CFD Simulations of Steam Cracking Furnaces Using Detailed Combustion Mechanisms

Computers and Chemical Engineering 30 (2006) 635–649

CFD simulations of steam cracking furnaces usingdetailed combustion mechanisms

G.D. Stefanidisa, B. Mercib, G.J. Heynderickxa,∗, G.B. Marina

a Laboratory for Petrochemical Engineering, Ghent University, Krijgslaan 281 Block S5, Ghent B9000, Belgiumb Fluid Mechanics Laboratory, Department of Fluid, Heat and Combustion Mechanics, Ghent University, St. Pietersnieuwstraat 41, Ghent B9000, Belgium

Received 11 April 2005; received in revised form 18 October 2005; accepted 18 November 2005

Abstract

A three-dimensional mathematical model has been developed for the simulation of flow, temperature and concentration fields in the radiationsection of industrial scale steam cracking units. The model takes into account turbulence–chemistry interactions through the Eddy DissipationConcept (EDC) model and makes use of Detailed Reaction Kinetics (DRK), which allows the detailed investigation of the flame structure.Furthermore, simulation results obtained with the EDC-DRK model are compared with simulation results obtained with a simplified modelc d, muchf in a smallerfl e simplifiedm shown thatw ller flamev s on others e–chemistryi g furnacesu©

K model

1

cetaifueg

a

ll andat ares, sim-enas are

in-“fire-eameac-ctioneen

,otht,4one-IM

0d

ombining the Eddy Break Up (EBU)/finite rate formulation with Simplified Reaction Kinetics (SRK). When the EBU-SRK model is useaster fuel oxidation and products formation is predicted. The location of the peak temperature is shifted towards the burner, resultingame and the confinement of the combustion process into a smaller area. This is most likely because of the inherent deficiency of thodel to correctly predict the overall (effective) burning rate when the turbulent mixing rate and the reaction rate are comparable. It ishen neither the “fast-chemistry” nor the “slow-chemistry” approximation is satisfied, the overall burning rate is overpredicted. The smaolumes obtained with the EBU-SRK model have important effects on the predicted temperature distribution in the furnace as well aignificant design parameters like the refractory wall and tube skin temperatures. It is suggested that more sophisticated turbulencnteraction models like the EDC model and more Detailed Reaction Kinetics should be used for combustion modeling in steam crackinnder normal firing conditions.2005 Elsevier Ltd. All rights reserved.

eywords: Steam cracking furnaces; Detailed combustion mechanisms; Turbulence–chemistry interactions; Eddy dissipation concept; Eddy break up

. Introduction

Steam cracking of hydrocarbons is a basic petrochemical pro-ess since it accounts for the major part of the production ofthylene and propylene, which are the main building blocks for

he petrochemical industry. Typical steam cracking furnaces arepproximately 12 m long, 3 m wide and 8 m high. Steam crack-

ng takes place in coils suspended in the radiation section of theurnace. The process gas that flows through the coils is heatedp to high temperatures by means of gas-fired long flame burn-rs distributed in the floor of the furnace and/or by means ofas-fired radiation burners in the side walls of the furnace.

An accurate simulation of the olefin yields, coke formationnd NOx emissions requires accurate simulations of the flue gas

∗ Corresponding author. Tel.: +32 9 264 4516; fax: +32 9 264 4999.E-mail address: [email protected] (G.J. Heynderickx).

and process gas flow patterns, of the process, tube, waflue gas temperature profiles as well as the heat fluxes thexchanged between the process gas and the flue gas. Thuulation of all the interacting chemical and physical phenomthat take place in the radiation box and the process tubenecessary.

At the Laboratory for Petrochemical Engineering (LPT)house developed software packages allow for coupledside” and “process-side” simulations of industrial scale stcracking furnaces. For the simulation of the cracking rtions inside the reactor tubes a detailed kinetic radical reascheme (CRACKSIM) containing over 1000 reactions betw128 components has been developed (Willems & Froment1988a, 1988b). Coke formation models were derived for blight and heavy hydrocarbon feedstocks (Plehiers & Fromen1990; Reyniers, Froment, Kopinke, & Zimmermann, 199).The radical reaction scheme can be combined with adimensional or a two-dimensional reactor model (COILS

098-1354/$ – see front matter © 2005 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2005.11.010

636 G.D. Stefanidis et al. / Computers and Chemical Engineering 30 (2006) 635–649

Nomenclature

A constant in the EBU modela stoichiometric reaction coefficientb stoichiometric reaction coefficientC concentration (mol/cm3)C1ε RNG k–ε model variable coefficientC2ε RNG k–ε model constantCµ RNG k–ε model constantCx, Cy, Cz variables in the six-flux radiation model

(J/s/m2)cp specific heat at constant pressure (J/kg/K)D molecular diffusivity (m2/s)Dt turbulent diffusivity (m2/s)Da Damkohler number

=characteristic flow time scale

characteristic reaction time scale= τflow

τchemE total energy per unit mass,E = h + 1

2ui + k − pρ

(J/kg)g gravitational constant,g = 9.81 (m/s2)Heff effective enthalpy per unit mass (J/kg)h mean static enthalpy per unit mass (J/kg)hm enthalpy of formation of speciesm per unit mass

of speciesm (J/kg)h* static enthalpy in the fine structures per unit mass

of fine structures (J/kg)h∗

m static enthalpy of speciesm in the fine structuresper unit mass of speciesm in the fine structures(J/kg)

k turbulent kinetic energy per unit mass (m2/s2)kα absorption coefficient (m−1)Ka Karlovitz number=

characteristic time scale of the laminar flame

Kolmogorov time scale

= τL

τKLem Lewis number of species

m = thermal diffusivity

mass diffusivity of speciesm= Dth

Dm

M molecular weight (kg/mol)NS total number of speciesPk production of turbulent kinetic energy term

