail: vasilis}[email protected].
undesirable, because it can create safety problems, reduce catalyst life, reduce reactor performance, and lead to reactor runaway if not properly controlled. Harold et al., 1995, summarize the options available to reduce the severity of hot spots in multi-tubular "xed-bed reactors by (1) (2) (3) (4) (5)
reduce coolant temperature; increase carrier (ballast) gas #ow rate; increase bed thermal conductivity; reduce tube diameter; and dilute the catalyst bed (activity pro"ling).
In addition to these options in industrial reactors, however, an inert diluent (ballast gas) is often used to facilitate hot spot control. 1.1. Ballast gas use In air-based oxidations the ballast gas is usually nitrogen, but in oxygen-based oxidations the ballast gas selection is more complex. A signi"cant amount of patent literature (Kingsley and Cleland, 1964; Severs, 1974; Ramachaadran et al., 1991; Palmer and Holzhauer, 1982;
0009-2509/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 4 9 2 - 8
3684
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
Etzkorn and Harkreader, 1988; Etzkorn and Harkreader, 1990) describes the use of ballast gas in various hydrocarbon controlled oxidation processes. We discuss next a few examples of ballast gas use. Our intent is not to be exhaustive on the matter, but rather to present the diversity of catalytic oxidation processes that advocate the use of ballast gases. Ethylene oxide production in "xed-bed reactors is currently the largest oxygen-based hydrocarbon oxidation process. Ethylene oxide production was converted from air-based to oxygen-based process in the early 1960s. Methane (Kingsley and Cleland, 1964) was selected as the most appropriate ballast gas on the base of its inertness under the reaction conditions, good thermal conductivity and heat capacity properties, and its positive e!ect on #ammability. It has been reported (Kingsley and Cleland, 1964) that a maximum ethylene oxide yield achieved as methane replaced nitrogen in the process ballast gas. The optimum yield depended on the ballast gas composition and the ethylene concentration in the reactor feed. The reason for the yield increase was the improved heat transfer properties of the methane ballast gas, which reduced the hot spot e!ect and increase selectivity. Vinyl acetate manufacture is also oxygen-based and alternative ballast gases have been proposed (Severs, 1974) for this process as well. The current technology uses an excess of ethylene in the reactor feed instead of a non-reacting alternate ballast gas. The unreacted ethylene is recycled and the excess ethylene concentration in the reactor feed does not adversely a!ect the reaction kinetics for this particular reaction. The same solution is also preferred (Yen et al., 1982) in the oxygen-based chlorination of ethylene to vinyl chloride. Oxygen-based vinyl chloride production is an improvement over the air-based production in part, due to better heat transfer properties of the reaction mixture. In most air-based oxidation processes, nitrogen is the ballast gas. Acrylic and methacrylic acid production are air-based processes that utilize steam as a component of the ballast gas (Farhad, 1987). It has been reported in recent patents (Etzkorn and Harkreader, 1988, 1990) that the use of an anhydrous ballast gas improves production. The heat capacity of the ballast gas was correlated (Etzkorn and Harkreader, 1988, 1990) with improved reactor performance. Hydrocarbons with higher heat capacity than steam were found to improve performance. Additional bene"ts included reduction of the maximum hot spot temperature and increased catalyst life. In order to increase the hydrocarbon concentration in the reactor feed for maleic anhydride production without the adverse hot spot e!ects, Ramachaadran et al. (1991) proposed to use a mixture of methane, nitrogen and CO as a ballast gas in the feed together with oxygen and the hydrocarbon. The particular mixture of methane}nitrogen}CO acts as a #ame suppressor allowing higher butane concentration to be used in the feed and facilitates
