NIST/ASME Steam Properties Database

Appendix C

INFORMATION ON WARNING AND ERROR LIMITS

All formulations used within the NIST/ASME Steam Properties database have a specified region of validity. In addition, most of them can be extrapolated to some extent without producing unreasonable results. Two different levels of boundaries are therefore incorporated in the software. The first level is the actual region of validity of the formulation. Calculations outside those boundaries still produce a result, but also produce a warning message. The second level are the boundaries beyond which no calculations are allowed. These boundaries are usually set because the calculations would be physically meaningless, or because computational problems would be encountered. The following sections describe the boundaries for various calculations.

Thermodynamic Properties

The formulation is recommended for temperatures between 273.15 K and 1273.15 K and for all positive pressures up to 1000 MPa. The absolute limits (beyond which no calculations are made) are temperatures of 190 K and 5000 K and a pressure of 1.0x10⁵ MPa. To avoid computational problems, a lower pressure limit of 1.0x10^-20 MPa is also set. There is also a warning region very close to the critical point, which is discussed separately below.

Transport Properties

The absolute limits for transport properties are the same as for the thermodynamic properties. The recommended validity range for the viscosity calculations is as follows:

The recommended validity range for the thermal conductivity calculations is:

273.15 K T 1073.15 K  for  p 100 MPa

273.15 K T 673.15 K  for  100 MPa < p 150 MPa
273.15 K T 523.15 K for 150 MPa < p 200 MPa
273.15 K T 398.15 K for 200 MPa < p 400 MPa

Dielectric Constant

The absolute limits for the dielectric constant calculations are the same as for the thermodynamic properties, except that the lower temperature limit is 238 K. The recommended range is temperatures from 238 to 873 K at pressures up to 1000 MPa.

Refractive Index

The absolute limits for the refractive index calculations are the same as for the thermodynamic properties.  The recommended range is temperatures from 261.15 K to 773.15 K at densities up to 1060 kg/m³.  There are also limits on the wavelength of light at which the refractive index may be computed.  The recommended range is from 0.2 mm to 1.1 mm.  The absolute limits are from 0.18 mm to 1.9mm.

Solid Phase Boundaries

If fluid phase calculations are requested in a region in which the actual equilibrium phase would be a solid (for example, for a supercooled liquid), a warning message is issued. If the temperature is more than 35 K below the fluid-solid saturation boundary at that pressure, no calculations are performed.

Near-Critical Region

The 1995 IAPWS formulation for thermodynamic properties is known to give unphysical behavior for some of the “derivative” properties (specifically, the isothermal compressibility, the isochoric and isobaric heat capacities, and the speed of sound) in a region very close to the critical point.  Property calculations in that region are therefore accompanied by a warning.  The region is defined by:

647.076 K < T < 652.096 K  for 320.39 kg/m³ <p< 323.61 kg/m³

Vapor-Liquid Saturation

Vapor-liquid saturation calculations are only valid for temperatures and pressures from the triple point (273.16 K, 611.657 Pa) to the critical point (647.096 K, 22.064 MPa).  In addition, numerical limitations prevent solving exactly for the saturation conditions very near the critical point. In that case, a warning is issued, and the saturation pressure and coexisting densities are given based on an interpolation constrained to give the correct values for pressure (22.064 MPa) and density (322 kg/m³) at the critical point. This warning should rarely be encountered; the software is able to solve rigorously for vapor-liquid coexistence at temperatures up to approximately 647.09599 K.

The database also allows calculations of the vapor-liquid saturation boundary extrapolated below the triple point, down to a temperature of 253.15 K. A warning is issued if calculations are performed in this region.

Surface Tension

The surface tension formulation is valid from the triple point to the critical point.  For the extrapolated vapor-liquid boundary below the triple point, the surface tension formulation is extrapolated and a warning is issued.

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