A new simulation method for the separation of binary mixtures in a four-column simulated moving bed

In this paper, a new resolution method for the dynamic simulation of a simulated moving bed is presented. A general rate model for each solute and each column is presented for the case of a linear isotherm. A hybrid resolution is developed, in which an analytical solution is used for the solid stationary phase, while the mobile fluid phase concentrations are obtained by numerical resolution. It is illustrated, through a numerical study, that the resolution method is robust. The method is validated by comparison with previously published experimental results. It is also shown that these numerical simulations are obtained much faster than those based on the physical separation process, allowing the use of this resolution method for on-line applications and process control.24221122

Adsorption of γ-Valerolactone: An Alternative for Solvent Recovery after Conversion of Lignocellulosic Biomass to Fermentable Sugars

The γ-valerolactone is an effective solvent in solubilizing lignocellulosic biomass fractions, although it inhibits microbial activity. To avoid the negative effects on the metabolism of microorganisms, even small quantities of γ-valerolactone need to be removed. This study examined the adsorption of γ-valerolactone on the commercial resin. The removal efficiency, adsorption equilibrium, pH effects, and fixed-bed column conditions were investigated. The highest removal efficiency of γ-valerolactone from sugar solution was 39.92 %, with 413.78 mg g−1 γ-valerolactone adsorption capacity, observed with commercial resin Dowex Optipore L-493 and pH 4.00. Dual-site Langmuir adsorption isotherm was found to be the best-fitting model for describing the adsorption mechanisms of γ-valerolactone on commercial resin. Thus, this study shows that γ-valerolactone could be removed from sugar solution by adsorption on commercial resin. In addition, the process is a viable alternative for the recovery of solvent and keeping the microbial activity in lignocellulosic biomass fractions

Simulation And Techno-economic Evaluation Of Large Scale 2.5-dimethylfuran Production From Fructose