heat removal. Oxygen or oxygen-enriched air can be used as the oxidant. When enriched air was used, nitrogen was partially replaced by methane and CO . When oxygen was used, nitrogen was completely replaced by methane and CO . Both ballast gas and unreacted butane can be recycled. An oxygen-based process with recycle was also described (Marshall, 1975; Palmer and Holzhauer, 1982) for the production of maleic anhydride by butane selective oxidation. The oxygen-based process was compared (Palmer and Holzhauer, 1982) to an air-based process with a recycle and to the conventional air-based process using the same catalyst. When pure oxygen was used the ballast gas was comprised of carbon oxides (CO and CO ), whereas, when air was used, the ballast gas was comprised of nitrogen and carbon oxides. In order to prevent build-up of inerts (CO , CO and N ) in the recycle a purge stream was withdrawn from the recycle stream at a rate equal to the rate of the build-up of inerts. The air-based process with recycle did not o!er signi"cant advantages. However, Palmer and Holzhauer (1982), report that the per gram production of catalyst was increased by 50% for an oxygen-based process using a ballast gas (CO and CO ) compared to the air-based process. 1.2. Heat and mass transfer modeling To our knowledge, limited attempts have been reported (Runhong and Yuen, 1993) to elucidate the e!ect of alternate ballast gases with reactor modeling techniques. This is surprising given the industrial signi"cance of ballast gas applications. Runhong and Yuen (1993), report simulations with one- and two-dimensional homogeneous models of an ethylene oxide reactor when nitrogen or methane are used as ballast gases. In reactor simulations, methane performed better than nitrogen by lowering the hot spot temperature maximum without a selectivity penalty. Runhong and Yuen (1993), used either nitrogen or methane as a ballast gas with di!erent operating conditions in each case. Thus, the e!ect on reactor performance of gradually substituting nitrogen with methane under identical process conditions was not obvious. In recent years increasingly sophisticated models have been developed (Finlayson and Rosendal, 1995; Froment and Papageorgiou, 1995; Bey and Eigenberger, 1997a) for heat and mass transfer modeling of "xed-bed reactors. Selection of the appropriate reaction kinetic and heat transfer parameters, to be used with a theoretical model, is critical. It still remains di$cult to estimate heat transfer coe$cients (Froment and De Wachs, 1972; Li and Finlayson, 1977; Bauer and Schlunder, 1978a,b; Dixon and Cresswell, 1979; Cresswell et al., 1982; Wakao and Kaguei, 1982; Dixon, 1985; Borkink and Westerterp, 1992; Bey and Eigenberger, 1997b) in a universally accepted fashion. The problem becomes even more complicated
3685
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
if one attempts to alter the ballast gas composition. Reaction kinetics are also di$cult to obtain for industrially relevant conditions. In our simulations we used reaction and heat transfer data for ethylene oxide and phthalic anhydride reactions available in the open literature (Runhong and Yuen, 1993; Calderbank et al., 1977; Li and Finlayson, 1977; Wakao and Kaguei, 1982). It is critical that the reactor model uses identical heat transfer parameters as the model that was used to estimate the kinetic parameters. The goal of our simulations was to elucidate the ballast gas e!ect on reactor performance in oxygen or air-based hydrocarbon oxidations and for di!erent reaction mechanisms. Only the e!ect on heat transfer of a single ballast gas was examined although it is obvious that mixtures of gases are used industrially. In particular, the partial oxidation of ethylene to ethylene oxide was used as an example of a parallel reaction mechanism where the partial oxidation of o-xylene to phthalic anhydride was used as an example of a more complicated mechanism with several intermediate species. In our simulation of ethylene oxidation we assumed the following reaction equations (kinetics by Runhong and Yuen, 1993): C H #0.5 O "C H O, (I) C H #3O "2CO #2H O. (II) For the xylene oxidation simulation we used kinetic parameters estimated by Calderbank et al. (1977), who assumed the following reaction network:
