Halite Fluid Inclusion Model
Author
Emmanuel Guillerm
Title
Halite Fluid Inclusion Model
Description
Predicts the liquid pressure, effect of surface tension on liquid-vapor homogenization temperature, and hydrostatic pressure correction, for fluid inclusions in halite crystals.
Category
Working Material
Keywords
HaliBubble, fluid inclusion, halite, equation of state, liquid pressure, homogenization temperature, Laplace pressure, hydrostatic pressure
URL
http://www.notebookarchive.org/2025-01-b23umu8/
DOI
https://notebookarchive.org/2025-01-b23umu8
Date Added
2025-01-24
Date Last Modified
2025-01-24
File Size
4.02 megabytes
Supplements
Rights
CC BY-NC-SA 4.0
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Halite Fluid Inclusion Model
Halite Fluid Inclusion Model
Emmanuel Guillerm
In[]:=
BeginPackage["NaCl`"];
In[]:=
Tst::usage="Tst (K) freezing point of pure water";Tamb::usage="Ambient temperature 298.15 K";Rm::usage="Universal gas constant, J mol-1 K-1";Mnacl::usage="Mnacl (kg/mol) molar mass of NaCl";Mnabr::usage="Mnabr (kg/mol) molar mass of NaBr";Mh2o::usage="Mh2o (kg/mol) molar mass of H2O";Mkcl::usage="Mkcl (kg/mol) molar mass of KCl";Mmgcl2::usage="Mmgcl2 (kg/mol) molar mass of MgCl2";Mcacl2::usage="Mcacl2 (kg/mol) molar mass of CaCl2";Mna2so4::usage="Mna2so4 (kg/mol) molar mass of na2so4";Mk2so4::usage="Mk2so4 (kg/mol) molar mass of K2SO4";Mmgso4::usage="Mmgso4 (kg/mol) molar mass of MgSo4";Mnahco3::usage="Mnahco3 (kg/mol) molar mass of NaHCO3";Msrcl2::usage="Msrcl2 (kg/mol) molar mass of SrCl2";TDSkgkgH2O::usage="TDSkgkgH2O[mnacl_,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_,mnabr_]; Total dissolved salts in kg/kgH2O as a function of molality";TDSkgkg::usage="TDSkgkg[mnacl_,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_,mnabr_]; Total dissolved salts in kg/kg as a function of molality";TDSgL::usage="TDSkgkg[T_,p_,mnacl_,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_]; Total dissolved salts in g/L as a function of molality, T (K) and p (MPa)";NaClmsatamb::usage="NaClmsatamb[T] molal solubility (mol/kg) of NaCl in H2O at T/K and ambient pressure from Farelo";deltaNaClmsatP::usage="deltaNaClmsatPsolubility change (mol/kgH2O) from P1 to P2 (MPa), assuming P change is the same for complex brines as for NaCl-H2O";NaClmsat::usage="Brine's halite solubility, mol.kgh2O-1";TDSmassfrac::usage="Total dissolved salts in kg/kg";NaClmsatmassfrac::usage="Brine's halite solubility, kg/kg";Thm::usage="halite melting temperature, °C; Driesner and Heinrich 2007";xNaClmsatP::usage="";NaClmsatP::usage="NaClmsatP[T,P] molal solubility (mol/kg) of NaCl in H2O as a function of T/K (273 - 1273K), P/MPa (0 - 500 MPa) from Driesner and Heinrich 2007";NaClmsatPmassfrac::usage="NaClmsatPmassfrac[T,P] mass fraction solubility (kg/kg) of NaCl in H2O at any T/K, P/MPa from Sawamura";NaClmsatPmolfrac::usage="NaClmsatPmolfrac[T,P] mole fraction solubility (mol/mol) of NaCl in H2O at any T/K, P/MPa from