Conceptual process synthesis (CPS) is an important issue in chemical processing industries. This paper is based on a schematic diagram of 2.5 dimethylfuran (DMF) production from fructose [ Y. R. Leshkov, C. J. Barrett, Z. L. Liu, J. A. Dumesic. Production of dimethylfuran for liquid fuels from biomass-derived carbohydrates. Nature (2007), doi:10.1038/nature05923]. It assessed the general steps of the life cycle of an 2.5-dimethylfuran (DMF) industrial production project. Chemical route synthesis, process development (thermodynamic modeling) and process engineering (defining basic equipment for economic evaluation) were investigated. The process flow diagram (PFD) was made in the commercial process simulator UNISimTM. A literature review on the process was carried out in order to determine which thermodynamic model would be suitable to represent the phase equilibrium. In the system studied (fructose, 1-butanol, sodium chloride, water, chloride acid, hydroxymethylfurfural, 2,5 dimethylfuran) the presence of the sodium chloride affects the phase equilibrium. In this work, consider the salt as simple molecule, rather than distributed charged ions in the solution. This allows the use of the UNIQUAC model. The binary interaction parameters of the model were estimated from experimental data in literature of liquid-liquid equilibrium. The process for DMF production was simulated with these parameters. The process separates water from the 1-butanol and water, 1-butanol and DMF. The material and energy balances were performed by UNISimTM software. Economic evaluation showed that a suitable operational condition could work with 174 mil t/y of fructose and could produce 155 mil t/y of DMF. The cost of DMF was 1.95 U$$/kg. The DMF value and the thermal energy consumption are key issues for a profitable operation of the plant. This analysis suggests that DMF production from fructose deserves serious consideration by investors. Copyright © 2014,AIDIC Servizi S.r.l.37475480Abrams, D.S., Prausnitz, J.M., Statistical thermodynamics of liquid mixtures: A new expression for the excess gibbs energy of partly or completely miscible systems (1975) AIChE Journal, 21, pp. 116-128Aznar, M., (1996) Liquid-Vapour Equilibrium of Electrolytic Systems by Group Contribution Methods, , Ph.D. Thesis, Federal University of Rio de Janeiro, Rio de Janeiro, BrazilCatté, M., Dussap, C.G., Achard, C., Gros, J.B., Excess properties and solid-liquid equilibria for aqueous solutions of sugars using a uniquac model (1994) Fluid Phase Equilibria, 96, pp. 33-50Cezário, G.L., Filho, R.M., Mariano, A.P., (2010) Design and Energetic Evaluation of the Distillation System for a Biobutanol Production Plant by Extractive Fermentation, , XVII Congress of Scientific Initiation from Campinas State University, Campinas, BrazilDebye, P., Huckel, E., (1923) Theory of Eletroctrolytes, Physics Zeitsch, 24, pp. 185-206Fowler, R.H., Guggenheim, E.A., (1949) Statistical Thermodynamics, , Cambridge University Press, Cambridge, United KingdomFredenslund, A.A., Gmehling, J., Rasmussen, P., (1977) Vapor-Liquid Using UNIFAC, , Elsevier, Amsterdamm, The NetherlandsLeshkov, Y.R., Barrett, C.J., Liu, Z.Y., Dumesic, J.A., Production of dimethylfuran for liquid fuels from biomass-derived carbohydrates (2007) Nature, 447, pp. 