Skip to main content
SpringerLink
Log in

Modeling Multicomponent Fluid Flow in Deforming and Reacting Porous Rock

  • Published:
Petrology Aims and scope Submit manuscript

Abstract

We propose a coupled hydro-mechanical-chemical model and its 1D numerical implementation. We demonstrate its application to the model filtration of a multicomponent fluid in deforming and reacting host rocks, considering changes in the densities, phase proportions, and the chemical compositions of the coexisting phases. The presented 1D numerical implementation is illustrated by the example of soapstone formation from serpentinite during the filtration of Н2О−CО2 fluid with a low CО2 concentration coupled with the viscous deformation of the mineral matrix, considering the MgO−SiO2−Н2О−CО2 system. The numerical results show the propagation of a porosity wave by means of a viscous (de)compaction mechanism accompanied by the formation of an elongated zone with higher filtration properties. After the formation of such a channel, the formation and propagation of the reaction fronts occur and are associated with the transformation of the mineral composition of the original rock. During H2O−CO2 fluid filtration, starting with 1 wt % dissolved CO2, carbonization of hydrated serpentinite starts, specifically antigorite transforms to magnesite and talc.

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.

REFERENCES

  1. Aranovich, L. Ya., Fluid–mineral equilibria and thermodynamic mixing properties of fluid systems, Petrology, 2013, vol. 21, no. 6, pp. 588–599.

    Article  Google Scholar 

  2. Aranovich, L.Y., The role of brines in high-temperature metamorphism and granitization, Petrology, 2017, vol. 25, pp. 486–497.

    Article  CAS  Google Scholar 

  3. Aranovich, L.Y. and Newton, R.C., H2O activity in concentrated NaCl solutions at high pressures and temperatures measured by the brucite–periclase equilibrium, Contrib. Mineral. Petrol., 1996, vol. 125, pp. 200–212.

    Article  CAS  Google Scholar 

  4. Aranovich, L.Y. and Newton, R.C., H2O activity in concentrated KCl and KCl–NaCl solutions at high temperatures and pressures measured by the brucite–periclase equilibrium, Contrib. Mineral. Petrol., 1997, vol. 127, pp. 261–271.

    Article  CAS  Google Scholar 

  5. Aranovich, L.Y. and Newton, R.C., Reversed determination of the reaction; phlogopite+quartz= enstatite+potassium feldspar+H2O in the ranges 750–875oC and 2–12 kbar at low H2O activity with concentrated KCl solutions, Am. Mineral., 1998, vol. 83, no. 3–4, pp. 193–204.

    Article  CAS  Google Scholar 

  6. Aranovich, L.Y. and Newton, R.C., Experimental determination of CO2-H2O activity-composition relations at 600–1000oC and 6–14 kbar by reversed decarbonation and dehydration reactions, Am. Mineral., 1999, vol. 84, no. 9, pp. 1319–1332.

    Article  CAS  Google Scholar 

  7. Aranovich, L.Y., Newton, R.C., and Manning, C.E., Brine-assisted anatexis: experimental melting in the system haplogranite–H2O–NaCl–KCl at deep-crustal conditions, Earth Planet. Sci. Lett., 2013, vol. 374, pp. 111–120.

    Article  CAS  Google Scholar 

  8. Aranovich, L.Y., Akinfiev, N.N., and Golunova, M., Quartz solubility in sodium carbonate solutions at high pressure and temperature, Chem. Geol., 2020, vol. 550. 119699.

    Article  CAS  Google Scholar 

  9. Beinlich, A., John, T., Vrijmoed, J.C., et al., Instantaneous rock transformations in the deep crust driven by reactive fluid flow, Nat. Geosci., 2020, vol. 13, no. 4, pp. 307–311.

    Article  CAS  Google Scholar 

  10. Bessat, A., Pilet, S., Podladchikov, Y.Y., and Schmalholz, S.M., Melt migration and chemical differentiation by reactive porosity waves, Geochem., Geophys., Geosyst., 2022, vol. 23, no. 2. e2021GC009963.

