Computer Simulation of FCC Riser Reactors*

S.L. Chang, S.A. Lottes, C.Q. Zhou,** B. Golchert, and M. Petrick

Argonne National Laboratory au9700 South Cass Avenue @: ’IT?

Argonne, IL 60439COz$

** Purdue Universi@ CaIumet +=3Hammond, IN 46323

“(E g

The submitted manuscript has been created by theUniversity of Chicago as Operator of Argonne NationaLaboratory (“Argonne”) under Contract No. W-31-109ENG-38 with the U.S. Department of Energy. The U.SGovernment retahs for itself, and others ectiw on itrbehalf, a paid-up, nonexclusive, irrevocable worfdwidflicense in said article to reproduce, prepare derivativ<works, distribute copies to the public, and performpublicly and display publicly, by or on behalf of thfGovernment. I

Submitted to

The 15th International Conference on Advanced Science and TechnologyApril 2-3, 1999, Argonne, IL

sponsored byArgonne National Laboratory, USA

National Tsing Hua University, TaiwanChinese Academic and Professional Association in Mid-America

* Work supported by U.S. Department of Energy, Assistant Secretary for Energy Efficiency andRenewable Energy, under Contract W-3 1-109-ENG-38.

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Computer Simulation of FCC Riser Reactors

S.L. Chang, S.A. Lottes, C.Q. Zhou,* B. Golchert, and M. Petrick

Argonne National Laboratory9700 South Cass Avenue

Argonne, IL 60439

* Purdue University CalumetHammond, IN 46323

AbstractA three-dimensional computational fluid dynamics

(CFD) code, ICRKF.LO, was developed to simulate themuhiphase reacting flow system in a f7uid catalyticcracking (FCC) riser reactor. The code solve flowproperties bused on fundamental conservation laws ofmass, momentum, and energy for gas, liquid, and solidphases. Useful phenomenological models weredeve[oped to represent the contro[[ing FCC processes,including droplet dispersion and evaporation, partic[e-soiid interactions, and intetfacial heat transfer betweengas, droplets, and particles. Techniques were alsodeveloped to j2tciiitate numerical calculations. Thesetechniques include a hybrid flow-kinetic treatment toinclude detai~ed kinetic calculations, a time-integralapproach to overcome numerical stl~ness problems ofchemical reactions, and a sectional coupling andblocked-cell technique for handling complex geometry.Tlte copvrighied lCRKFLO sof~are has been va)idatedwith experimental data from pilot- and commercial-scaleFCC units. The code can be used to evaluate the impactsof design and operating conditions on the production ofgasoline and other oilproduets.

Introduction

Computational fluid dynamics (CFD) simulation hasbecome a new and important tool to help deveIopadvanced energy conversionicombustion systems. Atypical example is the advancement of the fluid catalyticcracking (FCC) technology. The FCC technology thatproduces gasoline and other valuable oil products wasfirst developed in the 1940s. Since then, it has becomethe most important process used by the refinery industryto produce gasoline. The process has been greatlyimproved over the years by the U.S. refineries tocompete in global markets and meet more stringentenvironmental regulations. The FCC units in U.S.

refineries today produce about 40V0 of the nation’sgasoline supply. The advancement of catalysts has beenthe most significant reason for the advancement of FCCtechnology. Recently, refineries have shown muchinterest in improving feed injection systems anddeveloping short-resident e-time riser units [1].Advanced FCC processes are usually tested in a smallpilot-scale unit and gradually scaled up to a largecommercial unit. The capacity of a pilot-scale unit isabout 1 barrel per day (bpd), and the capacity of acommercial unit can be as high as 100,000 bpd. Thescale-up process requires several intermediate steps forconstruction, tests, and adjustments. These tests areexpensive and time-consuming. Detailed knowledge ofthe relationships between process operating parametersand flow conditions within the system can decrease thedevelopment time of new and/or upgraded FCC systems.Such knowledge can be obtained by analyses based on acomputer simulation that includes the controllingprocesses of an FCC system and the testing results ofpilot units.

Chemical kinetics and flow dynamics are twocontrolling processes of an FCC system. In older FCCriser units, the residence time is long and the flow is fillydeveloped in the riser. Under this circumstance, thechemical kinetics is the only controlling process in anFCC riser, and kinetic calculations can be made based onassumed or simplified flow fields. Since there arethousands of oil species in the cracking processes,models of lumped species and reduced kinetic reactionsare developed for a kinetic calculation. Weekman andNate [2] first introduced a three-lump (feed oil, gasoline,and dry gas) cracking kinetic model to predict gasolineproduction in an FCC riser unit. Later, Jacob et al. [3]developed a ten-lump cracking kinetic model to predictmore detailed distribution of oil species in an FCC risersystem. Recently, Nigam and Klein [4] and Quann andJaffee [5] have been developing ways to approachchemical kinetics computation and model building for

cracking reaction systems with hundreds or thousands ofoil species. These kinetic computations are usuallybased on simplified or assumed flow fields.

