NOTE: The following information is for Pure Compounds only. We are working on similar information for Binary Mixtures.

Fitted Equations for Specific Properties

Listed below are the properties for which evaluated data is generated by TDE. Each property is linked to a list showing the set of possible equations that can be fit to the data. The equation that is used for a specific query is the one that provides the best fit of the data. This equation is then used to provide evaluated data.

NOTE: All of this information is displayed here in an individual file so that you can do text searches by using the Find funtion from the Edit menu of your browser.

Purpose: Provide definitions of equations and equation parameters used for output of evaluated data.

Select a property to see all associated equations. Properties represented with equations in TDE output are:

Phase Boundary Pressure:
Density (Phase Boundary):
- Saturated Density (Liquid)
- Saturated Density (Gas)
Density (Single Phase):
- Density (Liquid)
- Density (Gas)
Enthalpy of Phase Change:
- Enthalpy of Vaporization (Liquid/Gas)
Heat Capacity:
- Saturated C_sat (Liquid)
- Constant pressure C_p^o (Ideal Gas)
Speed of Sound (Single Phase):
- Speed of Sound (Liquid)
- Speed of Sound (Gas)
Refractive Index (Single Phase):
- Refractive Index (Liquid)
Surface Tension:
- Surface Tension (Liquid/Gas)
Viscosity (Single Phase):
- Viscosity (Saturated Liquid)
- Viscosity (Low-pressure Gas)
Thermal Conductivity :
- Thermal Conductivity (Saturated Liquid)
- Thermal Conductivity (Gas)

Vapor Pressure: Liquid-Gas Phase Boundary Pressure

DEFAULT: Wagner 25 (sample parameter output)

p/p^o

p_c/p^o

T_c/T

₁

₂

^1.5

₃

^2.5

₄

⁵

T/T_c

p^o

Alternative 1: Antoine (sample parameter output)

p/p^o

p^o

Alternative 2: Yaws.VaporPressure (sample parameter output)

p/p^o

p^o

₁₀

Alternative 3: DIPPR 115 (sample parameter output)
ln(p/p^o) = a + b/T + c×ln(T) + d×T² + e/T² ; where p^o = 1 kPa

Alternative 4: DIPPR 101 (sample parameter output)
ln(p/p^o) = a + b/T + c×ln(T) + d×T^e ; where p^o = 1 kPa

Alternative 5: Wagner 36 (sample parameter output)
ln(p/p^o) – ln(p_c/p^o) = T_c/T (A₁ + A₂×t^1.5 + A₃×t³ + A₄×t⁶); where t = 1 - T/T_c and p^o = 1 kPa

Wagner 25 (Vapor Pressure: Output Details)

ln(p/p^o) – ln(p_c/p^o) = T_c/T (A₁ + A₂×t^1.5 + A₃×t^2.5 + A₄×t⁵); where t = 1 - T/T_c and p^o = 1 kPa

Evaluation Results:

The example is for fitted vapor pressures for benzene.

Antoine (Vapor Pressure: Output Details)

ln(p/p^o) = A + B/(T + C); where p^o = 1 kPa

Evaluation Results:

The example is for fitted vapor pressures for benzene.

Yaws (Vapor Pressure: Output Details)

lg(p/p^o) = a + b/T + c×lg(T) + d×T + e/T² ; where p^o = 1 kPa and lg = log₁₀

Evaluation Results:

The example is for fitted vapor pressures for benzene.

DIPPR 115 (Vapor Pressure: Output Details)

ln(p/p^o) = a + b/T + c×ln(T) + d×T² + e/T² ; where p^o = 1 kPa

Evaluation Results:

The example is for fitted vapor pressures for benzene.

DIPPR 101 (Vapor Pressure: Output Details)

ln(p/p^o) = a + b/T + c×ln(T) + d×T^e ; where p^o = 1 kPa

Evaluation Results:

The example is for fitted vapor pressures for benzene.

Wagner36 (Vapor Pressure: Output Details)

ln(p/p^o) – ln(p_c/p^o) = T_c/T (A₁ + A₂×t^1.5 + A₃×t³ + A₄×t⁶); where t = 1 - T/T_c and p^o = 1 kPa

Evaluation Results:

The example is for fitted vapor pressures for benzene.

