Skip to main content
SpringerLink
Log in

Multiphase Thermohaline Convection in the Earth’s Crust: I. A New Finite Element – Finite Volume Solution Technique Combined With a New Equation of State for NaCl–H2O

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

We present a new finite element – finite volume (FEFV) method combined with a realistic equation of state for NaCl–H2O to model fluid convection driven by temperature and salinity gradients. This method can deal with the nonlinear variations in fluid properties, separation of a saline fluid into a high-density, high-salinity brine phase and low-density, low-salinity vapor phase well above the critical point of pure H2O, and geometrically complex geological structures. Similar to the well-known implicit pressure explicit saturation formulation, this approach decouples the governing equations. We formulate a fluid pressure equation that is solved using an implicit finite element method. We derive the fluid velocities from the updated pressure field and employ them in a higher-order, mass conserving finite volume formulation to solve hyperbolic parts of the conservation laws. The parabolic parts are solved by finite element methods. This FEFV method provides for geometric flexibility and numerical efficiency. The equation of state for NaCl–H2O is valid from 0 to 750°C, 0 to 4000 bar, and 0–100 wt.% NaCl. This allows the simulation of thermohaline convection in high-temperature and high-pressure environments, such as continental or oceanic hydrothermal systems where phase separation is common.

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

Similar content being viewed by others

References

  • A. Anderko K.S. Pitzer (1993) ArticleTitleEquation-of-state representation of phase equilibria and volumetric properties of the system NaCl–H2O above 573 K, Geochim Cosmochim. Acta 57 1657–1680

    Google Scholar 

  • K. Aziz A. Settari (1979) Petroleum Reservoir Simulation Applied Science Publishers Barking

    Google Scholar 

  • W. Bai W. Xu R.P. Lowell (2003) ArticleTitleThe dynamics of submarine geothermal heat pipes Geophys. Res. Lett. 30 110 Occurrence Handle10.1029/2002GL016176

    Article  Google Scholar 

  • H.L. Barnes (1997) Geochemistry of Hydrothermal Ore Deposits EditionNumber3 John Wiley New York

    Google Scholar 

  • Bauer, O.: 2002, PROST 4.1, PROperties of Water and STeam. http://www.tt.tu-harburg.de/mitarbeiter/Ehemalige/engel/PROST/PROST.h tml, Technische Universität Hamburg–Harburg, Germany.

  • J. Bear (1972) Dynamics of Fluids in Porous Media Dover New York

    Google Scholar 

  • Belayneh, M., Matthäi, S.K. and Geiger, S.: Numerical simulation of viscous immiscible displacement in layered fractured limestone reservoir analogues. AAPG Bulletin, in press.

  • L. Bergamschi S. Mantica G. Manzini (1998) ArticleTitleA mixed finite element-finite volume formulation of the Black-Oil model SIAM J. Sci. Comput. 20 970–997

    Google Scholar 

  • J.L. Bischoff R.J. Rosenbauer (1985) ArticleTitleAn empirical equation of state for hydrothermal seawater (3.2 Percent NaCl) Amer. J. Sci. 285 725–763

    Google Scholar 

  • R.J. Bodnar C.W. Burnham S.M. Sterner (1985) ArticleTitleSynthetic fluid inclusions in natural quartz. III. Determination of phase equilibrium properties in the system H2O–NaCl to 1000°C and 1500 bars Geochim. Cosmochim. Acta 49 1861–1873

    Google Scholar 

  • Burri, A.: 2004, Implementation of a multiphase flow simulator using a fully upwind galerkin method within the CSP multiphysics toolkit, Unpublished Diploma Thesis, Eidgenössische Technische Hochschule Zürich, Switzerland.

  • P.L. Cloke S.E. Kesler (1979) ArticleTitleHalite trend in hydrothermal solutions Econ. Geol. 74 1823–1831

    Google Scholar 

  • Cordes, C. and Kinzelbach, W.: 1996, Comment on “Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity?”, R. Mosé, P. Siegel, P. Ackerer, and G. Chavent (eds.), Water Resour. Res. 32, 1905–1909.