In recent years, the residence time of FCC units hasbeen shortened significantly to improve theirperformance. Flow dynamics also becomes an importantprocess for controlling the cracking processes.Computer simulation of a multiphase reacting flowsystem like an FCC riser flow is formidable because itrequires a computer code to solve many coupled non-linear partial differential equations (PDEs) numerically.The numerical solution requires much computationalpower, both in speed and memory. The difficulty ismagnified by the limited understanding of the physics ofa multiphase flow. In the past decade, with theadvancement of the understanding of multiphase flow,the numerical techniques required to solve the PDEs, andcomputer hardware, newer versions of CFD codes werefound to be capable of modeling an FCC flow system.Theologos et al. [6] used a commercial CFD code tosimulate an FCC riser reactor. The simulation was atwo-phase flow (gas and particle) simulation withWeekman and Nate’s three-lump kinetic model. Thesimulation was used to predict engineering aspects of ariser reactor, including pressure drop, particle slipvelocity, and temperature distribution. However, thesimulation does not include an important element of theriser flow - the feed oil spray, and the number of lumpedspecies is limited.

Since 1993, ANL has been working with severalrefining companies to develop CFD capabilities tosupport advanced FCC development. A CFD codecalled lCRKFLO was developed based on an existingmultiphase reacting flow code. The code includes theformulation of a three-phase (gas, liquid, and particle)flow and a hybrid approach than can handle a largenumber of lumped oil species. It can predict oil productconcentrations of a riser based on locally computed flowproperties. The code has been validated with both pilot-and commercial-scale data. This paper presents thecode, its unique models and numerical approaches, thevalidation, and some selected results.

FCC Riser Flow Characteristics

A typical FCC unit includes three majorcomponents: a riser reactor, a stripper/separator, and aregenerator. Figure 1 shows a simple sketch of the FCCunit. Catalyst particles are transported to the bottom ofthe riser reactor from a regenerator. A spray of feed oilis injected into the riser to mix with catalyst particles andbe converted to lighter oil products. A small amount ofinert gas is used to lift particles in the entrance region ofthe riser. Oil droplets are vaporized when heated to theboiling point. Then, the oil vapor is cracked into variouslighter oil products by the catalyst and heat. Coke is aby-product of the cracking processes. The deposition of

coke on catalyst surface lowers catalyst activity. Theend of the riser is connected to a separator, in which oilproducts and spent catalyst particles (covered with coke)are separated. Oil products are sent to a distillationcolumn for further processing, and the spent particles aretransported to the regenerator to bum off the coke withair. After the coke deposit is burned off, the catalystparticles are hot and regenerated. Then, the catalyst isrecycled back to the riser reactor for the next run ofcracking. This study focuses on the riser flow.

regenerator

bustionair

Iifi gas

Figure 1 A TypicalFCCUnit

There are three major processes in a riser flow:mixing, vaporization, and the cracking reaction, asshown in Figure 2. The mixing process includes thecombined effects of interracial interactions (momentumand heat transfer between phases); flow convection andturbulent diffusion of gas, oil droplets, and catalystparticles. During the mixing process, the heat carried bythe catalyst particles is transferred to the gas and the oildroplets. Generally, the catalyst is heated up to atemperature much higher than the boiling point of thefeed oil. Consequently, the vaporization process isdominated by boiling and controlled by the heat transferrate to oil droolets.

011prcductsspent catalyst

FluidDynamicMcdel

Feed oil andhft gas

Cracking

o

eaction

Particle Drcplet Catalvst 1

InteractIonModels

Od vapor

c

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Coke Gasoline.. ●, Ot ducts

. ..; :●* Cata st%: parti Ies

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atalystulicles,

Feed otl andlit? gas

is

Figure 2 Major Processes in an FCC Riser Reactor

During the vaporization process, a liquid oil dropletreleasing oil vapor in the presence of a hot catalyst

particle. Following the vaporization process, thecracking process takes place. Four lumps including feedoil, gasoline (or light oil), dry gas, and coke are shown inFigure 2. Feed oil vapor contacts catalyst particles, andthe cracking reactions on the catalyst surface convert thefeed oil vapor to light oil vapor and dry gas. Coke is aby-product of the process. These processes all have animpact on the riser performance.

Simulation Approach

ICRKFLO is a three-dimensional CFD codedeveloped specifically for an FCC riser flow. Theformulation of the code includes major hydrodynamicand cracking processes of the FCC riser flow. Oil vaporspecies produced in the FCC cracking process cannumber in the thousands. Solving for all species isfrivolous and often causes severe numerical stiffnessproblems when it is coupled with the hydrodynamiccalculation. But solving for only a few species may notbe enough for the analysis of the product yields.

