SIMULATION OF FLUID CATALYTIC CRACKING RISERS A SIX LUMP MODEL

Transcription

1 Proceedings o the 11 th Brazilian Congress o Thermal Sciences and Engineering -- ENCIT 2006 Braz. Soc. o Mechanical Sciences and Engineering -- ABCM, Curitiba, Brazil,- Dec. 5-8, 2006 SIMULATION OF FLUID CATALYTIC CRACKING RISERS A SIX LUMP MODEL Paper CIT Cezar Otaviano Ribeiro Negrão Universidade Tecnológica Federal do Paraná UTFPR, Programa de Pós-graduação em Engenharia Mecânica e de Materiais PPGEM, Laboratório de Ciências Térmicas LACIT, Av. Sete de Setembro, 3165, , Curitiba-PR. negrao@ceetpr.br Fábio Baldessar Universidade Tecnológica Federal do Paraná UTFPR, Programa de Pós-graduação em Engenharia Mecânica e de Materiais PPGEM, Laboratório de Ciências Térmicas LACIT, Av. Sete de Setembro, 3165, , Curitiba-PR. Abstract. The current work presents the modeling o the riser o Fluid Catalytic Cracking (FCC) Units. The low and the cracking reactions are considered two-phased (luid and solid), one-dimensional and steady. Mass, momentum and energy equation are admitted or luid and solid phases. The inite dierence method was used or the solution o the ordinary dierential equations. A six lump kinetics model is employed to evaluate the gasoil, gasoline, LPG, uel gas, light cycle oil (LCO) and coke lumps. A eedstock vaporization approach is described. Comparisons o the six with a our lump model was conducted and o the vaporization model with instantaneous vaporization were conducted. The results reveal the vaporization has inluence on the product composition at the riser outlet. Besides, the kinetics models also is very important on the cracking reactions. Keywords. FCC, six lump model, vaporization, mathematical model, simulation. 1. Introduction The catalytic cracking (FCC) is one o the most important chemical processes developed during the last century. Today, FCC is responsible or almost 50% o all gasoline produced in the whole world. This process breaks the larger molecular weight ractions o oil into smaller ones, such as gasoline, LPG (Liqueied Petroleum Gas) and LCO (Light Cycle Oil). The FCC is a complex operation process due to the high sensitivity to its boundary conditions and several disturbances o dierent sources. The modeling o FCC is quite complicated because the complex luid dynamics (turbulence and gas-solid low) and the cracking and combustion kinetics. There are several works in the literature that deal with modeling o FCC units at dierent level o rigor. Weekman (1968) was one o the irsts, which presented a kinetic model or riser catalytic cracking a three lump model. Jacob and Weekman (1976) presented a ten lump model or the kinetics in the riser. All the riser kinetics models employed today are based on Weekman (1968) and Jacob and Weekman (1976) models, such as, the Lee s et al. (1989) our lump model, the Pitault s et al. (1994) and Juarez s et al. (1989) ive lump models and the Martignoni s (2000) six lump model. Others presented the modeling o all FCC. For example, the McFarlane et al. (1990) simulated dynamically the ESSO model IV FCC Unit, employing a our lump model or the riser; Malay et al. (1999) and Han and Chung (2001) used a our lump kinetics model, considered the low as one-dimensional in the riser and admitted the regenerator composed o two regions; Santos (2000) modeled the REFAP s (Reinery Alberto Pasqualini) FCC Unit and used the Jacob s and Weekman (1976) model or the riser and a two region model or the regenerator; Erthal (2003) applied the Han and Chung s (2001) model or the riser, the Melo s (2003) model or the stripper/separator vase and the Penteado s (2003) model or the regenerator. He simulated the FCC pilot plant o SIX/PETROBRAS. In the current work, a six lump and a eed stock vaporization models were added to the Erthal s riser model. Comparisons o the six and our lump models were conducted. Besides, the results o instantaneous vaporization with o vaporization model were compared. 2. FCC Description Figure 1 illustrates a FCC plant which is basically composed o: Riser, Separator vase, Stripper and Regenerator. The FCC operation can be summarized as ollow. At the riser inlet, the eedstock charge, at 200 o C, is placed in contact with a catalyst (particles) stream at a higher temperature (700 o C). The energy provided by the catalyst is enough to heat, vaporize and produce cracking reactions in the eedstock. Due to the high temperature and to the catalytic properties o the medium, the eedstock molecules are broken, resulting in lighter composites and coke. Coke consists basically o carbonic chains, not cracked, hydrogen and aromatic compounds with characteristics o graphite and it is responsible or deactivation o the catalyst. The catalyst is dragged by the vaporized load as a consequence o its density variation. In case the reactions were not interrupted, the products at the riser outlet would be only carbon,