  • G Marsiliy Particlede (1986) Quantitative Hydrogeology Academic Press New York

    Google Scholar 

  • P.T. Delaney (1982) ArticleTitleRapid intrusion of magma into wet rock: Groundwater flow due to pore pressure increases J. Geophys. Res. 87 7739–7756

    Google Scholar 

  • E.M. Dicks (1993) Higher order Godounov black-oil simulations for compressible flow in porous media University of Reading U.K.

    Google Scholar 

  • T. Driesner C.A. Heinrich (2003) ArticleTitleAccurate P-T-X-V-H correlations for the system NaCl–H2O from 0 to 800 °C, 0 to 500 Mpa, and 0 to 1 X N aCl, Acta Mineralog Petrograph. Abstr. Ser. 2 55–56

    Google Scholar 

  • Driesner, T. and Heinrich, C.A.: 2005, The system NaCl–H2O. I. Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000°C, 0 to 5000 bar, and 0 to 1 X N aCl, Geochim. Cosmochim. Acta, in revision.

  • Driesner, T.: The system NaCl–H2O. II. Molar volume, enthalpy, and isobaric heat capacity from 0 to 1000°C, 0 to 5000 bar, and 0 to 1 X N aCl Geochim. Acta, in revision.

  • L.J. Durlofsky (1993) ArticleTitleA triangle based mixed finite-element finite-volume technique for modeling two phase flow through porous media J. Comput. Phys. 105 252–266 Occurrence Handle10.1006/jcph.1993.1072

    Article  Google Scholar 

  • L.J. Durlofsky (1994) ArticleTitleAccuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities Water Resour.Res. 30 965–973 Occurrence Handle10.1029/94WR00061

    Article  Google Scholar 

  • C.R. Faust J.W. Mercer (1979a) ArticleTitleGeothermal reservoir simulation 1. Mathematical models for liquid- and vapor-dominated hydrothermal systems Water Resour. Res. 15 23–30

    Google Scholar 

  • C.R. Faust J.W. Mercer (1979b) ArticleTitleGeothermal reservoir simulation 2. Numerical solution techniques for liquid- and vapor-dominated hydrothermal systems Water Resour. Res. 15 31–46

    Google Scholar 

  • A.T. Fisher (1998) ArticleTitlePermeability within basaltic oceanic crust Rev. Geophysics 36 143–182

    Google Scholar 

  • P.A. Forsyth (1991) ArticleTitleA control volume finite element approach to NAPL groundwater contamination, SIAM J Sci. Comput. 12 1029–1057

    Google Scholar 

  • E. Gamma (2002) Design patterns: Elements of Reusable Object Oriented Software Addison-Wesley Reading, MA

    Google Scholar 

  • G. Garven M.S. Appold V.I. Toptygina T.J. Hazlett (1999) ArticleTitleHydrogeologic modeling of the genesis of carbonate-hosted lead-zinc ores Hydrogeol. J. 7 108–126 Occurrence Handle10.1007/s100400050183

    Article  Google Scholar 

  • S. Geiger R. Haggerty J.H. Dilles M.H. Reed S.K. Matthäi (2002) ArticleTitleNew insights from reactive transport modelling: the formation of the sericitic vein envelopes during early hydrothermal alteration at Butte, Montana Geofluids 2 185–201 Occurrence Handle10.1046/j.1468-8123.2002.00037.x

    Article  Google Scholar 

  • S. Geiger S. Roberts S.K. Matthäi C. Zoppou A. Burri (2004) ArticleTitleCombining Finite element and finite volume methods for efficient multiphase flow simulations in highly heterogeneous and structurally complex geologic media Geofluids 4 284–299 Occurrence Handle10.1111/j.1468-8123.2004.00093.x

    Article  Google Scholar 

  • S. Geiger T. Driesner C.A. Heinrich S.K. Matthäi (2006) ArticleTitleMultiphase thermohaline convection in the Earth’s crust: II. Benchmarking and application of a finite element – finite volume solution technique with a NaCl–H2O equation of state Transport Porous Media 63 417–443

