Calculate thermodynamic and electrostatic properties of water.
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character, computational setting or property(s) to calculate
numeric, temperature (K)
numeric, pressure (bar), or Psat for vapor-liquid saturation
These functions compute the thermodynamic (Gibbs energy and it derivatives) and electrostatic (dielectric constant and its derivatives) properties of liquid or supercritical \H2O as a function of temperature and pressure using equations of state taken from the literature.
The high-level function
water performs different computations, depending on the setting of
Thermodynamic and electrostatic properties are calculated using a FORTRAN subroutine taken from the SUPCRT92 software package (Johnson et al., 1992). See more information below.
Thermodynamic properties are calculated using an implementation in R code of the IAPWS-95 formulation (Wagner and Pruss, 2002), and electrostatic properties are calculated using the equations of Archer and Wang, 1990. See
IAPWS95 and more information below.
Thermodynamic and electrostatic properties are calculated using the Deep Earth Water (DEW) model (Sverjensky et al., 2014). The defaults for
P reflect the minimum values for applicability of the model; calculations at lower
P points fall back to using SUPCRT92. See
Calling the function with no arguments returns the current computational setting.
water("DEW") to make the setting; the previous setting (at the time of the function call) is returned invisibly.
Subsequent calculations with
water, or other functions such as
affinity, will use that setting.
water are one or more of those given below, depending on the computational setting; availability is shown by an asterisk.
Note that some of the properties that can actually be calculated using the different formulations are not implemented here.
rho, the units are those used by Johnson and Norton, 1991.
||Helmholtz energy||cal mol^-1||*||*||NA|
||Gibbs energy||cal mol^-1||*||*||*|
||Entropy||cal K^-1 mol^-1||*||*||NA|
||Internal energy||cal mol^-1||*||*||NA|
||Isochoric heat capacity||cal K^-1 mol^-1||*||*||NA|
||Isobaric heat capacity||cal K^-1 mol^-1||*||*||NA|
||Speed of sound||cm s^-1||NA||*||NA|
||Coefficient of isobaric expansivity||K^-1||NA||*||NA|
||Coefficient of isothermal compressibility||bar^-1||NA||*||NA|
||Dynamic viscosity||g cm^-1 s^-1||NA||*||NA|
||Thermal conductivity||cal cm^-1 s^-1 K^-1||NA||*||NA|
||Thermal diffusivity||cm^2 s^-1||NA||*||NA|
||Kinematic viscosity||cm^2 s^-1||NA||*||NA|
||Isochoric expansivity||bar K^-1||NA||*||NA|
||Z Born function||dimensionless||NA||*||NA|
||Y Born function||K^-1||*||*||NA|
||Q Born function||bar^-1||*||*||*|
||Isobaric temperature derivative||K^-2||NA||*||NA|
||X Born function||K^-2||*||*||NA|
||N Born function||bar^-2||*||NA||NA|
||U Born function||bar^-1 K^-1||*||NA||NA|
||Saturation vapor pressure||bar||*||*||NA|
||Isobaric expansivity||cm^3 K^-1||NA||*||NA|
||Isothermal compressibility||cm^3 bar^-1||NA||*||NA|
|of dielectric constant|
|of dielectric constant|
water.DEW with no arguments to list the available properties.
water.SUPCRT92 interfaces to the FORTRAN subroutine taken from the SUPCRT92 package (H2O92D.F) for calculating properties of water.
These calculations are based on data and equations of Levelt-Sengers et al., 1983, Haar et al., 1984, and Johnson and Norton, 1991, among others (see Johnson et al., 1992).
A value of
P set to Psat refers to one bar below 100 °C, otherwise to the vapor-liquid saturation pressure at temperatures below the critical point (Psat is not available at temperatures above the critical point).
water.SUPCRT92 provides a limited interface to the FORTRAN subroutine; some functions provided there are not made available here (e.g., using variable density instead of pressure, or calculating the properties of steam).
The stated temperature limits of validity of calculations in
water.SUPCRT92 are from the greater of 0 °C or the melting temperature at pressure, to 2250 °C (Johnson et al., 1992).
Valid pressures are from the greater of zero bar or the melting pressure at temperature to 30000 bar.
The present functions do not check these limits and will attempt calculations for any range of input parameters, but may return
NA for properties that fail to be calculated at given temperatures and pressures and/or produce warnings or even errors when problems are encountered.