2 Proceedings o ENCIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT methane and hydrogen, which do not have commercial value. Thereore, at the riser outlet, the mixture goes to a separator vase, where the products are separated rom catalyst by cyclones. Ater pass through a stripper, the particles are delivered to a regenerator where the coke is burnt and the catalyst is reheated. The reactivated catalyst goes back to the riser, completing the cycle. 3. Mathematical Model The riser model considers the gas-solid low as one-dimensional, two-phase and adiabatic. As the riser residence time is quite small compared to the response time o the other components, any change in the riser inlet will almost instantly aect the conditions at the riser outlet. Thereore, the riser model is considered quasi-static and the time change is neglected in the energy conservation equations. Products SEPARATOR VESSEL E-2 STRIPPER RISER Combustion gas REGENERATO R Spent Catalyst Air Regenerated Catalyst Gasoil and lit steam Figure 1 - Simpliied scheme o a FCC Unit Momentum Conservation The momentum conservation equation or both phases, gas and solid, can be written as: 2 ( ) ( ) d ρε i ivi d Pεi 4τ piεi = ρiεi g ± FDεi dz dz d r (1) where the index i means either the solid or luid phase, ε is the volumetric raction, z is the vertical position, ρ is the density and v is the low velocity. P is the pressure and d r is the riser inner diameter. τ pi is the shear stress between the wall and the phase i and F D is the drag orce Mass Conservation The mass conservation equation is required or the evaluation o the solid raction (ε c ) along the riser: ε = c c ρ va c c r (2) c is the catalyst mass low rate and A r is the riser cross- where v c is the catalyst velocity, ρ c is the catalyst density, section area. The luid raction is obtained by:

3 Proceedings o ENCIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT ε = 1 ε (3) c 3.3. Energy Conservation The luid phase temperature is evaluated by the heat balance: dh Ar = q Rρε + α A e T c T dz ( ) (4) where is the mass low rate o the luid. T g and T c are the gas and catalyst temperature, respectively. α is the convection heat transer coeicient, A e is the ratio o catalyst surace area and catalyst volume (Han and Chung, 2001) and q R is the heat o reaction, which depends on the kinetics model. For the our-lump kinetics model, the heat o reaction is (Han and Chung, 2001): q R = H12k12 ygo + H13k13 ygo + H14k14 ygo + H23k23 ygl + H24k24 y gl φc (5) where y go and y gl are, respectively, the gasoil and gasoline raction. The H ij s are enthalpy o reactions to convert i lump into j lump. The heat o reaction or the six lump kinetics model (Martignoni, 2000) is: q R H Ω M + H Ω M = ρε go go wgo cq cq wcq c φ (6) where M go and M cq are the gasoil and coke molecular mass, respectively. Ω go and Ω cq are the mass reaction ratios o gasoil and coke, respectively. H cp is the coke enthalpy o reaction and H go is the gasoil enthalpy o reaction. Two vaporization approaches are considered: i) instantaneous vaporization: the eedstock vaporizes as soon the catalyst get in contact with it and; ii) one-dimensional vaporization: the vaporization takes place as the eedstock lows. i) Instantaneous vaporization For the instantaneous vaporization o the eedstock at the riser inlet, the luid is considered an ideal gas and the luid enthalpy is admitted a unction o the temperature. Thereore, Eq. (4) becomes: dt c A q A T T dz ( ) RS p = RS RS Rρε + α e c (7) where c pg is the speciic heat o the gas phase. ii) One-dimensional vaporization For the one-dimensional vaporization, a distillation curve is employed (Baldessar, 2005): Xvap = T (8) where X vap is the gasoil vaporized raction (dimensionless) and T is the luid temperature ( o C). Equation (8) is valid rom 46.5 to o C. The gasoil liquid and gas phases take place together during a certain period within the riser and thereore, the enthalpy o the mixture is computed by: h = h X + (1 X ) h v vap vap l (9) where h and h l are, respectively, the enthalpy o the gas and liquid phases. By employing the Farah s (2003) data, the ollowing correlations were it: h T T 2 v = (10) h T T 2 l = (11)

