Equation Descriptions

Descriptions for Fitted Equations

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: Vapor Pressure (Liquid/Gas), Sublimation (Crystal/Gas), Condensed (Crystal/Liquid)
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: C_sat (Liquid), C_sat (Crystal), 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 1: Wagner 25 (Output details)

p/p^o

p_c/p^o

T_c/T

₁

₂

^1.5

₃

^2.5

₄

⁵

T/T_c

p^o

DEFAULT 2: PV Expansion: (Output details)
ln(p/p^o) = a₁ + a₂/T + a₃×ln(T) + a₄×T + a₅×T² + a₆×T⁶+ a₇/T⁴
Alternative 1: Antoine (Output details)

p/p^o

p^o

Alternative 2: Yaws.VaporPressure (Output details)

p/p^o

p^o

₁₀

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

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

Alternative 5: Wagner 36 (Output details)
ln(p/p^o) – ln(p_c/p^o) = T_c/T (A₁×t + 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×t + 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×t + 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: (Output details)
ln(p/p^o) = a₁ + a₂/T + a₃×ln(T) + a₄×T + a₅×T² + a₆×T⁶+ a₇/T⁴
Alternative 1: Antoine (Output details)
ln(p/p^o) = A + B/(T + C); where p^o = 1 kPa
Alternative 2: Yaws.VaporPressure (Output details)
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 (Output details)
ln(p/p^o) = a + b/T + c×ln(T) + d×T² + e/T² ; where p^o = 1 kPa
Alternative 4: DIPPR 101 (Output details)
ln(p/p^o) = a + b/T + c×ln(T) + d×T^e ; where p^o = 1 kPa

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

PolynomialExpansion: Phase boundary pressure for the crystal/liquid boundary

p/p^o = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1 and p^o = 1 kPa.

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: (Output details)
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 (Output details)
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 (Output details)
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 (Output details)
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: (Output details)
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: (Output details)
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): (Output details)
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, C = åc_i+1/Tⁱ, and R is the gas constant.
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, C = åc_i+1/Tⁱ, and R is the gas constant.

Evaluation Results:

The example is for fitted gas densities of pentane.

Enthalpy of Vaporization (Liquid/Gas)

DEFAULT: Watson Equation: (Output details)
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 (Output details)
H_vap = A×{1 - ( T / T_c )}ⁿ
Alternative 2: PPDS 12 (Output details)
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.

Watson Equation: 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 1: CSExpansion: (Output details)
C_sat = (åa_i+1× tⁱ) + b/t , where the summation is from i = 0 to nTerms -1.
DEFAULT 2: PolynomialHC: (Output details)
C_sat = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1.
Alternative 1: Yaws.PolynomialExpansion (Output details)
C_sat = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 2: DIPPR.PolynomialExpansion (Output details)
C_sat = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 3: PPDS 15 (Output details)
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.

C_sat (Crystal Phase)

DEFAULT: PolynomialHC: (Output details)
C_sat = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1.
Alternative 1: Yaws.PolynomialExpansion (Output details)
C_sat = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 2: DIPPR.PolynomialExpansion (Output details)
C_sat = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1

PolynomialHC: C_sat or C_p of any 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 quinoline.

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 any 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 or crystal 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 1: 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.
DEFAULT 2: PolynomialHC: (Output details)
C_sat = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1.
Alternative 1: Yaws.PolynomialExpansion (Output details)
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) (Output details)
C_p^o = a + b×{(c/T)/sinh(c/T)}² + d×{(e/T)/cosh(e/T)}²
Alternative 3: PPDS2 (Output details)
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, R is the gas constant, and y = T / (T + T_S), where T_S is a constant.
Alternative 4: Helmholtz (Output details)
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, R is the gas constant, 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: (Output details)
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: (Output details)
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: (Output details)
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: (Output details)
s = a₀× t^a₁×(1 + a₂ ×t) , where t = 1 - T/T_c and T_c is the critical temperature.
Alternative 1: Yaws.SurfaceTension (Output details)
s = exp(A)×{1 - ( T / T_c )}ⁿ
Alternative 2: HVPExpansion (Output details)
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

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: (Output details)
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 (Output details)
lg(h/h^o) = A + B/T + C×T + D×T ²
Alternative 2: DIPPR 101 (Output details)
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: (Output details)
h = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 1: Yaws.PolynomialExpansion (Output details)
h = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 2: DIPPR 102 (Output details)
h = A×T^B / (1+ C/T + D/T²)
Alternative 3: PPDS 5 (Output details)
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: (Output details)
l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 1: Yaws.ThermalConductivity (Output details)
lg(l/l^o) = A + B×(1 - T/C)^2/7
Alternative 2: Yaws.PolynomialExpansion (Output details)
l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 3: DIPPR.PolynomialExpansion (Output details)
l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 4: PPDS 8 (Output details)
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: (Output details)
l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 1: Yaws.PolynomialExpansion (Output details)
l = å a_i× T ⁱ, where the summation is from i = 0 to nTerms - 1
Alternative 2: PPDS 3 (Output details)
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.

Descriptions for Fitted Equations

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: Vapor or 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)

Watson Equation: 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)

Csat (Crystal Phase)

PolynomialHC: Csat or Cp of any phase

CSExpansion: For Csat of the Liquid phase

Yaws.PolynomialExpansion: For Csat of any phase

DIPPR.PolynomialExpansion: For Csat of the liquid or crystal 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

Watson Equation: 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)

C_sat (Crystal Phase)

PolynomialHC: C_sat or C_p of any phase

CSExpansion: For C_sat of the Liquid phase

Yaws.PolynomialExpansion: For C_sat of any phase

DIPPR.PolynomialExpansion: For C_sat of the liquid or crystal 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)