A hybrid approach is adopted to allow enough oilspecies to be included for a more realistic representationof the cracking process. In the two-step hybridapproach, a smaller number of major species are solved,coupled with the hydrodynamic calculation in the firststep and a much larger number of minor subspecies aresolved in the second step based on the flow fieldcalculated in the first step.

Hvdrodvnamic Formulation with ReducedReaction Mechanism

An FCC riser flow consists of gas, liquid, and solidphases. An FCC flow simulation should include all threephases. The gas species can be divided into two groups:major lumped species for the first-step calculation andminor subspecies for the second-step calculation. Themajor gas species

divided into a spectrum of size groups. The solid flowcontains the catalyst particles. The particles can also bedivided into various size groups.

The code calculates flow properties of all threephases. The gas flow properties to be calculated includepressure, density, temperature, velocity components, andspecies concentrations. The liquid properties includedroplet number density, temperature, and velocitycomponents for each size group. The solid propertiesinclude particle number density, temperature, velocitycomponents, and coke fraction for each size group. AnEulerian approach is employed to formulate governingequations of these properties. The governing equations

include the equations of state and those derived from theconservation laws of mass, momentum, and energy.

Gas Ecmations

The equations of state for the gas flow include theideal gas, the caloric, and the species unity equations.The ideal gas law gives a functional relationship amongpressure, temperature, and density. The caloric equationgives an expression of enthalpy in terms of temperature.The species unity equation says that the summation of allgas species mass fractions equals one.

The conservation equations derived for the gas flowinclude the continuity, momentum, enthalpy, and speciesequations. All the equations are elliptic-type partialdifferential equations. For convenience of numericalcalculation, the equations are put in a common form,

~ %3 Pu,#$-=) ‘ %,=, ax, ,

(1)

in which ~ is a general flow property for the scalar 1,velocity components u,, Uz, and us, enthalpy h, andspecies concentrations ~, G, fO,and fs; x,, xl, and X3arecoordinates; 0 is gas volume fraction; p and A areIaminar and turbulent viscosities; IS<is a diffusivitycoefficient for <; and S< is the source term of the &equation. Turbulent viscosity is determined from aturbulence model (see Multiphase k-e Section).

The source terms of the gas governing equations aremostly related to the interactions between phases and thecracking reactions. The source term of the continuityequation accounts for the mass generation from thedroplet evaporation (see Spray Evaporation Section).The source terms of the momentum equations accountfor the interracial drag forces from both droplets andparticles (see Interracial Interaction Section) and themomentum from the mass added by the evaporationprocess. The source terms of the enthalpy equationaccount for the droplet evaporation (see SprayEvaporation Section) and the interracial heat transferfrom both droplets and particles (see InterracialInteraction Section). The source terms of the feed oilequation account for the species generation from thedroplet evaporation (see Spray Evaporation Section) andthe species consumption of the cracking reaction (seeTime-Integral Lump Reaction Section). The source termof the dry gas equation accounts for the production ofdry gas from the cracking reaction (see Time-IntegralLump Reaction Section). The governing equations ofthe inert gases have no source term.

Dro~let Eauations

The liquid-phase formulation is based on anEulerian approach, which treats liquid droplets as acontinuous fluid. A spray of liquid oil is injected into anFCC riser. The spray consists of droplets of a size

spectrum. To compute liquid properties, the droplets aredivided into various size groups, k=l ,K. For the kthsizegroup, governing equations are derived to solve fordroplet number density n~~; velocity components ut~ i,where i= 1,3; and temperature To. A commo’nformulation of these equations for the droplets of the k’hsize group is given as:

–> -a -~ ---(fbpbk,k-r,~)=s,. (2)

in which ~ is a general droplet property for numberdensity, velocity components, or temperature; r isdroplet diffhsivity resulting from interaction withturbulence in the gas phase (See Turbulence Section),and S< is the sum of source terms.

The source terms of the droplet conservationequations are mostly related to the interactions betweenphases. The source terms of the droplet number densityequation account for the size shift of droplet numberdensity due to the evaporation process (see SprayEvaporation Section). The source term of the dropletmomentum equations accounts for the interracial dragforces from gas flow (see Interracial Interaction Section).The source terms of the temperature equation account forthe interracial heat transfer from both gas flow andparticles (see Interracial Interaction Section).

Particle Eauations

The solid-phase formulation is also based on anEulerian approach, treating solid particles as acontinuous fluid. Particles are also divided into varioussize groups. For each size group k, governing equationsare derived to solve for particle number density nP~,velocity components UP~i, i= 1,3, and temperature T :~,and coke fraction, C~. Coke has a strong impact on &ecracking reaction because it can deactivate the catalyst.A common formulation similar to Eq.(2) can be derivedfor the governing equations of the kthparticle size group.