(J/m3/s)Prt turbulent Prandlt numberpeff effective pressure,peff = p + 2

3ρk (Pa)Qrad net volumetric rate of radiative heat

release (J/m3/s)q∗

rad net radiative heat transfer rate from the fine struc-tures to the bulk fluid per unit mass of fine struc-tures (J/kg/s)

R ideal gas constant,R = 8.314 (J/mol/K)Rm, Rm average net production rate of species

m (mol/m3/s)rk,tot total rate of reactionk (mol/m3/s)rk,mix turbulent mixing rate of reactionk (mol/m3/s)rk,intr intrinsic rate of reactionk (mol/m3/s)

S inverse of the mean shear time scale (s−1)Sij mean strain rate tensorSMi source term for theith direction in the momentum

equation (kg/m2/s2)SE source term in the energy equation (J/m3/s)T temperature (K)T* temperature in the fine structures (K)u, v, w velocity component in thex, y and z direction

(m/s)ui, uj velocity component in theith orjth direction (m/s)x, y, z coordinate directionsxj coordinate in thej directionym mean mass fraction of speciesmy∗m mass fraction of species m in the fine structures

Greek symbolsαw wall absorptivityαε RNG k–ε model constantαk RNG k–ε model constantβ RNG k–ε model constantγ* mass fraction of the fine structuresε dissipation rate of turbulent kinetic energy per unit

mass (m2/s3)εw wall emissivityη turbulence to mean shear time scale ratioη0 RNG k–ε model constantλ molecular conductivity (J/m/s/K)λt turbulent conductivity (J/m/s/K)µ molecular viscosity (Pa s)µt turbulent viscosity (Pa s)ν kinematic viscosity (m2/s)ρ mean density (kg/m3)ρ* density in the fine structures (kg/m3)σ Stefan-Boltzmann constant, σ = 5.7× 10−8

(J/s/m2/K4)τ* characteristic time scale of the fine structures (s)ω∗

m net production rate of speciesm in the fine struc-tures (mol/m3/s)

1D/2D) solving the flow and species transport equations in thereactor (Van Geem, Heynderickx, & Marin, 2004). The calcula-tion of the accurate flow and temperature fields in the radiationbox is done with CFD simulation software (FLOWSIM) thatsolves the three-dimensional Reynolds Averaged Navier-Stokes(RANS) equations along with a two-equation turbulence model.Since radiation accounts for most of the heat flux towards thereactor tubes there is also a strong need for an appropriateradiation model. Finally, for a furnace with long flame burn-ers, where combustion occurs in the furnace itself, as opposedto furnaces with radiation burners, where combustion is local-ized in the burner cups, the CFD flow solver should also becombined with a combustion model including combustion kinet-ics and turbulent mixing. Examples of coupled “fire-side” and“process-side” simulations are given inHeynderickx, Oprins,

G.D. Stefanidis et al. / Computers and Chemical Engineering 30 (2006) 635–649 637

Marin, and Dick (2001), Oprins and Heynderickx (2003)andOprins, Heynderickx, and Marin (2001).

The focus in this work is on turbulent combustion model-ing in steam cracking furnaces. In the aforementioned papers,combustion was modeled using Simplified Reaction Kinetics(SRK) accounting for hydrocarbon and hydrogen oxidation(Westbrook & Dryer, 1981) in combination with the Eddy BreakUp (EBU)/finite rate formulation (Magnussen & Hjertager,1976). In this work, the combustion model is extended tomake use of Detailed Reaction Kinetics (DRK) in combina-tion with a turbulent–chemistry interaction model based on theEddy Dissipation Concept (EDC) (Gran & Magnussen, 1996).A representative segment of a steam cracking furnace is simu-lated both with the simplified and the more advanced turbulentcombustion model. This work investigates the effect of theinclusion of detailed combustion chemistry and of an advancedturbulence–chemistry interaction model in CFD simulations ofsteam cracking furnaces on the predicted wall, tube skin andflue gas temperature profiles as well as on the predicted speciesconcentration profiles. Moreover, the detailed combustion mech-anism is used to obtain an insight into the structure of the furnaceflames under normal furnace firing conditions.

2. Turbulent combustion in CFD simulations

Turbulent combusting flows are characterized by continuousfl tionG press erags re as ourct ceo comb sedc s inc

s. Infi actet nc-t citys (e.gF at itt odef n thv d tht culad hust termt urefl eth-o osedt ter-i s liket nteC theor ithr pen

sive even if multi-processor computers and advanced tabulationtechniques are used.

Much simplification is obtained when the shape of PDF ispre-assumed (e.g.Jones & Whitelaw, 1982). Usually, either the�-function or the Gaussian function is used for that purpose.In this case, the first two moments (mean and variance) of ascalar suffice to determine its PDF. Under the simplification ofequilibrium chemistry andLe = 1 for all species local speciesmass fractions and density are given as function of a so-calledmixture fraction, which is a conserved quantity. Therefore, onlytwo transport equations for the mean and the variance of themixture fraction need to be constructed and solved. This is apopular approach leading to fast calculations but is only applica-ble to non-premixed combustion systems and gives only reliableresults if the equilibrium assumption is satisfied.

A second class of turbulence–chemistry interaction methodsis based on a geometrical analysis of the flame. Those models arerelated to the flamelet assumption (e.g.Bray & Peters, 1994). Allreactions are considered to be sufficiently fast so that the lengthscale of the reaction zone is smaller than the Kolmogorov lengthscale. In this case, the flame can be considered as an ensemble ofvery thin, isotropic, one-dimensional laminar flame structures(‘flamelets’). The implementation of a flamelet model is notunique and depends on the type of the flame. Usually, the steadystate governing equation for scalars in the flamelets is solvedprior to the actual flame calculation resulting in the constructiono blesa ixturef pre-d stion.T s tod g tot

od-e tes tot tedm na t itl surem r thea heE ino hem-i ablet andh n( odys wasr rablew dMi )t on-c acei ,B ibes cales

uctuations in density, temperature and species concentraiven the strong non-linear nature of the reaction rate exions with respect to the state variables, closure of the avpecies reaction rates based on mean values of temperatupecies concentrations leads to poor predictions of the serm:Rm(T, Ci) �= Rm(T , Ci). Capturing the effect of turbulenn the average reaction rates is an important constituent ofustion modeling. Several approaches have been propoope with the problem of turbulence–chemistry interactionombustion applications.