Sawamura";NaCldensAG::usage="NaCldensAG[T,P,m] density (kg/m3) of m molal NaCl solution in H2O at any T/K, P/MPa, m/(mol/kg) from Al Ghafri (2012) empirical fit.";NaClcompAG::usage="NaClcompAG[T,P,m] isothermal compressibility(MPa-1) of m molal NaCl solution in H2O at any T/K, P/MPa, m/(mol/kg) from Al Ghafri (2012) empirical fit.";NaClwAG::usage="NaClwAG[T,P,m] speed of sound of m molal NaCl solution in H2O at any T/K, P/MPa, m/(mol/kg) from Al Ghafri (2012) empirical fit.; Cp from Archer";BrinedensAG::usage="BrinedensAG[T,P,mNaCl,mKCl,mMgCl2,mCaCl2,mNa2SO4,mNaHCO3,mSrCl2] density (kg/m3) of aqueous solution with m molal of each salt, at any T/K, P/MPa, m/(mol/kg) from Al Ghafri (2012+2013) empirical fit. Limits: T/298-473K; P/0-68.5 MPa; m/6-4.5-5-6-1.5-1-3 molal";BrineexpAG::usage="BrineexpAG[T,P,mNaCl,mKCl,mMgCl2,mCaCl2,mNa2SO4,mNaHCO3,mSrCl2] thermal expansion (°C-1) of aqueous solution with m molal of each salt, at any T/K, P/MPa, m/(mol/kg) from Al Ghafri et al(2012, 2013) empirical fit. Limits: T/283-473K; P/0-68.5 MPa; m/6-4.5-5-6-1.5-1-3 molal";BrinecompAG::usage="BrinecompAG[T,P,mNaCl,mKCl,mMgCl2,mCaCl2,mNa2SO4,mNaHCO3,mSrCl2] isothermal compressibility (MPa-1) of aqueous solution with m molal of each salt, at any T/K, P/MPa, m/(mol/kg) from Al Ghafri et al(2012, 2013) empirical fit. Limits: T/283-473K; P/0-68.5 MPa; m/6-4.5-5-6-1.5-1-3 molal";BrineIsochoreAG::usage="BrineIsochoreAG[T,P,mNaCl,mKCl,mMgCl2,mCaCl2,mNa2SO4,mNaHCO3,mSrCl2] isochore slope (°C/MPa) of aqueous solution with m molal of each salt, at any T/K, P/MPa, m/(mol/kg) from Al Ghafri et al(2012, 2013) empirical fit. Limits: T/283-473K; P/0-68.5 MPa; m/6-4.5-5-6-1.5-1-3 molal";BrinedensPitzer::usage="BrinedensPitzer[T/K,mna/molal,mk_,mmg_,mca_,mcl_,mbr_,mso4_,mhco3_,mco3_]. The Pitzer ion-interaction density equation of state at 1 atm from Krumgalz et al. (2000). Range:";BrineCpPitzer::usage="BrineCpPitzer[mna/molal,mk_,mmg_,mca_,mcl_,mbr_,mso4_,mhco3_,mco3_], J / (kg K). The Pitzer ion-interaction isobaric heat capacity at 25°c and 1 atm from Criss and Millero(1996, 1999). Range:";BrinecompadPitzer::usage="BrinecompadPitzer[mna/molal,mk_,mmg_,mca_,mcl_,mbr_,mso4_,mhco3_,mco3_], Pa-1. The Pitzer ion-interaction adiabatic compressibility at 25°c and 1 atm from Millero and Sharp (2013). Range:";BrinecompPitzer::usage="BrinecompPitzer[mna/molal,mk_,mmg_,mca_,mcl_,mbr_,mso4_,mhco3_,mco3_], Pa-1. The Pitzer ion-interaction isothermal compressibility at 25°c and 1 atm, calculated from the density, adiabatic compressibility, thermal expansion, and isobaric heat capacity. Range:";BrineexpPitzer::usage="BrineexpPitzer[T/K,mna/molal,mk_,mmg_,mca_,mcl_,mbr_,mso4_,mhco3_,mco3_], Pa-1. The Pitzer ion-interaction isobaric thermal expansion at 1 atm, according to the model of Krumgalz et al. (2000). Range:";NaCldensDries::usage="NaCldensDries[T/K,p/MPa,mnacl/molal], equation of Driesner 2007, ranges: T 0 - 1000 °C, p 0 - 500 MPa, mnacl