The particle number density equation has no sourceterm. The source terms of the particle momentumequations account for the drag force from the gas flowand the shear stress and solid pressure through particle-solid interactions (see Interracial Interaction Section).The source terms of the particle temperature equationaccount for the heat transfer to/from gas and droplets(see Interracial Interaction Section). The source term ofthe coke equation accounts for the production of cokefrom cracking reactions (see Time-Integral LumpReaction Section).

Phenomenolozical Models

Phenomenological models are used to determineturbulent diffusivity and the source/sink terms of theabove-mentioned governing equations. A time-integrallumped reaction model is used to calculate the

generation and consumption rates of the oil species andcoke as the source terms of the species and cokeequations. A spray evaporation model is used tocalculate the droplet evaporation rates and translates theevaporation rates into a droplet size distribution shift.The evaporation rate is used in the source term of the gascontinuity equation and the sink term of the gas enthalpyequation. The shifi of the droplet size distribution isused to formulate the source/sink terms of the dropletnumber density equations. A mutli-phase k-c turbulencemodel is used to calculate turbulent viscosities anddifl%sivities of species and heat. Models of interracialinteractions are used to calculate the rates of interracialmomentum and heat transfer for the momentum andenergy equations of all three phases.

Time-Intemal Lump Reaction Model

The reaction model was developed based on a four-Iump kinetic model developed by Dave et al. [7]. Thefour-lump kinetic model considers four lumped oilcomponents in two cracking reactions. The four oillumps are feed oil, light oil, dry gas, and coke. Feed oilis the heavier oil components and the light oil is thelighter oil components, based on the boiling point. Thecutoff boiling point is arbitrarily chosen, e.g., 494 K.Dry gas is the oil vapor components of carbon numberlower than Cj. Coke is a byproduct of the crackingreactions.

Two cracking reactions used here are reaction (a),the feed oil cracking reaction that converts feed oil tolight oil, dry gas, and coke, and reaction (b) the light oilcracking reaction that converts light oil to dry gas andcoke.

P04a, P,+aJP~+ ajC, (a)

P,~blP~ + b2C~ (b)

where PO,P/, P~, C~represent feed oil, light oil, dry gas,and coke, respectively; al, al, a, b,, and b2 are mass

Lstoichiometric coefficients; and , and k2 are reactionrates. Reaction rates are generally expressed inArrhenius formulae, and the associated rate constants canbe extracted from pilot-scale test data. A methodologyof extracting these kinetic constants will be brieflydescribed in the Extraction of Kinetic Constants Section.

The reaction time scale is generally much shorterthan the flow time scale. A flow calculation may suffersevere numerical instability or stifbess problems due tothe large difference between the flow and the reactiontime scales (see Numerical Convergence Section). Atime-integral approach was developed to improvenumerical convergence and stability. The approachconverts the reaction time scale to the flow time scale byintegrating the reaction rate over a computational cell ofthe flow field. This approach [8] has been shown toyield a great improvement in numerical convergence andstability of computations. In the integral reaction model,

reaction rate as a function of computational cellresidence time is derived, taking into account thereaction rate changes induced by changing speciesconcentration as the flow proceeds through the cell.With this model, the reaction rate cannot be grosslyoverpredicted, and all of the feed oil vapor in a cellcannot be consumed in an iteration step. Thus, theoscillatory behavior of the differential reaction model iseliminated, and the reaction portion of the CFD code isnumerically stabilized.

SmaY Evaporation Model

The spray evaporation model provides (1) a dropletsize distribution for the injection spray, (2) sprayevaporation rate as the source term for the continuity andfeed oil species equations, and (3) the droplet sizeshifting rate as the source term for the droplet numberdensity equations.

Experiments show that droplets have a bell-shapedsize distribution in a spray. As the droplet radiusincreases, the number density function increases fromzero at zero radius to a peak and decreases aflerward.Based on the distribution fimction, droplet size groupscan be defined. The droplet number density of the sizegroup k is defined as the number of droplets of a radiusbetween r~.fand r~.

Vaporization causes droplets to shift from larger tosmaller size groups at a computed rate and also results intransfer of vapor from the droplets into the gas phase.The source term in the gas continuity equation is theevaporation rate of the droplets per unit volume. In theICRKFLO code, the droplet evaporation model is basedon the fundamental physics of stationary single dropletevaporation and then modified for large groups ofdroplets in a convective environment using correlations.For each droplet size group, the number densitydecreases due to the evaporation of the size group, butincreases due to the evaporation of the next larger sizegroup. The rate of number density change becomes asource term for the droplet number density equation ofthe droplet size group k. More details of the spray modelare given in Reference 9.

Interracial Interaction Models

FCC riser flow is a three-phase flow, including gas,oil droplets, and catalyst particles. In such a flow, thereare numerous interactions between phases. Theinteractions could be exchanges of mass, such asevaporation and coke deposition and transport, orexchanges of momentum and energy. The code includesthree interracial interaction models: a particle-solidinteraction model, an interracial drag model, and aninterracial heat transfer model.

