Steam Cracking: Kinetics And Feed Characterisation

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Steam Cracking: Kinetics and Feed CharacterisationJoão Vilhena uto Superior Técnico, Lisbon, PortugalNovember 2015AbstractIn the present work a mathematical steam cracking furnace model is presented and several kineticschemes from literature, both molecular and radical, were implemented and validated against data fromindustrial ethane, propane and naphtha feedstocks processing furnaces. The results showed that, forgaseous feedstocks, the implemented kinetics were able to accurately predict product yields, with theradical scheme superseding the molecular one. Regarding naphtha cracking, however, the implementedradical kinetics from literature seemed to fail at predicting plant data. A steady-state study on alternativediluents relatively to steam was also carried out and it was concluded that there may actually be nodifference between diluents if one is not willing to further increase the coil outlet temperature, althoughhelium posed the best alternative if no constraints on temperature exist. At last, since the implementationof kinetic schemes require the molecular composition of the feed and because liquid feedstocks areusually characterised by other indices rather than a detailed hydrocarbon analysis, a feed characterisationmodel was developed. This model had the objective to determine the molecular composition of naphthafeedstocks given the commercial indices that usually characterise such petroleum fractions. The results,however, showed that the model is not able to accurately determine such compositions, having beenconcluded that a priori knowledge had to be included to improve its predictions.Keywords: Steam cracking, Ethane, Propane, Naphtha, Kinetics, Feed characterisation1. IntroductionThe steam cracking process is a cornerstone ofthe chemical industry as it generates highly valuable olefins – from which ethylene, propylene andbutadiene are the most relevant ones – from lowervalue feedstocks. Feedstocks for this process usually have fossil origin and range from gaseousfeedstocks, like ethane and propane, to liquid,heavier feedstocks, such as naphtha, gas oil andgas condensates [1].Ethylene is the major product of a steam cracking unit and it is almost exclusively produced by thisprocess. Being the largest volume building block,it is mainly used in the manufacture of polyethylene, ethylene oxide, vinyl acetate, ethylbenzeneand ethylene dichloride [2].Propylene, on the other hand, is considered aco-product of an olefins plant as nearly 60% ofits production is associated with ethylene’s manufacture [3]. Nevertheless, propylene is a valuable olefin – in fact, the most relevant steam cracking co-product – being involved in the production of polypropylene, acrylonitrile, propylene oxide, cumene and isopropanol [4].1.1. MotivationThe production of ethylene and propylene fromethane, propane and other light alkanes via pyrolysis is a vital element to the chemical industry. Ithas become even more prominent following the recent advances in the exploitation of shale gas inthe United States and elsewhere.On the other hand, the fact that refineries havebeen processing increasingly heavier crude oilshas brought much attention to liquid feedstocks,with heavier cuts such as atmospheric and vacuumgas oils being considered as possible hydrocarbonsources. Amongst the liquid feedstocks, naphthahas historically been by far the most widely used.In this regard, the need arises for the development of high-fidelity mathematical models, able tofully describe an olefins plant operation and whoseapplication in whole-plant optimisation is of the utmost interest of the petrochemical industry.1.2. ScopeThe current work was intended to bring a muchbetter understanding on literature kinetic schemesfor steam cracking, namely on how well do thesesuffice in accurately predicting product distribu1

tion for different feedstocks: ethane, propane andnaphtha. To accomplish this, a furnace mathematical model would have to be used in order to implement different kinetics and compare simulationresults against industrial data.Having the kinetics been studied, it was alsointended to perform a study on different diluentswhich could pose a beneficial alternative relativelyto steam.Finally, since a detailed molecular composition isrequired in these kind of models, this work was alsoexpected to involve the development and validationof a naphtha feed characterisation model whichcould provide such information based on easilyobtainable average properties of the mixture.Figure 2: Schematic diagram of a thermal crackingfurnace in a typical olefin plant [8].2. BackgroundSince the first refinery, built in Romania in 1856,crude oil has been fractionated in order to obtainlighter, more valuable cuts. However, the saturated hydrocarbons that are usually