    Google Scholar 

  • M.A. Grant M.L. Sorey (1979) ArticleTitleThe compressibility and hydraulic diffusivity of a water-steam flow Water Resour. Res. 15 684–686

    Google Scholar 

  • L. Haar J.S. Gallagher G.S. Kell (1984) NBS/NRC Steam Tables Hemisphere Publishing Corporation Washingdon, DC

    Google Scholar 

  • A. Harten (1983) ArticleTitleHigh resolution schemes for hyperbolic conservation laws J. Comput. Phys. 49 357–393

    Google Scholar 

  • Hayba, D.O. and Ingebritsen, S.E.: 1994, The Computer Model HYDROTHERM, A Three-Dimensional Finite-Difference Model to Simulate Ground-Water Flow and Heat Transport in the Temperature Range of 0 to 1200°C. U.S. Geological Survey Water-Resources Investigations Report 94–4045.

  • D.O. Hayba S.E. Ingebritsen (1997) ArticleTitleMultiphase groundwater flow near cooling plutons. J. Geophys. Res. 102 12235–12252 Occurrence Handle10.1029/97JB00552

    Article  Google Scholar 

  • J.W. Hedenquist J.B. Lowenstern (1994) ArticleTitleThe role of magmas in the formation of hydrothermal ore-deposits Nature 370 519–527 Occurrence Handle10.1038/370519a0

    Article  Google Scholar 

  • C.A. Heinrich D. Günther A. Audétat T. Ulrich R. Frischknecht (1999) ArticleTitleMetal fractionation between magmatic brine and vapor, determined by microanalysis of fluid inclusions Geology 27 755–758 Occurrence Handle10.1130/0091-7613(1999)027<0755:MFBMBA>2.3.CO;2

    Article  Google Scholar 

  • R. Huber R. Helmig (1999) ArticleTitleMulti-phase flow in heterogeneous porous media: A classical finite element method versus and implicit pressure-explicit saturation-based mixed finite element-finite volume approach Int. J. Numer. Meth. Fluids 29 899–920 Occurrence Handle10.1002/(SICI)1097-0363(19990430)29:8<899::AID-FLD715>3.0.CO;2-W

    Article  Google Scholar 

  • P.S. Huyakorn G.F. Pinder (1983) Computational Methods in Subsurface Flow Academic Press New York

    Google Scholar 

  • S.E. Ingebritsen W.E. Sanford (1999) Groundwater in Geologic Processes Cambridge University Press Cambridge

    Google Scholar 

  • T. Jupp A. Schultz (2000) ArticleTitleA thermodynamic explanation for black smoker temperatures Nature 403 880–883 Occurrence Handle10.1038/35002552

    Article  Google Scholar 

  • Y. Kawada S. Yoshida S. Watanabe (2004) ArticleTitleNumerical simulations of mid-ocean ridge hydrothermal circulation including the phase separation of seawater Earth Planets Space 56 193–215

    Google Scholar 

  • W. Kissling M. McGuinness A. McNabb G. Weir S. White R. Young (1992) ArticleTitleAnalysis of one-dimensional horizontal two-phase flow in geothermal reservoirs Transport Porous Media 7 223–253 Occurrence Handle10.1007/BF01063961

    Article  Google Scholar 

  • M. Küther (2002) Error estimates for numerical approximations to scalar conservation laws Universität Freiburg Germany

    Google Scholar 

  • K.C. Lewis RP. Lowell (2004) ArticleTitleMathematical modeling of phase separation of seawater near an igneous dike Geofluids 4 197–209 Occurrence Handle10.1111/j.1468-8123.2004.00086.x

    Article  Google Scholar 

  • E. Lüschen S. Sobolev U. Werner W. Söller et al. (1993) ArticleTitleFluid reservoir (questionable) beneath the KTB drillbit indicated by seismic shear-wave observations Geophys. Res. Lett. 20 923–926

    Google Scholar 

  • C.E. Manning S.E. Ingebritsen (1998) ArticleTitlePermeability of the continental crust: Implications of geothermal data and metamorphic systems Rev. in Geophys. 37 127–150