Those approaches can be classified in three categorierst, statistical approach, the mean scalar values are extrhrough the knowledge of one-point Probability Density Fuions (PDF’s). The shape of one joint scalar or joint velocalar PDF can be determined by its own transport equationox, 1996; Pope, 1985). This approach has the advantage th

reats the chemical source term exactly. It is not entirely mree though. The terms representing the transport of PDF ielocity space due to velocity and pressure fluctuations anransport of PDF in the reactive scalar space due to moleiffusion appear unclosed in the PDF transport equation. T

he closure problem is shifted from the chemical sourceo molecular mixing and mixing due to velocity and pressuctuations. The predictive capability of transport PDF mds heavily depends on the quality of modeling of the uncl

erms (Peters, 2000). The transport PDF equation is characzed by high dimensionality that renders classical techniquehe finite volume method inappropriate for its solution. Moarlo techniques are to be used. Although the method is

etically sound, its application to industrial CFD problems wealistic chemistry is expected to be computationally very ex

s.-ende

-to

ad

.

leer,

-

-

f flamelet libraries where values for the independent variare stored for a wide range of a passive scalar such as the m

raction in case of non-premixed combustion or anotheretermined progress variable in case of premixed combuhose libraries are later used during the CFD calculationetermine the local species distribution. Models belongin

his category are valid forDa � 1 andKa < 1.The third category of turbulence–chemistry interaction m

ls consists of models that relate the effective reaction raurbulent mixing levels. Probably the most widely celebraodel of this category is the modified EBU model ofMagnussend Hjertager (1976). Its popularity stems from the fact tha

eads to fast and robust calculations. It is a first-order cloodel and, like the flamelet models, was developed undessumption ofDa � 1. A recent extension of this model is tDC model (Gran & Magnussen, 1996) that was developedrder to be able to take into account detailed, finite rate c

stry. The latter model has the advantage of being applico both premixed and non-premixed combustion systemsas been successfully used in the past.Gran and Magnusse1996)used the model for simulating a non-premixed bluff btabilized flame. Good agreement with experimental dataeported. The performance of the EDC model was compaith the one of a transport PDF model.Chakraborty, Paul, anukunda (2000)used the model to simulate H2/air combustion

n a scramjet combustor. InHan, Wei, Schnell, and Hein (2003,he EDC is used for simulation of a hybrid reburn/selective natalytic reduction process in a pilot scale coal-fired furnn combination with a reduced kinetic model. InGiacomazziattaglia, and Bruno (2004), the EDC model is used to descringle-step combustion chemistry close to the dissipation s


in the context of Large Eddy Simulations (LES) and RANS sim-ulations of a premixed C3H8/air bluff-body flame.Rasmussen etal. (2004)use the EDC model for post-processing of a detailedkinetic mechanism onto converged flow and temperature pro-files derived from a CFD simulation with single-step chemistry.In the present work, the EDC model with detailed combustionchemistry is used in coupled flow-reaction simulations to modelcombustion in a steam cracking furnace. The same simulationsare performed with the simplified EBU-SRK model that wasused in the past. The differences in the results coming out of thetwo modeling approaches are interpreted in terms of the theo-retical background associated with them in order to examine thevalidity of the simplifications involved in the second approach.

An overview of the model equations, the implementa-tion of combustion chemistry in the in-house developed codeFLOWSIM and the numerical solution procedures are given inthe following sections.

3. Flow modeling

The calculation of the three-dimensional statistically station-ary turbulent flow field in the furnace is based on the solution ofthe RANS equations in compressible formulation, closed withthek–ε model derived from the Renormalization Group method(RNG) (Yakhot, Orszag, Thangam, Gatski, & Speziale, 1992).The equations of the RNGk–ε model are of the same form ast form sipat

wC

1

η emS netv

4. Radiation modeling

The six-flux model ofDe Marco and Lockwood (1975)is usedto calculate the radiative heat transfer in the furnace. As pointedout by Keramida, Liakos, Founti, Boudouvis, and Markatos(2000), the six-flux model can be applied to industrial gas fur-naces with relative ease; it is numerically robust and yieldsaccurate predictions. The model divides the total solid angleinto six solid angles of magnitude 2π in which the radiationintensity varies. Each one of the solid angles is centered aboutone of the co-ordinate directions. In this case, only three of theresulting six equations are independent. Another three equationsare found by integrating the radiative transfer equation in each ofthree pairs of infinitesimal solid angles in the co-ordinate direc-tions. The second-order Ordinary Differential Equations (ODEs)describing the six-flux model under the assumptions of (1) greymedium, (2) absence of scattering and (3) index of refractionequal to unity, are:

∂

∂x

(1

kα

∂Cx

∂x

)= kα(3Cx − Cy − Cz) − kασT 4 (6)

∂

∂y

(1

kα

∂Cy

∂y

)= kα(−Cx + 3Cy − Cz) − kασT 4 (7)

∂(

1 ∂Cz

)= kα(−Cx − Cy + 3Cz) − kασT 4 (8)

T ationo

α

α

α

w ativec eased ts

Q

T l-u el ofE

5

, thes lvingt

w

hose of the standardk–ε model. The transport equationsass, momentum, energy, turbulent kinetic energy and dis

ion rate of turbulent kinetic energy are:

∂

∂xj

(ρuj) = 0 (1)

∂

∂xj

(ρuiuj) = −∂peff

∂xi

+ ∂

∂xj

(2(µ + µt)Sij) + SMi (2)

∂

∂xj

(ρHeffuj) = ∂

∂xj

((λ + λt)

∂T

∂xj

)