saturation";NaCldensArch::usage="NaCldensArch[T,P,m] density (kg/m3) of m molal NaCl solution in H2O at any T/K, P/MPa, m/(mol/kg) from Archer's (1992) Pitzer EoS.";NaClcompArch::usage="NaClcompArch[T,P,m] isothermal compressibility(MPa-1) of m molal NaCl solution in H2O at any T/K, P/MPa, m/(mol/kg) from Archer's (1992) Pitzer EoS.";NaClwArch::usage="NaClwArch[T,P,m] speed of sound (m/s) of m molal NaCl solution in H2O at any T/K, P/MPa, m/(mol/kg) calculated with Archer's (1992) density and heat capacity EoS.";NaClindexrho::usage="NaClindexrho[T,ρ,m] refractive index at 589 nm of NaCl solutions in H2O at any T/K, ρ/(kg/m3), m/(mol/kg) based on Gladstone-Dale";NaClindexsatP::usage="NaClindexsatP[T,P] refractive index at 589 nm of saturated NaCl solution in H2O at any T/K, P/MPa based on Gladstone-Dale";NaClindexsatamb::usage="NaClindexsatamb[T] refractive index at 589 nm of saturated NaCl solution in H2O at T/K and ambient pressure based on Gladstone-Dale";NaClcamb::usage="NaClcamb[T,m] sound velocity (m/s) of NaCl solution in H2O at T/K, m/(mol/kg) and ambient pressure from Millero";NaClcsatamb::usage="NaClcsatamb[T] sound velocity (m/s) of saturated NaCl solution in H2O at T/K, m/(mol/kg) and ambient pressure from Millero and Farelo";NaClBrillouinamb::usage="NaClBrillouinamb[T,m,lambda] Brillouin shift (GHz) of NaCl solution in H2O at T/K, m/(mol/kg), λ/nm and ambient pressure";NaClBrillouinsatamb::usage="NaClBrillouinsatamb[T,lambda] Brillouin shift (GHz) of saturated NaCl solution in H2O at T/K, λ/nm and ambient pressure";Halitedens::usage="Halitedens[T,p] density (kg/m3) of NaCl crystal ";Haliteexp::usage="Haliteexp[T,p] thermal expansion (K-1) of NaCl crystal ";Halitecomp::usage="Halitecomp[T,p] compressibility (MPa-1) of NaCl crystal ";Tcoeff::usage="[Thinf_,Th_], volume expansion coefficient due to temperature from a temp Thinf to Th, linear; in °C";GrowthRateNaCl::usage="[T_,mNa_,mK_,mMg_,mCa_,mSO4_,mHCO3_,NaClratio_,S_] with T/K, concentrations of ions at halite saturation in mol/kgH2O, Na/Cl molal ratio, and S the supersaturation defined as the molal ratio of actual concentration to saturation concentration";BrineSurfaceTension::usage="BrineSurfaceTension[T,mnacl,mkcl,mmgcl2,mcacl2,mna2so4,mnahco3,mna2co3], units: N/m. T/K, solutes in mol/kgH2O. Surface tension of multi-electrolyte brine with model of Dutcher et al 2010. ";λ::usage="λ[Thobs,mnacl,mkcl,mmgcl2,mcacl2,mna2so4,mnahco3,msrcl2] (m) Berthelot Laplace length as modified from Caupin (2022): here we incorporate all source of compression, not only isothermal compressibility but also dissolution and cavity compliance . Function of Th,obs (°C), and molality of salts (mol/kgH2O).";BubbleRadius0::usage="[Thinf/°C,T/°C,mnacl/molal,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_,V/μm3], radius of the vapor bubble in an isochoric FI";BubbleRadius::usage="[Thinf/°C,T/°C,deltaSolubility/molal/°C,mnacl/molal,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_,V/μm3] (radius