Starting with version 0.9-9.4, a check for minimum pressure (in valTP function in H2O92D.f) has been bypassed so that properties of H2O can be calculated using
water.SUPCRT92 at temperatures below the 0.01 °C triple point.
A primary check is still enforced (Tbtm), giving a minimum valid temperature of 253.15 K.
water.IAPWS95 is a wrapper around
water.IAPWS95 provides for calculations at specific temperature and pressure; density, needed for
IAPWS95, is inverted from pressure using
The function also contains routines for calculating the Born functions as numerical derivatives of the static dielectric constant (from
For compatibility with geochemical modeling conventions, the values of Gibbs energy, enthalpy and entropy output by
IAPWS95 are converted by
water.IAPWS95 to the triple point reference state adopted in
SUPCRT92 (Johnson and Norton, 1991; Helgeson and Kirkham, 1974).
water.IAPWS95 also accepts setting
P to Psat, with the saturation pressure calculated from
WP02.auxiliary; by default the returned properties are for the liquid, but this can be changed to the vapor in
A data frame, the number of rows of which corresponds to the number of input temperature-pressure pairs.
Archer, D. G. and Wang, P. M. (1990) The dielectric constant of water and Debye-Hückel limiting law slopes. J. Phys. Chem. Ref. Data 19, 371–411. https://doi.org/10.1063/1.555853
Haar, L., Gallagher, J. S. and Kell, G. S. (1984) NBS/NRC Steam Tables. Hemisphere, Washington, D. C., 320 p. http://www.worldcat.org/oclc/301304139
Helgeson, H. C. and Kirkham, D. H. (1974) Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures. I. Summary of the thermodynamic/electrostatic properties of the solvent. Am. J. Sci. 274, 1089–1098. http://www.ajsonline.org/cgi/content/abstract/274/10/1089
Johnson, J. W. and Norton, D. (1991) Critical phenomena in hydrothermal systems: state, thermodynamic, electrostatic, and transport properties of H2O in the critical region. Am. J. Sci. 291, 541–648. http://www.ajsonline.org/cgi/content/abstract/291/6/541
Johnson, J. W., Oelkers, E. H. and Helgeson, H. C. (1992) SUPCRT92: A software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous species, and reactions from 1 to 5000 bar and 0 to 1000°C. Comp. Geosci. 18, 899–947. https://doi.org/10.1016/0098-3004(92)90029-Q
Levelt-Sengers, J. M. H., Kamgarparsi, B., Balfour, F. W. and Sengers, J. V. (1983) Thermodynamic properties of steam in the critical region. J. Phys. Chem. Ref. Data 12, 1–28. https://doi.org/10.1063/1.555676
Sverjensky, D. A., Harrison, B. and Azzolini, D. (2014) Water in the deep Earth: The dielectric constant and the solubilities of quartz and corundum to 60 kb and 1,200 \degC. Geochim. Cosmochim. Acta 129, 125–145. https://doi.org/10.1016/j.gca.2013.12.019
Wagner, W. and Pruss, A. (2002) The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31, 387–535. https://doi.org/10.1063/1.1461829
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## calculations along saturation curve T <- seq(273.15, 623.15, 25) # liquid density, from SUPCRT92 water("rho", T=T, P="Psat") # values of the saturation pressure, Gibbs energy water(c("Psat", "G"), T=T, P="Psat") # derivatives of the dielectric constant (Born functions) water(c("QBorn", "YBorn", "XBorn"), T=T, P="Psat") # now at constant pressure water(c("QBorn", "YBorn", "XBorn"), T=T, P=2000) ## comparing the formulations T <- convert(c(25, 100, 200, 300), "K") # IAPWS-95 oldwat <- water("IAPWS95") water(water.IAPWS95(), T=T) # Deep Earth Water (DEW) water("DEW") water(water.DEW(), T=T, P=1000) # SUPCRT92 (the default) water(oldwat) water(water.SUPCRT92(), T=T) ## calculating Q Born function # after Table 22 of Johnson and Norton, 1991 T <- rep(c(375, 400, 425, 450, 475), each=5) P <- rep(c(250, 300, 350, 400, 450), 5) w <- water("QBorn", T=convert(T, "K"), P=P) # the rest is to make a neat table w <- as.data.frame(matrix(w[], nrow=5)) colnames(w) <- T[1:5*5] rownames(w) <- P[1:5] print(w)
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