Desenvolvimento Espacial de Desenvolvimento Espacial de uma Onda de Perturbação em uma Onda de Perturbação em Escoamento Bifásico Escoamento Bifásico Óleo Óleo Pesado Pesado –– Água no Padrão Água no Padrão EstratificadoEstratificado

Marcelo Souza de Castro

Motivação Objetivo

� Estabilidade Hidrodinâmica do Padrão Estratificado ao longo de linhas de transporte de petróleo;

� Teórico:◦ Modelagem do escoamento

bifásico através do modelo de dois fluidos;

◦ Usar método das características para verificar o desenvolvimento espacial de uma onda de perturbação;

◦ Definição de um critério de transição espacial.

IntroduçãoIntrodução

transição espacial.

� Experimental:◦ Montar bancada

experimental para comparar com resultados teóricos.

Escoamento EstratificadoEscoamento Estratificado

ModelagemModelagem

� Utilização do modelo de dois Fluidos;

ModelagemModelagem� Método Híbrido

◦ Baseado no deslizamento entre as fases.

s>1

Óleo mais rápido que água; Velocidade da onda menor que a do

óleo

ModelagemModelagem

� Método Híbrido◦ Baseado no deslizamento entre as fases.

s<1

Água mais rápido que Água mais rápido que água;

Velocidade da onda menor que a do água

ModelagemModelagem� Método das Características

CHCL

ModelagemModelagem� Método das Características

ModelagemModelagem

� Método das Características

ModelagemModelagem� Método das Características◦ Caso: s<1

Modelagem• Método das Características

– Caso: s>1

Resultados NuméricosResultados Numéricos

� Usar método de diferenças finitas.

ExperimentalExperimental

� Readequação da gangorra;� Projeto e montagem de bocal para

escoamento estratificado;� Projeto e montagem de sistema de � Projeto e montagem de sistema de

amortecimento para o fluido;

ExperimentalExperimental

� Bocal:

Próximas EtapasPróximas Etapas

� Bancada Experimental;� Análise pelo método das

Características da equação da onda;� Levantamento de banco de dados;� Levantamento de banco de dados;� Utilização do método de Gaster

(1962) para critério de transição espacial.

Referências BibliográficasReferências Bibliográficas� Al Wahaibi, T. e Angeli, P., Transition beween strat ified and non-stratified horizontal oil-water flows , Part I: Stability analysis. Chemical

Engineering Science 62, 2915-2928, 2007.

� Angeli, P., Liquid-liquid dispersed flows in horizontal pipes, Ph.D. Thesis. Imperial College of Science, Technology and Medicine, 1996.

� Arirachakaran,S. et. al., An analysis of oil/water flow phenomena in horizontal pipes, SPE Paper 18836, SPE Prof. Prod. Operating Symp., Oklahoma, 1989.

� Barnea, D. e Taitel, Y, Transient-formulation modes and stability of steady-state annular flow, Chemical Engineering Science vol. 44,n. 2, 325-332, 1989.

� Barnea, D., Stability analysis of annular flow structure, using a discrete form of the “two-fluid model”, Int. J. Multiphase Flow 17, 705-716, 1991.

� Barnea, D. e Taitel, Y., Kelvin-Helmholtz stability criteria for stratified flow: viscous versus non-v iscous (inviscid) approaches, International Journal of Multiphase Flow, 19, n. 4, 639-649, 1993.

� Barnea, D. e Taitel, Y, Interfacial and Structural stability of separated flow, Int. J. Multiphase Flow 20, 387-414, 1994.

� Barnea, D. e Taitel, Y, Structural stability of str atified flow – the two-fluid model approach, Chemical Engineering Science vol. 49, 22, 3757-3764, 1994.

� Bergles, A.E. et. al., Two-phase Flow and Heat Transfer in The Power and Process Industries, Hemisphere;Mc Graw-Hill, 1981.

Betchov , R., e Criminale , W., O.. . Academic press. 1967.� Betchov , R., e Criminale , W., O.. Stability of parallel flow. Academic press. 1967.

� Brauner, N., Two phase Liquid-liquid annular flow, International Journal of Multiphase Flow, 17, n. 1, p. 59 - 76, 1991.

� Brauner, N e Maron, D.M., Flow pattern transitions in two-phase liquid-liquid flow in horizontal tubes , International Journal of Multiphase Flow, 18, n. 1, p. 123, 1992b.

� Brauner, N. e Maron, D.M., Stability analysis of st ratified liquid-liquid flow, International Journal of Multiphase Flow, 18, n. 1, p. 103, 1992a.

� Brauner, N., e Maron, D. M., Classification of Liquid-Liquid Two-phase Flow Systems and the Prediction of Flow Pattern Maps, 2nd International Symposium on Two-Phase Flow Modeling and Experimentation - ISTP’99, 2, pp.747-754, Pisa, Italy, 1999.

� Butterworth, D. e Hewitt, G.F., Two-phase Flow and Heat Transfer, Oxford University Press, reprinted 1978, Eds. 1977.

� Cheng, L., Ribatski, G. e Thome, J. R., Two phase flow patterns asn flow-patterns maps: Fundamentals and Applications, Applied Mechanics Review, Published online, 30 de Julho, vol, 61., 2008.

� Crowley, C.J., Wallis, G.B. e Barry, J.J., Dimensio nless form of a one-dimensional wave model for the stratified flow regime transition, International Journal of Multiphase Flow, 19, n. 2, pp. 369-376, 1993.