of the vapour bubble in a halite FI)";BubbleRadiusSpinodal::usage="[T/°C,mnacl/molal,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_,V/μm3] (*Radius of bubble at spinodal (Caupin 2022), in meters *)";BubbleRadiusBinodal::usage="[T/°C,mnacl/molal,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_,V/μm3] (*Radius of bubble at binodal (Caupin 2022), in meters *)";Thbino0::usage="[Thinf/°C,mnacl/molal,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_,V/μm3]. Binodal temperature for an isochoric FI.";Thspino0::usage="[Thinf/°C,mnacl/molal,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_,V/μm3]. Spinodal temperature for an isochoric FI";ΔThspino::usage="ΔThspino[Thobs,deltaSolubility,mnacl,mkcl,mmgcl2,mcacl2,mna2so4,mnahco3,msrcl2,V] (°C) Difference between Th,inf and spinodal Th, as a function of Th observed (Thobs, °C), NaCl solubility change per °C (mol/(kgH20.°C)), molality of salts (mol/kgH2O), fluid inclusion volume (μm3). ";ΔThbino::usage="ΔThbino[Thobs,deltaSolubility,mnacl,mkcl,mmgcl2,mcacl2,mna2so4,mnahco3,msrcl2,V] (°C) Difference between Th,inf and binodal Th, as a function of Th observed (Thobs, °C), NaCl solubility change per °C (mol/(kgH20.°C)), molality of salts (mol/kgH2O), fluid inclusion volume (μm3). ";dPdTisoΔP::usage="dPdTisoΔP[T/K,p/MPa,deltaSolubility/molal °C-1,mnacl/molal,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_]. ";deltaTLaplacePressure::usage="deltaTLaplacePressure[Thobs,deltaSolubility,mnacl,mkcl,mmgcl2,mcacl2,mna2so4,mnahco3,msrcl2,V] (°C) Difference between Th,inf and the average of spinodal and binodal Th; function of Th,inf (°C), NaCl solubility change per °C (mol/(kgH20.°C)), molality of salts (mol/kgH2O), fluid inclusion volume (μm3). Al Ghafri EoS. Analytical solution.";deltaTLaplacePressureNum::usage="deltaTLaplacePressureNum[Thinf,deltaSolubility,mnacl,mkcl,mmgcl2,mcacl2,mna2so4,mnahco3,msrcl2,V] (°C) Difference between Th,inf and the average of spinodal and binodal Th; function of Th,inf (°C), NaCl solubility change per °C (mol/(kgH20.°C)), molality of salts (mol/kgH2O), fluid inclusion volume (μm3). Al Ghafri EoS. Numerical solution.";TtrapNum::usage="TtrapNum[Thinf_,WaterHeight_,g_,deltaSolubility_,mnacl_,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_]; Temperature of entrapment of fluid inclusion as a function of Th,inf (°C; the homogenization temperature of an infinitely large system), water column height (m), g (m²/s), NaCl solubility change per °C (mol/(kgH20.°C)), and molalities of the seven salts NaCl, KCl, MgCl2, CaCl2, Na2SO4, NaHCO3, SrCl2 (mol/kgH2O)";deltaTHydrostaticPressure::usage="deltaTHydrostaticPressure[Thinf,WaterHeight,g,deltaSolubility,mnacl,mkcl,mmgcl2,mcacl2,mna2so4,mnahco3,msrcl2]; Analytical resolutio, for Temperature of entrapment of fluid inclusion as a function of Th,inf (°C; the homogenization temperature of an infinitely large system), water column height (m), g (m²/s), NaCl solubility change per °C (mol/(kgH20.