4 Proceedings o ENCIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT where h l and h g are in kj/kg and T, in ºC. Equations (10) and (11) are valid rom 46.5 to o C. As soon as h is known, the T can be evaluated by the combination o Eqs. (7), (8), (9) and (10). The energy balance or the solid phase can be evaluated by: dtc mc c pc = Arα Ae( Tg Tc) (12) dz 3.4. Conservation o Chemical Species The source or sink o each species can be computed by: dy = ρ ε A Ωφ dz i RS i c (13) where y i is the mass raction o each lump, ρ is the luid density, ε is the luid volumetric raction. φ c is the catalyst deactivation unction (Han and Chung, 2001) and Ω i is reaction rate o each lump per unit o mass, deined or the our lump model (Erthal, 2003): Ω = k y (14) n i ik i and or the six lump model (Martignoni, 2000): i 1 * n N j * nj ρc ( Mk ( C) ) ( Mk( C) ) ( 1 ε ) Ω = r i j ji j i ij i j= i j= i+ 1 m d (15) where k ij is the constant o kinetics calculated by the Ahrenius law, C * is a pseudo concentration (Martignoni, 2000) and n is the reaction order. 3.5 Density Although ater cracking the catalyst is covered by coke, its density is considered constant in the current work. On the other hand, the gas density is computed by the ideal gas equation: PM ρ = (16) RT where M is the molecular weight o the gas phase, R is the ideal gas constant. The molecular weight o the gas phase is calculated as a unction o the mass raction, y i, and o the molecular weight o each lump, M i : M = 1 yi M i (17) 4. Method o Solution The domain is divided into a series o nodes along the riser and the conservation equations are discretized by the inite dierence method. The boundary conditions o the problem are: pressure, temperatures and mass low rates o gasoil, catalyst and steam at the riser inlet. The discretized equations are thus solved sequentially rom the bottom to the top o the riser. Fluid and catalyst temperatures, catalyst and luid velocities lump ractions, volumetric solid raction, volumetric luid raction, gas density and pressure are computed at each node along the riser height. In compressible luid lows, the state equation (16) is usually employed to evaluate the low pressure and the continuity equation is used to compute the density. This procedure is appropriate because density is quite sensitive to pressure changes. In case o incompressible lows, the density is insensitive to pressure changes. Thereore, during an iterative solution, the density value is not correct at the beginning o the solution process and small density discrepancies will cause large pressure oscillation (equation (16)). Despite the riser low being compressible, the density changes basically by temperature and molecular mass variations. The pressure drop along the riser is mainly