Sublimation Pressure: Crystal-Gas Phase Boundary Pressure

DEFAULT: PV Expansion: (sample parameter output)

ln(p/p^o) = a₁ + a₂/T + a₃×ln(T) + a₄×T + a₅×T² + a₆×T⁶+ a₇/T⁴
Alternative 1: Antoine (sample parameter output)

ln(p/p^o) = A + B/(T + C); where p^o = 1 kPa
Alternative 2: Yaws.VaporPressure (sample parameter output)

lg(p/p^o) = a + b/T + c×lg(T) + d×T + e/T² ; where p^o = 1 kPa and lg = log₁₀
Alternative 3: DIPPR 115 (sample parameter output)

ln(p/p^o) = a + b/T + c×ln(T) + d×T² + e/T² ; where p^o = 1 kPa
Alternative 4: DIPPR 101 (sample parameter output)

ln(p/p^o) = a + b/T + c×ln(T) + d×T^e ; where p^o = 1 kPa

PV Expansion: Sublimation Pressure

ln(p/p^o) = a₁ + a₂/T + a₃×ln(T) + a₄×T + a₅×T² + a₆×T⁶+ a₇/T⁴

NOTE: The TDE program truncates this equation based upon the extent and quality of the fitted data.

Condensed Phase boundary pressure

DEFAULT: PolynomialPressure: (sample parameter output)

ln(p/p^o) = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 1:
There are no alternative equations for this property at this time.

PolynomialExpansion: Phase boundary pressure for the crystal/liquid boundary

ln(p/p^o) = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted phase-boundary pressures for benzene.

Density of the Liquid (on the Liquid/Gas phase boundary): d_sat

VDNS Expansion: (sample parameter output)

d_sat = d_c + a₁×t^0.35 + åa_i+1×tⁱ , where the summation is from i = 1 to nTerms -1.

d_c = the critical density and t = 1 - T/T_c, where T_c is the critical temperature.
Alternative 1: Rackett (sample parameter output)
d_sat = d_c×B^{– (1-T/T_c)^N}; where T_c and d_c are the critical temperature and critical density, respectively.

Alternative 2: PPDS 10 (sample parameter output)
d_sat = d_c + a₁×t^0.35 + a₂×t^2/3 + a₃×t + a₄×t^4/3;
d_c = the critical density and t = 1 - T/T_c, where T_c is the critical temperature.

Alternative 3: PPDS 17 (sample parameter output)
d_sat = (a₁ + a₂×t) ^{-1 - t^-2/7}/a₀ ; where t = 1 - T/T_c, and T_c is the critical temperature.

VDNS Expansion: For d_sat of the Liquid or Gas phase

d_sat = d_c + a₁×t^0.35 + åa_i+1×tⁱ ; where the summation is from i = 1 to nTerms -1.

d_c = the critical density and t = 1 - T/T_c, where T_c is the critical temperature.

NOTE: The TDE program truncates this equation based upon the extent and quality of the fitted data.

Rackett Equation: For d_sat of the Liquid phase

d_sat = d_c×B^{– (1-T/T_c)^N}; where T_c and d_c are the critical temperature and critical density, respectively.

PPDS 10: For d_sat of the Liquid phase

d_sat = d_c + a₁×t^0.35 + a₂×t^2/3 + a₃×t + a₄×t^4/3;

d_c = the critical density and t = 1 - T/T_c, where T_c is the critical temperature.

Evaluation Results:

The example is for fitted densities at vapor saturation for benzene.

PPDS 17: For d_sat of the Liquid phase

d_sat = (a₁ + a₂×t) ^{-1 - t^-2/7}/a₀ ; where t = 1 - T/T_c, and T_c is the critical temperature.

Evaluation Results:

The example is for fitted densities at vapor saturation for benzene.

Density of the Gas (on the Liquid/Gas phase boundary)

VDNSExpansion: (sample parameter output)

d_sat = d_c + a₁×t^0.35 + åa_i+1×tⁱ , where the summation is from i = 1 to nTerms -1.

d_c = the critical density and t = 1 - T/T_c, where T_c is the critical temperature.
Alternative 1: There are no alternative equations for this property at this time.