− ∂

∂xj

(NS∑

m=1

ρ(D + Dt)hm

∂ym

∂xj

)+ SE (3)

∂

∂xj

(ρkuj) = ∂

∂xj

(αk(µ + µt)

∂k

∂xj

)+ Pk − ρε (4)

∂

∂xj

(ρεuj) = ∂

∂xj

(αε(µ + µt)

∂ε

∂xj

)+ C1ε

ε

kPk − C2ερ

ε2

k(5)

here Pk = 2µtSijSij; µt = Cµρk2/ε; λt =µtcp/Prt; Prt = 0.9;µ = 0.0845; αk =αε = 1.39; C2ε = 1.68 and C1ε =.42− η(1−η/η0)

1+βη3 ; η = Skε

; S =√2SijSij; Sij = 12

(∂ui

∂xj+ ∂uj

∂xi

);

0 = 4.38; β = 0.012; ρHeff =ρE +peff.The source term in thomentum equation includes gravitation (SMx = SMy = 0 and

Mz =−ρg). The source term in the energy equation is theolumetric heat release due to radiation (Qrad).

-

∂z kα ∂z

he boundary conditions of the model considering conservf radiation energy at the furnace walls and coils are:

wCx ∓ 2

3kα

∂Cx

∂x(2 − αw) = εwσT 4

w (9)

wCy ∓ 2

3kα

∂Cy

∂y(2 − αw) = εwσT 4

w (10)

wCz ∓ 2

3kα

∂Cz

∂z(2 − αw) = εwσT 4

w (11)

here the− and + are associated with the positive and nego-ordinate directions. Finally, the local volumetric heat relue to radiation is expressed as a function of the coefficienCi:

˙ rad = 4

3kα(Cx + Cy + Cz) − 4kασT 4 (12)

he absorption coefficientkα is calculated in each control vome by means of the exponential band absorption moddwards, Glassen, Hauser, and Tuchscher (1967).

. Combustion modeling

For steam cracking furnaces with long-flame burnerspecies concentration fields are calculated by means of sohe species transport equations in averaged formulation:

∂

∂xj

(ρujym) = ∂

∂xj

(ρ(D + Dt)

∂ym

∂xj

)+ RmMm (13)

hereDt = Dµt/µ


Two models have been used to calculate the average netspecies production ratesRm for the combustion of a methane–hydrogen fuel mixture.

5.1. EBU-SRK model

In this model, the methane and hydrogen oxidation processis represented by a simplified reaction scheme:

CH4 + 1.5O2 → CO + 2H2O (14)

CO + 0.5O2 → CO2 (15)

H2 + 0.5O2 → H2O (16)

with corresponding intrinsic reaction rate equations:

r14,intr = 1.5 × 1013 e−125604/RT C−0.3CH4

C1.3O2

(17)

r15,intr = 3.98× 1020 e−167472/RT CCOC0.5H2OC0.25

O2(18)

r16,intr = 1013C0.5O2

CH2 (19)

The intrinsic reaction rates for the two-step mechanism describ-ing methane combustion (Eqs.(17) and(18)) were derived byW rsi osed anNW eya

s ,r dH

r

ws

fied.F low-c ur-b rater cal-c pecc oneo u-p ingr sulta odelc dic-t eeda sionoM

5.2. EDC-DRK model

In this model, the detailed combustion mechanism ofChenand Dibble (1991)is used. This mechanism involves 35 elemen-tary reactions among 16 species: CH4, H2O, CO2, H2, CO, O2,N2, O, H, OH, HO2, H2O2, CH3, CH2O, CH3O and HCO.

The EDC model is used to introduce turbulence–chemistryinteractions. The model is based on a general reactor conceptfor the calculation of the average net species production rates inturbulent reactive flows. Combustion takes place in the regionsof the turbulent field where the highest molecular fluxes occur.Those regions are associated with the smallest turbulence struc-tures, the so-called fine-structures. Through a step-wise descrip-tion of the turbulence energy cascade process from large toprogressively smaller eddies, an expression for the mass frac-tionγ* of the fine-structures and for the characteristic time scaleτ* for mass exchange between the fine-structures and the bulkfluid is derived, dependent upon the turbulence quantities andthe viscosity:

γ∗ = 9.67(vε

k

)3/4(21)

τ∗ = 0.41(v

ε

)1/2(22)

These quantities are subsequently used in the reactor modelingo idesa fine-s turbu-l ls liket siso derivetM

likeF bec nd thes d asa nergyw SRp eara nces isr riva-t ebraice theOi

T tures.I ert ateq ted.

estbrook and Dryer (1981). The set of kinetic parameten Eq. (19) was found to give reaction rates close to thetermined based on the parameters in the ASPEN, KDBIST databases (Aspen Plus, 2002; Kang et al., 2003; Mallard,estley, Herron, & Hampson, 2003). As a consequence, th

re used in this work.In each control volume the total rate of reactionk, rk,tot, is

et to be the minimum ofrk,mix andrk,intr where the mixing ratek,mix, is given by the modified EBU model ofMagnussen anjertager (1976):

k,mix = Aε

kρ min

(yfuel

Mfuel,b

a

yoxidizer

Moxidizer

)(20)

hereA is an empirical constant calibrated to be 4 andb/a is thetoichiometric ratio between fuel and oxidizer.