Table 1 Parameters for simulations of the ethylene oxide and phthalic anhydride cases Parameter
Ethylene oxide
Phthalic anhydride
¸ (m) R (m) R d (m) N e G (kg/m s) Reaction kinetics
7.7 0.0127 0.004 0.52 18 Runhong and Yuen (1993) Li and Finlayson (1977) 22 atm
0.85 0.0127 0.003 0.56 1.318 Calderbank et al. (1977) Wakao and Kaguei (1982) 1 atm
a ,j U CP P
a multiple reaction system take the form Gy dX G"r (X , ¹ ), ! (1) G G P M dz j 8a d¹ P"! CP #(!H) r (X , ¹ ), (2) Gc G G P N dz r A R where ¹ is the reaction-averaged temperature and a is P calculated from the following equation:
4a B ln(1!a) A(¹ !¹ )" !ln(1!a)# . P U Bi 3A
(3)
The parameters A and B for multiple reaction systems at ¹"¹ are given from: P * * A" ln(H) and B" ln(H), (4) *¹ *¹ where
(III) where CO represents carbon oxides (CO and CO ). V 2. Model development Detailed two-dimensional heterogeneous models that account for radial and axial heat and mass transfer have been presented (Finlayson and Rosendal, 1995; Froment and Papageorgiou, 1995; Bey and Eigenberger, 1997). Since this was an introductory study and only the qualitative e!ect of ballast gas use was investigated, we selected to use a one-dimensional model (a model) based on asymptotic analysis (Herskowitz and Hagan, 1988; Herskowitz, et al., 1988) of the radial temperature pro"le. The details of the model are given elsewhere (Herskowitz, et al., 1988). The "nal mass and energy balances for
L H" (!DH ) r . (5) G G G The parameters used to solve the above equations for the ethylene oxide and phthalic anhydride processes are given in Table 1. The estimation of the e!ective radial conductivity (j ) and the wall heat transfer coe$cient CP (a ) are further discussed in the next section. U 3. Results and discussion The two physical parameters signi"cantly a!ected by the reaction mixture composition and closely related to heat transfer are the gas thermal conductivity and heat capacity. Heat capacity and thermal conductivity of gas mixtures were calculated according to methods presented in Perry's Handbook (1984). In a homogeneous "xed-bed reactor simulation heat transfer is characterized by two parameters: (a) the wall heat transfer coe$cient (a ) U and (b) the bed radial conductivity (j ). The e!ect of CP
3686
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
increased heat capacity and thermal conductivity on a and j was investigated using empirical or semiemU CP pirical correlations (Froment and De Wachs, 1972; Bey and Eigenberger, 1997; Westerterp, 1997; Wakao and Kaguei, 1982; Bauer and Schlunder, 1978a, b; Cresswell et al., 1982; Li and Finlason, 1977). It was found that di!erent correlations predict di!erent values for j and CP a , when ballast gas composition changes. Correlations U based on the Re number (Froment and De Wachs, 1972; Froment and Bischo!, 1990), though more accurate for the gas mixture they were derived for, are not suitable to predict j and a when the gas mixture composition CP U changes. Table 2 summarizes results of several correlations (Bey and Eigenberger, 1997; Westerterp, 1997; Wakao and Kaguei, 1982; Bauer and Schlunder, 1978a, b; Cresswell et al., 1982; Li and Finlason, 1977), incorporating the Pr number. Heat transfer parameters j and CP a were predicted for a mixture containing initially 18% U molar oxygen, 1% xylene and balance nitrogen. The ballast gas molar composition was varied by replacing nitrogen with methane in 10% increments and monitoring the change in the