Density (Liquid Phase)

Tait Equation: (sample parameter output)

d = d_sat / [1 - c×ln{(b + p) / (b + p_sat)}] ; where

b = åB_i+1×t ⁱ, c = åC_i+1×t ⁱ, and t = (T-T_center)/100, where T_center is a constant parameter.
Summations are from i = 0 to (nTerms -1), where nTerms is the number of B or C terms.
d_sat = the density of the saturated liquid and p_sat = the saturation vapor pressure.
Alternative 1: There are no alternative equations for this property at this time.

Tait Equation: Density (Liquid Phase)

d = d_sat / [1 - c×ln{(b + p) / (b + p_sat)}] ; where

b = åB_i+1×t ⁱ, c = åC_i+1×t ⁱ, and t = (T-T_center)/100, where T_center is a constant parameter.
Summations are from i = 0 to (nTerms -1), where nTerms is the number of B or C terms.
d_sat = the density of the saturated liquid and p_sat = the saturation vapor pressure.

Density (Gas Phase)

DEFAULT: Virial Equation (VirialV):
(sample parameter output)

d = 1000×Mw / V_m; where Mw is the molar mass and V_m is the molar volume.

Z = 1000×p×V_m/(R×T) = 1 + B/V_m + C/V_m²,

where B = åb_i+1/Tⁱ and C = åc_i+1/Tⁱ
Alternative 1:
There are no alternative equations for this property at this time.

VirialV: For density of the gas phase.

d = 1000×Mw / V_m; where Mw is the molar mass and V_m is the molar volume.

Z = 1000×p×V_m/(R×T) = 1 + B/V_m + C/V_m², where B = åb_i+1/Tⁱ and C = åc_i+1/Tⁱ

Evaluation Results:

The example is for fitted gas densities of pentane.

Enthalpy of Vaporization (Liquid/Gas)

DEFAULT: HVP Expansion: (sample parameter output)

ln(H_vap/H_vap^o) = a₁ + åa_i ×T_r^i-1×ln(1-T_r) , where the summation is from i = 2 to nTerms -1

T_r = T/T_c, T_c is the critical temperature, and H_vap^o = 1 kJ/mol
Alternative 1: Yaws.VaporizationH (sample parameter output)

H_vap = A×{1 - ( T / T_c )}ⁿ
Alternative 2: PPDS 12 (sample parameter output)

H_vap/R = a₁×t^1/3 + a₂×t^2/3 + a₃×t + a₄×t² + a₅×t⁶

where t = 1 - T/T_c, T_c is the critical temperature, and R is the gas constant.

HVPExpansion: For H_vap for the liquid-gas phase boundary

ln(H_vap/H_vap^o) = a₁ + åa_i ×T_r^i-1×ln(1-T_r) , where the summation is from i = 2 to nTerms -1

T_r = T/T_c, T_c is the critical temperature, and H_vap^o = 1 kJ/mol

Evaluation Results:

The example is for fitted enthalpies of vaporization for benzene.

Yaws.VaporizationH: For H_vap for the liquid-gas phase boundary

H_vap = A×{1 - ( T / T_c )}ⁿ

Evaluation Results:

The example is for fitted enthalpies of vaporization for pentane.

PPDS12: For H_vap for the liquid-gas phase boundary

H_vap/R = a₁×t^1/3 + a₂×t^2/3 + a₃×t + a₄×t² + a₅×t⁶

where t = 1 - T/T_c, T_c is the critical temperature, and R is the gas constant.

Evaluation Results:

The example is for fitted enthalpies of vaporization for benzene.

C_sat (Liquid Phase)

DEFAULT: CSExpansion: (sample parameter output)

C_sat = (åa_i+1× tⁱ) + b/t , where the summation is from i = 0 to nTerms -1.
Alternative 2: Yaws.PolynomialExpansion (sample parameter output)

C_sat = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 3: DIPPR.PolynomialExpansion (sample parameter output)

C_sat = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 3: PPDS 15 (sample parameter output)

C_sat / R = a₀/t + a₁ + a₂×t + a₃×t² + a₄×t³ + a₅×t⁴

where t = 1 - T/T_c, T_c is the critical temperature, and R is the gas constant.

CSExpansion: For C_sat of the Liquid phase

C_sat = (åa_i+1× tⁱ) + b/t , where the summation is from i = 0 to nTerms -1.

Evaluation Results:

The example is for fitted heat capacities at vapor saturation for benzene.