°C)), and molalities of the seven salts NaCl, KCl, MgCl2, CaCl2, Na2SO4, NaHCO3, SrCl2 (mol/kgH2O). Al Ghafri EoS.";deltaTHydrostaticPressureNum::usage="deltaTHydrostaticPressureNum[Thinf,WaterHeight,g,deltaSolubility,mnacl,mkcl,mmgcl2,mcacl2,mna2so4,mnahco3,msrcl2]; Analytical resolutio, for Temperature of entrapment of fluid inclusion as a function of Th,inf (°C; the homogenization temperature of an infinitely large system), water column height (m), g (m²/s), NaCl solubility change per °C (mol/(kgH20.°C)), and molalities of the seven salts NaCl, KCl, MgCl2, CaCl2, Na2SO4, NaHCO3, SrCl2 (mol/kgH2O). Al Ghafri EoS. Numerical solution.";dPdTisoTh::usage="[T/°C,deltaSolubility/mol.kgw-1,mnacl/molal,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_]. Slope of the monophasic FI in the P-T field (MPa/°C), at its intersection with the SLVE, using Al Ghafri (2012, 2013) EoS. Analytical solution.";pmonophasic::usage="[Thinf/°C,T/°C,deltaSolubility/molal °C-1,mnacl/molal,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_]; Internal pressure in the monophase halite FI (units: MPa). EoS of Al Ghafri, 25-200°C, 0-68 MPa, up to saturation.Halite dissolution equation of Driesner and Heinrich 2007 (0 - 1000 °C, 0-500 MPa). Analytical equation, integrated from Th,inf to T; pressure is kept at 0 MPa.";pmonophasicNum::usage="[Thinf_,T_,deltaSolubility_,mnacl_,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_]; Internal pressure in the monophase halite FI (units: MPa). Function of Th,inf (°C), T (°C), NaCl solubility change per °C (mol/(kgH20.°C)), and molalities of the seven salts NaCl, KCl, MgCl2, CaCl2, Na2SO4, NaHCO3, SrCl2 (mol/kgH2O). EoS of Al Ghafri, 25-200°C, 0-68 MPa, up to saturation.Halite dissolution equation of Driesner and Heinrich 2007 (0 - 1000 °C, 0-500 MPa)";TbeqNumIsochore::usage="[Thinf,Pb,mnacl,mkcl,mmgcl2,mcacl2,mna2so4,mnahco3,msrcl2]. Units: °C, MPa, molal.";TbeqNum::usage="[Thinf,Pb,deltaSolubility,mnacl,mkcl,mmgcl2,mcacl2,mna2so4,mnahco3,msrcl2]. Units: °C, MPa, molal. Temperature of equilibrium under burial pressure Pb. At this temperature, the FI liquid pressure compensates Pb.";pmonophasicburialNumIsochore::usage="[Tbeq,T,Pb,mnacl,mkcl,mmgcl2,mcacl2,mna2so4,mnahco3,msrcl2]. Units: °C, MPa, molal.";pmonophasicburialNum::usage="[Tbeq/°C,T/°C,Pb/MPa,deltaSolubility/molal/°C,mnacl/molal,mkcl_,mmgcl2_,mcacl2_,mna2so4_,mnahco3_,msrcl2_]. Liquid pressure in the monophasic halite FI when buried under conditions {T, Pb}";Plim::usage="[FIsize_] The absolute value of the internal pressure (MPa) at which a halite FI starts plastic deformation (irreversible damage), according to Guillerm et al. (2020). Function of size of FI (side of square, in μm)";FIsize::usage="[ΔP_] The maximum size of undamaged FIs as a function of the maximum stress undergone by the FIs.";
The parameters for the functions are temperature in K, pressure in MPa and molality m in mol of solute/kg of solvent.
