Revista Mexicana de Ingeniería Química, Vol. 22, No. 3 (2023), Sim2347

Entropy and Hurst analysis for the determination of two-phase flow time series complexity

A. Marin-Lopez, H. Puebla, J. A. Martínez-Cadena, J. Alvarez-Ramirez

https://doi.org/10.24275/rmiq/Sim2347

 

Abstract

The complexity in time series of two-phase flow is associate with the interaction of gas bubbles and liquid phase, this interaction shows characteristic that depend on different condition such as low rate, physical properties phases, geometry, and tube inclination, etc. This work uses singular value decomposition (SVD) entropy and rescaled range analysis (R/S) to evaluated complexity in voltage signals of four flow patterns. Entropy helps to understand the complexity of each flow pattern, while R/S analysis allows detecting long-range correlations that exist in a time series. Results shows the entropy by SVD and R/S analysis in time series are interesting techniques that can use for the identification of flow patterns with the advantage that are easy to use and implement due to their low computational cost.

Keywords: flow-pattern, fractal analysis, entropy, voltage series.

 

References

  • Aguilar, A., Riesco, J., Pérez, V., Ramírez, J., Rodríguez, J., & Ramírez, A. (2014). Patrones en dos Fases para Tuberías verticales. de Cuerpos Académicos, 46.
  • Al-Ruhaimani, F., Pereyra, E., Sarica, C., Al-Safran, E. M., & Torres, C. F. (2017). Experimental analysis and model evaluation of high-liquid-viscosity two-phase upward vertical pipe flow. SPE Journal, 22(03), 712-735.
  • Alvarez-Ramirez, J., Alvarez, J., Rodriguez, E., & Fernandez-Anaya, G. (2008). Time-varying Hurst exponent for US stock markets. Physica A: statistical mechanics and its applications, 387(24), 6159-6169.
  • Alvarez-Ramirez, J., Alvarez, J., & Rodriguez, E. (2008). Short-term predictability of crude oil markets: a detrended fluctuation analysis approach. Energy Economics, 30(5), 2645-2656.
  • Alvarez-Ramirez, J., Cisneros, M., Ibarra-Valdez, C., & Soriano, A. (2002). Multifractal Hurst analysis of crude oil prices. Physica A: Statistical Mechanics and its Applications, 313(3-4), 651-670.
  • Alvarez-Ramirez, J., & Rodriguez, E. (2021). A singular value decomposition entropy approach for testing stock market efficiency. Physica A: Statistical Mechanics and its Applications, 583, 126337.
  • Caraiani, P. (2014). The predictive power of singular value decomposition entropy for stock market dynamics. Physica A: Statistical Mechanics and its Applications, 393, 571-578.
  • C. Kleinstreuer, P. Griffith, Two-Phase Flow: Theory and Applications, Taylor and Francis, New York, NY 2004.
  • Cheng, L., Ribatski, G., & Thome, J. R. (2008). Two-phase flow patterns and flow-pattern maps: fundamentals and applications. Applied Mechanics Reviews, 61(5).
  • Franca, F., Acikgoz, M., Lahey Jr, R. T., & Clausse, A. (1991). The use of fractal techniques for flow regime identification. International Journal of Multiphase Flow, 17(4), 545-552.
  • Firouzi, M., & Hashemabadi, S. H. (2009). Exact solution of two-phase stratified flow through the pipes for non-Newtonian Herschel–Bulkley fluids. International communications in heat and mass transfer, 36(7), 768-775.
  • Gneiting, T., & Schlather, M. (2004). Stochastic models that separate fractal dimension and the Hurst effect. SIAM review, 46(2), 269-282.
  • Hewitt, G. F. (1982). Handbook of Multiphase systems. Hemisphere, Washington, DC.
  • Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Transactions of the American society of civil engineers, 116(1), 770-799.
  • Mandelbrot, B. T. (1965). Une classe de processus stochastiques homothetiques a soi-application a la loi climatologique de he Hurst. Comptes Rendus Hebdomadaires des Seances de l Academie des Sciences, 260(12), 3274-3277.
  • Mandelbrot, B. T., Van Ness J. W., Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10 (1968) 422–437.
  • Meraz, M., Rodriguez, E., Femat, R., Echeverria, J. C., & Alvarez-Ramirez, J. (2015). Statistical persistence of air pollutants (O3, SO2, NO2 and PM10) in Mexico City. Physica A: Statistical Mechanics and its Applications, 427, 202-217.
  • Moguel‐Castañeda, J. G., Rocha‐Lara, C. E., Ramirez‐Castelan, C. E., Soto‐Cortes, G., Hernandez‐Martinez, E., & Puebla, H. (2021). Two‐phase flow‐patterns identification in oil/gas pipelines based on fractal analysis. The Canadian Journal of Chemical Engineering, 99(4), 874-883.
  • O'Donovan, A., & Grimes, R. (2020). Two-phase flow regime identification through local temperature mapping. Experimental Thermal and Fluid Science, 115, 110077.
  • Peles, Y. P., & Haber, S. (2000). A steady state, one dimensional, model for boiling two phase flow in triangular micro-channel. International Journal of Multiphase Flow, 26(7), 1095-1115.
  • Rao, M., Chen, Y., Vemuri, B. C., & Wang, F., (2004). Cumulative residual entropy: a new measure of information. IEEE transactions on Information Theory, 50(6), 1220-1228.
  • Soedarmo, A., Soto-Cortes, G., Pereyra, E., Karami, H., & Sarica, C. (2018). Analogous behavior of pseudo-slug and churn flows in high viscosity liquid system and upward inclined pipes. International Journal of Multiphase Flow, 103, 61-77.
  • Sabatini, A. M. (2000). Analysis of postural sway using entropy measures of signal complexity. Medical and Biological Engineering and Computing, 38(6), 617-624.
  • Stanley, H. E., Amaral, L. N., Goldberger, A. L., Havlin, S., Ivanov, P. C., & Peng, C. K. (1999). Statistical physics and physiology: monofractal and multifractal approaches. Physica A: Statistical Mechanics and its Applications, 270(1-2), 309-324.
  • S. Z. Rouhani, M. S. Sohal, Prog. Nucl. Energy 1983, 11, 219.
  • Serizawa, A., Feng, Z., & Kawara, Z. (2002). Two-phase flow in microchannels. Experimental Thermal and Fluid Science, 26(6-7), 703-714.
  • Wall, M. E., Rechtsteiner, A., & amp; Rocha, L. M., (2003). Singular value decomposition and principal component analysis. A practical approach to microarray data analysis, 91-109. Springer, Boston, MA.
  • Wang, Z. (1984). Fast algorithms for the discrete W transform and for the discrete Fourier transform, IEEE Transactions on Acoustics, Speech, and Signal Processing, 4, 803-816.
  • Wu, B., Firouzi, M., Mitchell, T., Rufford, T. E., Leonardi, C., & Towler, B. (2017). A critical review of flow maps for gas-liquid flows in vertical pipes and annuli. Chemical Engineering Journal, 326, 350-377.
  • Xue, Y., Li, H., Li, L., & Chen, T. (2014). A review of studies on the flow patterns of gas-liquid two phases flow in vertical tubes. International Journal of Microscale and Nanoscale Thermal and Fluid Transport Phenomena, 5(3/4), 179.