Yaws.PolynomialExpansion: For C_sat of the liquid phase

C_sat = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted heat capacities at vapor saturation for benzene.

DIPPR.PolynomialExpansion: For C_sat of the liquid phase

C_sat = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted heat capacities at vapor saturation for benzene.

PPDS 15: For C_sat of the liquid phase

C_sat / R = a₀/t + a₁ + a₂×t + a₃×t² + a₄×t³ + a₅×t⁴

where t = 1 - T/T_c, T_c is the critical temperature, and R is the gas constant.

Evaluation Results:

The example is for fitted heat capacities at vapor saturation for benzene.

C_p^o(Ideal Gas)

DEFAULT: Wilhoit Equation
C_p^o / R = a₀ + (a₁ /T ²) × exp( -a₂ /T ) + a₃ × y² + {a₄ - a₅ /(T - a₇)²} × y ⁸
where y = (T - a₇)/(T + a₆) and R is the gas constant.
See Thermodynamics of Organic Compounds in the Gas State (Volumes I and II) by M. Frenkel, G. J. Kabo, K. N. Marsh, G. N. Roganov, and R. C. Wilhoit. Publsihed by the Thermodynamics Research Center (TRC), College Station: TX. 1994.
Alternative 1: Yaws.PolynomialExpansion (sample parameter output)

C_p^o = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 2: AlyLee (which is also DIPPR 107) (sample parameter output)

C_p^o = a + b×{(c/T)/sinh(c/T)}² + d×{(e/T)/cosh(e/T)}²
Alternative 3: PPDS2 (sample parameter output)

C_p^o/R = C_low + (C_low - C_¥)×y² ×{1 + (y - 1) å(a_i × y_i)} ; where the summation is from i = 0 to 4.

C_low and C_¥ are equation constants, and y = T / (T + T_S), where T_S is a constant.
Alternative 4: Helmholtz (sample parameter output)

C_p^o/R = 1 + t - {åa_i×n_i×(n_i - 1)×t^{^n_i}}_{(n_i¹ 0 or 1)} + åb_i×(c_i×t)²×exp(c_i×t) / {exp(c_i×t) - 1}²;

where t = T_c/T, T_c = the critical temperature, and the summations are from i = 1 to nTerms.

C_p^o(Ideal Gas)

C_p^o = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

The example is for fitted heat capacities in the ideal-gas state at p = 100 kPa for pentane.

Aly & Lee Equation (same as DIPPR 107):
C_p^o(Ideal Gas)

C_p^o = a + b×{(c/T)/sinh(c/T)}² + d×{(e/T)/cosh(e/T)}²

Reference: Aly, F. A.; Lee, L. L. Fluid Phase Equil. 1981, 6, 169-179.

The example is for fitted heat capacities in the ideal-gas state at p = 100 kPa for pentane.

PPDS 2: C_p^o(Ideal Gas)

C_p^o/R = C_low + (C_low - C_¥)×y² ×{1 + (y - 1) å(a_i × y_i)} ; where the summation is from i = 0 to 4.

C_low and C_¥ are equation constants, and y = T / (T + T_S), where T_S is a constant.

Evaluation Results:

The example is for fitted heat capacities in the ideal-gas state at p = 100 kPa for pentane.

Helmholtz: C_p^o(Ideal Gas)

C_p^o/R = 1 + t - {åa_i×n_i×(n_i - 1)×t^{^n_i}}_{(n_i¹ 0 or 1)} + åb_i×(c_i×t)²×exp(c_i×t) / {exp(c_i×t) - 1}²;
where t = T_c/T, T_c = the critical temperature, and the summations are from i = 1 to nTerms.

The example is for fitted heat capacities in the ideal-gas state at p = 100 kPa for 2-methylpyrrole.

Speed of Sound (Liquid Phase)

DEFAULT: RSSL Expansion: (sample parameter output)

u = A + B×T + C×(d - d_sat) + D×d²,

where d is the density of the liquid and d_sat is the density of the saturated liquid.
Alternative 1:
There are no alternative representations for this property at this time.

Speed of Sound (Liquid Phase)

u = A + B×T + C×(d - d_sat) + D×d²,

where d is the density of the liquid and d_sat is the density of the saturated liquid.

The example is for fitted speeds of sound for benzene.

