Skip to main content

Advertisement

SpringerLink
Log in

Magnetic resonance measurement of fluid dynamics and transport in tube flow of a near-critical fluid

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

An ability to predict fluid dynamics and transport in supercritical fluids is essential for optimization of applications such as carbon sequestration, enhanced oil recovery, “green” solvents, and supercritical coolant systems. While much has been done to model supercritical velocity distributions, experimental characterization is sparse, owing in part to a high sensitivity to perturbation by measurement probes. Magnetic resonance (MR) techniques, however, detect signal noninvasively from the fluid molecules and thereby overcome this obstacle to measurement. MR velocity maps and propagators (i.e., probability density functions of displacement) were acquired of a flowing fluid in several regimes about the critical point, providing quantitative data on the transport and fluid dynamics in the system. Hexafluoroethane (C2F6) was pumped at 0.5 ml/min in a cylindrical tube through an MR system, and propagators as well as velocity maps were measured at temperatures and pressures below, near, and above the critical values. It was observed that flow of C2F6 with thermodynamic properties far above or below the critical point had the Poiseuille flow distribution of an incompressible Newtonian fluid. Flows with thermodynamic properties near the critical point exhibit complex flow distributions impacted by buoyancy and viscous forces. The approach to steady state was also observed and found to take the longest near the critical point, but once it was reached, the dynamics were stable and reproducible. These data provide insight into the interplay between the critical phase transition thermodynamics and the fluid dynamics, which control transport processes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Albert K, Braumann U, Tseng LH, Nicholson G, Bayer E, Spraul M, Hofmann M, Dowle C, Chippendale M (1994) Online coupling of supercritical-fluid chromatography and proton high-field nuclear-magnetic-resonance spectroscopy. Anal Chem 66(19):3042–3046

    Article  Google Scholar 

  • Allen LA, Glass TE, Dorn HC (1988) Direct monitoring of supercritical fluids and supercritical chromatographic separations by proton nuclear magnetic-resonance. Anal Chem 60(5):390–394

    Article  Google Scholar 

  • Bae YY, Kim HY (2009) Convective heat transfer to CO2 at a supercritical pressure flowing vertically upward in tubes and an annular channel. Exp Therm Fluid Sci 33(2):329–339. doi:10.1016/j.expthermflusci.2008.10.002

    Article  Google Scholar 

  • Bae JH, Yoo JY, Choi H (2005) Direct numerical simulation of turbulent supercritical flows with heat transfer. Phys Fluids 17(10). doi:10.1063/1.2047588

  • Barmatz M, Hahn I, Lipa JA, Duncan RV (2007) Critical phenomena in microgravity: past, present, and future. Rev Mod Phys 79:1–52. doi:10.1103/RevModPhys.79.1

    Article  Google Scholar 

  • Beysens DA (2005) Near-critical point hydrodynamics and microgravity. In: Kowalewski TA (ed) Mechanics of the 21st century (Proceedings of the 21st international congress of theoretical and applied mechanics), 15–21 August 2004, Warsaw, Poland. Springer, Netherlands, pp 117-130

  • Bruch A, Bontemps A, Colasson S (2009) Experimental investigation of heat transfer of supercritical carbon dioxide flowing in a cooled vertical tube. Int J Heat Mass Transf 52(11–12):2589–2598. doi:10.1016/j.ijheatmasstransfer.2008.12.021

    Article  Google Scholar 

  • Brunner G (2005) Supercritical fluids: technology and application to food processing. J Food Eng 67(1–2):21–33. doi:10.1016/j.jfoodeng.2004.05.060

    Article  Google Scholar 

  • Callaghan PT (1991) Principles of nuclear magnetic resonance microscopy. Oxford University Press, New York

    Google Scholar 

  • Callaghan PT (2011) Translational dynamics and magnetic resonance: principles of pulsed gradient spin echo NMR. Oxford University Press, Oxford

    Book  Google Scholar 

  • Codd SL, Manz B, Seymour JD, Callaghan PT (1999) Taylor dispersion and molecular displacements in poiseuille flow. Phys Rev E Stat Phys Plasmas Fluids 60(4):R3491–R3494

    Article  Google Scholar 

  • Dang CB, Hihara E (2004) In-tube cooling heat transfer of supercritical carbon dioxide. Part 2. Comparison of numerical calculation with different turbulence models. Int J Refrig 27(7):748–760. doi:10.1016/j.ijrefrig.2004.04.017