982-986Lozowski, D., Economic indicators (2013) Chemical Engineering, 120, pp. 63-64Mock, B., Evans, L.B., Chen, C.C., Thermodynamic representation of phase equilibria of mixedsolvent electrolyte systems (1986) AIChE Journal, 32, pp. 1655-1664Peters, M.S., Timmerhaus, K.D., West, R.E.W., (2003) Plant Design and Economics for Chemical Engineers, , McGraw-Hill, New York, USAPitzer, K.S., Thermodynamics of electrolytes i. Theoretical basis and general equation (1973) Journal Physics Chemical, 77, pp. 268-277Qureshi, N., Hughes, S., Maddon, I.S., Cotta, M.A., Energy-efficient recovery of butanol from model solutions and fermentation broth by adsorption (2005) Bioprocess and Biosystems Engineering, 27, pp. 215-222Renon, H., Prausnitz, J.M., Local compositions in thermodynamics excess functions for liquid mixtures (1968) AIChE Journal., 14, pp. 135-144Turton, R., Bailie, R.C., Whiting, W.B., Shauwitz, J.A., (2003) Analysis, Synthesis, and Design of Chemical Processes, , Prentice Hall, New JerseySantis, R., Marrelli, L., Muscetta, P.N., Liquid-liquid equilibria in water-aliphatic alcohol systems in the presence of sodium chloride (1976) Chemical Engineering Journal, 11, pp. 207-214Santis, R., Marrelli, L., Muscetta, P.N., Influence of temperature on the liquid-liquid equilibrium of the water-n butyl alcohol-sodium chloride system (1976) Journal of Chemical and Engineering Data, 21, pp. 324-327Schaub, G., Vetter, A., Biofuels for automobiles-An overview (2003) Chemical Engineering Technology, 31, pp. 721-729www.honeywell.com, UNISim Honeywell 2007, Accessed 05/03/1

Computational Fluid Dynamics Of A Semi Batch Reactor For Heavy Oil Hydroconversion

This work presents the numerical results of the computational fluid dynamics of a semi batch reactor used for hydroconversion of heavy oil. The reactor is a multicomponent system, and it is modeled as a pseudo two phase system (gas+slurry). The equations used are the continuity equations, the momentum equation (Navier-Stokes), and the k-ε for turbulence. The numerical method used to solve the mathematical method was the finite volume, where the problem was divided in two domains, in order to account for the moving part of the impeller. The numerical results indicated convergence of the procedure for the velocity profiles. © 2009 American Institute of Physics.1148 2281284Yamada, T.S., Guirardello, R., Kinetics and fluid dynamics for oil residue hydroconversion in commercial software (2007) IntemationalJoumal of Reactor Engineering, 5, pp. 1-10Bertodano, M.L., Lahey, R.T., Jones, O.C., Development of a k-s model for bubbly two phase flow (1994) Trans. ASME J. Fluids Eng, 116, p. 128Bertodano, M.L., Lahey, R.T., Jones, O.C., Phase distribution in bubble two phase flow in vertical ducts (1994) Int. J. Multiphase F/ow, 20, p. 805Grace, J.R., Weber, M.E., Hydrodynamics of drops and bubbles (1982) Handbook of Multiphase Systems, , ed. G. Hetsroni, HemispherePedersen, K.S., Fredenslund, A., Thomassen, P., (1990) Properties of Oils and Natural Gases, , Gulf Publishing Company, Book DivisionAlmeida, R.M., Guirardello, R., Hydroconversion kinetics of Marlim vacuum residue (2005) Catalysis Today, 109 (1-4), pp. 104-111Launder, B.E., Spalding, D.B., The numerical computation of turbulent flows, Comput (1974) Methods Appl. Mech. Eng, 3, pp. 269-28