Particle-Solid Interaction Model: The model has thecapability to predict a unique U-shaped particledistribution in a riser flow. In a riser flow, catalystparticles frequently collide with each other, and someparticles settle near the wall to form a U-shapeddistribution. The collision effect is neglected in mostCFD codes. This model derives a diffusive term by solidcollision based on the gradient of the local particle massflux. Solid diffisive terms are added to the particlemomentum equations.

Solid Pressure Model: Particles can be packed in ariser where the velocity is low or flow direction changes.When packed, particles are directly in contact with theneighboring particles and exert a solid pressure on otherparticles. The solid pressure is assumed to be a functionof local solid volume fraction when solid volumefraction exceeds a packed value, e.g., 0.6. The solidpressure is used in the source terms of the particlemomentum equations.

Interracial Heat Transfer Model: The model handlesthe heat transfer between (1) gas and droplets, (2) gasand particles, and (3) droplets and particles. Thegas/droplet and gas/particle heat transfer models useconventional Nusselt formulae with the slip velocity tocalculate the heat transfer rate. The slip velocity is thevelocity difference between gas and droplet or particle.The droplet or particle heat transfer model is new. Itaccounts for the conduction heat transfer between aparticle and droplet. This heat transfer is significantwhen droplets are much larger than particles or viceversa. The new model assumes particles collide with adroplet in the flow and conduction heat transfer occursfor each collision. The number of collisions betweenparticles and a droplet can be calculated based on aneffective collision volume. The effective collisionvolume is the sphere of a radius equal to the sum of theparticle and droplet radii. The collision between aparticle and a droplet results in conductive heat transferfrom the hot particle to the cold droplet. The heattransfer rate is calculated using the Fourier Law of heatconduction. The conduction heat flux is added to thesource terms of the droplet energy equation, and an equalamount of heat flux is subtracted from the source termsof the particle energy equation.

Interracial Drag Model: Oil droplets and catalystparticles are driven by the drag force from the gas flow.The drag force is used in the source terms of the gas,liquid, and solid momentum equations. Empiricalequations are commonly used to comelate the drag forcewith the slip velocity. The empirical drag coefficient isexpressed as a fi.mction of Reynolds and transfernumbers.

Multi~hase k-e Turbulent Model

A turbulent flow consists of a spectrum of rotationaleddies. The eddies, having a size ranging from a tiny,

‘?

techniques are employed to construct regions of complexgeometry in the mesh or mesh sections.

Grid Selection

The grid employed in the computation is a staggeredsystem. A momentum cell is used to solve for gasvelocity components, and a scalar cell is used to solvefor other flow properties. For each FCC flow simulation,a grid sensitivity study is conducted to select the finalgrid system, which gives independent numerical resultsto three significant decimal digits upon further gridrefinement. This approach conserves computational timewhile still providing adequately accurate results. Animportant feature of the control volume approach usedby the ICRKFLO code is that it is conservative in termsof mass, energy, species, and all variables solved for viathe transport equations, both locally and globally to avery high degree, regardless of grid size.

Blocked-Cell Technictue

Grid nodes can be excluded from a CFD calculationby marking them as blocked cells. A blocked cell isimpermeable to fluid flow and can be used to constructirregular boundq sutiaces. Rectangular blocked cellscan be easily implemented. However, a sloped contouris hard to fit smoothly with these cells, and stair-stepcomer cells are generated. Multiphase flow calculationsusing this approach tend to show unrealistic particlepileup in the comer cells, and sometimes the particlepileup leads to severe numerical instability.

A new triangular blocked-celI approach wasdeveloped to alleviate the numerical instability problemby fitting a diagonal or curved boundary contour moresmoothly. Formulation of a triangular blocked-cell issimilar to that of an open flow cell. The majordifference is that the flow volume and the propertydiffusivity length of a triangular blocked cell are onlyhalf of those of a regular flow cell. Slip or non-slipconditions are assumed for the liquid and solid phases onthe contoured wall. A sloped contour can be well fittedby triangular blocked ceIIs. Calculations were done bysolving the converging flow field using the newtriangular blocked-cell approach and the traditionalrectangular blocked-cell approach. Some calculationsusing the rectangular blocked-cell approach experiencedsevere numerical instability because the particles piledup in comer cells. For the same problem, the triangularblocked-cell approach achieved a stable, highlyconverged solution. Triangular blocked cells becomewedges in a three-dimensional grid.

Sectional Coupling Technique

A sectional coupling approach was developed forthe flow simulation of long riser reactors with bends.The approach consists of two major steps: (1) riser isrepresented by several straight tube sections, and (2) theflow field in each section is calculated using a CFDcode, e.g., ICRKFLO, in sequence, with the exit flowconditions of the previous section are used as the inletflow conditions for the next section. More detaileddiscussion can be found in Reference 13.