Speed of Sound (Gas Phase)

DEFAULT: RSSG Expansion: (sample parameter output)

u = A + B×T + C×p + D×p/T ;

where T is the temperature and p is pressure.
Alternative 1:
There are no alternative representations for this property at this time.

Speed of Sound (Gas Phase)

u = A + B×T + C×p + D×p/T ;

where T is the temperature and p is pressure.

The example is for fitted speeds of sound for pentane in the gas phase.

Refractive Index n_D (Liquid)

DEFAULT: RIXExpansion: (sample parameter output)

n_D = A + B×t + å C_i×wⁱ ;the summation is from i = 1 to nTerms

where t = T - 298.15 K and w = WL - 589.26 (WL = wavelength in nm)
Alternative 1:
There are no alternative equations for this property at this time.

RIXExpansion: Refractive Index n_D (Liquid)

n_D = A + B×t + å C_i×wⁱ ;the summation is from i = 1 to nTerms

where t = T - 298.15 K and w = WL - 589.26 (WL = wavelength in nm)

Evaluation Results:

The example is for fitted surface tensions for pentane.

Surface Tension s (Liquid/Gas)

DEFAULT: PPDS 14: (sample parameter output)

s = a₀× t^a₁×(1 + a₂ ×t) , where t = 1 - T/T_c and T_c is the critical temperature.
Alternative 1: Yaws.SurfaceTension (sample parameter output)
s = exp(A)×{1 - ( T / T_c )}ⁿ
Alternative 2: HVPExpansion (sample parameter output)
ln(s/s^o) = a₁ + åa_i ×T_r^i-1×ln(1-T_r) , where the summation is from i = 2 to nTerms -1

T_r = T/T_c, T_c is the critical temperature, and s^o = 1 N/m

PPDS14: For surface tension s for the liquid/gas interface

s = a₀× t^a₁×(1 + a₂ ×t) , where t = 1 - T/T_c and T_c is the critical temperature.

Evaluation Results:

The example is for fitted surface tensions for benzene.

Yaws.SurfaceTension: For surface tension s for the liquid/gas interface

Alternative 1: Yaws.SurfaceTension (sample parameter output)

s = exp(A)×{1 - ( T / T_c )}ⁿ

Evaluation Results:

The example is for fitted surface tensions for benzene.

HVPExpansion: For surface tension s for the liquid/gas interface

ln(s/s^o) = a₁ + åa_i ×T_r^i-1×ln(1-T_r) , where the summation is from i = 2 to nTerms -1

T_r = T/T_c, T_c is the critical temperature, and s^o = 1 N/m

The example is for fitted surface tensions for benzene.

Viscosity (Saturated Liquid)

DEFAULT: PPDS 9: (sample parameter output)

ln(h/h^o) = a₁ ×X^1/3 + a₂ ×X^4/3 + ln(a₅) , where X = (a₃ - T) / (T - a₄) and h^o = 1 Pa×s
Alternative 1: Yaws.Viscosity (sample parameter output)

lg(h/h^o) = A + B/T + C×T + D×T ²
Alternative 2: DIPPR 101 (sample parameter output)

ln(h/h^o) = a + b/T + c×ln(T) + d×T^e ; where h^o = 1 Pa×s

PPDS9: Viscosity h of the saturated liquid

ln(h/h^o) = a₁ ×X^1/3 + a₂ ×X^4/3 + ln(a₅) , where X = (a₃ - T) / (T - a₄) and h^o = 1 Pa×s.

Evaluation Results:

The example is for fitted viscosities for the saturated liquid phase of benzene.

Yaws.Viscosity: Viscosity h of the saturated liquid

lg(h/h^o) = A + B/T + C×T + D×T ²

Evaluation Results:

The example is for fitted viscosities for the saturated liquid phase of benzene.

DIPPR101: Viscosity h of the saturated liquid

ln(h/h^o) = a + b/T + c×ln(T) + d×T^e ; where h^o = 1 Pa×s

Evaluation Results:

The example is for fitted viscosities for the saturated liquid phase of benzene.

Viscosity (Gas at low pressures; p < 6 bar)

DEFAULT: TransportPolynomial: (sample parameter output)

h = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 1: Yaws.PolynomialExpansion (sample parameter output)

h = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 2: DIPPR 102 (sample parameter output)

h = A×T^B / (1+ C/T + D/T²)
Alternative 3: PPDS 5 (sample parameter output)

h = a₀×T_r / {1 + a₁×(T_r - 1)× T_r^{^a₂}}^1/6; where T_r = T/T_c and T_c is the critical temperature.