Comparison Of Several Glycerol Reforming Methods For Hydrogen And Syngas Production Using Gibbs Energy Minimization

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)This paper focuses on the comparison of different glycerol reforming technologies aimed to hydrogen and syngas production. The reactions of steam reforming, partial oxidation, autothermal reforming, dry reforming and supercritical water gasification were analyzed. For this, the Gibbs energy minimization approach was used in combination with the virial equation of state. The validation of the model was made between the simulations of the proposed model and both, simulated and experimental data obtained in the literature. The effects of modifications in the operational temperature, operational pressure and reactants composition were analyzed with regard to composition of the products. The effect of coke formation was discussed too. Generally, higher temperatures and lower pressures resulted in higher hydrogen and syngas production. All reforming technologies demonstrated to be feasible for use in hydrogen or synthesis gas production in respect of the products composition. The proposed model showed good predictive ability and low computational time (close to 1 s) to perform the calculation of the combined chemical and phase equilibrium for all systems analyzed.39311796917984CAPES; São Paulo Research Foundation; 2011/20666-8; FAPESP; São Paulo Research FoundationFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Saxena, R.C., Seal, D., Kumar, S., Goyal, H.B., Thermo-chemical routes for hydrogen rich gas from biomass: A review (2008) Renew Sustain Energy Rev, 12, pp. 1909-1927Ma, F., Hanna, M.A., Biodiesel production: A review (1999) Bioresour Technol, 70, pp. 1-15Pagliaro, M., Ciriminna, R., Kimura, H., Rossi, M., Della Pina, C., From glycerol to value added products (2007) Angew Chem Int Ed, 46, pp. 4434-4440Vaidya, P.D., Rodrigues, A.E., Glycerol reforming for hydrogen production: A review (2009) Chem Eng Technol, 32, pp. 1463-1469Zhang, B., Tang, X., Li, Y., Xu, Y., Shen, W., Hydrogen production from steam reforming of ethanol and glycerol over ceria supported metal catalysts (2007) Int J Hydrogen Energy, 32, pp. 2367-2373Buffoni, I.N., Pompeo, F., Santori, G.F., Nichio, N.N., Nickel catalysts applied in steam reforming of glycerol for hydrogen production (2009) Catal Commun, 10, pp. 1656-1660Adhikari, S., Fernando, S.D., Haryanto, A., Hydrogen production from glicerin by steam reforming over nickel catalysts (2008) Renew Energy, 33, pp. 1097-1100Thyssen, V.V., Maia, T.A., Assaf, E.M., Ni supported on La2O3-SiO2 used to catalyze glycerol steam reforming (2013) Fuel, 105, pp. 358-363Iriondo, A., Barrio, V.L., Cambra, J.F., Arias, P.L., Guemez, M.B., Sanchez, M.C., Glycerol steam reforming over Ni catalysts supported on ceria and ceria promoted alumina (2010) Int J Hydrogen Energy, 35, pp. 11622-11633Pompeo, F., Santori, G.F., Nichio, N.N., Hydrogen production by glycerol steam reforming with Pt/SiO2 and Ni/SiO2 catalysts (2011) Catal Today, 172, pp. 183-188Pompeo, F., Santori, G.F., Nichio, N.N., Hydrogen and/or syngas from steam reforming of glycerol. Study of platinum catalysts (2010) Int J Hydrogen Energy, 35, pp. 8912-8920Wang, H., Wang, X., Li, M., Li, S., Wang, S., Ma, X., Thermodynamic analysis of hydrogen production from glycerol autothermal reforming (2009) Int J Hydrogen Energy, 34, pp. 5683-5690Wang, W., Thermodynamic analysis of glycerol partial oxidation for hydrogen production (2010) Fuel Process Technol, 91, pp. 1401-1408Yang, G., Yu, H., Peng, F., Wang, H., Yang, J., Xie, D., Thermodynamic analysis of hydrogen generation via oxidative steam reforming of glycerol (2011) Renew Energy, 36, pp. 2120-2127Byrd, A.J., Pant, K.K., Gupta, R.B., Hydrogen production from glycerol by reforming in supercritical water over Ru/Al2O3 catalyst (2008) Fuel, 87, pp. 2956-2960Chakinala, A.G., Brilman, D.W.F., Van Swaaij, W.P.M., Kersten, S.R.A., Catalytic and non catalytic supercritical water gasification of microalgae and glycerol (2009) Indust Eng Chem Res, 49, pp. 1113-1122Guo, S., Guo, L., Cao, C., Yin, J., Lu, Y., Zhang, X., Hydrogen production from glycerol by supercritical water gasification in a continuos flow tubular reactor (2012) Int J Hydrogen Energy, 37, pp. 5559-5568Van