2584 Ind. Eng. Chem. Res. 1994,33, 2584-2590

Coke Formation in the Thermal Cracking of Hydrocarbons. 4. Modeling of Coke Formation in Naphtha Cracking

Geert C. Reynierst and Gilbert F. Fromenti Laboratorium uoor Petrochemische Techniek, Universiteit Gent, Krggslaan 281, S 5, B9000 Gent, Belgium

Frank-Dieter Kopinke and Gerhard Zimmermann Abteilung Hochtemperaturreaktionen a m Institut fur Technische Chernie der Universitat Leipzig, 0-04303 Leipzig, Permoserstrasse 15, Germany

An extensive experimental program has been carried out in a pilot unit for the thermal cracking of hydrocarbons. On the basis of the experimental information and the insight in the mechanisms for coke formation in pyrolysis reactors, a mathematical model describing the coke formation has been derived. This model has been incorporated in the existing simulation tools at the Laboratorium voor Petrochemische Techniek, and the run length of an industrial naphtha cracking furnace has been accurately simulated. In this way the coking model has been validated.

Introduction

One of the main problems in the thermal cracking of hydrocarbons for olefin production is the formation of a coke layer on the inner wall of the coils. This leads in the first place to a decrease of the heat flux to the reacting gas mixture and second also to an increase of the pressure drop over the reactor. Periodically the furnace operation has to be stopped and the coke has to be burnt off by means of a mixture of steam and air.

In the previous papers in this series (Kopinke et al., 1988, 1993a,b) relative rates of coke formation from various types of carbon atoms (aliphatic, aromatic, ...I were determined. The relative rates were determined by adding a small but precisely defined amount of a I4C- labeled component to a naphtha feed.

The present paper provides a mechanistic interpreta- tion of the experiments performed by Kopinke et al. and of additional experimental information obtained in the pilot plant for thermal cracking of the Laboratorium voor Petrochemische Techniek.

Experimental information and mechanistic interpre- tation were combined to develop a model describing quantitatively the coking process in thermal cracking coils. The coking model was combined with a kinetic model for the pyrolysis of liquid feedstocks, a reactor model and a furnace model. The combination of these models allows the accurate prediction of the run length of a furnace for the thermal cracking of naphtha.

Experimental Procedure and Results

The pilot plant for thermal cracking at the Labora- torium voor Petrochemische Techniek has been de- scribed elsewhere (Van Damme and Froment, 1982). The unit is very flexible as to feedstock and operating conditions. A rigorous procedure was followed in the coking experimentation reported in the present paper:

1. An oxidative pretreatment of the reactor walls was applied prior to each experiment. Twice-distilled water was fed at a rate of 1 k g h to the coil which was kept at 600 "C.

* Author to whom correspondence should be addressed. ' Present address: ENSIM N.V., Noorderlaan 127, B2030

E-mail: gf@elptes3.rug.ac.be.

Antwerp, Belgium.

2. Next, the coil was heated, still under a flow of steam, to the desired temperature profile.

3. Next the hydrocarbon feed was introduced. This caused a disturbance of the temperature profile, due to the endothermic reactions. This transient period was kept as short as possible. Within 15 min the reactor was again in steady state.

4. The operating conditions were kept constant for a period of 6 h. During this period, several analyses of the reactor effluent were carried out. The pressure and temperature profiles in the reactor were continuously monitored.

5 . After 6 h the hydrocarbon feed was stopped. This, again caused an upset in the temperature profile. Hence, a stabilization period of 15 min was required.

6. Finally, the coke formed during the experiment was burnt off by means of a mixture of steam and air. The carbon monoxide and carbon dioxide concentrations in the reactor effluent were measured continuously by infrared analyzers, together with the total volumetric effluent flow. Decoking mainly took place in a reaction front wandering through the reactor. The temperature in the reaction front amounted to about 1000 "C.

Forty-five experiments were carried out, with widely different feedstocks and operating conditions. Feed- stocks ranged from CH4 to n- and i-Cs, C2H4, benzene, and mixtures thereof, naphtha and kerosene. The coil outlet temperature ranged from 820 to 960 "C, the coil outlet pressure ranged from 1.5 t o 3.6 bar absolute and the diluent was either H2O or N2.