found in thesefractions lack the chemical reactivity needed forthe development of several other petrochemicals ofvarying complexity. Therefore, industrial processessuch as steam cracking have been developed inorder to convert these compounds into more reactive unsaturated hydrocarbons, such as olefins andaromatics [5, 6].After being cooled in the TLEs, the radiantcoil effluent enters the recovery front-end sectionwhere it is first submitted to further cooling. In thecase of liquid feedstocks, for process reasons, thecracked gas leaves the TLEs at higher temperatures and thus require an oil quench followed bya primary fractionator in order to reduce temperature down to 230 C and condense pyrolysis fueloil. Gaseous feedstocks, on the other hand, do notrequire any of these operations, being thus cooledfrom about 300 C to about 200 C in secondaryTLEs [1, 9].2.1. Steam cracking processThe hydrocarbon product stream, in order to beEthylene is almost exclusively produced by thersubjectedto downstream processing, then needsmally cracking petroleum hydrocarbons in the prestobecooledto near ambient temperature by conence of steam (over 97% of the annual volume), intactingwithalarge descending water stream in aa process known as steam cracking or pyrolysis [7],subsequentwaterquench tower [1].whose simplified flowsheet is shown in Figure 1.Next,aseriesofcompression stages and acidFirst, the hydrocarbon feedstock enters the furgasremovalunitscompressthe cracked gas tonace in the convection section (Figure 2), where itabout35barandremoveCO2 and H2 S from theis pre-heated, mixed with dilution steam, and thegasstream,whichissubsequentlydried in molecresulting mixture further heated to incipient crack ularsievebedstoremovepracticallyall the watering temperatures of 500-680 C . The feed immedi[1,9].ately heads to fired tubular reactors hanged vertiFinally, the gas is chilled and separated into itscally in the radiant section of the furnace (radiantcoils), where high firebox temperatures of 1000- product streams by means of a fractionation train.1200 C favour highly-endothermic pyrolytic de- In order to further increase light olefins yield, acetycomposition reactions, which convert the feed into lene, methylacetylene and propadiene are usuallyvaluable products [1]. The usage of steam de- converted in catalytic hydrogenation units [1, 9].creases hydrocarbon partial pressure which in turnreduces coke-forming reactions thriving in such 2.2. Cracking reactionsGenerally cracking refers to those reactions inconditions, thus avoiding premature furnace shutwhich large molecule hydrocarbons are cracked,down due to excessive coke build-up.The cracked gas then leaves the radiant coil at thus yielding smaller hydrocarbon compounds.800-850 C and is abruptly cooled to 550-650 C These reactions can be divided into two classes:by indirect quenching in transfer-line exchangers thermal cracking – in which large hydrocarbon(TLEs), so that further cracking of valuable reaction breakdown is induced by high temperatures – andcatalytic cracking – in which a selective catalystproducts and coke formation are prevented [1].plays the major role in the hydrocarbon decomposition. Steam cracking relies on thermal crack2

Ethane/propane ionationAcid-gasremovalDilution nation &hydrogenationEthylenePropyleneCrude C4ByproductsLight distillatePyrolysis gasolinePyrolysis fuel oilFigure 1: Simplified flowsheet of the steam cracking process; elements in blue only exist in liquid feedstockscracking plants (adapt. [1])ing reactions in the presence of steam to convertlow-value hydrocarbons into valuable olefins whilstkeeping coke forming reactions to a minimum.Since the pioneer work of F.O. Rice in the 1930s[10], it is well known that the largest part of gasphase hydrocarbon pyrolysis proceeds through afree radical mechanism which is inherently characterized by a vast number of species and reactions.Although specific reactions taking place in a freeradical scheme depend on the feed employed, themechanisms are simply summarized with the following three main reaction classes [11]:(b) Radical addition/decomposition· R1· R2 R3 R1 R2 R3Radicals may react with olefins, thusforming heavier, less saturated, radicalsand/or the opposite may occur, i.e. theC-C bond of large molecules at the β position relatively to the radical is ruptured(β scission), thereby producing an olefinand a new radical.(c) Radical isomerization reactions1. Initiation and termination reactions·R1 R2 R1 R2·R3· R4· R3 R4(3)R1· R2 R3 R4 R5 R6(1a)· R1 R2 R3 R4 R5 R6(1b)R1· R2 R3 R4 R5 R6· R1 R2 R3 R4 R5 R6R1· R2 R3 R4 R5 R6These unimolecular reactions involve eitherthe C-C bond scission, thus forming twosmaller radicals (Eq. 1a), or the formation of anew bond (C-C or C-H) as two radicals cometogether and produce a single molecule (Eq.1b).