Bennekon, J.G., Venderbosch, R.H., Assink, D., Heeres, H.J., Reforming of methanol and glycerol in supercritical water (2011) J Supercrit Fluids, 58, pp. 99-113Voll, F.A.P., Rossi, C.C.R.S., Silva, C., Guirardello, R., Souza, R.O.M.A., Cabral, V.F., Thermodynamic analysis of supercritical water gasification of methanol, ethanol, glycerol, glucose and cellulose (2009) Int J Hydrogen Energy, 34, pp. 9737-9744Wang, X., Li, M., Wang, M., Wang, H., Li, S., Wang, S., Thermodynamic analysis of glycerol dry reforming for hydrogen and synthesis gas production (2009) Fuel, 88, pp. 2148-2153Fernández, Y., Arennilas, A., Bermúdez, J.M., Menéndez, J.A., Comparative study of conventional and microwave assisted pyrolysis, steam and dry reforming of glycerol for syngas production, using a carbonaceous catalyst (2010) J Anal Appl Pyrolysis, 88, pp. 155-159Kale, G.R., Kulkarni, B.D., Thermodynamic analysis of dry autothermal reforming of glycerol (2010) Fuel Process Technol, 91, pp. 520-530Valliyappan, T., Bakhshi, N.N., Dalai, A.K., Pyrolysis of glycerol for the production of hydrogen or syngas (2008) Bioresour Technol, 99, pp. 4476-4483Adhikari, S., Fernando, S., Gwaltney, S.R., Filip To, S.D., Bricka, R.M., Steele, P.H., A thermodynamic analysis of hydrogen production by steam reforming of glycerol (2007) Int J Hydrogen Energy, 32, pp. 2875-2880Holladay, J.D., Hu, J., King, D.L., Wang, Y., An overview of hydrogen productions technologies (2009) Catal Today, 139, pp. 244-260Rass-Hansen, J., Johansson, R., Moller, M., Christensen, C.H., Steam reforming of technical bioethanol for hydrogen production (2008) Int J Hydrogen Energy, 33, pp. 4547-4554Adhikari, S., Fernando, S., Haryanto, A., Production of hydrogen by steam reforming of glicerin over alumina supported metal catalysts (2007) Catal Today, 129, pp. 355-364Adhikari, S., Fernando, S., Haryanto, A., A comparative thermodynamic and experimental analysis on hydrogen production by steam reforming of glicerin (2007) Energy Fuels, 21, pp. 2306-2310Slinn, M., Kendall, K., Mallon, C., Andrews, J., Steam reforming of biodiesel by-product to make renewable hydrogen (2008) Bioresour Technol, 99, pp. 5851-5858Oliveira, E.L.G., Grande, C.A., Rodrigues, A.R.E., Methane steam reforming in large pore catalyst (2010) Chem Eng Sci, 65, pp. 1539-1550Sanchez, E.A., Comelli, R.L.A., Hydrogen by glycerol steam reforming on a nickel alumina catalyst: Deactivation processes and regeneration (2012) Int J Hydrogen Energy, 37, pp. 14740-14746Dieuzeide, M.L., Iannibeli, V., Jobbagi, M., Amadeo, N., Steam reforming of glycerol over Ni/Mg/γ-Al2O3 catalysts. Effect of calcination temperatures (2012) Int J Hydrogen Energy, 37, pp. 14926-14930Bobadilla, L.F., Álvarez, A., Domínguez, M.I., Romero-Sarria, F., Centeno, M.A., Montes, M., Influence of the shape of Ni catalyst in the glycerol steam reforming (2012) Appl Catal B - Environ, 123, pp. 379-390Cheng, G.K., Foo, S.Y., Adesina, A.A., Steam reforming of glycerol over Ni/Al2O3 catalysts (2011) Catal Today, 178, pp. 25-33Wang, C., Dou, B., Chen, H., Song, Y., Xu, Y., Du, X., Hydrogen production from steam reforming of glycerol by Ni-Mg-Al based catalysts in fixed bed reactor (2013) Chem Eng J, 220, pp. 133-142Wang, C., Dou, B., Chen, H., Song, Y., Xu, Y., Du, X., Renewable hydrogen production from steam reforming of glycerol by Ni-Cu-Al, Ni-Cu-Mg, Ni-Mg catalysts (2013) Int J Hydrogen Energy, 38, pp. 3562-3571Ahmed, S., Krumpelt, Hydrogen from hydrocarbon fuels for fuel cells (2001) Int J Hydrogen Energy, 26, pp. 291-301Carrettin, S., McMorn, P., Johnston, P., Griffin, K., Kiely, C.J., Hutchings, G.J., Oxidation of glycerol using supported Pt, Pd and Au catalysts (2003) Phys Chem Chem Phys, 5, pp. 1329-1336Rennard, D.C., Kruger, J.S., Schmidt, L.D., Autothermal catalytic partial oxidation of glycerol to syngas and non-equilibrium products (2009) Chem Sus Chem, 2, pp. 89-98Rabenstein, G., Hacker, V., Hydrogen for fuel cells from ethanol by steam reforming, partial oxidation and combined auto-thermal reforming: A thermodynamic analysis (2008) J Power Sources, 185, pp. 1293-1304Qi, A., Wang, S., Fu, G., Wu, D., Autothermal reforming of n-octane on Ru-based catalysts (2005) Appl Catal A - Gen, 293, pp. 71-82Dauenhauer, P.J., Salge, J.R., Schmidt, L.D., Renewable hydrogen by autothermal steam reforming of volatile carbohydrates (2006) J Catal, 