5 Proceedings o ENCIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT caused by riction and does not aect density. Thus, the algorithm to solve compressible lows is not appropriate or this case and an alternative one should be applied. The density will be computed by employing the state equation (16) and a pressure correction algorithm based on the continuity equation will be used (Patankar, 1980). The pressure is thus corrected according to the ollowing equation: ( ρ ε ) ( ) i i 1 i i i 2 2 P = P + K v A m n n (18) the superscript i corresponds to the current iteration, n is the node being evaluated and K is an under-relaxation actor which must be appropriately chosen. is the gasoil mass low rate which is a constant known value. A high value o K may not conduct to convergence and a very tiny value makes the solution process very slow. Usually, the division o i i i K by ten increases three times the solution time. As long as value is dierent rom the ρ vε A value, the pressure is corrected. Thereore, the pressure is corrected to satisy the continuity equation. The convergence in each grid node is evaluated by two criteria: a) Relative residue o the momentum conservation equation or a particular node, or both phases, luid and solid: i i i Pnε j, n + Psε j, s 4τ i i i j, n i i j ( vj, n vj, s) ρj, ngε j, n ± FDεc, n A z z dr Error mv j j, s (19) and, b) Relative residue o the mass conservation equation: R mass i i i i ρvρε A = Error (20) where the numerator o the equations are, respectively, the residues o momentum and mass o the node. The denominators are, respectively, the momentum value at the previous evaluated node, s and the luid mass low rate, which is a known value. The subscripts n and s are, respectively, the current and the previous evaluated nodes. The convergence is considered when all three residues (mass, momentum o luid and solid phases) are smaller than the Error value. 5. Results and Discussions This section presents comparisons o the current work with the Erthal s (2003) results that employ a our lump kinetics model and instantaneous vaporization. Sensitivity analyses o the kinetics and vaporization models are conducted. Table 1 presents the operational and boundary conditions o the riser (Martignoni, 2000) and will be employed to compare with the Erthal s (2003) results. The ollowing approaches are considered in the comparison: a) The our lump kinetics model with instantaneous vaporization (Erthal s (2003) results); b) The our lump kinetics model with one-dimensional vaporization; c) The six lump kinetics model with one-dimensional vaporization; This section discusses the composition o the products, velocity and temperatures along the riser. Two analyses are considered: the sensitivity o the model results, regarding the vaporization approaches and kinetics models Comparison o Vaporization Models Figures 2 and 3 show the comparison o the product compositions along the riser or the our lump model with instantaneous and one-dimensional vaporization. The one-dimensional vaporization model aects the composition o the gasoil by 10% at the riser outlet. The higher consumption o gasoil in the one-dimensional vaporization is the result o higher temperatures reached at the end o vaporization. One can see the gasoil mass raction changes almost instantly to 0.89, which corresponds to approximately 50% o total eedstock. The other 11% is regarded to steam content. The vaporization continues almost linearly reaching 93% o the mass raction the complete evaporation o the gasoil. From this point on, the cracking reactions and the gasoil amount start to diminish. On the other hand, in the instantaneous vaporization, the gasoil mass raction reaches 0.93 at the riser inlet and its amount starts to reduce immediately because o the cracking reactions. On the one-dimensional vaporization model, 49% o eedstock