    Article  Google Scholar 

  • de Gennes PG (ed) (1975) Phase transition and turbulence: an introduction. In: Proceedings of the NATO advanced study institute on fluctuations, instabilities, and phase transitions. Plenum Press, New York

  • Duffey RB, Pioro IL (2005) Experimental heat transfer of supercritical carbon dioxide flowing inside channels (survey). Nucl Eng Des 235(8):913–924

    Article  Google Scholar 

  • Dvoyashkin M, Valiullin R, Karger J (2007a) Supercritical fluids in mesopores—new insight using NMR. Adsorption 13(3–4):197–200. doi:10.1007/s10450-007-9064-y

    Article  Google Scholar 

  • Dvoyashkin M, Valiullin R, Karger J, Einicke WD, Glaser R (2007b) Direct assessment of transport properties of supercritical fluids confined to nanopores. J Am Chem Soc 129 (34):10344. doi:10.1021/ja074101+

  • Fard MH (2009) CFD modeling of heat transfer of CO2 at supercritical pressures flowing vertically in porous tubes. Int Commun Heat Mass 37(1):98–102. doi:10.1016/j.icheatmasstransfer.2009.08.004

    Article  MathSciNet  Google Scholar 

  • Fukushima E, Roeder SBW (1981) Experimental pulse NMR: a nuts and bolts approach. Addison-Wesley, Reading, MA

    Google Scholar 

  • He S, Kim WS, Jackson JD (2008) A computational study of convective heat transfer to carbon dioxide at a pressure just above the critical value. Appl Therm Eng 28(13):1662–1675. doi:10.1016/j.applthermaleng.2007.11.001

    Article  Google Scholar 

  • Hohenberg PC, Halperin BI (1977) Theory of dynamic critical phenomena. Rev Mod Phys 49(3):435–479

    Article  Google Scholar 

  • Howell JR, Lee SH (1999) Convective heat transfer in the entrance region of a vertical tube for water near the thermodynamic critical point. Int J Heat Mass Transf 42(7):1177–1187

    Article  MATH  Google Scholar 

  • Hussain R, Pintelon TRR, Mitchell J, Johns ML (2011) Using NMR displacement measurements to probe CO2 entrapment in porous media. AIChE J 57(7):1700–1709. doi:10.1002/aic.12401

    Article  Google Scholar 

  • Jackson JD, Hall WB (ed) (1979) Influences of buoyancy on heat transfer to fluids in vertical tubes under turbulent conditions. In: Turbulent forced convection in channels and bundles. Hemisphere Publishing Corp, New York

  • Jain PK, Rizwan U (2008) Numerical analysis of supercritical flow instabilities in a natural circulation loop. Nucl Eng Des 238(8):1947–1957. doi:10.1016/j.nucengdes.2007.10.034

    Article  Google Scholar 

  • Jiang PX, Xu YJ, Lv J, Shi RF, He S, Jackson JD (2004) Experimental investigation of convection heat transfer of CO2 at super-critical pressures in vertical mini-tubes and in porous media. Appl Therm Eng 24(8–9):1255–1270. doi:10.1016/j.applthermaleng.2003.12.024

    Article  Google Scholar 

  • Jiang PX, Shi RF, Xu YJ, He S, Jackson JD (2006) Experimental investigation of flow resistance and convection heat transfer of CO2 at supercritical pressures in a vertical porous tube. J Supercrit Fluids 38(3):339–346. doi:10.1016/j.supflu.2005.12.004

    Article  Google Scholar 

  • Jiang PX, Shi RF, Zhao CR, Xu YJ (2008a) Experimental and numerical study of convection heat transfer of CO2 at supercritical pressures in vertical porous tubes. Int J Heat Mass Transf 51(25–26):6283–6293. doi:10.1016/j.ijheatmasstransfer.2008.05.014

    Article  MATH  Google Scholar 

  • Jiang PX, Zhang Y, Shi RF (2008b) Experimental and numerical investigation of convection heat transfer Of CO2 at supercritical pressures in a vertical mini-tube. Int J Heat Mass Transf 51(11–12):3052–3056. doi:10.1016/j.ijheatmasstransfer.2007.09.008

    Article  Google Scholar 

  • Jiang PX, Zhang Y, Xu YJ, Shi RF (2008c) Experimental and numerical investigation of convection heat transfer of CO2 at supercritical pressures in a vertical tube at low Reynolds numbers. Int J Therm Sci 47(8):998–1011. doi:10.1016/j.ijthermalsci.2007.08.003