244, pp. 238-247Douette, A.M.D., Turn, S.Q., Wang, W., Keffer, V.I., Experimental investigation of hydrogen production from glycerin reforming (2007) Energy Fuels, 21, pp. 3499-3504Edwards, J.H., Maitra, A.M., The chemistry of methane reforming with carbon dioxide and its current and potential applications (1995) Fuel Process Technol, 42, pp. 269-289Mizuno, T., Goto, M., Kodama, A., Hirose, T., Supercritical water oxidation of a model municipal solid waste (2000) Indust Eng Chem Res, 39, pp. 2807-2810Kruse, A., Supercritical water gasification (2008) Biofuels Bioprod Biorefining, 2, pp. 415-437Savage, P.E., Heterogenous catalysis in supercritical water (2000) Catal Today, 62, pp. 167-173Calzavara, Y., Joussot-Dubien, C., Boissonnet, G., Sarrade, S., Evaluation of biomass gasification in supercritical water process for hydrogen production (2005) Energy Convers Manag, 46, pp. 615-631Guo, Y., Wang, S.Z., Xu, D.H., Gong, Y.M., Ma, H.H., Tang, X.Y., Review of catalytic supercritical water gasification for hydrogen production from biomass (2010) Renew Sustain Energy Rev, 14, pp. 334-343Hao, X.H., Guo, L.J., Mao, X., Zhang, X.M., Chen, X.J., Hydrogen production from glucose used as a model compound of biomass gasified in supercritical water (2003) Int J Hydrogen Energy, 28, pp. 55-64Clifford, T., (1998) Fundamentals of Supercritical Fluids, , Oxford University Press New YorkMay, A., Salvadó, J., Torras, C., Montané, D., Catalytic gasification of glycerol in supercritical water (2010) Chem Eng J, 160, pp. 751-759Smith, W.R.M., Missen, R.W., (1982) Chemical Reaction Equilibrium Analysis: Theory and Algorithms, , JohnWiley & SonsPitzer, K.S., Curl, R.F., The volumetric and thermodynamic properties of fluids III. Empirical equation of the second virial coefficient (1957) J Am Chem Soc, 20, pp. 263-272Tsonopoulos, C., An empirical correlation of second virial coefficients (1974) AIChE J, 20, pp. 263-272Castello, D., Fiori, L., Supercritical water gasification of biomass: Thermodynamic constraints (2011) Bioresour Technol, 102, pp. 7574-7582Castillo, J., Grossmann, I.E., Computation of phase and chemical equilibria (1981) Comput Chem Eng, 5, pp. 99-108Freitas, A.C.D., Guirardello, R., Oxidative reforming of methane for hydrogen and synthesis gas production: Thermodynamic equilibrium analysis (2012) J Nat Gas Chem, 21, pp. 571-580Lu, Y., Guo, X., Zhang, X., Yan, Q., Thermodynamic modeling and analysis of biomass gasification for hydrogen production in supercritical water (2007) Chem Eng J, 131, pp. 233-244Nichita, D.V., Gomez, S., Luna, E., Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method (2002) Comput Chem Eng, 26, pp. 1703-1724Rossi, C.C.R.S., Berezuk, M.E., Cardozo-Filho, L., Guirardello, R., Simultaneous calculation of chemical and phase equilibria using convexity analysis (2011) Comput Chem Eng, 35, pp. 1226-1237Freitas, A.C.D., Guirardello, R., Supercritical water gasification of glucose and cellulose for hydrogen and syngas production (2012) Chem Eng Trans, 27, pp. 361-366Castier, M., Solution of isochoric-isoenergetic flash problem by direct entropy maximization (2009) Fluid Phase Equilibria, 276, pp. 7-17White, W.B., Johnson, S.M., Danzig, G.B., Chemical equilibrium in complex mixtures (1958) J Chem Phys, 28, pp. 751-755Brooke, K., Meeraus, D., Raman, R., (1998) GAMS - A User's ManualPolling, B.P., Prausnitz, J.M., O'Connel, P.J., (2000) The Properties of Gases and Liquids, , 5th ed. McGraw Hill New YorkReid, R.P., Prausnitz, J.M., Sherwood, T.K., (1987) The Properties of Gases and Liquids, , 4th ed. McGraw Hill New YorkDippr, (2000) DIADWM Public V. 1.2. Design Institute for Physical Property Data. Information and Data Evaluation ManagerAdhikari, S., Fernando, S.D., To, S.D.F., Bricka, R.M., Steele, P.H., Haryanto, A., Conversion of glycerol to hydrogen via a steam reforming process over nickel catalysts (2008) Energy Fuels, 22, pp. 1220-1226Wang, X., Li, M., Li, S., Wang, H., Wang, S., Ma, X., Hydrogen production by glycerol steam reforming with/without calcium oxide sorbent: A comparative study of thermodynamic and experimental work (2010) Fuel Process Technol, 91, pp. 1812-1818Freitas, A.C.D., Guirardello, R., Thermodynamic analysis of supercritical water gasification of microalgae biomass for hydrogen and syngas production (2013) Chem Eng Trans, 32, pp. 553-55