TransportPolynomial: For viscosity h of the gas at low pressures (p < 600 kPa)

h = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

Yaws.PolynomialExpansion: For viscosity h of the gas at low pressures (p < 600 kPa)

h = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

DIPPR 102: For viscosity h of the gas at low pressures (p < 600 kPa)

h = A×T^B / (1+ C/T + D/T²)

Evaluation Results:

The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

PPDS 5: For viscosity h of the gas at low pressures (p < 600 kPa)

h = a₀×T_r / {1 + a₁×(T_r - 1)× T_r^{^a₂}}^1/6; where T_r = T/T_c and T_c is the critical temperature.

Evaluation Results:

The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

Thermal Conductivity l: (Liquid)

DEFAULT: TransportPolynomial: (sample parameter output)

l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 1: Yaws.ThermalConductivity (sample parameter output)

lg(l/l^o) = A + B×(1 - T/C)^2/7
Alternative 2: Yaws.PolynomialExpansion (sample parameter output)

l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 3: DIPPR.PolynomialExpansion (sample parameter output)

l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 4: PPDS 8 (sample parameter output)

l = a₁ + å(a_i+1 ×t^i/3) , where the summation is from i = 1 to nTerms -1 and t = 1 - T/T_c

TransportPolynomial: For thermal conductivity l of the saturated liquid

l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted thermal conductivities for the saturated liquid phase of benzene.

Yaws.ThermalConductivity: For thermal conductivity l of the saturated liquid

lg(l/l^o) = A + B×(1 - T/C)^2/7

Evaluation Results:

The example is for fitted thermal conductivities for the saturated liquid phase of benzene.

Yaws.PolynomialExpansion: For thermal conductivity l of the saturated liquid

l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted thermal conductivities for the saturated liquid phase of benzene.

DIPPR.PolynomialExpansion: For thermal conductivity l of the saturated liquid

l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted thermal conductivities for the saturated liquid phase of benzene.

PPDS8: For thermal conductivity l of the saturated liquid

l = a₁ + å(a_i+1 ×t^i/3) , where the summation is from i = 1 to nTerms -1 and t = 1 - T/T_c

Evaluation Results:

The example is for fitted thermal conductivities for the liquid phase of benzene.

Thermal Conductivity (Gas at low pressures; p < 6 bar)

DEFAULT: TransportPolynomial: (sample parameter output)

l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 1: Yaws.PolynomialExpansion (sample parameter output)

l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 2: PPDS 3 (sample parameter output)

l = T_r^0.5 (åa_i / T_rⁱ)^-1 , where the summation is from i = 1 to 3,

and T_r = T/T_c, where T_c is the critical temperature.

TransportPolynomial: For thermal conductivity l of the gas at low pressure (p < 600 kPa)

l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

Yaws.PolynomialExpansion: For thermal conductivity l of the gas at low pressure (p < 600 kPa)

l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

PPDS 3: For thermal conductivity l of the gas at low pressure (p < 600 kPa)

l = T_r^0.5 (åa_i / T_rⁱ)^-1 , where the summation is from i = 1 to 3,

and T_r = T/T_c, where T_c is the critical temperature.

Evaluation Results:

The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

NOTE: The following information is for Pure Compounds only. We are working on similar information for Binary Mixtures.

Fitted Equations for Specific Properties

Vapor Pressure: Liquid-Gas Phase Boundary Pressure

Wagner 25 (Vapor Pressure: Output Details)

Antoine (Vapor Pressure: Output Details)

Yaws (Vapor Pressure: Output Details)

DIPPR 115 (Vapor Pressure: Output Details)

DIPPR 101 (Vapor Pressure: Output Details)

Wagner36 (Vapor Pressure: Output Details)

Sublimation Pressure: Crystal-Gas Phase Boundary Pressure

PV Expansion: Sublimation Pressure

Condensed Phase boundary pressure

PolynomialExpansion: Phase boundary pressure for the crystal/liquid boundary

Density of the Liquid (on the Liquid/Gas phase boundary): dsat

VDNS Expansion: For dsat of the Liquid or Gas phase

Rackett Equation: For dsat of the Liquid phase

PPDS 10: For dsat of the Liquid phase

PPDS 17: For dsat of the Liquid phase

Density of the Gas (on the Liquid/Gas phase boundary)

Density (Liquid Phase)

Tait Equation: Density (Liquid Phase)

Density (Gas Phase)

VirialV: For density of the gas phase.