6 Proceedings o ENCIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT vaporizes within the irst inite dierence node due to the high quantity o heat transerred to it. The vaporization inishes 10cm above the riser inlet. The cracking reactions only take place ater the complete vaporization. Table 1. Boundary conditions, thermophysical properties and geometry data o the riser (Martignoni, 2000). Boundary conditions Mass low rate o gasoil (kg/h) 170 Mass low rate o steam (kg/h) 11 Inlet pressure at the riser inlet (bar) 2.5 Steam inlet temperature (K) 500 Gasoil inlet temperature (K) 500 Inlet temperature o catalyst (K) 993 Thermophysical properties Catalyst density (kg/m 3 ) 1400 Catalyst speciic heat (kj/kg K) 1.09 Gasoil density (kg/m 3 ) 26 Steam density (kg/m 3 ) 0.7 Steam speciic heat (kj/kg K) 2.0 Dynamic viscosity o the gaseous phase (kg/m s) 1.4x10-5 Geometry Height o the riser (m) 18 Diameter o the riser (m) The beginning o the gasoline ormation occurs almost simultaneously in both models, as shown in Figure 4 and 5. On the one-dimensional vaporization model, the temperature is higher than on the instantaneous vaporization and thereore the cracking reactions accelerate. The same tendency shown or the gasoline was observed or the uel gas and coke the ormation start at the same position or both models. Besides, the one-dimensional vaporization model presents higher gasoline and uel gas production and higher gasoil consumption. The higher temperature o the onedimensional vaporization is responsible or that. Additionally, the one-dimensional vaporization model presents a lower velocity at the riser inlet than the instantaneous vaporization model, as the vaporization does not take place at once (see Figure 7). Ater the complete vaporization, the increase o the density causes an acceleration o the luid and its velocity reaches a higher value than the instantaneous vaporization counterpart. This takes place along the irsts centimeters rom the riser inlet. Aterwards, both curves become similar. However, because o the initial acceleration, the one-dimensional vaporization velocity remains higher. Figure 6 shows the behavior o the luid velocity or both models along the whole riser Kinetics Model Comparison In order to compare the our and six lump models, the composition o gasoil and LCO are added orming one lump and uel gas and LPG, another one. Note the dierence between the models is basically on those lumps. The comparison assumes one-dimensional vaporization in the riser. Figure 8 and 9 show the evolution o gasoil and gasoline composition along the riser. As shown, the gasoil composition ater vaporization is almost the same or both models. Aterwards, the six-lump kinetics model reduces rapidly the gasoil mass raction. In the six lump model, almost all cracking reactions take place near the riser inlet. From 4.0 m high on, the gasoil mass raction becomes almost constant. On the hand, the our-lump model produces an almost constant gasoil mass raction reduction. Thereore, at the riser outlet both models provide the same gasoil mass raction. The gasoline composition shows a similar proile. In other words, the gasoline mass raction or the six lump model increases very ast near the riser inlet almost all gasoline is ormed by 4.0 m high. Ater 10,0 m high, the composition almost does not change, indicating the remaining o the riser length is not necessary. Although the gasoline ormation rate or the our-lump model is smaller its mass raction is almost the same at the riser outlet the dierence is under 3%. The uel gas mass raction proile along the riser is similar to the gasoline one. The values or both kinetics models at the riser outlet are shown in Table 2. As shown, the dierences are small or either gasoil, gasoline or uel gas. The percent dierence is reerred to the total mass o the gases at the riser outlet. As shown in Figures 8 and 9, the results o the our lump model shows a large derivative at the riser outlet, indicating a taller riser would be necessary to reach the complete conversion. However, measured data show the products are basically ormed near the riser inlet (Martignoni, 2000). Thereore, the six-lump model would be more appropriate or the current case. The gas velocity or the six lump model presents a higher acceleration near the riser inlet because the greater reduction o the gas density. On the other hand, the gas velocity or the our-lump model has a sudden change ater vaporization but does not reach its counterpart value. In the latter, the cracking reactions are distributed along the riser