An approach to calculate solid-liquid phase equilibrium for binary mixtures

An approach is presented to calculate solid-liquid phase equilibrium for binary mixtures, using expressions for the temperature as a function of the molar fraction. For Margules model the expression gives explicitly the temperature, while for other liquid phase activity models an iterative procedure is required to calculate the temperature. The method is very easy to apply and it can be used for mixtures that have peritectic and eutectic points, or just a eutectic point. The approach was applied to five case studies with binary mixtures of fatty acids and triglycerides. The results were in good agreement with experimental data. (C) 2009 Elsevier B.V. All rights reserved.2811122

Modelling And Simulation Of A Multiphase Fluidized Bed Reactor By Variational Principles

This paper shows the study of a computational fluid dynamics approach through the investigationand evaluation of the intrinsic characteristics of the optimization associated with the variational principle method when applied to a multiphase fluidized bed reactor modelling and simulation operating in a slurry bubble column mode. The optimization criterion associated in the method is based on the minimization of the amount of energy. The variationalmethodhas advantagesin modellingand fitting parameters (constants) of equations in the critical regions of the flow, where other methods may not give good results, and regions under the influence of the equipmentwall or other disturbences. The disadvantage of this method is that there is no general methodapplicable in all processes, just for particular cases. The type of reactor evaluated is employed in hydroconversion and hydrotreatment processes. There are few experimental results available in the literature for real situations. The simulated computational results are comparedwith the experimental results from the literature of an fluidized system formed by water-air-glass spheres. Also, computational results are comparedwith the result obtained for a hydroconversion reactor solved by means of the finite volume method. The results obtained show that the variational method is capable of simulating a multiphase fluidized bed reactor as well as other methods. This show that it is possible to explore the optimizationcharacteristics of the variationalprinciples. © 1999 Elsevier Science Ltd.23SUPPL. 1S411S414Carbonell, M.M., (1996) Modelagem e simulaciio de reator j/uidizado trifasico aplicado ao processo de hidroconversiio de oleos pesados, , M.Sc. dissertation, UNICAMP, BrazilCarbonell, M.M., Guirardcllo, R., Modelling of a slurry bubble column reactor applied to the hydroconversion of heavy oils (1997) Chemical Engineering Science, 52, pp. 4179-4185Chen, Z., Zheng, C., Feng, Y., Modeling of three-phase fluidized beds based on local bubble characteristics measurements (1995) Chemical Engineering Science, 50, pp. 231-236Dudukovic, M.P., Devanathan, N., Bubble column reactors: some recent developments (1993) Chemical Reactor Technology for Environmentally Safe Reactors and Products, pp. 353-377. , eds. H. 1. Lasa, G. Dogu and A. Ravella, Kluwer Academic Publishers, DordrcchtEcer, A., Rout, R.K., Investigation of solution of Navier-Stokes equations using a variational formulation (1983) Int. J.for Num. Meth. in Fluids, 3, pp. 23-31Zhu, J., Drag and mass transfer for flow of a Carreau fluid past a swarm of newtonian drops (1995) Int. J. Multiphase FlolV, 21, pp. 935-940Finlayson, B.A., (1972) The method of weighted residuals and variational principles, , McGraw-Hill Inc., New YorkGal-Or, B., Weihs, D., Variational analysis of high mass transfer rates from spherical particles boundary-layer (1972) Int. J. Mass Heat Transfer, 15, p. 20272044Gaschc, H.E., Edinger, C., Kompel, H., Hofmann, H., A fluid dynamically based model of bubble column reactors (1990) Chern. Engng. Technol., 13, pp. 341-349GorIa, R.S.R., Madden, P.E., A variational approach to non-steady non-newtonian flow in a circular pipe (1984) J. Non-Newtonian Fluid Mech., 16, pp. 251-265Grienberger, 1., Holmann, H., Investigations and modelling of bubble columns (1992) Chern. Engng. Sci., 47, pp. 2215-2220Menzel, T., Weide, T., Staudacher, O., Wein, O., Onken, U., Reynolds shear stress for modeling of bubble column reactors (1990) Ind. Engng. Chern. Res., 29, pp. 988-994Reti, Z., Reti, P., Variational inequalities as models of chemical reactors (1982) Hung. J. Ind. Chern., 10, pp. 243-250Reichardt, H., (1951) Z.Angew. Math. Mech, 31, p. 208Schwarz, M.P., Turner, W.J., Applicability of the k-e turbulence model to gas-stirred baths (1988) Appl. Math. Modelling, 12, pp. 273-279Tarmy, B.L., Chang, M., Coulaloglou, C.A., Ponzi, P.R., (1984) The Three Phase Hydrodynamic Characteristics ofthe EDS Coal Liquefaction Reactors: Their Development and Use in Reactor Scaleup, , Institution of Chemical Engineers Symposium on Chemical Reaction Engineering, Edinburg, 10-13, SeptemberTorvik, R., Svendsen, H.F., Modelling of sluny reactors. A fundamental approach (1990) Chern. Engng. Sci., 45, pp. 2325-2332Yang, C.T., Variational theories in hydrodynamics and hydraulics (1994) J. Hydraulic Engng., 120. , jun