From the set of experiments a number of industrially important conclusions can be drawn:

1. Under identical conditions ethane yields more coke than propane or n-butane. From the discussion of the mechanism of coke formation, it will become clear that this is linked to the type of radicals produced with the different feedstocks. In ethane cracking, hydrogen, methyl, vinyl, and ethyl radicals are important. All these are small and active radicals. In cracking longer chain paraffins allyl radicals are also formed. Allyl radicals are more stable and less reactive.

2. Isoparaffinic feedstocks yield more coke than the corresponding normal paraffinic feedstocks.

3. Steam, used as a diluent, is not inert toward coke. Experiments were carried out under exactly the same conditions except that in one case steam dilution was used and in the other case nitrogen, for the same molar

0888-5885/94/2633-2584$04.50/~ 0 1994 American Chemical Society

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Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2585

A, - C CxHy

Figure 1. Mechanism of filament growth.

flow rate. In all cases the experiment with nitrogen dilution yielded more coke than the one with steam dilution. The difference in coke yield is strongly de- pendent on the type of feedstock used and on the operating conditions. It is clear, however that steam is able to remove part of the coke formed at temperatures exceeding 850 C.

4. The rate of coke formation increases with pressure. This indicates that bimolecular reactions are important. In free radical reaction schemes, the main bimolecular reactions are hydrogen abstractions and addition reac- tions.

Development of a Coking Model

The experimental observations and a detailed litera- ture survey point to a complex mechanism of coke formation in thermal cracking. Three mechanisms contribute to the deposition of a coke layer.

Heterogeneous Catalytic Mechanism. During the startup of a furnace, the reacting gas mixture is in contact with the bare reactor walls. Incoloy 800H, frequently used as the material of construction, contains 31 wt % nickel. By chemisorption, species from the gas phase form a metal-hydrocarbon complex on the nickel crystallites at the inner tube wall. This complex decomposes and yields carbonaceous material on the metal surface. The carbon migrates through the metal particle by diffusion and precipitates a t the grain boundaries. The driving force for the diffusion is a difference in thermodynamic activity between the car- bon at the metal surface and the carbon at the grain boundaries (Bianchini and Lund, 1989). Diffusion is the rate-determining step of the process. The precipitated carbon causes stress in the metal structure. Eventually, the stress becomes so large that the nickel crystallite is removed from the metal structure. As more carbon is deposited, a carbon filament, carrying a metal particle on top of it, is formed. This is shown in Figure 1. In the coke layer from an industrial reactor for the thermal cracking of naphtha, a dense network of filaments has been observed with filaments having a diameter be- tween 2 and 5 pm and a length between 20 pm and l mm.

The rate of carbon deposition in this initial phase is very high. In an electrobalance type of reactor, also available at the Laboratorium voor Petrochemische Techniek, initial coking rates of more than 50 g/m2h have been observed in the thermal cracking of ethane at 810 C. After 15 min, however, the coking rate decreases, to reach an asymptotic value of less than 10 g/(m2 h).

The filament network forms a porous structure. Deficiencies in the graphitic structure act as active sites on the outer walls of the filaments. On these active sites coke deposition continues via the heterogeneous non- catalytic mechanism. The influence of the metal par-

*+ - --.- * t

Figure 2. Growth of carbon layer.

ticles on the coke formation decreases steadily as the metal surface becomes covered by a carbon layer. A remanent catalytic activity is always present, however.

Heterogeneous Noncatalytic Mechanism. This mechanism is the most important one in the coke formation. The overall structure of the filament coke is graphitic. This implies the degradation of the hy- drocarbons to an aromatic structure by condensation and dehydrogenation.

At the gadcoke interface the polyaromatic layer is not yet completely dehydrogenated. At this surface hydro- gen abstraction reactions by free radicals from the gas phase can occur. Hydrogen, methyl, and ethyl radicals are the most active species. As a consequence, the concentration of the active sites a t the coke surface becomes a function of the gas phase composition. This explains the experimental observation according to which feedstocks generating more active radicals also yield more coke.

At the free radical positions on the coke surface, certain gas phase molecules (coke precursors) react via an addition mechanism. All unsaturated molecules from the gas phase are potential precursors. In Figure 2, an example of the reaction sequence is shown with l-hexene as a precursor.

The long aliphatic side chain of these molecules is subject to decomposition. The remaining part of the molecule reacts in a few steps to a ring structure, in which the dehydrogenation reactions proceed very rap- idly. In this way the aromatic structure continues to grow further and the free radical site at the coke surface is regenerated by further hydrogen abstraction.