  11. Beuchert, M.J. and Podladchikov, Y.Y., Viscoelastic mantle convection and lithospheric stresses, Geophysic. J. Int., 2010, vol. 183, no. 1, pp. 35–63.

    Article  Google Scholar 

  12. Bhatnagar, P., Nonlinear Wates in One-Dimensional Dispersive Systems, Clarendon Press, 1979.

    Google Scholar 

  13. Brown, M., The contribution of metamorphic petrology to understanding lithosphere evolution and geodynamics, Geosci. Front., 2014, vol. 5, no. 4, pp. 553–569.

    Article  Google Scholar 

  14. Gordon, S. and McBride, B.J., Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications, Part 1: Analysis. 1994, no. NAS 1.61:1311.

  15. Connolly, J.A.D., Computation of phase equilibria by linear programming: a tool for geodynamic modeling and its application to subduction zone decarbonation, Earth Planet. Sci. Lett., 2005, vol. 236, no. 1–2, pp. 524–541.

    Article  CAS  Google Scholar 

  16. Connolly, J.A.D., A primer in Gibbs energy minimization for geophysicists, Petrology, 2017, vol. 25, no. 5, pp. 526–534.

    Article  Google Scholar 

  17. Dobretsov, N.L., Glaukofanslantsevye i eklogit-glaukofanslantsevye kompleksy SSSR (Blueschist and Eclogite–Blueschist Complexes of the USSR), Sobolev, V.S., Eds., Novosibirsk: Nauka, 1974.

    Google Scholar 

  18. Dong, J.J., Hsu, J.Y., Wu, W.J., et al. Stress-dependence of the permeability and porosity of sandstone and shale from TCDP Hole-A, Int. J. Rock Mechanics Mining Sci., 2010, vol. 47, no. 7, pp. 1141–1157.

    Article  Google Scholar 

  19. Duretz, T., Räss, L., Podladchikov, Y.Y., and Schmalholz, S.M., Resolving thermomechanical coupling in two and three dimensions: spontaneous strain localization owing to shear heating, Geophys. J. Int., 2019, vol. 216, no. 1, pp. 365–379.

    Article  Google Scholar 

  20. Fletcher, R.C. and Hofmann, A.W., Simple models of diffusion and combined diffusion-infiltration metasomatism, Geochem. Transp. Kinetics, 1974, vol. 634, pp. 243–259.

    CAS  Google Scholar 

  21. Gerya, T., Introduction to Numerical Geodynamic Modelling (Cambridge University Press, 2019), pp. 179–241.

    Book  Google Scholar 

  22. Ghorbani, J., Nazem, M., and Carter, J.P., Numerical modelling of multiphase flow in unsaturated deforming porous media, Comp. Geotechn., 2016, vol. 71, pp. 195–206.

    Article  Google Scholar 

  23. Green, H.W., Psychology of a changing paradigm: 40+ years of high-pressure metamorphism, Int. Geol. Rev., 2005, vol. 47, no. 5, pp. 439–456.

    Article  Google Scholar 

  24. Hartz, E.H. and Podladchikov, Y.Y., Toasting the jelly sandwich: The effect of shear heating on lithospheric geotherms and strength, Geology, 2008, vol. 36, no. 4, pp. 331–334.

    Article  Google Scholar 

  25. Holland, T.J.B. and Powell, R., An internally consistent thermodynamic data set for phases of petrological interest, J. Metamorph. Geol., 1998, vol. 16, no. 3, pp. 309–343.

    Article  CAS  Google Scholar 

  26. Hu, H., Jackson, M.D., and Blundy, J., Melting, compaction and reactive flow: controls on melt fraction and composition change in crustal mush reservoirs, J. Petrol., 2022, vol. 63, no. 11. egac097.