    Article  Google Scholar 

  • Jiang PX, Zhao CR, Shi RF, Chen Y, Ambrosini W (2009) Experimental and numerical study of convection heat transfer of CO2 at super-critical pressures during cooling in small vertical tube. Int J Heat Mass Transf 52(21–22):4748–4756. doi:10.1016/j.ijheatmasstransfer.2009.06.014

    Article  Google Scholar 

  • Klusman RW (2003) Evaluation of leakage potential from a carbon dioxide EOR/sequestration project. Energy Convers Manag 44(12):1921–1940. doi:10.1016/s0196-8904(02)00226-1

    Article  Google Scholar 

  • Kuethe DO, Pietrass T, Behr VC (2005) Inert fluorinated gas T-1 calculator. J Magn Reson 177(2):212–220. doi:10.1016/j.jmr.2005.07.022

    Article  Google Scholar 

  • Kurganov VA, Kaptil’ny AG (1992) Velocity and enthalpy fields and eddy diffusivities in a heated supercritical fluid flow. Exp Therm Fluid Sci 5:465–478

    Article  Google Scholar 

  • Kurganov VA, Kaptilnyi AG (1993) Flow structure and turbulent transport of a supercritical pressure fluid in a vertical heated tube under the conditions of mixed convection—experimental-data. Int J Heat Mass Transf 36(13):3383–3392

    Article  Google Scholar 

  • Landau LD, Lifshitz EM (1959) Fluid mechanics, vol 26. Pergamon Press, London

    Google Scholar 

  • Lee SH, Howell JR (1996a) Gravitational effects on laminar convection to near-critical water in a vertical tube. J Thermophys Heat Transf 10(4):627–632

    Article  Google Scholar 

  • Lee SH, Howell JR (1996b) Laminar forced convection at zero gravity to water near the critical region. J Thermophys Heat Transf 10(3):504–510

    Article  Google Scholar 

  • Lemmon EW, McLinden MO, Friend DG (2013) Thermophysical properties of fluid systems in NIST chemistry webbook, NIST standard reference database, vol 69. National Institute of Standards and Technology, Gaithersburg, MD 20899. http://webbook.nist.gov/chemistry/. Accessed 6 May 2013

  • Liao SM, Zhao TS (2002) An experimental investigation of convection heat transfer to supercritical carbon dioxide in miniature tubes. Int J Heat Mass Trans 45(25):5025–5034

    Article  Google Scholar 

  • Madani H, Valtz A, Coquelet C, Meniai AH, Richon D (2008) Vapor–liquid equilibrium data for the (hexafluoroethane + 1,1,1,2-tetrafluoroethane) system at temperatures from 263 to 353 K and pressures up to 4.16 MPa. Fluid Phase Equilib 268(1–2):68–72. doi:10.1016/j.fluid.2008.08.011

    Article  Google Scholar 

  • Maiwald M, Li HP, Schnabel T, Braun K, Hasse H (2007) On-line H-1 NMR spectroscopic investigation of hydrogen bonding in supercritical and near critical CO2-methanol up to 35 MPa and 403 K. J Supercrit Fluids 43:267–275. doi:10.1016/j.supflu.2007.05.009

    Article  Google Scholar 

  • Newling B (2008) Gas flow measurements by NMR. Prog Nucl Magn Reson Spectrosc 52:31–48

    Article  Google Scholar 

  • Okamoto K, Ota J, Sakurai K, Madarame H (2003) Transient velocity distributions for the supercritical carbon dioxide forced convection heat transfer. J Nucl Sci Technol 40(10):763–767

    Article  Google Scholar 

  • Okwen RT, Stewart MT, Cunningham JA (2009) Analytical solution for estimating storage efficiency of geologic sequestration of CO2. Int J Greenh Gas Con 4(1):102–107. doi:10.1016/j.ijggc.2009.11.002

    Article  Google Scholar 

  • Onuki A (1998) Nonequilibrium phase transitions in extreme conditions: effects of shear flow and heat flow. J Phys Condens Mat 10(49):11473–11490

    Article  Google Scholar 

  • Onuki A (2002) Phase transition dynamics. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Onuki A, Kawasaki K (1978) Fluctuations in non-equilibrium steady states with laminar shear-flow—classical fluids near the critical-point. Sup Prog Theor Phys 64:436–441

    Article  Google Scholar 

  • Orr FM, Taber JJ (1984) Use of carbon-dioxide in enhanced oil-recovery. Science 224(4649):563–569