This mechanism explains the formation of a deposit consisting of graphitic layers containing carbon atoms in sp2 hybridization. The hydrogen content of such a deposit is very low, in agreement with industrial observations. Several other reaction sequences, an example of which is shown in Figure 3, yield cross- linked graphitic structures. The cross-linking of aro- matic layers explains why samples of coke layers from industrial coils are extremely hard and can hardly be drilled.

It is clear that the number of possible reaction paths is extremely large. Every molecule from the gas phase is in principle a potential coke precursor. Since the number of species in the reaction mixture is very large, especially when cracking liquid feedstocks, it is impos- sible to take into account all those reactions in develop- ing a model for the coke formation.

Free radicals contribute to coke formation via termi- nation reactions with the coke macroradical. This

2586 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 * + H -

b&+a-. A

Figure 3. (a) Cross-linking with sp3 linking with sp2 carbon atom.

contribution is relatively unimportant, however, as is clear from a comparison of the concentration of the free radicals in the reaction mixture (typically 10-6-10-3 wt %) with the coke yield, which is of the order of 0.1 wt %. Free radicals mainly act in hydrogen abstraction reactions.

Homogeneous Noncatalytic Mechanism. This third mechanism implies the formation of polynuclear aromatics in the gas phase via free radical reactions. These large molecules grow in the gas phase to tar droplets that can be liquid or even solid at the conditions prevailing in a thermal cracking reactor. Part of the droplets impinge on the tube wall. Some rebound into the gas phase, but it is more likely that they adhere to the surface and are incorporated in the coke layer, since the outer surface of the droplets is not completely dehydrogenated. Hence, hydrogen abstraction reactions by gas phase radicals are possible and the coke layer can grow further.

This mechanism is considered important only in the cracking of heavy liquid feedstocks, such as atmospheric or vacuum gas oil, or else when the temperature exceeds 900 C.

Quantitative Formulation of the Rate of Coking In what follows the modeling of the coking in thermal

cracking reactors will concentrate on the main mecha- nism, the heterogeneous noncatalytic mechanism. Tak- ing into account all the possible reaction pathways would Iead to an unrealistically high number of kinetic parameters, and their estimation would not be possible or at least inaccurate.

The number of reactions can be decreased by restrict- ing the number of coke precursors.

Paraffins are the main components in a naphtha feedstock. These components do not disappear through addition reactions, so that their direct contribution to coke formation is low. Moreover, the coking rate is highest in the high-temperature section of the reactor.

In this section the paraffin content in the reacting mixture has decreased to a large extent.

For the same reasons, naphthenes can also be ne- glected as direct precursors to coke.

Unsaturates are a very important class of coke precursors. They are reaction products of the pyrolysis reactions so that their concentration in the high- temperature zone of the reactor is high. Furthermore, unsaturates are reactive and are good candidates for radical addition. C4 components, which are present in high concentration, are important coke precursors. Longer chain unsaturated components decompose rap- idly to smaller components.

Aromatics form a second class of important coke precursors. The aromatic ring structure is close to the structure of the coke matrix. Further, (branched) aromatics are reactive components, especially at the high temperatures prevailing in thermal cracking coils.

The basis of the modeling is the presence of active sites at the coke surface. These are in reality radical positions. The coke is mainly graphitic in structure. The free radical sites at the surface are all phenylic or benzylic sites. As an approximation, the activity of these sites is considered to be equal.

Addition reactions occurring at these sites regenerate the free radical position, so that the total number of active sites is constant. What follows then is a sequence of dehydrogenation and cyclization reactions causing the incorporation of the carbon atoms of the coke precursor into the coke layer.

The essential elements of the reaction of a precursor with an active site at the coke surface are (a) the growth of the coke layer with a number of carbon atoms equal t o the carbon number of the precursor and (b) the regeneration of the active site at the coke surface.