Two major disadvantages of the model can be identiirst, the model represents the extreme limits of “fast- or shemistry” only. Inevitably, the contribution of either the tulent mixing rate or the intrinsic reaction rate to the totalk,tot is neglected. Moreover, the intrinsic reaction rate isulated based on the average values of temperature and soncentrations. Second, the model is only compatible withr two-step globalirreversible reaction schemes. When coling of the EBU model with detailed kinetic schemes containeversible elementary reactions is attempted, erroneous rere likely to be obtained; limiting rates computed by the mould drive the system in the direction opposite to the oneated by chemical kinetics. In other words, the system procway from chemical equilibrium. A more extensive discusn the EBU model and its limitations can be found inBrink,ueller, Kilpinen, and Hupa (2000).

d

ies

s

s

f the fine structures. It is concluded that the model provlink between the small-scale turbulence structures (or

tructures), where reactions take place, and the grid-scaleence structures that can be described by turbulence modehe RNGk–ε, which is used in this work. A detailed analyf the turbulence energy cascade model that was used to

he expressions Eqs.(21)and(22)can be found inErtesvag andagnussen (2000).When the EDC model is to be integrated in a CFD code

LOWSIM every single computational cell is considered toomposed of a reactive space, namely the fine-structures aurrounding fluid that is inert. The reactive space is modelePerfectly Stirred Reactor (PSR) exchanging mass and eith the surrounding inert fluid. Thus, the solution of a Problem in every single cell involving the system of non-linlgebraic equations consisting of the mass and energy balaequired. To make the simulations more robust, temporal deives are added in the balances and the set of non-linear algquations is transformed into an initial value problem whereDE set of mass and energy balances (Eqs.(23) and(24)) is

ntegrated from a known initial state to steady-state.

dy∗m

dt= ym − y∗

m

(1 − γ∗)τ∗ + ω∗mMm

ρ∗ (m = 1, . . . , NS) (23)

dh∗

dt=∑NS

m=1(ymhm − y∗mh∗

m)

(1 − γ∗)τ∗ + q∗rad (24)

he superscript asterisk refers to quantities in the fine strucf there is no superscript (ref. Eq.(13)) averaged quantities ovhe cell are meant. In Eq.(24) the net radiative heat transfer r˙∗radfrom the fine-structures to the surrounding fluid is neglec


In this work, the implicit Euler method is used for time march-ing when solving the set of ODE’s. As only the steady-statesolution is needed, relatively large time steps can be taken, thusreducing the required number of iterations and the required CPUtime.

Solution of the system of Eqs.(23)and(24)provides valuesfor the variables in the fine structures (T ∗, y∗

m, m = 1, . . ., NS)and for the net species production ratesω∗

m in the fine-structures.Eventually, the average net species production rates,Rm, that aresubstituted in the species transport equations (Eq.(13)), whichare integrated over each control volume, are calculated from:

Rm = γ∗

(1 − γ∗)τ∗ (y∗m − ym) (25)

Thus, the effect of turbulence on the source terms,RmMm, ofthe species transport equations (Eq.(13)) is taken into accountthrough the determination of the mass fraction and of the char-acteristic time scale of the fine structures.

In principle, the EDC model can be combined with one- ortwo-step global mechanisms. However, the combination of theEDC model with the specific two-step mechanism for methaneoxidation described in Section5.1was found to be problematicdue to the negative concentration exponent for methane in Eq.(17), which satisfies the experimentally observed rich flamma-bility limit of the methane/air mixture. From a numerical pointof view, the negative exponent can create problems since the rateo thanc ationf .A inedv herea obalm ofv nenh inetieb ausa allet ixinr

E int ed isb

5m

umpt andt outt them comp ationo sa ctior g as

mixing and not reaction is the rate-limiting step. Combustion isseen by the model as a sequential process. First, the eddy breakup process leads to enhanced molecular mixing at the small tur-bulence scales, the so-called fine-structures, and then reactionoccurs in the fine-structures. Then the overall rate should begiven from:

rk,tot =(

1

rk,mix+ 1

γ∗(ρ/ρ∗)rk,intr(Ci∗, T ∗)

)−1

(26)

This equation, however, may cause numerical problems in thecalculation of the overall rate and therefore it is not used in theliterature. Moreover, the state of the fine structures cannot becalculated in the context of the EBU model. The model neglectsthe second term in Eq.(26), which always leads to overesti-mation of the overall rate if the “fast-chemistry” assumption(rk,mix � rk,intr(C∗

i , T∗)) is invalid. This is likely to happen at

low temperature combustion (T < 1300 K) in the beginning ofthe reaction zone. The model also provides a simple “fix” forthe “slow-chemistry” limit whenever the reaction rate is smallerthan the mixing rate. In this case, the overall rate is set to be thereaction rate, which is calculated based on the average values ofthe state variables over the control volume. This is valid only forperfectly mixed components in the control volume where thetemperature and concentration fluctuations go to zero. Again,neglect of the turbulent fluctuations causes overprediction oft“ BUm om-b lentlyt nei-t tioni

6

ddedi iter-a ationo mem d byt -v bym1 is-c ua-t oint-ww tionm e lat-t val-u asest thes -i ellsa les( to

f methane consumption increases without limit as the meoncentration goes to zero. For that reason the PSR simulailed to converge when the reaction rate Eq.(17) was usedrtificial truncation of the rate expression at a predetermalue did not solve the problem either. On this score, tre no simulation results with the EDC model and the glechanism of Section5.1. To our knowledge, no other set

alues for the methane and oxygen concentration expoave been proposed in the literature for use into technical kxpressions. Remark that when reaction rate Eq.(17) is com-ined with the EBU model this problem does not arise bect small fuel concentrations the mixing rate becomes sm

han the reaction rate and the total rate is set equal to the mate.

Finally, it was shown byGran and Magnussen (1996)that theBU model (Eq.(20)) is a limiting case of the EDC model

he event of one-step irreversible reaction under the “mixurnt” (=“fast-chemistry”) assumption.

.3. Analysis of possibilities and limitations of the EBUodel

This paragraph is focused on the investigation of the assions hidden in the mathematical formulations of the EBUhe finite rate chemistry/EBU models. The target is to bringhe inaccuracies that should be expected in the event thatodels are used when mixing and reaction time scales arearable. This discussion is also important for the interpretf the results that are presented in Section8. The EBU model i“fast-chemistry” model and assumes that the effective rea

ate is only determined by the turbulent mixing rate as lon

es

tsc

erg

-

se-

n

he overall rate (Bakker, Haidari, & Marshall, 2001) unless theperfect-mixing” assumption holds. Given the fact that the Eodel can only be combined with one- or two-step global c

ustion mechanisms, the fuel consumption rate and equivahe products formation rate is bound to be overpredicted ifher the “fast-chemistry” nor the “slow-chemistry” assumps satisfied.