j and a values. The parameters CP U for the phthalic anhydride reactor reported in Table 1 were used in the calculation of j and a . The last line in CP U Table 2 represents the average % increase of j and CP a for a 1% increase of the methane concentration. U Although there is disagreement among di!erent correlations (Table 2) they all predict a signi"cant improvement in j and a equal to about 0.14}1.28 and 0.9}1.27%, CP U respectively, for every 1% methane concentration increase. Heat capacity and thermal conductivity of the gas mixture increase linearly as nitrogen concentration decreases and as a result j and a increase. The Bey and CP U Eigenberger (1997) correlation, which has a week (Pr ) dependence to the Pr number, predicted the smallest a increase. More work is needed to incorporate the U ballast gas e!ect in j and a correlations. For the CP U ethylene oxide simulations reported in this work we used correlations for j and a reported by Li and Finlayson CP U
(1977), because that correlation was also used in the derivation of kinetic parameters (Runhong and Yuen, 1993). For the phthalic anhydride simulation we used correlations by Wakao and Kaguei (1982), because it was found that when they were used in simulations the results agree with results reported by Calderbank et al. (1977). The correlations by Wakao and Kaguei can also predict j and a when the composition of the ballast gas CP U changes. 3.1. Ethylene oxide reactor simulations With the aid of the model we tested how ethylene oxide yield can be a!ected by the ballast gas composition. Fig. 1 illustrates the model results for ethylene oxide selectivity, ethylene conversion and hot spot temperature as a function of increasing methane concentration. The reactor feed consisted of 15% ethylene, 7% oxygen, 10.55% carbon dioxide with nitrogen or nitrogen}methane mixtures make up the rest. The reactor feed temperature was at 5133K and the coolant temperature was 5263K. It becomes evident (Fig. 1 left) that the selectivity (per pass) increases as methane substitutes for nitrogen until it exponentially reaches a limiting value. The simulations predict that ethylene conversion per pass decreases (Fig. 1 left). In the industrial process most of the unreacted ethylene is recycled, thus, a selectivity increase will lead to an overall yield increase for the process. Fig. 1 (right) also depicts the hot spot temperature evolution as methane replaces nitrogen. We observe that the maximum temperature decreases as methane concentration in the reaction mixture increases. Reduction of the hot spot temperature results in a selectivity increase because higher temperatures favor the undesirable reaction to carbon dioxide. These results agree qualitatively with experimental results presented elsewhere (Kingsley and Cleland, 1964) for the ethylene oxide process yield as methane replaces nitrogen in the ballast gas. The experimentally observed yield maximum (Kingsley and Cleland,
Table 2 Prediction of the wall heat transfer coe$cient (a ) and the e!ective radial conductivity (j ) from various correlations as methane substitutes nitrogen U CP in a mixture containing initially 18% oxygen, 1% o-xylene and balance nitrogen Westertep (1997)
0% CH 10% CH 20% CH 30% CH 40% CH % increase per 1% CH
Bey and Eigenberger (1997)
a U
j CP
a U
275 300 324 349 374 0.90
0.74 0.83 0.92 1.00 1.12 1.28
248 251 254 258 262 0.14
j CP
Wakao and Kaguei (1982) a U
j CP
205 229 254 280 309 1.27
0.53 0.58 0.64 0.70 0.77 1.13
Bauer and Schlunder (1978a, b) a U
Cresswell et al. (1982)
Li and Finlayson (1977)
j CP
a U
j CP
a U
j CP
0.97 1.10 1.20 1.30 1.42 1.16
408 439 471 504 539 0.8
1.10 1.20 1.30 1.40 1.54 1.00
120 134 148 163 179 1.23
1.70 1.90 2.10 2.30 2.53 1.22
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
3687
Fig. 1. Model results for ethylene oxide selectivity, ethylene conversion (left) and hot spot temperature (right) as a function of increasing methane concentration.