An example of such a reaction with ethylene as a precursor can be written

P + C,H4-2C + P+ 2H, and the corresponding rate equation for carbon forma- tion:

The concentration of the free radicals at the coke surface is unknown. The coke has a macroradical character, mainly due to hydrogen abstraction by the radicals from the gas phase. The influence of free radicals as abstracting species in the coke formation can be accounted for by introducing a multiplication factor containing the concentration of the main reaction products of the two most active radicals. The most abundant and reactive of these are H and CH3. The concentration of hydrogen and methane are taken to be proportional to that of H and CHf, respectively. The following expression can then be written for the rate of coke formation out of an ethylene precursor:

A similar approach for the other precursors leads to a coke model containing 12 reactions in parallel. The rate of coke formation may then be expressed as

Ind. Eng. Chem. Res., Vol. 33, No. 11,1994 2687

The precursors are classified into groups depending upon their characteristic function (double bond, triple bond, aromatic ring, ... ).

The reactions of coke radicals with precursors belong- ing to the same group are considered to have the same activation energy. A reference component is chosen in each group. The reference factors for the coke formation out of the other members of the group are related to that of the reference component through the relative reactivities for coke formation derived by Kopinke et al. (1988, 19931, thus reducing the number of independent parameters to be estimated from the experimental data.

Simulation of the Run Length of a Furnace for the Thermal Cracking of Naphtha

The coking model is combined with the kinetic model for the pyrolysis of liquid feedstocks which generates the local concentrations of Hz, CHI, and the coke precursors along the coil. The structure of this model has been described by Clymans and Froment (1984) and Hillewaert et al. (1988). The rigorous kinetic model enter in the plug flow continuity and energy equations for the reactor simulation. The heat flux to the reactor is generated by a detailed furnace model (Plehiers and Froment, 1988; Rao et al., 1988). This combination of models allows an accurate and detailed simulation of a thermal cracking unit.

Table 1 presents the basic information about the industrial furnace, the split coil reactors, and the operating conditions. No further data are required to set up the simulation model for the radiation section, except the location of the burners in the walls and the location of the reactor coils in the furnace. This information is provided in Figure 4.

The furnace geometry is complex. Because of sym- metry only half of the furnace and four reactor coils need to be simulated. The approach followed for run length simulations has been described in detail elsewhere (Plehiers et al., 1990). The continuity equation for carbon is integrated by incrementing the time in discrete steps. The coking rate is considered to be constant in each time interval. For this simulation, time intervals of 200-300 h were appropriate. In total, 280 h of CPU time was required on a Data General Eclipse MV15000/8 computer to carry out the complete run length simulation.

The operating policy of the furnace consisted of keeping the ethylene production constant in time. Figure 5 shows the ethylene yield averaged over the four reactors. It is constant over the whole run length within 0.1 wt % absolute or 0.3% relative. The feed rates were also kept constant over the run length.

Significant differences were found, however, among the individual coils. The ethylene yields from the four coils are shown in Figure 6. The initial differences are due to a distinct location of each coil with respect to the burners. This results in differences in the radiative heat transfer fluxes to each reactor and, hence, in different naphtha conversions and ethylene yields. The evolution with time of the ethylene yield from each reactor is not identical. The growth of the coke layer is not the same for each coil, and as a consequence the amount of heat transferred to the reacting process gas and the pressure level in the reactors evolve in a different way. These are factors which affect the ethylene yield and selectiv- ity.

Table 1. Basic Information for the Run Length Simulation

Furnace Data height (mm) 9090 length (mm) 14400 width (mm) 2500 number of burners 160 thickness of refractory (mm) 230 thickness of insulation (mm) 50

Fuel Conditions fuel composition (~01%)

methane 95 hydrogen 5

initial fuel gas flow rate (kmoyh) air excess (%I 10 uniform side wall firing

Reactor Configuration 8 coils, split coil design total length (mm) 53890 number of passes 6

198.4

passes 1-4: split section total length (mm) 35920 internal diameter (mm) 80.0 external diameter (mm) 95.6

total length (mm) 17970 internal diameter (mm) 114.3 external diameter (mm) 129.9

Operating Conditions hydrocarbon flow rate per coil (kgh) 2785 steam dilution (kg/kg) 0.7 coil inlet temperature ("C) 620 coil outlet pressure (bar abs) 1.45

Material Properties emissivity of furnace wall 0.60 emissivity of tubes 0.95 thermal conductivity (W/(m K))

passes 5,6: single tube section

0.0193 + 118.0 x 10-6T (K) 0.0452 + 111.1 x 10-6T(K) refractory insulation

tubes -1.257 + 0.04327T(K) coke 6.46

1600 specific gravity of coke (kg/m3)

specific gravity d(15/15) 0.7057 PNA analysis (wt %)

n-paraffins 33.0 isoparafhs 37.0 naphthenes 18.0 aromatics 12.0

IBP 36.0 50% 94.5 FBP 161.0

Feedstock Characterization

boiling range ("C)

Figure 7 shows the heat consumption of the furnace. To keep the ethylene production constant, in spite of the growing coke layer and its increasing heat transfer resistance, requires an increase of the heat input. The ethylene production cost, therefore, rises with time.