. Numerical methods—solution procedure

The flow, combustion and radiation models are emben three different modules that are successively used in antive cycle, till convergence is reached. Spatial discretizf the flow domain is done by means of the finite-voluethod using a non-structured tetrahedral grid create

he Gmsh software (Geuzaine & Remacle, 2001). The conection operator in all transport equations is discretizedeans of a first-order flux-difference splitting scheme (Dick,990; Dick & Steelant, 1997). Second-order terms are dretized centrally. The linearized set of partial differential eqions in the flow and combustion models are solved pise with the LAPACK routines (Anderson et al., 1999),hich employ the LU decomposition and back substituethod, using a Gauss–Seidel relaxation scheme. Th

er means that at any iteration level the most recentes for the variables are used, which in general incre

he convergence rate. Applying this relaxation scheme toolution of the system of Eqs.(1)–(5) involves first sweepng forward and then backward through the list of cnd solving the system for the vector of primitive variabρ, u, v, w, p, k, ε). No special consideration was given


reordering of the cells before the Gauss–Seidel method wasapplied. The cell list remained as ordered by the grid generationprogram.

7. Furnace geometry and operating conditions

The objective of this work is two-fold. First, to investigatewhether turbulence–chemistry interactions and detailed chem-istry effects in the flame modeling of steam cracking furnacesinfluence the evolution of important dependent variable profiles,such as tube, wall and flue gas temperatures and fuel/flue gasspecies concentrations. Second, to obtain a clear conception ofthe flame structure. For that reason, a representative segmentof a naphtha cracking furnace is simulated using the two com-bustion models described in Sections5.1 and 5.2. The segmentcontains two flame burners that are positioned on the left and theright side of six reactor tubes. Fuel and air are premixed beforeentering the radiation section. 53222 tetrahedral cells are usedto discretize the physical space between the segment walls, thesymmetry planes and the reactor tubes. Local grid refinement isapplied in the flame region above the two burners and near thesolid boundaries.

In this work, no coupled furnace-reactor simulations (e.g.Heynderickx et al., 2001; Oprins et al., 2001) are performed,since only a segment of the furnace is simulated. Therefore, a

Fig. 2. Top view of the simulated segment.

fixed process gas temperature profile, taken from previous reac-tor calculations, is applied and is considered to be part of theboundary conditions of the simulations.

A schematic representation of the furnace and the simulatedsegment is given inFig. 1. The top view of this volume elementis presented inFig. 2. The basic simulation conditions are givenin Table 1.

8. Results and discussion

Simulation results from the application of the mathemat-ical models described in Sections3–5 to CH4/H2 premixedflames in a representative segment of a steam cracking furnaceunder normal firing conditions are presented. The results aremainly given in terms of temperature and species concentrationprofiles.

In Fig. 3, the calculated temperature profiles with the twocombustion models in a vertical cross section through the burn-ers are presented. A more extended reaction zone is predictedwith the EDC-DRK model. The latter implies slower combus-tion of the fuel leading to lower temperatures in a small regionclose to the burners and higher temperatures further away fromthe burner. In order to quantify those differences, vertical and

Fig. 1. Schematic representation of the furnace and the simulated segment.

horizontal temperature profiles in the same vertical cross sectionare shown inFigs. 4 and 5.

In Fig. 4, the vertical temperature profile along the center-l thatt thet rox-

ine of the right-hand side burner is presented. It is shownhe temperature evolution with the EDC-DRK model lagsemperature evolution with the EBU-SRK model up to app


Table 1Simulation conditions

Furnace segmentHeight (m) 6.796Length (m) 1.2Width (m) 3.0Thickness of refractory (m) 0.23Thickness of insulation (m) 0.05Number of burners 2

ReactorNumber of reactor tubes 6Total reactor length (m) 38.68External tube diameter (m) 0.12Internal tube diameter (m) 0.10

Firing conditions (one burner)Fuel gas flow rate (kg/s) 0.4226Fuel equivalence ratio 0.94Fuel gas composition (wt%)CH4 94.3H2 5.7

Material propertiesEmissivity of furnace wall 0.85Emissivity of tube skin 0.6Thermal conductivity of refractory wall (W/m/K) 0.394Thermal conductivity of insulation (W/m/K) 0.19Thermal conductivity of tube skin (W/m/K) −8.432 + 3.04×

10−2T (K)

Fig. 4. Vertical temperature profile along the centerline of the right-hand sideburner. Simulation conditions are given inTable 1.

imately 1.7 m above the burner opening. At this height the twolines cross and further downstream the temperature predictedwith the EDC-DRK model remains higher but the temperaturedifference between the two models decreases with height. Themaximum temperature predicted with the EDC-DRK modelis 1918 K at approximately 2 m height whereas the maximumtemperature predicted with the EBU-SRK is 1878 K at approx-imately 1.4 m height. Temperature differences up to 900 K arepredicted in the region between the burner opening and the cross-ing point of the two temperature lines.

Fig. 3. Temperature profile in a vertical cross section through the burners. (a) E
DC-DRK model and (b) EBU-SRK model. Simulation conditions are given in Table 1.


Fig. 5. Horizontal temperature profiles in a vertical cross section through the burners at several heights. Simulation conditions are given inTable 1.

In Fig. 5, horizontal temperature profiles in the same crosssection are presented. At 0.6 m height (Fig. 5a) similar trendsare observed as inFig. 4. Namely, much higher temperatures arepredicted with the EBU-SRK model in the region close to the

burners. The two temperature lines cross at approximately 0.3 mto the left of the right-hand side burner and 0.3 m to the rightof the left-hand side burner. In the region between the crossingpoints and the reactor tubes the temperatures predicted with the

F h the s ai

ig. 6. Calculated flow profile projected on a vertical cross section throug
n Table 1.
burners. EDC-DRK model and (b) EBU-SRK model. Simulation conditionre given


Fig. 7. Internal tube skin temperature profile along the reactor. Simulation con-ditions are given inTable 1.