1964) is a function of several process parameters (per pass yield, separation system, recycle, purge rate, reactants purity), therefore, a direct quantitative comparison with experimental results is not possible without knowing of all the process details. Also kinetic parameters used in this work (Runhong and Yuen, 1993) are not representative of the catalyst used in the experimental studies (Kingsley and Cleland, 1964). The results (Fig. 1), however, demonstrate a positive e!ect on selectivity and hot spot temperature for the methane ballast gas. 3.2. Phthalic anhydride reactor simulations Production of phthalic anhydride (PA) via controlled oxidation of o-xylene with air is a well studied oxidation process. In phthalic anhydride production process proper care must be taken to ensure that the hydrocarbon-air feed mixture is outside the #ammability envelope or an elaborate safety system must be employed to prevent and/or relieve a de#agration. Operating within the #ammability envelope is possible (Lurgi, 1994) by carefully designing the reactor feed system, by using proper rupture disks to relieve pressure and by using redundant interlocks. The lower #ammability limit of o-xylene in air is 1 mol%. The model was used to predict behavior of "xed-bed reactors in the air-based controlled oxidation of o-xylene to phthalic anhydride, in which the properties of the feed gas mixture were altered by introduction of a methane ballast gas. We employed this example for the purpose of illustrating the ballast gas e!ect on heat transfer, however, several other factors (e.g. #ammability, catalyst performance, process economics) need to be evaluated before one can actually utilize a ballast gas for heat
transfer control in an industrial controlled oxidation process. Fig. 2 presents calculations for o-xylene partial oxidation to PA as a function of the methane concentration in the ballast gas. A feed molar concentration 1.5% in o-xylene, 18% in O , and balance N and CH mixtures was assumed. A total gas feed rate of 1.318 kg/m s was assumed. The reactor wall temperature and the feed temperature were 6933K. We observe from Fig. 2 (left) that xylene conversion and phthalic anhydride selectivity decrease as methane concentration in the ballast gas increases. The hot spot temperature (Fig. 2 right) also decreases as methane concentration in the ballast gas increases. The conversion and the hot spot temperature trends are similar to those observed in the ethylene case. The product selectivity trend (Fig. 2 left), however, is opposite to the one observed in the ethylene oxidation case. This di!erence is explained if one considers the more complicated reaction mechanism that we used for the xylene oxidation (reaction (III)). In this case not only the undesirable reaction rates, that form carbon oxides, are depressed by the lower temperatures encountered along the reactor but the reaction rates of the intermediate species, are depressed as well. The di!erence in the temperature pro"les along the reactor is depicted in Fig. 3 for nitrogen ballast gas (left) and for nitrogen with 10% methane ballast gas (right). We observe that the temperature maximum is lower when the ballast gas contains methane. The temperature maximum that is observed (9003K) when nitrogen only is used, would result in fast catalyst deactivation during actual reactor operation (Calderbank et al., 1977). Catalyst dilution was proposed as a solution for hot spot temperature control, and was proved e!ective in
3688
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
Fig. 2. Model results for phthalic anhydride selectivity, o-xylene conversion (left) and hot spot temperature (right) as a function of increasing methane concentration.
Fig. 3. Temperature pro"les along the reactor length for phthalic anhydride when nitrogen is used as a ballast gas (left) and when a nitrogen with 10% methane mixture is used as ballast gas (right).
theoretical simulations (Calderbank et al., 1977). The hot spot temperature maximum is reduced from 9003K (Fig. 3 left) to 8503K (Fig. 3 right) when a ballast gas containing 10% methane is used. Although conversion and selectivity are somewhat lower the catalyst life will be preserved. Further increase of the methane concentration in the ballast gas will further reduce the hot spot temperature but also reduce product yield. Thus, for a given set of process conditions, there is a methane/nitrogen ballast gas composition, that will optimize both hot spot temperature and phthalic anhydride production.
4. Conclusions Theoretical results from ethylene oxide and phthalic anhydride reactor simulations indicate that ballast gas use is an e!ective tool for improving heat removal and
hot spot temperature control in "xed-bed reactor processes. Di!erent reaction mechanisms may be a!ected di!erently by changes in the ballast gas composition as it is evident from the comparison of the ethylene oxidation and the o-xylene oxidation cases. In this work the e!ect of a single ballast gas was examined, although, the ballast gas composition is a critical parameter that requires optimization. In an industrial reactor the ballast gas selection will be guided by reactor performance evaluation, process parameters (recycle, purge, #ammability) and economic optimization. Therefore, it may not always be economical to use the best ballast gas available. Future work should focus on the development of reliable heat transfer correlations that account for composition changes, and also on the study of the ballast gas e!ect with heterogeneous models, in order to provide accurate design guidelines for reaction and process engineers.