· R1 R2 R3 R4 R5 R6· R1· R2 R3 R2 R3 R1 (4a)(4b)(4c)(5)Isomerization reactions of radicals compete with the decomposition reactions,being responsible for the transfer of theactive radical position to another. Thiscan be accomplished whether by intramolecular H-abstractions (Eqs. 4a- 4c)or by an internal addition of the radicalposition on unsaturated bonds (Eq. 5).2. Propagation reactionsOnce initiation occurs, radicals undergo a series of propagation reactions in which a radicalreacts with a molecule and produces a smallermolecule and a new radical, keeping the reaction chain going.3. ImplementationThis work was developed and carried out ingPROMSProcessBuilder , having been thor··R1 R2 R1 R2(2)oughly used for both model development, flowAccording to these reactions, smaller re- sheeting and results acquisition, along with theactive radicals abstract a hydrogen atom external physical properties packages MultiflashTMfrom a molecule, thus forming both a new and gSAFT . gPROMS Optimisation and Parameter Estimation tools were also employed.molecule and a new radical.(a) Hydrogen abstraction reactions3

3.1. Model equationsA description of the model equations containedwithin the mathematical furnace model used in thiswork is presented. This first-principles model iscomposed of several sub-models which each oneperforming different and separate calculations tobring the whole furnace model together.The component mass balance in a plug-flow reactor (PFR) is defined as (Eq. 6):d[Ni A] M Wi Arf orm,idzprocess heat transfer film coefficient, the coke thermal conductivity and the tube wall thermal conductivity, respectively. The Dittus-Boelter correlationwas used to obtain hprocess .For the heat flux q comes equation 11:q Nt ht(11)where Nt is the total mass flux, ht is the specificenthalpy of the process stream, obtained by the external physical properties package MultiflashTM .The momentum equation, which determines thepressure P variation with axis z, is defined byequation 12:(6)where Ni stands for the component mass flux, Ais the cross-sectional area of the tube, M Wi is thecomponent molecular weight and rf orm,i the com ponent rate of formation (or disappearance, if negdv v 2 Aρ 2fFn B fbd[PA] NA (12)ative).tdzdz2RLThe reaction rate for a given reaction j, rj , isgiven by equation 7:where v is the process gas linear velocity, ρ isthe process gas density, fF is the Fanning frictionfactor, L is the reactor length and nB and fb areNP roductsNReactantsYYthenumber and friction factor of bends, respecnnrj kf,j(Ck j,k ) kb,j(Cl j,l )tively. The Churchill equation was used to obtainkl(7) fF whilst fb was calculated using the Nekraskovwhere kf,j and kb,j are the forward and backward equation.At last, the external heat flux, qext , is relatedreaction constants for a given reaction j, respectively, nj,k is the individual component reaction or- to the tube metal temperature and the effectivetemperature of the flames produced by the furder and C the component molar concentration.The component rate of formation, rf orm,j , used nace burners through equation 13, derived fromin the component mass balance, is computed us- the Stefan-Boltzmann law:ing the following equation 8:rf orm,i NReactionsXqext ϵσ(Tf4lame T M T 4 )(rj νi,j )(13)being ϵ the emissivity, σ the Stefan-Boltzmann constant and Tf lame the effective flame temperature.(8)jwhere νi,j stands for the stoichiometric coefficientof component i in reaction j.The energy balance, on the other hand, is described by equation 9:3.2. Ethane crackingIn this section, the molecular and radical kinetics for ethane cracking published by Sundaram andFroment in 1977 [12] and 1978 [13], respectively,were used. Apart from validating these literatured[qA] qext 2πRe(9) kinetics, it was intended to verify to what extentdzdo radical schemes’ predictions supersede thosewhere Re is the external radius of the tube, qext , of molecular ones.The industrial furnace configuration and operatthe external heat flux supplied to the tube and qing conditions considered in this ethane crackingthe heat flux. qext is calculated by equation 10:kinetics study were published by Yancheshmeh etal. [14].T M T TprocessTherefore, once the furnace model has been set (10)qext ln(Ri/R)ln(Re/Ri )1andinputs provided, the above mentioned kinetRe hprocess Rλcokeλwallics were implemented and simulation results comwith Ri standing for the inner radius of the tube, R pared against plant data reported by Yancheshmehfor the radius from the center to the deposited coke (Table 1).surface, T M T standing for the outer wall temperInteresting conclusions may be withdrawn fromature of the tube, Tprocess for the process stream Table 1. The radical kinetics seem to clearly sutemperature and hprocess , λcoke and λwall being the persede the molecular ones as conversion, selec4