EDC-DRK model are higher but the temperature differences aregradually alleviated as the center of the furnace is approached.In the center of the furnace, where the tubes are located, a clearlocal minimum in the flue gas temperature is observed, the so-called heat sink expanding over the total furnace height, due tothe presence of the tubes. The temperature profiles at the heightof 3.5, 5 and 6.5 m (Fig. 5b–d) are outside of the flame zonewhere only flue gas is present. As already mentioned, the temperatures predicted with the EDC-DRK model are always highethan the temperatures predicted with the EBU-SRK model. Moreimportant is to notice the increasing asymmetry of the temper-ature profile with the furnace height. That can be attributed tothe flow pattern in the furnace, shown inFig. 6. A large recir-culation zone is predicted by both combustion models in theupper left part of the furnace and it is somewhat extended whenthe EBU-SRK model is used. The recirculation zone starts fromthe left wall at a height of 3.5 m approximately and expandsto the upper wall of the furnace and towards the reactor tubes.This recirculation zone is due to the asymmetric outlet of theflue gas in the furnace. Due to the high residence time of theflue gas in the recirculation zone, the temperature in this regionbecomes uniform (seeFig. 3) and the temperature difference pre-dicted with the two combustion models remains constant (see thenearly flat part of the lines on the left-hand side of the horizontaltemperature profiles inFig. 5c and d). On the contrary, the tem-perature differences outside of the recirculation zone predictedw rlineo morep effecto cen-t omess wall.T gioni theh tem-p dn

In Fig. 7, the internal tube skin temperature profile along thereactor length in the furnace segment is presented. As expectedbased on the presented flue gas temperature profiles, higher inter-nal tube skin temperatures are predicted with the EDC-DRK

Fig. 8. Vertical temperature profiles on the A wall at different axial positions(y-direction,Fig. 1). Simulation conditions are given inTable 1.

ith the two models decrease when going from the centef the burners towards the tubes, but this effect becomesronounced higher up in the furnace. This is because thef the recirculation zone on the temperature levels at the

er of the furnace, where the reactor tubes are located, bectronger at higher heights, i.e. close to the upper furnacehe flue gas temperature distribution in the reactor tube re

s important because it is an important factor determiningeat flux distribution towards the tubes and the tube skinerature profile, which is presented inFig. 7 and discusseext.

-r


Fig. 9. Shaded contour plots of the CH4 and H2 concentrations in a vertical cross section through the burners. The black isolines correspond to different CH4 andH2 concentration levels. (a) EDC-DRK model and (b) EBU-SRK model. Simulation conditions are given inTable 1.

model all along the reactor length. The ascending temperaturetrend that is predicted is due to the increasing process gas temper-ature. Six local minima are calculated with both models, whichcorrespond to the points where the reactor passes the top of thefurnace and the flue gas temperatures are low. Six local max-ima are calculated on each one of the six tubes, 1.5–2 m abovethe furnace floor. Those are also the peak temperature heightsof the two flames. The highest internal tube skin temperaturedifferences, up to 20 K, between the two combustion models arepredicted at the top part of each tube where the flue gas temper-atures differ most. This issue has already been discussed in theprevious paragraph.

The effect of the different combustion models on the walltemperatures is presented inFig. 8. In this figure, the temperaturevariation with height on the A wall (Fig. 2) at three differentaxial positions (y-direction,Fig. 1) are presented. Following thepresented flue gas temperature profiles, the wall temperaturespredicted with the EDC-DRK model are constantly higher inall three cases. The temperature differences are between 25 and60 K. Higher A wall temperatures are predicted between 1 and2 m height above the furnace floor because this zone faces theright-hand side flame directly. The maximum A wall temperaturepredicted with the EDC-DRK model is 1585 K aty = 0.6 m (crosssection through the burners) andz = 1.15 m (on the opposite ofthe peak temperature zone of the flame). The A wall temperatures

decrease with height and reach the lowest values just below theoutlet. The form of the temperature profiles on the C wall issimilar to that of the A wall and therefore they are not presentedin this paper.

The temperature differences predicted with the two combus-tion models and presented in the previous paragraphs suggestdifferent fuel combustion rates. The concentration profiles ofthe two fuel components, that is methane and hydrogen, in thesame cross section where the temperature profiles have beenpresented are shown inFig. 9. The results are presented in greyscaling and the black isolines named A–C correspond to differ-ent CH4 and H2 concentration levels. It is readily noticed thatcombustion progress for both fuel components is slower in thecase of the EDC-DRK model, leading to larger flames whenthis model is used. Indicatively, it is mentioned that 75% of theamount of CH4 at the inlet has been consumed at 0.85 m height(line B) with the EBU-SRK model whereas the same amountof methane is predicted to have been consumed at 1.2 m heightwith the more advanced EDC-DRK model. The differences arestriking in the case of H2. For example, 99% of H2 has alreadybeen burnt at 0.9 m height (line C) with the EBU-SRK whereasthe peak of the line C with the EDC-DRK is almost three timeshigher.

Similar results are obtained for the concentration profiles ofthe major combustion products, namely CO2 and H2O (Fig. 10).


Fig. 10. Shaded contour plots of the CO2 and H2O concentrations in a vertical cross section through the burners. The white isolines indicate the progress of CO2

and H2O formation at different levels. (a) EDC-DRK model and (b) EBU-SRK model. Simulation conditions are given inTable 1.

The white isolines A–C indicate the progress of CO2 and H2Oformation at three different levels, which are 50, 75 and 99%,respectively, of their maximum values. Slower formation of bothproducts is predicted in the case of the EDC-DRK model. Forinstance, 99% of CO2 has been formed at 2 m height (line C)with the EBU-SRK model and at 2.3 m height with the EDC-DRK model. Moreover, it can be seen that the differences inthe H2O evolution with the two combustion models are evenmore pronounced. The differences in the temperature and con-centration profiles that have been presented so far with the twocombustion models can by explained by means of the physicsthat are associated with them. This discussion has already beendone in Section5.3.