V. Papavassiliou, M.L. Wagner/Chemical Engineering Science 54 (1999) 3683}3689
Notation a U Bi c N d N G H ¸ M P r r R Re ¹ X y e j CP
wall heat transfer coe$cient Biot number heat capacity catalyst particle diameter mass velocity heat of reaction reactor length average molecular weight total pressure reaction rate reactor tube radius Reynolds number temperature conversion feed mole fraction of hydrocarbon catalytic bed porosity e!ective radial conductivity
Subscripts i w r t
species wall reaction averaged tube
References Bauer, R., & Schlunder, E.U. (1978a). Int. Chem. Engng, 18, 181}188. Bauer, R., & Schlunder, E.U. (1978b). Int. Chem. Engng, 18, 189}204. Bey, O., & Eigenberger, G. (1997a). Chem. Engng Sci., 52, 1365}1376. Bey, O., & Eigenberger, G. (1997b). Vortrag, ECCE-1, May 4}7.
3689
Borkink, J.G., & Westerterp, K.R. (1992). Chem. Engng Sci., 47, 2337}2342. Calderbank, P.H., Chandrasekharan, K., & Fumagalli, C. (1977). Chem. Engng Sci., 32, 1435}1443. Cresswell, D.L., Newson, E.J., & Wellauer, T. (1982). Chemical reaction engineering, ACS Symp. Ser. No. 196, (pp. 527}542). Dixon, A.G., & Cresswell, D.L. (1979). A.I.Ch.E. Jr., 25, 663}676. Dixon, A.G. (1985). A.I.Ch.E. Jr., 31, 826}834. Etzkorn, W.G., & Harkreader, G.G. (1988). European Patent, 293224A1. Etzkorn, W.G., & Harkreader, G.G. (1990). European Patent, 361372A1. Farhad, N. (1987). Acrylic acids and acrylic esters. SRI report 6C. Finlayson, B.A., & Rosendal, B. (1995). Comput. Chem. Engng, 19, 1207}1218. Froment, G.F., & De Wachs, (1972). Chem. Engng Sci., 27, 567}576. Froment, G.F., & Bischo!, K.B. (1990). Chemical reactor analysis and design. New York: Wiley. Froment, G.F., & Papageorgiou, J.N. (1995). Chem. Engng Sci., 50, 3043}3056. Harold, M.P., & Lerou, J.J., & Mills, P.L. (1995). Catalytic oxidations, (pp. 291}369). Herskowitz, M., & Hagan, P.S. (1988). A.I.Ch.E. Jr., 34(8). Herskowitz, M., Hagan, P.S., & Pirkle, C. (1988). SIAM Jr. Appl. Math., 48, 1083}1101. Kingsley, H.A., & Cleland, F.A. (1964). ;.S. Patent 3119837. Li, C.H., & Finlayson, B.A. (1977). Chem. Engng Sci., 32, 1055}1066. Lurgi, A.G. (1994). Lurgi brochure, Phthalic anhydride. Marshall, E.F. (1975). ;S Patent 3904652. Palmer, D., & Holzhauer, J. (1982). ;S patent 4342699. Perry, R.H., & Green, D. (1984). Perry's chemical engineering handbook. (6th ed.). New York: McGraw Hill. Ramachaadran, R., Shukla, Y., & MacLean, D.L. (1991). ;S Patent 4987239. Runhong, Q., & Yuen, T. (1993). Shiyou Huagong (Petrochemical Engineering). (vol. 22, pp. 792}798. Severs, G.M. (1974). ;S patent 3855280. Wakao, N., & Kaguei, S. (1982). Heat and mass transfer in packed beds. London: Gordon and Breach. Yen, Y., Hsu, L.C., & Chiou, C. (1982). SRI Report 5C.