7 Proceedings o ENCIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT providing a higher acceleration aterwards. The gas velocity proile or both kinetics models are shown in Figure 10. The gas velocity is also very similar or both models at the riser outlet. The temperature proile or the six lump model changes suddenly and aterwards its value remains almost constant, indicating the cracking reactions take place near the riser inlet. For the our-lump model, the temperature proile is similar to its counterpart near the riser inlet, however, ater the reaching the maximum, the temperature starts to decrease as the cracking reactions continue to occur (see Figure 11). 5.3 Comparison with Experimental Results Figures 12 and 13 show a comparison o the measured data using the six-lump model results or dierent riser heights. Note the dierences are considerable. As the kinetic constants are dependent on the eedstock and catalyst, the discrepancies must be related to a dierent eedstock employed in the development o such constants Figure 2. Gasoil mass raction along the riser or the two vaporization models. Figure 3. Gasoil mass raction along the irst 200 mm rom the riser inlet or the two vaporization models. Table 1. Mass raction o the dierent products at the riser outlet or both kinetics models. 4 lumps 6 lumps Dierence (%) Gasoil Gasoline Fuel Gas In order to reduce the discrepancies, Souza (2004) itted the six-lump model to the measured data by solving an inverse problem. He matched the model to experimental data provided by PETROBRAS (2001), correcting the value o H go and the kinetic constants (see details in Souza (2004)). A new comparison was thus conducted, considering the constants o Souza (2004). Figures 14 and 15 show a new comparison and also include the Souza s (2004) results. Note that the correction approximates considerably the computed values to the experimental results. Despite the Souza s (2004) hydrodynamic model being incompressible and two-dimensional, dierent rom the present one-dimensional and compressible model, the results are quite close. Thereore, one can say the mass ractions o the products are slightly dependent on the low hydrodynamic and strongly dependent on the kinetic o the reactions. 6. Conclusions This work presents a simulation model or a luid catalytic cracking riser. A comparison o two kinetic models (six and our-lump models) is discussed. The conservation equations o momentum, energy and mass are employed in the modeling and the low is considered two-phased (solid and luid phases), one-dimensional and quasi-static. The inite dierence method was used to solve the ordinary dierential equations. The results showed to be very sensitive to the vaporization model, because o the temperature proile. The higher the temperature provided by the one-dimensional vaporization model the higher eedstock conversion at the riser outlet. Thereore, the vaporization is an issue that should receive attention. Although the our and six-lump models produce similar results at the riser outlet the irst does not predict two lumps o great commercial interest LPG and LCO. Besides, the six-lump model yields a higher conversion near the riser inlet, causing asymptotic proiles o product composition at the riser outlet. On the other hand, the composition rate is

8 Proceedings o ENCIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT almost constant along the whole riser or the our-lump model. According to experimental data (PETROBRAS, 2001), the cracking reactions occur mostly near the riser inlet, demonstrating the six-lump model is more appropriate to represent the kinetics than the our-lump one. Figure 4. Gasoline mass raction along the riser or the two vaporization models. Figura 5. Gasoline mass raction along 1.0m rom the riser inlet or the two vaporization models. Figure 6. Fluid velocity variation along the whole riser or both vaporization models. Figure 7. Fluid velocity variation along 200mm rom the riser inlet or both vaporization models.

9 Proceedings o ENCIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT Figure 8. Gasoil mass raction or both kinetics model along the riser. Figure 9. Gasoline mass raction or both kinetics models along the riser. Figure 10. Fluid velocity or both kinetics models along the riser.

10 Proceedings o ENCIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT Figure 11. Fluid temperature or both kinetics models along the riser. The six-lump model, as proposed by Martignoni (2000), presents discrepancies with experimental data. The discrepancies are mainly related to the dierent eedstock and catalyst, employed in the development o the model. In order to reduce the discrepancies, Souza (2004) proposed to it the model to the experimental values. The Souza s (2004) itted data produced a signiicant improvement to the current model, approximating the computed values to the experimental ones. 7. Acknowledgements The authors would like to thank CAPES or the master degree scholarship provided to Eng. Fabio Baldessar and to PETROBRAS or the necessary inormation to accomplish the work. Additionally, the authors acknowledges the inancial support o ANP/FINEP by means o the Human Resource Program o ANP or the gas and oil sector PRH ANP/MCT (PRH 10 UTFPR). Figure 12 Measured and computed gasoline and LCO mass ractions at dierent riser heights.

11 Proceedings o ENCIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT Figure 13 Measured and computed LPG, coke and uel gas at dierent riser heights. Figure 14 Measured and computed gasoline and LCO mass ractions at dierent riser heights with the itted data o Souza (2004). Figure 15 Measured and computed LPG, uel gas and coke mass ractions at dierent riser heights with the itted data o Souza (2004).

