Thermodynamic Speed of Sound for Multiphase Multi-Reactive Equilibrium Systems

  • José Luiz de MedeirosEmail author
  • Lara de Oliveira Arinelli
  • Ofélia de Queiroz Fernandes Araújo


Rigorous formulas for the thermodynamic sound speed are developed via a steady-state, unidimensional, isentropic, multiphase, and multi-reactive equilibrium plug-flow. A correspondence between a multiphase multi-reactive plug-flow element and an equilibrium closed system (ECS), with two equilibrium state coordinates, is the main theoretical resource being used. Within ECS framework, momentum and energy flow balances lead to the sound speed derivation for complex equilibrium streams. The sound speed is also investigated in the critical neighborhood using the Landau Model to prove the absence of ± singularities at the critical point, despite critical lambda-shaped ± singularities of \(\overline{C}_{P}\) and density derivatives. A method is also detailed for calculating the sound speed of multiphase and multi-reactive streams using ECS thermodynamic properties provided by multiphase Flash(P, T) of HYSYS 8.8 simulator. Unit operation extensions (UOE) are proposed for estimating the multiphase and multi-reactive sound speed via HYSYS. With HYSYS, multiphase and/or multi-reactive equilibria, including liquid water segregation, are solved to feed the ECS sound speed formula. Multiphase examples are solved: natural gas, oil–water–gas, and supersonic separator for adjustment of water and hydrocarbon dew-points of natural gas. Multi-reactive multiphase sound speeds are predicted in supersonic reactors for methane pyrolysis and for two-phase methanol oxidation to formaldehyde.


  1. Arinelli, L.O., Trotta, T.A.F., Teixeira, A.M., de Medeiros, J.L., Araújo, O.Q.F.: Offshore processing of CO2 rich natural gas with supersonic separator versus conventional routes. J. Nat. Gas Sci. Eng. 46, 199–221 (2017). Scholar
  2. Bedard, R.L., Naunheimer, C., Gavin P. Towler, G.P.: Methane conversion apparatus and process using a supersonic flow reactor. US Patent 2014/0058160A1, 2014Google Scholar
  3. Cao, X., Yang, W.: The dehydration performance evaluation of a new supersonic swirling separator. J. Nat. Gas Sci. Eng. 1–10 (2015). Scholar
  4. Castier, M.: Thermodynamic speed of sound in multiphase systems. Fluid Phase Equilib. 306, 204–211 (2011). Scholar
  5. Cheng, A.T.Y.: Process for accelerating fast reactions using high-intensity plug-flow tubular reactors. Patent EP0995489 A2, 2000Google Scholar
  6. Crowl, D.A., Louvar, J.F.: Chemical Process Safety: Fundamentals with Applications, 2nd edn. Prentice Hall, USA (2002)Google Scholar
  7. de Medeiros, J.L., Arinelli, L.O., Araújo, O.Q.F.: Speed of sound of multiphase and multi-reactive equilibrium streams: a numerical approach for natural gas applications. J. Nat. Gas Sci. Eng. 46, 222–241 (2017). Scholar
  8. Ehinmowoa, A.B., Orodub, O.D., Anaweb, P.A.L., Ogunleyec, O.O.: Attenuating severe slug flow at large valve opening for increased oil production without feedback control signal. J. Petrol. Sci. Eng. 146, 1130–1141 (2016)CrossRefGoogle Scholar
  9. Fox, R.W., McDonald, A.T., Pritchard, P.J.: Introduction to Fluid Mechanics, 6th edn. Wiley, New York, USA (2004)zbMATHGoogle Scholar
  10. Hammer, M., Wahl, P.E., Anantharaman, R., Berstad, D., Lervåg, K.Y.: CO2 capture from off-shore gas turbines using supersonic gas separation. Energy Procedia 63, 243–252 (2014). Scholar
  11. Landau, L.D.: On the Theory of Phase Transitions. Translated from Landau L.D. “Collected Papers”, vol. 1, pp. 234–252. Nauka, Moscow (1969)Google Scholar
  12. Leung, J.C., Grolmes, M.A.: The discharge of two-phase flashing flow in a horizontal duct. AIChE J. 33(3), 524–527 (1987). Scholar
  13. Libby, P.A.: Theoretical analysis of turbulent mixing of reactive gases with application to supersonic combustion of hydrogen. ARS J. 32(3), 388–396 (1962). Scholar
  14. Machado, P.B., Monteiro, J.G.M., Medeiros, J.L., Epsom, H.D., Araujo, O.Q.F.: Supersonic separation in onshore natural gas dew point plant. J. Nat. Gas Sci. Eng. 6, 43–49 (2012). Scholar
  15. Mcmurtrey, L.J.: Nuclear powered water jet engine. US Patent US 3151596 A, 1964Google Scholar
  16. Nichita, D.V., Broseta, D., Leibovici, C.F.: Reservoir fluid applications of a pseudo-component delumping new analytical procedure. J. Pet. Sci. Eng. 59, 59–72 (2007)CrossRefGoogle Scholar
  17. Nichita, D.V., Khalid, P., Broseta, D.: Calculation of isentropic compressibility and sound velocity in two-phase fluids. Fluid Phase Equilib. 291(1), 95–102 (2010)CrossRefGoogle Scholar
  18. OGJ: Petrobras signs LOI to charter FPSO for Libra field. Oil Gas J. (2014)Google Scholar
  19. Powers, J.M., Paolucci, S.: Accurate spatial resolution estimates for reactive supersonic flow with detailed chemistry. AIAA J. 43(5), 1088–1099 (2005). Scholar
  20. Raniere, F.D., Schuman, M.D.: Method of controlling pyrolysis temperature. US Patent 4,724,272, 1988Google Scholar
  21. Romm, L., Somorjai, G.A.: High-temperature short-contact-time supersonic nozzle chemistry of light aliphatic hydrocarbons. Top. Catal. 20(1–4), 53–63 (2002)CrossRefGoogle Scholar
  22. Schinkelshoek, P., Epsom, H.D.: Supersonic gas conditioning—commercialisation of twister technology. GPA Annual Convention Proceedings, pp. 739–745. Grapevine, Texas, USA (2008)Google Scholar
  23. Secchi, R., Innocenti, G., Fiaschi, D.: Supersonic Swirling Separator for natural gas heavy fractions extraction: 1D model with real gas EOS for preliminary design. J. Nat. Gas Sci. Eng. 34, 197–215 (2016). Scholar
  24. Shandor, M., Stone, A.R., Walker, R.E.: Secondary gas injection in a conical rocket nozzle. AIAA J. 1(2), 334–338 (1963). Scholar
  25. Turner, J.: F-18 Hornet High-Speed (Transonic) Flyby (2009). Accessed 1 Aug 2017
  26. Wilkinson, J.: Wilk4: breaking the sound barrier (and Vapor Cones around Jets) (2012). Retrieved 31 Oct 2012
  27. Wood, A.B.: A Textbook of Sound: Being an Account of the Physics of Vibrations with Special Reference to Recent Theoretical and Technical Developments. The Macmillan Company, New York (1930)zbMATHGoogle Scholar
  28. Yang, Y., Wen, C., Wang, S., Feng, Y.: Numerical simulation of real gas flows in natural gas supersonic separation processing. J. Nat. Gas Sci. Eng. 21, 829–836 (2014). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • José Luiz de Medeiros
    • 1
    Email author
  • Lara de Oliveira Arinelli
    • 1
  • Ofélia de Queiroz Fernandes Araújo
    • 1
  1. 1.Escola de QuímicaFederal University of Rio de Janeiro (UFRJ)Rio de JaneiroBrazil

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