Table 1: Comparison between literature and simulation[15].Likewise, once the furnace model has been setand inputs provided, the above mentioned kinetics were implemented and simulation results compared against plant data reported by Van Damme(Table 2).results for ethane cracking.COP (bara)Conv. (%)Select. (%)Plantdata [14]Molecularkinetics [12]Radicalkinetics 8.8%Table 2: Comparison between literature and simulationresults for propane cracking.Yields (dry mol%)H2CH4C2 H2C2 H4C2 H6C3 H6C3 H8C4 H6AADmain aaCOP (bara)Conv. (%)Select. (%)Plantdata [15]Molecularkinetics [12]Radicalkinetics .872.800.000.011.01-166.6%10.1%Yields (dry mol%)H2CH4C2 H2C2 H4C2 H6C3 H6C3 H8C4 H6C4 H8 sC4 H10 sC5 Average absolute deviation of the main product yields: ethylene, propylene, hydrogen and methanetivity and every product yield are much more accurately predicted, with an AADmain of 8.8% againstthe 19.9% of the molecular scheme. These resultsthus support the statement that radical schemesare more predictive than the molecular ones andthus the increasing trend there has been in developing and implementing such schemes.Nevertheless, the radical scheme for ethanecracking still fails at predicting some product yieldssuch as methane, acetylene, propane and butadiene. Although it would be interesting to tune somekey kinetic parameters to better match these individual yields and verify the extensiveness of thetuned reaction set to other industrial cases, thatwork would fall out of the scope of the current workand consequently will not be considered.The results summarised in Table 1 thereforevalidate not only the implemented radical kineticsfrom Sundaram and Froment [13] but also the firstprinciples furnace model itself.AADmain aaAverage absolute deviation of the main product yields: ethylene, propylene, hydrogen and methaneSurprisingly, Table 2 shows an enormous discrepancy between results predicted by molecularkinetics and by radical kinetics, with the molecularones being completely unable to predict any entryof industrial data.Although one could foresee a higher struggle ofthese schemes to predict propane cracking results– due to the higher complexity relatively to ethanecracking – one could not have anticipated such disparity between plant data and simulation resultsusing molecular kinetics, even more so when it isshown in the paper that this scheme is able to accurately predict industrial data.A likely explanation therefore lies in the fact thatthe published kinetic parameters were tuned usinga rather narrow set of experimental/plant data and,therefore, are not able to predict results outside agiven range of operating conditions.Radical kinetics-wise, it is noted that it is ableproduce results with an acceptable agreementwith industrial data, with an AADmain of 10.1%.Nevertheless, although ethylene, propylene andmethane yields are rather well met, ethane conversion, in spite of being within 10% deviation, is stillbeing significantly underpredicted.3.3. Propane crackingIn this section, the molecular and radical kinetics for propane cracking published, along withthe ethane cracking ones, by Sundaram and Froment in 1977 [12] and 1978 [13], respectively, wereused. Once again, the objective was to analyse theperformance of literature kinetics in terms of product distribution prediction and to verify if radical kinetics pose a more predictive alternative relativelyto the molecular ones.The industrial furnace configuration and operating conditions considered in this propane crackingkinetics study were published by Van Damme et al.5

Table 3: Comparison between literature and simulationThis means if one was to meet the same conversion, one would not probably get the same reasonable agreement in terms of product yields. Moreover, ethylene selectivity, which is already beingoverpredicted, would further increase its deviationrelatively to the industrial value.Apart from the above observations, the predictions of other product yields are quite unsatisfactory, with most of deviations relatively to plant datasurpassing 80%.Once again, although falling out of the scope ofthe current work, it would be of one’s interest tooptimise some key kinetic parameters to match industrial data and evaluate the extensiveness of theoptimised reaction set to other industrial cases.The results from Table 1 thus somewhat validate the implemented radical kinetics from Sundaram and Froment [13]. The first-principles furnace model is once again validated.results for naphtha cracking.Plantdata [18]Towfighi’skinetics [16]Joo’skinetics [17]0.41.550.421.750.421.76H2CH4C2 H2C2 H4C2 H6C3 H6C3 H8C4 H6C4 H8 sC4 H10 560.232.9919.36AADmain a-68.7%52.3%Residence (s)COP (bara)Yields (dry mol%)3.4. Naphtha crackingHere, two different radical kinetic schemes fornaphtha cracking will have their ability to accuratelypredict product distribution evaluated by comparison against published industrial data. Molecularschemes do not accurately represent the complexcracking phenomena occurring in liquid feedstockspyrolysis