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Needs["IAPWS95DLL`"]Needs["NumericalCalculus`"]
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check Archer 92, I created an error while changing the code
General
General
Constants
Constants
Formula
Formula
Solubility
Solubility
Solubility of NaCl in H2O: Farelo 1993 (S[T]) and Sawamura 2007 (S[T,P])
Solubility of NaCl in H2O: Farelo 1993 (S[T]) and Sawamura 2007 (S[T,P])
Volumetric properties
Volumetric properties
Crystal host volumetric and mechanical properties
Crystal host volumetric and mechanical properties
H2O EoS: IAPWS95 as computed by Frédéric
H2O EoS: IAPWS95 as computed by Frédéric
NaCl-H2O EoS of Driesner 2007
NaCl-H2O EoS of Driesner 2007
Density empirical fit from Al Ghafri, Maitland and Trusler, J. Chem. Eng. Data. 2012NaCl: 298.15 < T < 472 K, 0.1 < P < 68.5 MPa, 0 < m 6 molalKCl: 298.15 < T < 472.96 K, 0 < P < 68.1 MPa, 0 < m< 4.49 molalMgCl2: 283.15 < T < 472.96 K, 0 < P < 68.1 MPa, 0 < m < 5 molalCaCl2: 283.15 < T < 472.96 K, 0 < P < 68.1 MPa, 0 < m < 6 molal
Density empirical fit from Al Ghafri, Maitland and Trusler, J. Chem. Eng. Data. 2012NaCl: 298.15 < T < 472 K, 0.1 < P < 68.5 MPa, 0 < m 6 molalKCl: 298.15 < T < 472.96 K, 0 < P < 68.1 MPa, 0 < m< 4.49 molalMgCl2: 283.15 < T < 472.96 K, 0 < P < 68.1 MPa, 0 < m < 5 molalCaCl2: 283.15 < T < 472.96 K, 0 < P < 68.1 MPa, 0 < m < 6 molal
Pitzer common constants and equations
Pitzer common constants and equations
Archer (1992): Apparent molar volume, density, and apparent molar heat capacity and heat capacity of NaCl(aq)
Archer (1992): Apparent molar volume, density, and apparent molar heat capacity and heat capacity of NaCl(aq)
DENSITY: Pitzer multi-electrolyte2 7 2024: Krfum2000 advises to use Krum96 values of the coefficients at 25°C, instead of T-fitted Krum2000’s values. Check that.For some salts, Krum2000 recommends to use only 298.15K parameters. Check that
DENSITY: Pitzer multi-electrolyte2 7 2024: Krfum2000 advises to use Krum96 values of the coefficients at 25°C, instead of T-fitted Krum2000’s values. Check that.For some salts, Krum2000 recommends to use only 298.15K parameters. Check that
ADIABATIC COMPRESSIBILITY: Pitzer multi-electrolyte
ADIABATIC COMPRESSIBILITY: Pitzer multi-electrolyte
HEAT CAPACITY: Pitzer multi-electrolytefrom Pitzer (1983) and May et al (2011)
HEAT CAPACITY: Pitzer multi-electrolytefrom Pitzer (1983) and May et al (2011)
Isothermal compressibility
Isothermal compressibility
Pitzer EoS: P T x
Pitzer EoS: P T x
Growth Rate: Equation of Joswiak et al. (2018)
Growth Rate: Equation of Joswiak et al. (2018)
Works for lower end of supersaturation values (between ~1 and 1.01)
Chemical and volumetric properties
Chemical and volumetric properties
Parameters
Parameters
Growth Rate equation
Growth Rate equation
Surface tension
Surface tension
Pure water (Vargaftik et al. 1983, 273K - 647.15K; Dutcher et al. 2010, 193 - 273K)Units: mN m-1
Pure water (Vargaftik et al. 1983, 273K - 647.15K; Dutcher et al. 2010, 193 - 273K)Units: mN m-1
Solutes (species 2 to 7: NaCl, KCl, MgCl2, CaCl2, Na2SO4, NaHCO3)
Solutes (species 2 to 7: NaCl, KCl, MgCl2, CaCl2, Na2SO4, NaHCO3)
Laplace pressure
Laplace pressure
Laplace pressure correction term, Method 1: solving bubble radius
Laplace pressure correction term, Method 1: solving bubble radius
Laplace pressure correction term using and extending Caupin et al (2022)
Laplace pressure correction term using and extending Caupin et al (2022)
Analytical equation
