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Mathematical modelling of gas flow and determination of axial gas dispersion coefficients using numerical inverse laplace transform and maple in a typical commercial apparatus

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, a new simple method for determination of flow parameters, axial dispersion coefficients DL and Péclet numbers Pe was presented. This method is based on an accurate measurement model considering pulse tracer response. Our method makes it possible to test the character of gas flow motion and precisely measure flow parameters for different pressures and temperatures. The idea of combining the transfer function, numerical inversion of the Laplace transform and optimisation method gives many benefits like a simple and effective way of finding solution of inverse problem and model coefficients. The calculated values of flow parameters (DL and/or Pe) suggest that in the considered case the gas flow is neither plug flow nor perfect mixing under operation condition. The obtained outcomes agree with the gas flow theory. Calculations were performed using the CAS program type, Maple.
Rocznik
Strony
223--–232
Opis fizyczny
Bibliogr. 26 poz., rys.
Twórcy
autor
  • Rzeszow University of Technology, Faculty of Chemistry, Department of Chemical and Process Engineering, al. Powstancow Warszawy 6, 35-959 Rzeszow
  • Rzeszow University of Technology, Faculty of Chemistry, Department of Chemical and Process Engineering, al. Powstancow Warszawy 6, 35-959 Rzeszow
Bibliografia
  • 1. Abate J., Valko P., 2004. Multi-precision Laplace transform inversion. Int. J. Numer. Meth. Engng., 60, 979–993. DOI: 10.1002/nme.995.
  • 2. Ali M., Awais M., 2014. Laplace transform method for unsteady thin film flow of a second grade fluid through a porous medium. J. Mod. Phys., 5, 103–106. DOI: 10.4236/jmp.2014.53017.
  • 3. Bellman R.E., Kalaba R.E., Lockett J., 1967. Numerical inversion of Laplace transforms. IEEE Trans. Autom. Control, 12, 624–625. DOI: 10.1109/TAC.1967.1098700.
  • 4. Boupha K., Jacobs J.M., Hatfield K., 2004. MDL Groundwater software: Laplace transforms and the De Hoog algorithm to solve contaminant transport equation. Comput. Geosci., 30, 445–453. DOI: 10.1016/j.cageo.2004.02.001.
  • 5. Cheng A.H-D., Sidauruk P., 1994. Approximate inversion of the Laplace transform. Mathematica Journal, 4(1), 76–82.
  • 6. Chen J.S., Liu C.W., Chenb C.S., Yehc H.D., 1996. A Laplace transform solution for tracer tests in a radially convergent flow field with upstream dispersion. J. Hydrol., 183, 263–275. DOI: 10.1016/0022-1694(95)02972-9.
  • 7. Chiang L.-W., 1989. The application of numerical Laplace inversion methods to groundwater flow and solute transport problems. New Mexico Institute of Mining and Technology, New Mexico.
  • 8. Cohen A.M., 2007. Numerical methods for Laplace transform inversion. Springer, Boston, MA. DOI: 10.1007/978-0-387-68855-8.
  • 9. Davies B., Martin B., 1979. Review Numerical Inversion of the Laplace transform: A survey and comparison of methods. J. Comput. Phys., 33, 1–32. DOI: 10.1016/0021-9991(79)90025-1.
  • 10. Duffy D.G., 1993. On the numerical inversion of Laplace transform: comparison of three new methods on characteristic problems from applications. ACM Trans. Math. Software, 19, 333–359. DOI: 10.1145/155743.155788.
  • 11. Endah R.M., Surjanto S. D., 2017. Performance of Gaver-Stehfest numerical Laplace inversion method on option pricing formulas. Int. J. Comput. Sci. Appl. Math., 3, 71–76. DOI: 10.12962/j24775401.v3i2.2215.
  • 12. Escobar F.H., Leguizamo F.A., Cantillo J.H., 2014. Comparison of Stehfest’s and Iseger’s algorithms for Laplacian inversion in pressure well tests. J. Eng. Appl. Sci., 9(6), 919–922.
  • 13. Hassanzadeh H., Pooladi-Darvish M., 2007. Comparison of different numerical Laplace inversion methods for engineering applications. Appl. Math. Comput., 189, 1966–1981. DOI: 10.1016/j.amc.2006.12.072.
  • 14. Knight J.H., Raiche A.P., 1982. Transient electromagnetic calculations using the Gaver- Stehfest inverse Laplace transform method. Geophys., 47, 47–50. DOI: 10.1190/1.1441280.
  • 15. Kocabas I., 2011. Application of iterated Laplace transformation to tracer transients in heterogeneous porous media. J. Franklin Inst., 348, 1339–1362. DOI: 10.1016/j.jfranklin.2010.04.002.
  • 16. Montella C., 2008. LSV modelling of electrochemical systems through numerical inversion of Laplace transforms, I: The GSLSV algorithm. J. Electroanal. Chem., 614, 121–130. DOI: 10.1016/j.jelechem.2007.11.010.
  • 17. Narayanan G.V., Beskos D.E., 1982. Numerical operational methods for time-dependent linear problems. Int. J. Numer. Methods Eng., 18, 1829–1854. DOI: 10.1002/nme.1620181207.
  • 18. Smith N., Brancik L., 2016. Comparative study on one-dimensional numerical inverse Laplace transform methods for electrical engineering. Elektrorevue, 18(1), 1–6.
  • 19. Taiwo O., King R., 2003. Determination of kinetic parameters for the adsorption of a protein on porous beads using symbolic computation and numerical Laplace inversion. Chem. Eng. Process., 42, 561–568. DOI: 10.1016/S0255-270(02)00068-5.
  • 20. Taiwo O., Schultz J., Krebs V., 1995. A comparison of two methods for the numerical inversion of Laplace transforms. Comp. Chem. Eng., 19, 303–308. DOI: 10.1016/0098-1354(94)00055-S.
  • 21. Wang Q., Zhan H., 2015. On different numerical inverse Laplace methods for solute transport problems. Adv.Water Resour., 75, 80–92. DOI: 10.1016/j.advwaters.2014.11.001.
  • 22. Wójcik M., Szukiewicz M., Kowalik P., 2015. Application of numerical Laplace inversion methods in chemical engineering with Maple® . J. Appl. Comp. Sci. Methods, 7, 5–15. DOI: 10.1515/jacsm-2015-0006.
  • 23. Wójcik M., Szukiewicz M., Kowalik P., Próchniak W., 2017. The efficiency of the Gaver-Stehfest method to solve one-dimensional gas flow model. Adv. Sci Technol. Res. J., 11(1), 246–252. DOI: 10.12913/22998624/68138.
  • 24. Wyns P., Foty D.P., Oughstun K.E., 1989. Numerical analysis of the precursor fields in linear dispersive pulse propagation. J. Opt. Soc. Am. A, 6, 1421–1429. DOI: 10.1364/JOSAA.6.001421.
  • 25. Yang F., Wang X., Liu H., 2011. Application of Laplace transform in well test interpretation – an example of Tahe oil field cavity – fractured reservoirs in Tarim Basin. 2011 International Conference on Multimedia Technology (ICTM), IEEE, Hangzhou, China, 26–29 July 2011, 1988–1991. DOI: 10.1109/ICMT.2011.6002378.
  • 26. Zhang J., 2007. Some innovative numerical approaches for pricing American options. University of Wollongong Thesis Collection, Wollongong, Australia.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6d4fcde5-3eb4-42ac-a2cf-7ce467ae331a
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