and, therefore, will not be considered.Towfighi and Karimzadeh published in 1993 [16]a naphtha cracking radical scheme comprising 150reactions and involving 22 molecular and 18 radicalspecies, covering the pyrolysis of species up to C6 .Furthermore, Joo published in 2000 [17] a seemingly more complex kinetic set describing the freeradical mechanisms occurring in naphtha pyrolysis,totalling 233 reactions. This radical scheme coversthe thermal cracking of species up to C8 , involving31 molecular and 48 radical species.The industrial furnace configuration, operatingconditions and detailed naphtha composition considered in this naphtha cracking radical kineticsstudy was published by Niaei et al. [18].Having the furnace model been set and inputs provided, the above mentioned kinetics wereimplemented and simulation results comparedagainst plant data reported by Niaei (Table 1).Apparently neither of the kinetic schemes seemsto accurately predict the product distribution. Infact, the published scheme by Towfighi andKarimzadeh remarkably fails to predict most of theyields, with the exception of methane and ethylene.From all the yields, the one corresponding to theC5 non-aromatic fraction, noted by ”Others”, hasthe largest deviation, being greatly overpredicted.On the other hand, the reported scheme fromJoo – which takes into account 81 more reactionsaAverage absolute deviation of the main yields: hydrogen,methane, ethylene, ethane, propylene, 1,3-butadiene, aromatics and ”others”.and almost twice the chemical species than theone from Towfighi and Karimzadeh – seems toshow a better agreement with plant data reportedby Niaei et al. [18], with an AADmain of 52.3%against 68.7% from Towfighi and Karimzadeh’sscheme, even though methane and ethylene yieldsare worsened. Once again, the C5 non-aromaticfraction yield is being considerably overpredicted.It is also noteworthy that in the reference paper the authors used the same industrial caseto validate their own mathematical model, achieving a quite reasonable agreement with plant data(AADmain 4.4%).It is stated that the detailed mechanistic kinetic model used by the authors involved 1230 reactions and 122 chemicalspecies. However, the references of the used kinetic model point to the radical scheme of Towfighiand Karimzadeh [16] and to the one reported bySundaram and Froment, whose total number of reactions combined does not exceed 300.This observation, along with the fact that thecracking of meaningful naphtha components is nottaken into account by neither of the implementedkinetic schemes, supports the suspicion that not allinformation regarding the complete kinetic modelsmay have been entirely disclosed. As a matter offact, many kinetic models are often proprietary andconfidential and, in this sense, may not be of theauthors’ interest to publicly disclose information sothat others can exactly reproduce their results.6

Dulient ratio (mol/molethane)In order to be able to predict product yields, notonly more reactions would probably have to beadded but also a kinetic parameter tuning processwould have to be carried out. Once again, although interesting, this would fall out of the scopeof the current work and, therefore, will not be 0.00CH45557.56062.56567.570Conversion (%)3.5. Alternative diluents studySteam plays a crucial role in the steam cracking furnace but its usage is costly and, in thissense, there has been an increasing trend in studying other diluents which may pose an alternativeto steam, with increased ethylene selectivity andlower energy consumption.A steady-state study was carried out in order tosolely analyse the influence of two physical properties of a diluent: molecular weight and heat capacity. Apart from carbon dioxide, several other diluting agents were taken into account (Table 4).Figure 3: Molar diluent ratios at different ethaneconversions (1.1bar P , 845 C COT ).C2H4 selectivity 67.570Conversion (%)Table 4: Molecular weights of diluting agents beingstudied.Figure 4: Ethylene selectivity at different ethaneDiluentMW (g/mol)Cp1000K 4.0130.320.871.841.232.754.3Energy consumption(MJ/kgC2H4)conversions (1.1bar P , 845 C COT mCO2N2HeH2CH45557.56062.56567.570Conversion (%)This study was based on the ethane industrialcase reported by Yancheshmeh [14] and on theradical kinetics published by Sundaram and Froment [13]. The study consisted of several steadystate optimisations, each one corresponding to adifferent fixed valued for conversion, in which thehydrocarbon feed flowrate, coil inlet pressure andinlet temperature were kept constant.The objective was to maximise ethylene selectivity by allowing the model to vary each diluent ratio(relatively to hydrocarbon), being the optimisationsubjected to both pressure drop ( 1.1 bar) and coiloutlet temperature constraints ( 845 C ). The corresponding results are summarised in Figures 3-5.Interesting observations