12 Proceedings o ENCIT ABCM, Curitiba, Brazil, Dec. 5-8, 2006 Paper CIT Reerences Erthal, R.H., 2003, Dynamic Modeling and Simulation o a Fluid Catalytic Cracker Converter, Master Dissertation, Post-graduate Program o Mechanical and Materials Engineering, Research and Post-graduate Department, CEFET- PR, Curitiba, Brazil (in Portuguese). Farah, M.,A., 2003, Fundamental Calculations in Process Engineering, Trainees Program Report o Petrobras, Rio de Janeiro, RJ (in Portuguese). Han, I.S., Chung, C.B., 2001, Dynamic modeling and simulation o a luidized catalytic cracking process. Part I: Process modeling, Chemical Engineering Science Vol.56, pp Lee, L.S., Chen, Y.W., Huang, T.N., 1989, Four-Lump Kinetic Model or Fluid Catalytic Cracking Process, The Canadian Journal o Chemical Engineering, Vol. 67. Jacob, S.M., Weekman, V.W., 1976, A lumping and Reaction Scheme or Catalytic Cracking, AIChE Journal, Vol. 22, No. 4, pp Juarez, J.A., Isunza, F.L., Rodriguez E.A., 1999, 5-lump Kinetic Model or Gas Oil Catalytic Cracking, Applied Catalysis A: General, Vol. 177, pp Malay, P., Milne B. J., ROHANI S., 1999, The Modiied Dynamic o a Riser Type Fluid Catalytic Unit, The Canadian J. o Chemical Eng., Vol. 77, pp Martignoni, W.P., 2000, Development o Modeling and Simulation o FCC Risers 1D model, Petrobrás Report (in Portuguese). McFarlane, R.C., Bartee, J.F., Georgakis, C., 1990, Dynamic Simulator or a Model IV Fluid Catalytic Cracking Unit American Institute o Chemical Engineering, Lehingh University, Bethelehem, Pennsylvania. Melo, R.F., 2003, Dynamic Modeling o Separator Vase/Stripper o a FCC Unit, Master Dissertation, Post-graduate Program o Mechanical and Materials Engineering, Research and Post-graduate Department, CEFET-PR, Curitiba, Brazil (in Portuguese). Patankar, S. V., 1980, Numerical Heat Transer and Fluid Flow, Taylor and Francis. Penteado, J.C., 2003 Dynamic Modeling o a FCC Regenerator, Master Dissertation, Post-graduate Program o Mechanical and Materials Engineering, Research and Post-graduate Department, CEFET-PR, Curitiba, Brazil (in Portuguese). Pitault, I., Nevicato, D., Forissier, M., Bernad, J.M., 1994 Kinetic Model Based on a Molecular Description or Catalytic Cracking o Vacuum Gas, Chemical Engineering Science, Vol. 49, No. 27A, pp Santos, M., 2000, Dynamic Model or Control o FCC UOP STACKED Converter Master Dissertation, Department o Chemical Engineering, UFRGS, Porto Alegre, Brazil (in Portuguese). Souza, J. A. (2004). Numerical simulation and thermodynamics optimization o luid catalytic cracking risers or the maximum uel production, PhD thesis, Federal University o Paraná - UFPR, Curitiba, Brazil (in Portuguese). Souza, J. A Numerical simulation and thermodynamics optimization o luid catalytic cracking risers or the maximum uel production, PhD thesis, Federal University o Paraná - UFPR, Curitiba, Brazil (in Portuguese). Weekman Jr., V.W., 1968, A Model o Catalytic Cracking Conversion in Fixed, Moving and Fluid Bed Reactors, I&EC Process Design and Development, Vol. 7, No. 1, pp Copyright Notice The author is the only responsible or the printed material included in his paper.