Numerical Conver~ence

A riser flow simulated by the authors generallyincludes four gas species, five to ten droplet size groups,a single particle size group, and a coke species carried byparticles. An FCC riser flow calculation is considered tohave converged if the local and global mass balances ofthe three phases are smaller than a set of predeterminedcriteria. A convergence study was conducted todetermine convergence criteria, defined by the averagemass residual of all computational cells. To have areasonably converged solution, the criteria need to be 1010(in dimensionless form, normalized by the inlet massflow rate) for the gas phase and 109 for both the liquidand solid phases. Generally in this application, withreasonable boundary conditions (inlet flow rates etc.), aconverged solution can be obtained in about 2000 globaliterations. Each global iteration includes ten gas phaseiterations and three liquid and solid phase iterations. Ona PentiumTMII 300 personal computer with 64 megabytesof random access memory, using a 32-bit FORTRANcompiler, a flow computation of about 10,000 nodestakes about 6 hours. The computational time increaseswith increased nodes. If a numerical instability isencountered, a computation never converges.

Numerical Instabilities

Numerical instabilities are often encountered in aflow calculation. Many of them are due to programmingemors; some are a consequence of the non-linearity ofthe equations; some are caused by singularities in theflow system; and some arise horn the discretized numbersystem on the computer. The programming errors, aslong as one can find them are easy to correct. As for theother two types of numerical problems, to find them isone thing and to resolve them is another. The resolutionof these numerical problems usually requires thedevelopment of new formulations and/or new numericalroutines.

Programm ing Errors: The authors found two veryeffective procedures to find and correct programmingerrors. One procedure concerning the flow symmetryincludes the following steps: (1) run a fill symmetricflow calculation, (2) compare the computed flowproperty numbers at two corresponding locations, and

(3) if the results are asymmetric, trace the computationalsteps back to the initial occurrence of the asymmetry.The other procedure concerning the mass and energybalances includes the following steps: (1) check globalmass and energy balances, and (2) if mass or energy doesnot balance, isolate the source of the imbalance and fixit.

Numerical Stiffness due to Fast Reactions: Reactionand flow time scales are often different by one or moreorders of magnitude. The difference of time scales cancause severe numerical stifiess problems. If thedifferential Arrhenius rate formulation is directly used inthe source term of a lumped species equation during theflow field computation, a numerical calculation oftendiverges or becomes unstable. The numerical problemcan be explained as follows. If a computational cell hasa high concentration of feed oil vapor and a hightemperature in the early stages of an iteration routine,then a very high reaction rate is predicted from thedifferential rate equation. This procedure, predictingonly an initial reaction rate for the cell, may lead to agreatly overpredicted reaction rate. This overpredictionmay occur even when an upper bound is placed on thereaction rate via the eddy breakup model. Theoverprediction is often great enough to cause all the feedoil vapor to be consumed in that cell for that iteration.So,.in the next iteration, the cell will contain oil productsonly, and the predicted reaction rate for that nextiteration step will be zero because of the zero reactantconcentration. During that next iteration with predictedzero reaction rate, the flow may bring in a largeconcentration of feed oil vapor, which will remain toyield a high reactant concentration in the third iterationof this sequence. Clearly, this sequence ofcomputational events may repeat endlessly, causingeither divergence of the computation or a continuingoscillation. A time-integral approach was developed toimprove numerical convergence and stability (see Time-Integral Lumped Reaction Model Section).

Exit Boundarv Fiow Conditions: The free flowboundary condition is often used as a reasonableapproximation at the outflow exit for a non-reacting flowcalculation because the computation is or can bestructured so that the flow is nearly filly developed atthe exit boundary. However, the free flow boundarycondition for a multiphase reacting flow calculation isnot as successfid. In the simulation of reacting flows,reaction often continues up to or very close to the exitplane (if it did not, the reactor would be larger thannecessary), and consequently the flow is often neveradequately developed to the point where the free flowboundary condition can be applied. In these cases, thecalculation generally converges poorly and sometimesdiverges. In calculating an FCC riser flow with the freeflow boundary condition, the authors found that thecalculation was not converged and the average massresidual was only 10-6. Instead of using the fi-ee flow

conditions, a velocity gradient was assumed at theoutflow exit. The gradient was calculated by balancingglobal mass flow after every solution iteration. By usingthe new boundary treatment, the FCC flow calculationconverged with an average mass residual less than 10-1O.For multiphase reacting flow systems, outflow boundarytreatments need to be examined care fidly, andappropriate treatments need to be developed.