Figure 8 gives the evolution of the coil inlet pressures for the individual reactors. To keep the coil outlet pressure constant, the inlet pressure has to be raised. This leads to a higher pressure level in the reactor, favoring the secondary (ethylene-consuming) reactions over the primary (ethylene-producing) reactions. Sec- ondary reactions are mostly bimolecular, while primary reactions proceed via a monomolecular mechanism.

The most pronounced increase in coil inlet pressure is found in coil 2, in which it amounts to 0.35 bar, a 23% relative increase with respect to the initial pressure drop of 1.51 bar.

2688 Ind. Eng. Chem. Res., Vol. 33, No. 11,1994

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1 4 t Figure 9. Initial heat flux profiles. to a higher temperature level in these reactors and in a higher feedstock conversion.

Figure 10 shows the evolution of the heat flux profiles as a function of time for reactor 4. The heat flux increases in the split tube section of the reactors, whereas in the single tube section the heat flux de- creases with time.

The rise of the heat fluxes in the first part of the

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Figure 5. Evolution with time of average ethylene yield.

The initial heat flux profiles are shown in Figure 9. The heat input is highest for reactors 2 and 4, leading

Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2689 F - 0 ST

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reactor results from the requirement of achieving a higher conversion, so as to keep the ethylene yield constant, in spite of the increase in pressure. It compensates for the decrease of the heat fluxes in the second part of the reactor caused by the coke formation. The coke layer reaches its maximum thickness in the second part of the coil.

It should be stressed that these results can only be obtained from a detailed furnace and reactor simulation. Assuming a translation of the heat flux profile with time, as is normally done when performing only reactor simulation, leads to an overestimate of the coking rates and to predicted run lengths which are too short.

The evolution of the coking rates with time is shown in Figure 11 (reactor 4). The coke formation takes place at the temperature of the gadcoke interface. The coking rates are high in the second part of the reactor. As a consequence, the coke layer grows fast there and creates an additional resistance to heat transfer. Further, the coke layer also causes a decrease of the tube cross- sectional area and this leads to higher linear gas velocities in this section, causing an improved convective heat transfer from the interface to the reacting gases. These two effects lead to a decrease with time of the interface temperatures in the single tube section of the reactor. Together with the interface temperatures, the coking rate also decreases with time.

In the split part of the reactor the coke layer is less important. Increasing the heat fluxes with time in- creases the gadcoke interface temperatures and the coking rates. The coke layer tends to become more uniform along the tube with time.

The simulated thickness of the coke layer is given in Figure 12 for reactor 4. The coke reaches its maximum thickness on the last pass, immediately after the last lower U-bend in the reactor. At the end of the run the coke thickness is 8.7 mm, corresponding to a reduction in diameter of more than 15%.

Figure 12. Evolution of profiles of thickness of coke layer in coil 4.

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The evolution with time of the coke layer is reflected in the external wall temperatures. These are shown for reactor 4 in Figure 13. The temperature rises with time to meet the heat flux requirements, in spite of the additional resistance to the heat transfer resulting from the coke deposition. Initially, the temperatures are highest in the high-temperature section of the reactor, where the coking rates are highest and the coke layer reaches its maximum thickness. The largest increase in the external wall temperatures is observed in this section. The maximum value is reached at a reactor length of 47 m. Initially the maximum value is ap- proximately 1000 "C.

Figure 14 shows the evolution with time of the maximum external wall temperature for the four simu- lated reactors. This value should be watched carefully during operation, since there is a limitation imposed by the metallurgy. In the present case the limiting value is 1090 "C and it is reached on reactor 4 after 1900 h or about 80 days of operation, after which decoking is necessary. The simulated value is in excellent agree- ment with the observed plant value, which was 85 days.