A second goal of this work was to obtain an insight intothe flame structure. The detailed combustion mechanism isused to obtain an understanding of the detailed structure of theCH4/H2/air premixed flames in the furnace.Fig. 11shows themost important species concentration profiles along the center-line of the right-hand side burner. InFig. 11a, the concentrationprofiles of the main C-containing species CH4, CO, CO2 arepresented. It is observed that the maximum CO concentration is

approximately situated at the same height where the CH4 con-centration goes to zero. Moreover, the concentration profiles ofCO, CO2 and CH4 as well as that of H2O (Fig. 11b) becomenoticeably steeper above 1 m height approximately. It is alsoremarked that the CO curve is always below the CO2 curvealthough the opposite would be expected in the beginning of thereaction zone since CO2 is mainly formed by the oxidation ofCO. To interpret the above results,Fig. 12should be consideredtogether with the flow field presented inFig. 6. In Fig. 12, theaverage net species production rates of the fuel components andthe main combustion products (Rm) along the centerline of theright-hand side burner are presented. It is important to noticethat the bulk of chemical activity is between 1 and 2.5 m height,which explains why the fuel species and products concentrationprofiles (Fig. 11a and b) as well as the temperature rise (Fig. 4)become steeper above 1 m height. It can be seen inFig. 4that thetemperature at 1 m height is 840 K approximately. The temper-ature rise from the inlet temperature of 343 up to 840 K wherecombustion starts, is due to conductive heat fluxes from the hightemperature region back to the preheat zone and due to convec-tive heat fluxes associated with the circulating hot flue gas from


Fig. 11. Vertical species mass fraction profiles along the centerline of the right-hand side burner. (a)yCO2, yCH4 and yCO; (b) yH2O, yOH2 andyH2O2; (c) yCH2O,yCH3O andyCH3; (d) yO, yH and yOH. Model: EDC-DRK. Simulation conditions are given inTable 1.

Fig. 12. Calculated vertical profiles of some selected average net species produc-tion rates along the centerline of the right-hand side burner. Model: EDC-DRK.Simulation conditions are given inTable 1.

the reaction zone (Fig. 6). Those large recirculation zones arealso responsible for the presence of CO2 in the preheat zone (upto 1 m height) in higher amounts than CO, whereas results fromone-dimensional premixed flame calculations (without recir-culation) show that CO2 formation lags CO formation in thebeginning of the reaction zone. InFig. 12 it is seen that themaximum product formation rates (CO2 and H2O) are calcu-lated exactly where the maximum destruction rates of the fuelspecies (CH4 and H2) occur. Above that height (approximately1.3 m) the chemical activity declines and at 2.5 m it is completed.At this height, the CO2 and H2O concentrations have reachedtheir maximum values (Fig. 11a and b). Besides, the peak ofthe CO2 formation rate almost corresponds spatially with thepeak of the CO concentration (Fig. 11a) because CO2 is formedthrough the recombination reaction of CO with OH radicals. It isalso noted that C-intermediate species such as CH3, CH2O andCH3O (Fig. 11c) as well as H-intermediate species such as OH2and H2O2 (Fig. 11b) coexist in the same interval between 0 and2.5 m. Moreover, their peak concentration values are found tobe at the same height of approximately 1.2 m. Finally, the calcu-lations with the detailed combustion mechanism have revealedthat the OH mass fraction is roughly one order of magnitudehigher than the mass fraction of O and two orders of magnitudehigher than the mass fraction of H (Fig. 11d), which suggeststhat for the fuel and the firing conditions considered, OH is thedominant radical in the H2–O2 pool.


9. Conclusions

A three-dimensional mathematical model has been devel-oped for the simulation of flow, temperature and concentrationfields in the radiation section of industrial scale steam crackingunits. The model takes into account turbulence–chemistry inter-actions through the Eddy Dissipation Concept model and makesuse of Detailed Reaction Kinetics, which allows the detailedinvestigation of the flame structure. Furthermore, simulationresults obtained with the EDC-DRK model are compared withsimulation results obtained with a simplified model combin-ing the Eddy Break Up/finite rate formulation with SimplifiedReaction Kinetics. When the EBU-SRK model is used, muchfaster fuel oxidation and products formation is predicted. Thelocation of the peak temperature is shifted towards the burner,resulting in a smaller flame and the confinement of the com-bustion process into a smaller area. This is most likely becauseof the inherent deficiency of the simplified model to correctlypredict the overall (effective) burning rate when the turbulentmixing rate and the reaction rate are comparable. It is shownthat when neither the “fast-chemistry” nor the “slow-chemistry”approximation is satisfied the overall burning rate is overpre-dicted. The fact that smaller flame volumes are calculated withthe EBU-SRK model has an important effect on the predictedtemperature distribution in the furnace as well as on other sig-nificant design parameters like the refractory wall and tube skint catet odela comb firingc

A

tificR ughp rcheo

R

A a, J.,ty

A gy,

B via

B es.

B nd

C om-S

C ech-In M.

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H ee-ners.

J cting

K e,

rsity,

K tos,

M 03).alData,

M elingand

O ee-

O ee-rack-

P .P f an

P

R Johan-chem-

emperatures. It is therefore concluded that more sophistiurbulence–chemistry interaction models like the EDC mnd more Detailed Reaction Kinetics should be used forustion modeling in steam cracking furnaces under normalonditions.

cknowledgements

The authors wish to acknowledge the Fund for Scienesearch—Flanders (FWO-N) for financial support throroject No. G.0070.03. Bart Merci is Postdoctoral Reseaf the FWO-N.

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CFD Simulations of Steam Cracking Furnaces Using Detailed Combustion Mechanisms