    Google Scholar 

  • G. Marsiliy Particlede (1986) Quantative Hydrogeology Academic press New York

    Google Scholar 

  • S.K. Matthäi S. Roberts (1996) ArticleTitleThe influence of fault permeability on single-phase fluid flow near fault-sand intersections: Results from steady-state high-resolution models of pressure-driven fluid flow AAPG Bulletin 80 1763–1779

    Google Scholar 

  • Matthäi, S.K., Aydin, A., Pollard, D.D. and Roberts, S.: 1998, Numerical simulation of departures from radial drawdown in a faulted sandstone reservoir with joints and deformation bands, in: G. Jones, Q.J. Fisher, and R.J. Knipe, (eds), Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs, Geological Society London, Special Publications 147, 157–191.

  • Matthäi, S.K., Geiger, S. and Roberts, S.: 2001, Complex Systems Platform: CSP3D3.0: User’s Guide. http://e-collection.ethbib.ethz.ch/show? type=4bericht&nr=239, Eidgenössische Technische Hochschule Zürich, Switzerland.

  • S.K. Matthäi (2003) ArticleTitleFluid flow and (reactive) transport in fractured and faulted rock J. Geochem. Exploration 78-79 179–182

    Google Scholar 

  • S.K. Matthäi C.A. Heinrich T. Driesner (2004a) ArticleTitleIs the Mount Isa copper deposit the product of forced brine convection in the footwall of a major reverse fault? Geology 32 357–360

    Google Scholar 

  • Matthäi, S.K., Mezentsev, A. and Belayneh, M.: 2004b, Control-volume finite-element two-phase experiments with fractured rock represented by unstructured 3D hybdrid meshes, SPE Paper presented at the SPE Reservoir Simulation Symposium Houston, Texas, U.S.A, SPE93341.

  • S.K. Matthäi M. Belayneh (2004c) ArticleTitleFluid flow partitioning between fractures and a permeable rock matrix Geophys. Res. Lett. 31 L07602 Occurrence Handle10.1029/2003GL019027

    Article  Google Scholar 

  • P. Möller S.M. Weise E. Althaus W. Bach et al. (1997) ArticleTitlePaleofluids and recent fluids in the upper continental crust: Results from the German Continental Deep Drilling Program (KTB) J. Geophys. Res. 102 18233–18254 Occurrence Handle10.1029/96JB02899

    Article  Google Scholar 

  • T.N. Narasimhan P.A. Witherspoon (1976) ArticleTitleAn integrated finite difference method for analyzing fluid flow in porous media Water Resour. Res. 12 57–64

    Google Scholar 

  • B.E. Nesbitt K. Muehlenbachs (1991) ArticleTitleStable isotopic constraints on the nature of the syntectonic fluid regime in the Canadian Cordillera Geophys. Res. Lett. 18 963–966

    Google Scholar 

  • D.A. Nield A. Bejan (1992) Convection in Porous Media Springer-Verlag Berlin

    Google Scholar 

  • C. Oldenburg K. Pruess (1998) ArticleTitleLayered thermohaline convection in hypersaline geothermal systems Transport Porous Media 33 29–63 Occurrence Handle10.1023/A:1006579723284

    Article  Google Scholar 

  • C. Oldenburg K. Pruess (1999) ArticleTitlePlume separation by transient thermohaline convection in porous media Geophys. Res. Lett. 26 2997–3000 Occurrence Handle10.1029/1999GL002360

    Article  Google Scholar 

  • C. Oldenburg K. Pruess (2000) ArticleTitleSimulation of propagating fronts in geothermal reservoirs with the implicit Leonard total variation scheme Geothermics 29 1–25 Occurrence Handle10.1016/S0375-6505(99)00048-6

    Article  Google Scholar 

  • M.J. O’Sullivan K. Pruess M.J. Lippman (2001) ArticleTitleState of the art of geothermal reservoir simulation Geothermics 30 395–429

    Google Scholar 

  • C. Palliser R. McKibbin (1998a) ArticleTitleA model for deep geothermal brines, I: T-p-X state-space description Transport Porous Media 33 65–80

