Basins of Attraction in the Calculation of Critical Points

Caroline N. Parajara; Gustavo B. Libotte; Gustavo Mendes Platt; Francisco D. Moura Neto

doi:10.15866/ireche.v9i3.14901

Basins of Attraction in the Calculation of Critical Points

Caroline N. Parajara⁽¹⁾, Gustavo B. Libotte⁽²⁾, Gustavo Mendes Platt^(3*), Francisco D. Moura Neto⁽⁴⁾

^(*) Corresponding author

Authors' affiliations

DOI: https://doi.org/10.15866/ireche.v9i3.14901

Abstract

Critical point calculations are extremely useful in Chemical Engineering context, since the correct prediction of the critical coordinates are important in various situations (for instance, in enhanced oil recovery). In this work, we proposed the use of the basins of attraction to show the convergence behavior of two strategies for critical point calculations in a system with two critical points, formed by methane + hydrogen sulfide. This kind of diagram – with complex convergence patterns – justifies the development of robust methodologies to solve systems of algebraic equations with multiple solutions.
Copyright © 2017 Praise Worthy Prize - All rights reserved.

Keywords

Critical Points; Basins of Attraction; Newton Methods

Full Text:

PDF

References

M. S. Soliman, Fractal erosion of basins of attraction in couple non-linear systems, J. Sound Vib. (1995) 182 729-740.
http://dx.doi.org/10.1006/jsvi.1995.0229

E. Spedicato, Z. Huang, Numerical experience with Newton-like methods for nonlinear algebraic systems, Computing (1990) 58 69-89.
http://dx.doi.org/10.1007/bf02684472

G. M. Platt, I. N. Bastos, R. P. Domingos, Calculation of double retrograde vaporization: Newton’s methods and hyperheuristic approach, J. Nonlinear Systems and Applications (2012) 3 107-120.
http://dx.doi.org/10.1155/2012/682087

R. A. Heidemann, A. M. Khalil, The calculation of critical points, AIChE Journal 26(5) (1980) 769-779.
http://dx.doi.org/10.1002/aic.690260510

P. Dimitrakopoulos, W. Jia, C. Li, An improved computational method for the calculation of mixture liquid-vapor critical points, Int. J. Thermophys. (2014) 35 865-889.
http://dx.doi.org/10.1007/s10765-014-1680-7

B. A. Stradi, Interval mathematics applied to critical point transitions, Revista de Matemática: Teoría Y Aplicaciones (2005) 12(1-2) 29-44.
http://dx.doi.org/10.15517/rmta.v12i1-2.248

S. M. Walas, Phase Equilibria in Chemical Engineering (Butterworth-Heinemann, 1985).
http://dx.doi.org/10.1016/b978-0-409-95162-2.50018-x

H. Nishiumi, T. Arai, Generalization of the binary interaction parameter of the Peng-Robinson equation of state by component family, Fluid Phase Equilibr. (1988) 42 43-62.
http://dx.doi.org/10.1016/0378-3812(88)80049-9

S. Sutherland, An introduction to Julia and Fatou sets (In: Fractals, Wavelets, and their Applications, Springer, 2014).
http://dx.doi.org/10.1007/978-3-319-08105-2_3

A. Lucia, X. Guo, P. J. Richey, R. Derebail, Simple process equations, fixed-point methods, and chaos, AIChE Journal (1990) 36(5) 641-654.
http://dx.doi.org/10.1002/aic.690360502

K. A. Green, S. Zhou, K. D. Luks, The fractal response of robust solutions techniques to the stationary point problem, Fluid Phase Equilibr. (1993) 84 49-78.
http://dx.doi.org/10.1016/0378-3812(93)85117-5

Refbacks

There are currently no refbacks.

Username
Password
Remember me