� Crowley, C.J., Wallis, G.B. e Barry, J.J., Validati on of a one-dimensional wave model for the stratifi ed-to-slug flow regime transition, with consequences for wave growth and slug frequency, International Journal of Multiphase Flow, 18, n. 2, pp. 249-271, 1992.

� Delhaye, J. M., Basic equations for two-phase flow modeling, in: Two-Phase Flow and Heat Transfer in the Power and Process Industries, Editado por A. E. Bergles, Hemisphere Pub. Corp., 1981.

� Drazin, P. G., e Reid, W. H.. Hydrodynamic stabilit y. Cambridge University Press, 1981.

� Elseth, G., An experimental study of oil-water flow in horizontal pipes, Ph.D. Thesis. The Norwegian University of Science and Technology, 2001.

� Fairusov, Y.V. et. al., Flow pattern transitions in horizontal pipelines carrying oil-water mixtures: full-scale experiments, Journal of Energy Resources Technology, 122, pp. 169-175, 2000.

� Galimov, A. Y., Drew, D. A., Lahey Jr. R. T. and Moraga, F. J., The analysis of interfacial waves, Nuclear Engineering and Design 235, 1283 – 1292, 2005.

Referências BibliográficasReferências Bibliográficas� Gaster, M, On the generation of Spatially Growing W aves in Boundary Layer, J. Fluid Mechanics, 22, pp. 443-441, 1964

� Gaster, M, On the Effects of Boundary-Layer Growth on Flow Stability, J. Fluid Mechanics, 66, pp. 465-480, 1974

� Govier, G.W., e Aziz, K., The Flow of Complex Mixtures in Pipes, Van Nostrand-Reinhold, 1972.

� Gu, H.Y. e Guo, L.J., Stability of stratified Gas-Liquid Flow in Horizontal and near Horizontal pipes, J. Chem. Eng., 15(5), 619-625, 2007.

� Hackbusch, K. W., On a Method of Characteristics for Solving a Hyperbolic Equation of Second Order, Computing, 20, pp. 47-60, 1978.

� Hewitt, G.F., Measurement of Two-phase Flow Parameters, Academic Press, 1978.

� Ishii, M., Thermo-fluid Dynamic Theory of Two-phase Flow, Eyrolles, 1975.

� Jones, A. V. e Prosperetti, A., On the suitability of first-order differential models for two-phase flow prediction. Int. J. Multiphase Flow 11, 133-148, 1985.

� Jones, A. V. e Prosperetti, A., The linear stability of general two-phase flow models--II. Int. J. Multiphase Flow 13, 161-171, 1987.

� Joseph, D. D., Bannwart, A. C. e Liu, Y. J., Stability of annular flow and slugging, Int. J. Multiphase Flow 22, 1247-1254, 1996.

� Kunii, D., e Levenspiel, O., Fluidization Engineering. Inc. USA, John Wiley & Sons, 1969.

� Linn, C. C., The Theory of Hydrodynamic stability. Cambridge University Press, 1955.� Linn, C. C., The Theory of Hydrodynamic stability. Cambridge University Press, 1955.

� Lovick, J., e Angeli, P., Two-phase Liquid Flows at the Partially Dispersed Flow Regime, 4th International Conference of Multiphase Flow, New Orleans, maio 27-junho 1, 2001.

� Mattheij, R. M., et al, Partial Differential Equations,: Modelling, Analy sis, Computation. SIAM, 2005

� Petalas N. e Aziz K., A mechanistic model for multiphase flow in pipes, Journal of Canadian Petroleum Technology, 39, n. 6, pp. 43-55, 2000.

� Rodriguez, O. M. H. e Bannwart, A. C., 1 Analytical model for interfacial waves in vertical core flow, Journal of Petroleum Science and Engineering 54, 173-182, 2006.

� Rodriguez, O. M. H. e Bannwart, A. C., 2 Experimental study on interfacial waves in vertical core flow, Journal of Petroleum Science and Engineering 54, 140-148, 2006.

� Rodriguez, O. M. H. e Bannwart, A. C., Stability Analysis of Core-Annular flow and neutral stability wave number, AIChE Journal, 54, pp 20-31, 2008.

� Schlichting, H., Boundary Layer Theory. McGraw-Hill, 1979.

� Taitel, Y. e Dukler, A. E., A model for predicting flow regime transitions in horizontal and near hori zontal gas-liquid flow. A.I.Ch.E. Journal, 22, pp. 47-55, 1976.

� Taitel, Y., Barnea, D. e Dukler, A. E., Modeling flow pattern transitions for steady upward gas-liquid flow in vertical tubes, A.I.Ch.E. Journal, 26, pp. 345-354, 1980.

� Trallero, J. L., Oil-Water Flow Patterns in Horizon tal Pipes, Ph.D. thesis, The University of Tulsa, T ulsa, Oklahoma, 1995.

� Trallero, J.L., Sarica, C., e Brill, J.P., A Study of Oil/water Flow Patterns in Horizontal Pipes, SPE Production & Facilities, SPE 36609, agosto, 1997.

� Wallis, G.B. One-dimensional Two-Phase Flow, EUA, McGraw Hill, 1969.

� Watson, J, On spatially-Growing Finite Disturbancces in Plane Poiseuille Flow,