    Google Scholar 

  • C. Palliser R. McKibbin (1998b) ArticleTitleA model for deep geothermal brines, II: Thermodynamic properties – density Transport Porous Media 33 129–154

    Google Scholar 

  • C. Palliser R. McKibbin (1998c) ArticleTitleA model for deep geothermal brines, III: Thermodynamic properties – enthalpy and viscosity Transport Porous Media 33 155–171

    Google Scholar 

  • O.M. Phillips (1991) Flow and Reactions in Permeable Rocks Cambridge University Press Cambridge

    Google Scholar 

  • Pruess, K.: 1987, TOUGH User’s Guide, U.S. Nuclear Regulatory Commission, Report NUREG/CR-4645.

  • Pruess, K.: 1991, TOUGH2 – A General Purpose Numerical Simulator for Multiphase Fluid and Heat Flow, Lawrence Berkeley Laboratory Report, LBL–29400.

  • Raffensperger, J.P.: 1996, Numerical simulation of sedimentary basin-scale hydrochemical processes, in: M.Y. Corapcioglu, (ed.), Advances in Porous Media 3, 185–305.

  • Reed, M. H.: 1997, Hydrothermal alteration and its relation to ore fluid composition, in H. L. Barnes, Geochemistry of Hydrothermal Ore Deposits, 3rd edn, 303–365.

  • P.S.Z. Rogers K.S. Pitzer (1982) ArticleTitleVolumetric properties of aqueous sodium chloride solutions J. Phys. Chem. Refer. Data 11 15–81

    Google Scholar 

  • A. Sarkar J.A. Nunn J.S. Hanor (1995) ArticleTitleFree thermohaline convection beneath allochtonous salt sheets – An agent for salt dissolution and fluid flow in Gulf-Coast sediments J. Geophys. Res. 100 18085–18092 Occurrence Handle10.1029/95JB01857

    Article  Google Scholar 

  • Schoofs, S.: 1999, Thermochemical convection in porous media. An application to hydrothermal systems and magmatic intrusions, Geologica Ultraiectina, 179.

  • S. Schoofs F.J. Spera U. Hansen (1999) ArticleTitleChaotic thermohaline convection in low-porosity hydrothermal systems Earth and Planetary Sci. Lett. 174 213–229

    Google Scholar 

  • S. Schoofs R.A. Trompert U. Hansen (2000) ArticleTitleThermochemcial convection in and beneath intracratonic basins: Onset and effects J. Geophys. Res. 105 25567–25585 Occurrence Handle10.1029/2000JB900272

    Article  Google Scholar 

  • S. Schoofs U. Hansen (2000) ArticleTitleDepletion of a brine layer at the base of the ridge-crest hydrothermal system Earth Planetary Sci. Lett. 180 341–353 Occurrence Handle10.1016/S0012-821X(00)00184-9

    Article  Google Scholar 

  • W.E. Seyfried J.S. Seewald M.E. Berndt K. Ding D.I. Foustoukos (2003) ArticleTitleChemistry of hydrothermal vent fluids from the main endavour field, northern juan de Fuca Ridge: geochemical controls in the aftermath of June 1999 seismic events J. Geophys. Res. 108 2429 Occurrence Handle10.1029/2002JB001957

    Article  Google Scholar 

  • J.R. Shewchuk (2002) ArticleTitleDelaunay refinement algorithms for triangular mesh generation Comput. Geom. Theory Appl. 22 21–74

    Google Scholar 

  • K.I. Shmulovich B.W.D. Yardley G.G. Gonchar (1995) Fluids in the Crust: Equilibrium and Transport Properties Chapman and Hall London

    Google Scholar 

  • S. Sourirajan G.C. Kennedy (1962) ArticleTitleThe system H2O–NaCl at elevated temperatures and pressures Amer. J. Sci. 260 115–141

    Google Scholar 

  • Steefel, C.I. and MacQuarrie, K.T.B.: 1996, Approaches to modeling of reactive transport in porous media, in: P.C. Lichtner, C.I. Steefel, and E.H. Oelkers, (eds), Reactive Transport in Porous Media, Reviews In Mineralogy 34, pp. 131–182.