Other Numerical Instabilities: Other numericalinstability problems that the authors have experienced ina CFD calculation are listed here without discussion: (1)flow reversal point where a velocity component changessign, (2) stagnation point where zero velocity iscalculated, (3) high heat transfer rate between phases, (4)the onset of droplet vaporization, (5) the time scaledifference between the flow of different phases, and (6)the difference between a continuous finction used in theformulation and a discretized fimction used in thecomputation. Due to the length limit on this paper, thediscussion of these problems will be deferred to futurepublications.

Code Validation

A CFD code solves approximate algebraic equationswith iteration routines. Even when a numericalcomputation converges, the result may still be differentfrom the true solution of the governing equations.Validation with experimental data is needed to justifyconfidence in a numericaI simulation.

ICRKFLO has been validated with experimentaldata obtained from pilot- and commercial-scale FCCunits. Good agreement was found between computedresults and experimental data.

An FCC riser flow exhibits a U-shaped radial solidvolume fraction profile. Many CFD codes havedifficulty in predicting such a profile. By using the newparticle-solid interaction model, ICRKFLO can predictthe U-shaped profile very well. The pressure dropspredicted by ICRKFLO also are found to be in goodagreement with the measured values [14].

In a study of a thermal cracking process, ICRKFLOdemonstrated its capability to predict product yields offour major lumps, pressure drop, and temperatures [15].In a recent study of FCC riser flows, an experimental testmatrix was selected and experiments were run. Thepredicted subspecies concentrations showed goodagreement with experimental data (see Results andDiscussion).

Results and Discussion

A CFD code for FCC riser reactor can be used forseveral purposes: (1) to provide detailed flowinformation that is related to the performance of thesystem; (2) to evaluate the impact of operatingconditions, e.g., temperature, catalyst to oil ratio, etc., on

the performance of the system; (3) to determine optimaloperating conditions of the system; and (4) to exploreinnovative concepts to improve the performance of thesystem.

A major function of the ICRKFLO code is to predictproduct yields of a FCC riser reactor. Figure 3 shows thecomputed and measured product yields at variousoperating temperatures and catalyst-to-oil (C/0) ratios ofan FCC riser. In the figure, the yields are plotted againstvarious products, i.e., gasoline, diesel, liquid petroleumgas (LPG), and heavy oil. Product yields of twooperating conditions are compared. At the highertemperature and C/O ratio, there is more LPG andgasoline and less diesel and feed oil. The dotted lines inFigure 3 represent the experimental measurements. Thepredicted product yields show good agreement with theexperimental data.

high4 A ‘-

----highT&C/O(m)