  27. Isaeva, A.V., Dobrozhanskii, V.A., Khakimova, L.A., and Podladchikov, Yu.Yu., Numerical modeling of phase equilibria of multicomponent hydrocarbon systems using direct Gibbs energy minimization, Gas. Promyshl., 2021, no. 2, pp. 20–29.

  28. Jacobs, G.K. and Kerrick D.M., Methane: an equation of state with application to the ternary system H2O–CO2–CH4, Geochim. Cosmochim. Acta, 1981, vol. 45, no. 5, pp. 607–614.

    Article  CAS  Google Scholar 

  29. Katz, R.F., Magma dynamics with the enthalpy method: Benchmark solutions and magmatic focusing at mid-ocean ridges, J. Petrol., 2008, vol. 49, no. 12, pp. 2099–2121.

    Article  CAS  Google Scholar 

  30. Keller, T. and Suckale, J., A continuum model of multi-phase reactive transport in igneous systems, Geophys. J. Int., 2019, vol. 219, no. 1, pp. 185–222.

    Article  Google Scholar 

  31. Khakimova, L., Isaeva, A., Dobrozhanskiy, V., and Podladchikov, Y., Direct energy minimization algorithm for numerical simulation of carbon dioxide injection, SPE Russian Petroleum Technology Conference. OnePetro, 2021. D031S013R003.

  32. Klein, F. and Garrido, C.J., Thermodynamic constraints on mineral carbonation of serpentinized peridotite, Lithos, 2011, vol. 126, no. 3–4, pp. 147–160.

    Article  CAS  Google Scholar 

  33. Korzhinskii, D.S., Principle of alkali mobility during magmatic phenomena, On the 70 th Anniversary of the Academician D.S. Belyankin, Moscow: AN SSSR, 1946, pp. 242–261.

    Google Scholar 

  34. Korzhinskii, D.S., Dependence of metamorphism on depth in the volcanogenic formations, Tr. Lab. Vulkanol. Akad. Nauk SSSR (Proc. Lab. Volcanol. Akad. Nauk SSSR), Moscow: Akad. Nauk SSSR, 1961, pp. 5–11.

    Google Scholar 

  35. Lacinska, A.M., Styles, M.T., Bateman, K., et al., An experimental study of the carbonation of serpentinite and partially serpentinised peridotites, Front. Earth Sci., 2017, vol. 5, pp. 37.

    Article  Google Scholar 

  36. Lopatnikov, S.L. and Cheng, A.H.D., Variational formulation of fluid infiltrated porous material in thermal and mechanical equilibrium, Mechan. Materi., 2002, vol. 34, no. 11, pp. 685–704.

    Article  Google Scholar 

  37. Landau, L.D. and Lifshitz, E.M., Fluid Mechanics: Landau and Lifshitz: Course of Theoretical Physics, New York: Elsevier, 2013, vol. 6, pp. 13.

    Google Scholar 

  38. Malvoisin, B., Podladchikov, Y.Y., and Vrijmoed, J.C., Coupling changes in densities and porosity to fluid pressure variations in reactive porous fluid flow: Local thermodynamic equilibrium, Geochem., Geophys., Geosyst., 2015, vol. 16, no. 12, pp. 4362–4387 (2015).

  39. Malvoisin, B., Podladchikov, Y.Y., and Myasnikov, A.V., Achieving complete reaction while the solid volume increases: A numerical model applied to serpentinisation, Earth Planet. Sci. Lett., 2021, vol. 563. 116859.

    Article  CAS  Google Scholar 

  40. Moulas, E., Podladchikov, Y.Y., Aranovich, L.Y., and Kostopoulos, D., The problem of depth in geology: When pressure does not translate into depth, Petrology, 2013, vol. 21, pp. 527–538.

    Article  Google Scholar 

  41. Orr, F.M., Theory of gas injection processes, Copenhagen: Tie-Line Publications, 2007, vol. 5, pp. 61–123.

    Google Scholar 

  42. Padrón-Navarta, J.A., Sánchez-Vizcaíno, V.L., and Hermann, J. et al., Tschermak’s substitution in antigorite and consequences for phase relations and water liberation in high-grade serpentinites, Lithos, 2013, vol. 178, pp. 186–196.