Enthalpy of Vaporization (Liquid/Gas)

HVPExpansion: For Hvap for the liquid-gas phase boundary

Yaws.VaporizationH: For Hvap for the liquid-gas phase boundary

PPDS12: For Hvap for the liquid-gas phase boundary

Csat (Liquid Phase)

CSExpansion: For Csat of the Liquid phase

Yaws.PolynomialExpansion: For Csat of the liquid phase

DIPPR.PolynomialExpansion: For Csat of the liquid phase

PPDS 15: For Csat of the liquid phase

Cpo(Ideal Gas)

Cpo(Ideal Gas)

Aly & Lee Equation (same as DIPPR 107): Cpo(Ideal Gas)

PPDS 2: Cpo(Ideal Gas)

Helmholtz: Cpo(Ideal Gas)

Speed of Sound (Liquid Phase)

Speed of Sound (Liquid Phase)

Speed of Sound (Gas Phase)

Speed of Sound (Gas Phase)

Refractive Index nD (Liquid)

RIXExpansion: Refractive Index nD (Liquid)

Surface Tension s (Liquid/Gas)

PPDS14: For surface tension s for the liquid/gas interface

Yaws.SurfaceTension: For surface tension s for the liquid/gas interface

HVPExpansion: For surface tension s for the liquid/gas interface

Viscosity (Saturated Liquid)

PPDS9: Viscosity h of the saturated liquid

Yaws.Viscosity: Viscosity h of the saturated liquid

DIPPR101: Viscosity h of the saturated liquid

Viscosity (Gas at low pressures; p < 6 bar)

TransportPolynomial: For viscosity h of the gas at low pressures (p < 600 kPa)

Yaws.PolynomialExpansion: For viscosity h of the gas at low pressures (p < 600 kPa)

DIPPR 102: For viscosity h of the gas at low pressures (p < 600 kPa)

PPDS 5: For viscosity h of the gas at low pressures (p < 600 kPa)

Thermal Conductivity l: (Liquid)

TransportPolynomial: For thermal conductivity l of the saturated liquid

Yaws.ThermalConductivity: For thermal conductivity l of the saturated liquid

Yaws.PolynomialExpansion: For thermal conductivity l of the saturated liquid

DIPPR.PolynomialExpansion: For thermal conductivity l of the saturated liquid

PPDS8: For thermal conductivity l of the saturated liquid

Thermal Conductivity (Gas at low pressures; p < 6 bar)

TransportPolynomial: For thermal conductivity l of the gas at low pressure (p < 600 kPa)

Yaws.PolynomialExpansion: For thermal conductivity l of the gas at low pressure (p < 600 kPa)

PPDS 3: For thermal conductivity l of the gas at low pressure (p < 600 kPa)

Density of the Liquid (on the Liquid/Gas phase boundary): d_sat

VDNS Expansion: For d_sat of the Liquid or Gas phase

Rackett Equation: For d_sat of the Liquid phase

PPDS 10: For d_sat of the Liquid phase

PPDS 17: For d_sat of the Liquid phase

HVPExpansion: For H_vap for the liquid-gas phase boundary

Yaws.VaporizationH: For H_vap for the liquid-gas phase boundary

PPDS12: For H_vap for the liquid-gas phase boundary

C_sat (Liquid Phase)

CSExpansion: For C_sat of the Liquid phase

Yaws.PolynomialExpansion: For C_sat of the liquid phase

DIPPR.PolynomialExpansion: For C_sat of the liquid phase

PPDS 15: For C_sat of the liquid phase

C_p^o(Ideal Gas)

C_p^o(Ideal Gas)

Aly & Lee Equation (same as DIPPR 107):
C_p^o(Ideal Gas)

PPDS 2: C_p^o(Ideal Gas)

Helmholtz: C_p^o(Ideal Gas)

Refractive Index n_D (Liquid)

RIXExpansion: Refractive Index n_D (Liquid)