Analytical equation
Monophasic Fluid Inclusion pressure (Guillerm 2019)
Monophasic Fluid Inclusion pressure (Guillerm 2019)
Isochore + thermal expansion
Isochore + thermal expansion
Compliance
Compliance
Dissolution-precipitation
Dissolution-precipitation
Last compliance
Last compliance
Analytical Formula for pressure calculation: dP/dT at Th,inf
Analytical Formula for pressure calculation: dP/dT at Th,inf
Hydrostatic pressure correction
Hydrostatic pressure correction
Burial FI pressure
Burial FI pressure
Threshold of plastic deformation (Guillerm et al 2020; Guillerm 2019)
Threshold of plastic deformation (Guillerm et al 2020; Guillerm 2019)
Refractive index, Brillouin
Refractive index, Brillouin
Refractive index and Gladstone-Dale analysis
Refractive index and Gladstone-Dale analysis
Sound velocity based on F. J. Millero et al., J. Sol. Chem. 1987which gives a fit of data for NaCl from 0 to 100°C and 0.2 to 6.1 molality
Sound velocity based on F. J. Millero et al., J. Sol. Chem. 1987which gives a fit of data for NaCl from 0 to 100°C and 0.2 to 6.1 molality
Brillouin shift for comparison with the experiments
Brillouin shift for comparison with the experiments
Model-data comparisons
Model-data comparisons
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Density
Density
Volumetric derivatives(Thermal expansion: αp; Isothermal compressibility: βT; Adiabatic compressibility: βs)
Volumetric derivatives(Thermal expansion: αp; Isothermal compressibility: βT; Adiabatic compressibility: βs)
Adiabatic compressibility
Adiabatic compressibility
Heat capacity
Heat capacity
Extrapolation tests
Extrapolation tests
Speed of sound in NaCl-H2O: calculations with Archer's model give the closest w to uMillero[273<T<373K,6molal]. There is still a deviation that we can see along binodal, with Archer lower by about 1% at 0°C; this deviation reduces at high temperature. This can be due to an overestimation of Subscript[β, T], as suggested in the Plot3D comparing Archer and Al Ghafri (at low T, the dρ/dp deviation between Archer and Al Ghafri is maximal).This results in a strong difference on the Δw/ΔT: along binodal between 0 and 35°C, we have 0.49m.(s.°C )-1 for Millero against 0.85m/s.°C calculated with Archer. This is certainly one of the reasons why the calculated isochoric speed of sound calculated with Archer has also larger dw/dT than the one we measure with Brillouin spectroscopy: ~2.05 m/s.°C with Brillouin spectro, and ~2.50 m/s.°C
Speed of sound in NaCl-H2O: calculations with Archer's model give the closest w to uMillero[273<T<373K,6molal]. There is still a deviation that we can see along binodal, with Archer lower by about 1% at 0°C; this deviation reduces at high temperature. This can be due to an overestimation of Subscript[β, T], as suggested in the Plot3D comparing Archer and Al Ghafri (at low T, the dρ/dp deviation between Archer and Al Ghafri is maximal).This results in a strong difference on the Δw/ΔT: along binodal between 0 and 35°C, we have 0.49m.(s.°C )-1 for Millero against 0.85m/s.°C calculated with Archer. This is certainly one of the reasons why the calculated isochoric speed of sound calculated with Archer has also larger dw/dT than the one we measure with Brillouin spectroscopy: ~2.05 m/s.°C with Brillouin spectro, and ~2.50 m/s.°C
Cite this as: Emmanuel Guillerm, "Halite Fluid Inclusion Model" from the Notebook Archive (2025), https://notebookarchive.org/2025-01-b23umu8
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