    Article  Google Scholar 

  43. Panfilov, M., Physicochemical fluid dynamics in porous media, Applications in Geosciences and Petroleum Engineering, John Wiley & Sons, 2018, pp. 51–88.

    Book  Google Scholar 

  44. Perchuk, L.L., Magmatizm, metamorfizm, i geodinamika (Magmatism, Metamorphism, and Geodynamics), Moscow: Nauka, 1993.

  45. Perchuk, L.L., Lokal’nye ravnovesiya i P-T evolyutsiya glubinnykh metamorficheskikh kompleksov (Local Equilibria and P–T Evolution of Deep-Seated Metamorphic Complexes), Moscow: IGEM RAN, 2006.

  46. Perchuk, L.L., Local mineral equilibria and P-T paths: Fundamental principles and applications to high-grade metamorphic terranes, Geol. Soc. Amer., 2011, vol. 207, pp. 61–84.

    Google Scholar 

  47. Perchuk, L.L. and Podladchikov, Yu.Yu., P-T metamorphic paths and related geodynamic models, Vestn. Mosk. Gos. Univ., Ser. 4. Geol., 1993, no. 5, pp. 24–39.

  48. Perchuk, L.L., Podladchikov, Yu.Yu., and Polyakov, A.N., Geodynamic modeling of some metamorphic processes, J. Metamorph. Geol., 1992, vol. 10, pp. 311–318.

    Article  Google Scholar 

  49. Perchuk, L.L., Gerya, T.V., van Reenen, D.D., et al. Formation and evolution of Precambrian granulite terranes: a gravitational redistribution model, Geol. Soc. Am. Mem., 2011, vol. 207, pp. 289–310.

    Google Scholar 

  50. Pesavento, F., Schrefler, B. A., and Sciumè, G., Multiphase flow in deforming porous media: A review, Arch. Comp. Meth. Eng., 2017, vol. 24, pp. 423–448.

    Article  Google Scholar 

  51. Petrini, K. and Podladchikov, Y., Lithospheric pressure-depth relationship in compressive regions of thickened crust, J. Metamorph. Geol., 2000, vol. 18, no. 1, pp. 67–77.

    Article  Google Scholar 

  52. Picazo S., Malvoisin B., Baumgartner L., and Bouvier A.S., Low temperature serpentinite replacement by carbonates during seawater influx in the Newfoundland Margin, Minerals, 2020, vol. 10, no. 2, pp. 184.

    Article  CAS  Google Scholar 

  53. Plümper, O., John, T., Podladchikov, Y.Y. et al., Fluid escape from subduction zones controlled by channel-forming reactive porosity, Nat. Geosci., 2017, vol. 10, no. 2, pp. 150–156.

    Article  Google Scholar 

  54. Schmalholz, S.M. and Podladchikov, Y., Metamorphism under stress: The problem of relating minerals to depth, Geology, 2014, vol. 42, no. 8, pp. 733–734.

    Article  Google Scholar 

  55. Räss, L., Simon, N.S.C., and Podladchikov, Y.Y., Spontaneous formation of fluid escape pipes from subsurface reservoirs, Sci. Repts., 2018, vol. 8, no. 1, pp. 11116.

    Article  Google Scholar 

  56. Räss, L., Duretz, T., and Podladchikov, Y.Y., Resolving hydromechanical coupling in two and three dimensions: spontaneous channelling of porous fluids owing to decompaction weakening, Geophysic. J. Int., 2019, vol. 218, no. 3, pp. 1591–1616.

    Article  Google Scholar 

  57. Räss, L., Utkin, I., Duretz, T., et al., Assessing the robustness and scalability of the accelerated pseudo-transient method, Geosci. Model Develop., 2022, vol. 15, no. 14, pp. 5757–5786.