    Article  Google Scholar 

  • Parker ME, Meyer JP, Meadows SR (2009) Carbon dioxide enhanced oil recovery injection technologies. In: Gale J, Herzog H, Braitsch J (eds) Greenhouse gas control technologies 9 (Energy Procedia), vol 1, pp 3141–3148

  • Pioro IL, Khartabil HF, Duffey RB (2004) Heat transfer to supercritical fluids flowing in channels—empirical correlations (survey). Nucl Eng Des 230(1–3):69–91

    Article  Google Scholar 

  • Rassi EM, Codd SL, Seymour JD (2012) MR measurement of critical phase transition dynamics and supercritical fluid dynamics in capillary and porous media flow. J Magn Reson 214:309–314. doi:10.1016/j.jmr.2011.09.045

    Article  Google Scholar 

  • Ravagnani A, Ligero EL, Suslick SB (2009) CO2 sequestration through enhanced oil recovery in a mature oil field. J Petrol Sci Eng 65:129–138

    Article  Google Scholar 

  • Saikawa K, Kijima J, Uematsu M, Watanabe K (1979) Determination of the critical-temperature and density of hexafluoroethane. J Chem Eng Data 24(3):165–167

    Article  Google Scholar 

  • Stanley HE (1971) Introduction to phase transitions and critical phenomena. Oxford University Press, New York

    Google Scholar 

  • Stejskal EO, Tanner JE (1965) Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J Chem Phys 42:288

    Article  Google Scholar 

  • Suekane T, Furukawa N, Tsushima S, Hirai S, Kiyota M (2009) Application of MRI in the measurement of two-phase flow of supercritical CO2 and water in porous rocks. J Porous Media 12(2):143–154

    Article  Google Scholar 

  • Tanaka H, Tsuge A, Hirata M, Nishiwak N (1973) Effects of buoyancy and of acceleration owing to thermal-expansion on forced turbulent convection in vertical circular tubes—criteria of effects, velocity and temperature profiles, and reverse transition from turbulent to laminar-flow. Int J Heat Mass Transf 16(6):1267–1288

    Google Scholar 

  • Van der Meer LGH (1995) The CO2 storage efficiency of aquifers. Energy Convers Manag 36(6–9):513–518

    Article  Google Scholar 

  • Yonker CR, Linehan JC (2005) The use of supercritical fluids as solvents for NMR spectroscopy. Prog Nucl Magn Reson Spectrosc 47(1–2):95–109. doi:10.1016/j.pnmrs.2005.08.002

    Article  Google Scholar 

  • Zappoli B (2003) Near-critical fluid hydrodynamics. CR Mech 331(10):713–726. doi:10.1016/j.crme.2003.05.001

    Article  MATH  Google Scholar 

  • Zappoli B, Amiroudine S, Gauthier S (1999) Rayleigh–Taylor-like instability in near-critical pure fluids. Int J Thermophys 20(1):257–265

    Article  Google Scholar 

  • Zhou N, Krishnan A (1995) Laminar and turbulent heat transfer in flow of supercritical CO2. In: 1995 national heat transfer conference, Portland, OR, 1995. ASME, pp 53–63

Download references

Acknowledgments

The authors would like to thank the members of the Magnetic Resonance Laboratory at Montana State University for assistance and support. S.L.C. acknowledges support by the National Science Foundation under CBET Grant 1335534. S.L.C. and J.D.S. acknowledge support, in part, by the Department of Energy under Grant DEFG02-11ER90025. J.M.B. acknowledges support by the Department of Energy under Grant DEFE0000397. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Department of Energy or the National Science Foundation. Equipment was funded by the National Science Foundation and the M.J. Murdock Charitable trust.

Author information

Authors and Affiliations

  1. Mechanical and Industrial Engineering Department, Montana State University, 314 Roberts Hall, Bozeman, MT, 59717, USA

    Joshua M. Bray, Erik M. Rassi & Sarah L. Codd

  2. Department of Chemical and Biological Engineering, Montana State University, Bozeman, MT, USA

    Joshua M. Bray & Joseph D. Seymour

Authors
  1. Joshua M. Bray
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik M. Rassi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joseph D. Seymour
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sarah L. Codd
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sarah L. Codd.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bray, J.M., Rassi, E.M., Seymour, J.D. et al. Magnetic resonance measurement of fluid dynamics and transport in tube flow of a near-critical fluid. Exp Fluids 55, 1777 (2014). https://doi.org/10.1007/s00348-014-1777-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00348-014-1777-6

Keywords

Search

Navigation