  • G. Strang (1968) ArticleTitleOn construction and comparison of difference schemes SIAM J. Numer. Anal. 5 506–517 Occurrence Handle10.1137/0705041

    Article  Google Scholar 

  • J.M. Strauss G.M. Schubert (1977) ArticleTitleThermal convection of water in a porous medium: Effects of temperature- and pressure-dependent thermodynamic transport properties J. Geophys. Res. 82 3411–3421

    Google Scholar 

  • K. Stüben (2002) User’s Manual SAMG Release 21b1, July 2002 Fraunhofer Institute SCAI, St. Augustin Germany

    Google Scholar 

  • P.K. Sweby (1984) ArticleTitleHigh resolution schemes using flux limiters for hyperbolic conservation laws SIAM J. Numer. Anal. 21 995–1011 Occurrence Handle10.1137/0721062

    Article  Google Scholar 

  • J.A. Trangenstein J.B. Bell (1989a) ArticleTitleMathematical structure of the black-oil model for petroleum reservoir simulation SIAM J. Appl. Math. 49 749–783 Occurrence Handle10.1137/0149044

    Article  Google Scholar 

  • J.A. Trangenstein J.B. Bell (1989b) ArticleTitleMathematical structure of compositional reservoir simulation SIAM J. Sci. Stat. Comput. 10 817–845 Occurrence Handle10.1137/0910049

    Article  Google Scholar 

  • V. Trommsdorff G. Skippen P. Ulmer (1985) ArticleTitleHalite and sylvite as solid inclusions in high-grade metamorphic rocks Contributions Mineral. Petrol. 89 24–29

    Google Scholar 

  • T. Ulrich D. Günther C.A. Heinrich (2002) ArticleTitleEvolution of a porphyry Cu-Au deposit, based on LA-ICP-MS analysis of fluid inclusions: Bajo de la Alumbrera, Argentina (v. 96, p. 1743, 2001) Econ. Geol. 97 1888–192

    Google Scholar 

  • Von Damm, K.L.: 1995, Controls on the chemistry and temporal of seafloor hydrothermal fluids, in: S.E. Humphris, R.A. Zierenberg, L.S. Mullineaux, and R.E. Thomson (eds.), Seafloor Hydrothermal Systems, Geophysical Monograph 91, 222–247.

  • W. Xu (2004) ArticleTitleModeling dynamic marine gas hydrate systems Amer. Mineral. 89 1271–1279

    Google Scholar 

  • R. Young (1993) ArticleTitleTwo-phase geothermal flows with conduction and the connection with Buckley–Leverett theory Transport Porous Media 12 261–278 Occurrence Handle10.1007/BF00624461

    Article  Google Scholar 

  • O.C. Zienkiewicz R.L. Taylor (2000) The Finite Element Method Vol. 3: Fluid Dynamics Butterworth-Heinemann London

    Google Scholar 

  • Zyvoloski, G.A., Robinson, B.A., Dash, Z.V. and Trease, L.L.: 1996, Users Manual for the FEHMN Application. Los Alamos National Laboratory, LA-UR-94-3788.

Download references

Author information

Authors and Affiliations

  1. Department of Earth Sciences, Institute for Isotope Geology and Mineral Resources, ETH Zürich, Sonneggstr. 5, CH-8092, Zürich, Switzerland

    Sebastian Geiger, Thomas Driesner & Christoph A. Heinrich

  2. Department of Earth Science and Engineering, Imperial College, London, SW7 2AZ, U.K.

    Stephan K. Matthäi

Authors
  1. Sebastian Geiger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Driesner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christoph A. Heinrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Stephan K. Matthäi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sebastian Geiger.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Geiger, S., Driesner, T., Heinrich, C.A. et al. Multiphase Thermohaline Convection in the Earth’s Crust: I. A New Finite Element – Finite Volume Solution Technique Combined With a New Equation of State for NaCl–H2O. Transp Porous Med 63, 399–434 (2006). https://doi.org/10.1007/s11242-005-0108-z

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-005-0108-z

Keywords

Search

Navigation