The temperature limit is reached on one reactor only. For the other reactors there still is a margin of some 10

2590 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994

"C, meaning that their run length could have been extended for 5-7 days. In commercial operation, it might be worthwhile to decrease the cracking severity on reactor 4, so as to prolong the production cycle.

Conclusions Literature data and experimental observations were

combined to obtain mechanistic insight into coke forma- tion in thermal cracking. Three mechanisms contribute. Initially a filament layer is formed by interaction of gas phase species with metal particles from the reactor wall. The main mechanism is the interaction between active sites on the coke layer with gas phase species. The active sites are free radicals and originate from hydro- gen abstraction by small active gas phase radicals, such as hydrogen and methyl radicals. At the free radical sites unsaturated precursors from the gas phase react via addition, followed by a set of dehydrogenation and cyclization reactions finally yielding a graphitic coke layer. A third mechanism involves the formation of droplets in the gas phase which then impinge and adhere t o the surface and are incorporated in the coke layer. This last contribution is thought to be important only in the cracking of very heavy liquid feedstocks.

The mechanistic considerations and the experimental information were used to develop a kinetic model in which a set of 12 coke precursors form coke via a set of parallel reactions.

This coking model was combined with a kinetic model for the cracking, a reactor model and a furnace model to simulate the run length of a furnace for the thermal cracking of naphtha. Detailed and accurate information can be obtained from this simulation. The growth of a coke layer is accurately simulated, and so is the evolu- tion of the external tube skin temperatures. The simulated and experimental run lengths agree within 5%.

Simulations of this kind can be used to optimize furnace operation for various feedstocks and operating conditions. They can be used as a guide for the adaptation of the operating variables aiming at prolong- ing the run length of the furnace.

Literature Cited

Bianchini, E. C.; Lund, C. R. F. Kinetic Implications of Mecha- nisms Proposed for Catalytic Carbon Filament Growth. J . Catal.

Clymans, P. J.; Froment G. F. Computer Generation of Reaction Paths and Rate Equations in the Thermal Cracking of Normal and Branched Paraffins. Comput. Chem. Eng. 1984,8 (2), 137- 142.

Figueiredo, J. L.; Orfao, J. J. M. Carbon Deposits on Metal Catalysts-Mechanisms of Formation and Gasification. Catal.

Hillewaert, L. P.; Dierickx, J. L.; Froment, G. F. Computer Generation of Reaction Schemes and Rate Equations for Thermal Cracking. AIChE J . 1988,34 (11, 17-24.

Kopinke, F. D.; Zimmermann, G.; Nowak, S. On the Mechanism of Coke Formation in Steam Cracking-Conclusions from Re- sults obtained by Tracer Experiments. Carbon 1988, 26 (21,

Kopinke, F. D.; Zimmermann, G.; Reyniers, G.; Froment, G. F. Relative Rates of Coke Formation from Hydrocarbons in Steam Cracking of Naphtha. 2. Paraffins, Naphthenes, Mono-, Di-, and Cycloolefins, and Acetylenes. Ind. Eng. Chem. Res. 1993a, 32 (11, 56-60.

Kopinke, F.-D.; Zimmermann, G.; Reyniers, G.; Froment, G. F. Relative Rates of Coke Formation from Hydrocarbons in Steam Cracking of Naphtha. 3. Aromatic Hydrocarbons. Ind. Eng. Chem. Res. 1993b,32 (ll), 2620-2625.

Plehiers, P. M.; Froment, G. F. Firebox Simulation of Olefin Units. Presented at the AIChE Spring National Meeting, March 6-10, 1988.

Plehiers, P. M.; Reyniers, G. C.; Froment, G. F. Simulation of the Run Length of an Ethane Cracking Furnace. Ind. Eng. Chem. Res. 1990, 29 (41, 636-641.

Rao, M. V.; Plehiers, P. M.; Froment, G. F. The Coupled Simulation of Heat Transfer and Reaction in a Pyrolysis Furnace. Chem. Eng. Sci. 1988,43 (6), 1223-1229.

Van Damme, P. S.; Froment, G. F. Thermal Cracking Computer Control in Pilot Plants. Chem. Eng. Prog. 1982, 78 (91, 77-82.

1989,177, 455-466.

Today 1989, 5, 385-393

117-124.

Received for review December 9, 1993 Revised manuscript received March 9, 1994

Accepted July 6 , 1994@

@ Abstract published in Advance ACS Abstracts, September 15, 1994.