can be made from Figures 3-5. It is observed that for low conversionsthe molar diluent ratios and ethylene selectivity follow the descending order of the molecular weightwhilst for high conversions these steeply decreaseand become coincident towards higher conversionvalues. Energy consumption, on the other hand,seems not to follow in order in particular.Figure 5: Specific energy consumption (relatively toethylene produced) at different ethane conversions(1.1bar P , 845 C COT ).First, at low conversions pressure drop hit theupper bound. This happened since the model triesto minimise not only the hydrocarbon partial pressure but also the residence time by increasing thediluent ratio as much as possible.Hence, the denser the diluent, the lower will bethe molar ratio for the same pressure drop. Because the molar diluent ratio is lower, the velocitywill also be lower, consequently leading to higherresidence times and lower selectivities. Furthermore, because of higher residence times, a lowerCOT is required to achieve a given conversion,which contributes to lower energy consumption.Energy consumption, however, must also takeinto account the heat capacity of the diluent. Oneis now able to understand why methane is the one7

leading to the highest energy consumption – it haslow density and the highest heat capacity – andwhy nitrogen is the one with the lowest energy consumption – it is relatively dense and has a relativelylow heat capacity.Finally, at high conversions the coil outlet temperature was the variable hitting the upper bound.This can easily be explained because of thestrong relation between temperature and conversion. Since temperature is being constrained, theonly existing solution to meet the fixed conversionsis to increase residence time and the model accomplishes this by abruptly lowering diluent ratios.With decreasing diluent ratios, comes lower pressure drop, lower selectivities and lower energy consumption.Moreover, since COT hits its upper bound athigh conversions, heat capacity effect on energyconsumption will become predominant over density and this is the reason behind the helium becoming the least energy demanding diluent at highconversions.At last, because residence time has to increaseto meet the high conversions being specified, thehigher the conversion, the less slack there will befor the diluent ratio to change between diluents. Asa matter of fact, at the limit, to meet maximum conversion, all the diluent ratios would have to be zeroand this justifies why variables became coincidenttowards very high conversion values.The main conclusion one may draw from theseresults is that, at high conversions, if one is notwilling to let COT increase above a certain value,there may actually be no difference between diluents. On the other hand, if COT is allowed to increase, helium seems the best alternative to steamas it leads to significantly higher ethylene selectivities and lower specific energy consumption.dM wL,idt(15a)T f (wL,i )(15b)where F is the total vapour flowrate, wV,i is thevapour mass fraction of component i, wL,i the liquid mass fraction of component i and M and T thetotal mass and temperature inside the distilling, respectively. The volume percent recovered is calculated based on the volume difference relativelyto the initial volume of the mixture in the distillingflask.The physical properties packages MultiflashTMand gSAFT were initially considered, having acareful analysis proved that Multiflash’s RedlichKwong-Soave Advanced (RKSA) thermodynamicmodel provided the most accurate results.Having the model been developed, it is now possible to evaluate its performance using experimental data. An analytical report from a sweetenednaphtha sample [19] was obtained and deemed tobe appropriate for this purpose. This data possessed not only the commercial indices but alsothe corresponding detailed hydrocarbon analysis,thus all the information required to validate the developed model.The validation of the feed model was performedusing the powerful gPROMS ’ Parameter Estimation tool. This entity uses a set of measurements(commercial indices) and estimates a defined setof parameters (feed component mass fractions) sothat a maximum likelihood goal, which involves theminimisation of a dedicated objective function, isachieved. In addition to the commercial indices,Shannon’s entropy criterion has also been includedin the Parameter Estimation entity.The parameter estimation results are summarised in Figure 6 and Tables 5 and 6.4. Feed characterisationThe implementation of kinetic sc

Ethylene is the major product of a steam crack-ing unit and it is almost exclusively produced by this process. Being the largest volume building block, it is mainly used in the manufacture of polyethy-lene, ethylene oxide, vinyl acetate, ethylbenzene and ethylene

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