low IJ x

~~~

—high T& C/O (c),’ . . . . .r’ - low T & C/O (m), !

: : ,, ~ low T & C/O (C).-; : -- .- .,.

. .

.---

LPG gasoline diesel heavy oil

Figure 3 Comparison of Computed and MeasuredProduct Yields at Various Operating Conditions

ICRKFLO has been used for various optimizationstudies. Figure 4 shows an example of the investigationof the impact of feed oil injection conditions on theproduct yields. Calculated yields of feed oil andgasoline are plotted versus spray injection Reynoldsnumber. In the figure, the diamond and square pointsrepresent computed feed and light oil concentrations,respectively. These points appear to be very wellcorrelated and can be represented by two simple curvesas shown in the figure, a solid line for light oilconcentration and a dotted line for feed oilconcentration. A minimum and a maximum are foundon the feed oil and the light oil curves, respectively.Since the oil conversion rate of an FCC unit is generallydefined as one minus the feed oil concentration, theminimal feed oil yield is also the maximal oil conversionrate. This computational result suggests that maximumoil conversion rate and gasoline yield can be achieved byadjusting the feed injection Reynolds number.

55

I

+ FeedOil■ Gasoline

50

0.0 0.2 0.4 0.6 0.8 I ,0 1.2

RM .0E+6

Figure 4 Product Yields vs. Injection Reynolds Number

ICRKFLO can also be used for the investigation ofinnovative FCC concepts, e.g., short-contact-timereactors and multistage reactors. Computational results[16] show that hydrodynamic processes, i.e., mixing andevaporation, have a strong impact on the product yieldsin a short-contact-time FCC riser unit.

Summary

Argonne National Laboratory has developed acopyrighted code, ICRKFLO, for the development ofadvanced multiphase reacting flow systems. It employsa hybrid hydrodynamic-chemical kinetic couplingtechnique and has been successfully applied to thesimulation of FCC riser flows. ICRKFLO solves forflow properties of all three phases (gas, liquid, and solid)locally in an FCC riser flow, with models governing thetransport of catalyst particles and feed oil droplets, thevaporization of the feed oil droplets, the cracking of theoil vapor, and the formation and deposition of coke onparticles. The code was validated by comparingcomputational results with experimental data for variouscases. The validated code was used to study the impactsof operating and design conditions on the product yieldsof an FCC riser reactor. The ICRKFLO computer codecan be a very usefi,d tool to use in optimizing riserperformance for specific operating conditions andperformance goals, such as maximizing valuable productyields.

Acknowledgments

This work was supported by U.S. Department ofEnergy (DOE), Assistant Secretary for EnergyEftlciency and Renewable Energy, under Contract W-31- 109-ENG-38 and managed by the DOE OffIce ofIndustrial Technology.

References

[1] Bienstock, M.G., D.C. Draemel, P.K. Ladwig, R,D.Patel, and P.H. Maher, “A History of FCC ProcessImprovement through Technology Development andApplication,” AIChE Spring National Meeting, Houston,TX (1993).[2] Weekrnrm, V.W., and D.M. Nate, “Kinetics ofCatalytic Cracking Selectivity in Fixed, Moving, andFluid Bed Reactors;’ AIChE Journal, 16(3):397-404(1970).[3] Jacob, S.M., B. Gross, S.E. Voltz, and V.W.Weekman, “A Lumping and Reaction Scheme forCatalytic Cracking: AIChE Journal, 22(4):701-713(1976).[4] Nigam, A., and M.T. Klein, “A Mechanism-Oriented Lumping Strategy for Heavy HydrocarbonPyrolysis: Imposition of Quantitative Stmcture-Reactivity Relationships for Pure Components,” Ind.Eng. Chem. Res., 32:1297-1303 (1993).[5] Quann, R.J., and S.B. Jaffee, “Building UsefidModels of Complex Reaction Systems in PetroleumRefming~’ Chemical Engineering Science, 51(10):1615-1635 (1996).[6] Theologos, K.N., I.D. Nikou, A.I. Lygeros, andN.C. Markatos, “Simulation and Design of FluidCatalytic-Cracking Riser-Type Reactors,” AIChEJournal, 43(2):486-494 (1993).[7] Dave, N.C., G.J. Duf@, and P. Udaja, “A Four-Lump Kinetic Model for the Cracking/Coking ofRecycled Heavy Oil,” Fuel, 72(9): 1331-1334 (1993).[8] Chang, S.L., and S.A. Lottes, “Integral CombustionSimulation of a Turbulent Reacting Flow in a Channelwith Cross-Stream Injection,” Numerical Heat TransferPart A, 24(1):25-43 (1993).[9] Chang, S.L., S.A. Lottes, C.Q. Zhou, and M.Petrick, “Evaluation of Multiphase Heat Transfer andDroplet Evaporation in Petroleum Cracking Flows;’HTD-VO1.335, Proceedings of the ASME Heat TransferDivision 4:17-27, International Mechanical Engineering

Congress and Exposition, Atlanta, GA (November 17-22, 1996).[10] Patankar, S.V., and D.B. Spalding, “A CalculationProcedure for Heat, Mass and Momentum Transfer inThree-dimensional Parabolic Flows: Int. J. Heat MassTransfer, 15:1787 (1972).[11] Zhou, X.Q., and H.H. Chiu, “Spray GroupCombustion Processes in Air Breathing PropulsionCombustors:’ AIAAISAEIASME 19th Joint PropulsionConference, Seattle, WA, AIAA-83-1323 (1983).[12] Chang, S.L., C.Q. Zhou, S.A. Lottes, B. Golchert,and M. Petrick, “Methodologies of Extracting KineticConstants for Multiphase Reacting Flow Simulation”Proceedings of 1997 Conference of CombustionFundamentals and Applications, Point Clear, AL, pp.348-353 (April 27-29, 1997).[13] Chang, S.L., C.Q. Zhou, S.A. Lottes, J.X.Bouillard, and M. Petrick, “A Sectional CouplingApproach for the Simulation of Multiphase ReactingFlow in a Bent Reactor:’ HTD-VOI. 335, Proceedings ofthe ASME Heat Transfer Division 4:361-373,International Mechanical Engineering Congress andExposition, Atlanta, GA (November 17-22, 1996).[14] Golchert, B.M., S.L. Chang, and M. Petrick,“Investigation of Particle/Gas Flow Characteristics inLong Pipelines,” AIChE 1998 Annual Meeting, Miami,FL (November 15-20, 1998).[15] Chang, S.L., S.A. Lottes, and M. Petrick,“Development of a Three-Phase Reacting FlowComputer Model for Analysis of Petroleum Cracking,”Proceedings of 1995 Mid-America Chinese ProfessionalAnnual Convention, Itasca, IL, pp. 281-288 (June 23-25,1995).[16] Chang, S.L., S.A. Lottes, C.Q. Zhou, and M.Petrick, “A Numerical Study of Short Residence TimeFCC Riser Flows with a New Flow/Kinetics ModelingTechnique,” HTD-VO1. 361, Proceedings of the ASMEHeat Transfer Division 2:83-90, InternationalMechanical Engineering Congress and Exposition,Anaheim, CA (November 15-20, 1998).