    Article  Google Scholar 

  58. Roded, R., Paredes, X., and Holtzman, R., Reactive transport under stress: Permeability evolution in deformable porous media, Earth Planet. Sci. Lett., 2018, vol. 493, pp. 198–207.

    Article  CAS  Google Scholar 

  59. Schmalholz, S.M., Moulas, E., Plümper, O., et al., 2D hydro-mechanical-chemical modeling of (de) hydration reactions in deforming heterogeneous rock: The periclase–brucite model reaction, Geochem., Geophys., Geosyst., 2020, vol. 21, no. 11, e2020GC009351.

  60. Tropper, P. and Manning, C.E., Paragonite stability at 700°C in the presence of H2O–NaCl fluids: constraints on H2O activity and implications for high pressure metamorphism, Contrib. Mineral. Petrol., 2004, vol. 147, pp. 740–749.

    Article  CAS  Google Scholar 

  61. Vrijmoed, J.C. and Podladchikov, Y.Y., Thermolab: A thermodynamics laboratory for nonlinear transport processes in open systems, Geochem., Geophys., Geosyst., 2022, vol. 23, no. 4. e2021GC010303.

  62. Weinberg, R.F. and Podladchikov, Y., Diapiric ascent of magmas through power law crust and mantle, J. Geophys. Res.: Solid Earth, 1994, vol. 99, no. B5, pp. 9543–9559.

    Article  Google Scholar 

  63. White, R.W., Powell, R., and Phillips, G.N., A mineral equilibria study of the hydrothermal alteration in mafic greenschist facies rocks at Kalgoorlie, Western Australia, J. Metamorph. Geol., 2003, vol. 21, no. 5, pp. 455–468.

    Article  CAS  Google Scholar 

  64. Whitham, G.B., Linear and Nonlinear Waves, New York: Wiley and Sons, 1974.

    Google Scholar 

  65. Xu, T., Apps, J.A., and Pruess, K., Mineral sequestration of carbon dioxide in a sandstone–shale system, Chem. Geol., 2005, vol. 217, no. 3–4, pp. 295–318.

    Article  CAS  Google Scholar 

  66. Yarushina, V.M., Makhnenko, R.Y., Podladchikov, Y.Y. et al., Viscous behavior of clay-rich rocks and its role in focused fluid flow, Geochem., Geophys., Geosyst., 2021, vol. 22, no. 10. e2021GC009949.

  67. Yarushina, V.M. and Podladchikov, Y.Y., (De)compaction of porous viscoelastoplastic media: Model formulation, J. Geophys. Res.: Solid Earth, 2015, vol. 120, no. 6, pp. 4146–4170.

    Article  Google Scholar 

  68. Zimmerman, R.W., Compressibility of Sandstones, New York: Elsevier, 1991.

    Google Scholar 

Download references

ACKNOWLEDGEMENTS

The authors thank J.C. Vrijmoed, T.V. Gerya, V.I. Malkovsky, and L.Ya. Aranovich for thorough reviewing the manuscript and valuable comments and recommendations on the presentation of the material, which led us to improve the quality of the paper.

Funding

This study was financially supported by Grant 075-15-2022-1106 from the Ministry of Science and Higher Education of the Russian Federation.

Author information

Authors and Affiliations

  1. University of Lausanne, Lausanne, Switzerland

    L. Khakimova & Yu. Podladchikov

  2. Skolkovo Institute of Science and Technology, Moscow, Russia

    L. Khakimova

  3. Lomonosov Moscow State University, Moscow, Russia

    L. Khakimova & Yu. Podladchikov

Authors
  1. L. Khakimova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. Podladchikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Khakimova.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Translated by E. Kurdyukov

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khakimova, L., Podladchikov, Y. Modeling Multicomponent Fluid Flow in Deforming and Reacting Porous Rock. Petrology 32, 2–15 (2024). https://doi.org/10.1134/S0869591124010053

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0869591124010053

Keywords:

Search

Navigation