Property Estimation Methods¶

Petroleum Fractions¶

Molecular weight¶

Riazi and Al Sahhaf method¶

\[ MM=\left[\frac{1}{0.01964}(6.97996-\ln(1080-T_{b})\right]^{3/2}, \]

where

\(MM\) Molecular weight (kg/kmol)

\(T_{b}\) Boiling point at 1 atm (K)

If the specific gravity ( \(SG\) ) is available, the molecular weight is calculated by

\[ \begin{eqnarray} MM & = & 42.965[\exp(2.097\times10^{-4}T_{b}-7.78712SG+ \\ & & +2.08476\times10^{-3}T_{b}SG)]T_{b}^{1.26007}SG^{4.98308} \end{eqnarray} \]

Winn¶

\[ MM=0.00005805PEMe^{2.3776}/d15^{0.9371}, \]

\ where

\(PEMe\) Mean Boiling Point (K)

\(d15\) Specific Gravity @ 60 °F

Riazi¶

\[ \begin{eqnarray} MM & = & 42.965\exp(0.0002097PEMe-7.78d15+0.00208476\times PEMe\times d15)\times \\ & & \times PEMe^{1.26007}d15^{4.98308} \end{eqnarray} \]

Lee-Kesler¶

\[ \begin{eqnarray} t_{1} & = & -12272.6+9486.4d15+(8.3741-5.9917d15)PEMe\\ t_{2} & = & (1-0.77084d15-0.02058d15^{2})\times \\ & & \times(0.7465-222.466/PEMe)\times10^{7}/PEMe\\ t_{3} & = & (1-0.80882d15-0.02226d15^{2})\times \\ & & \times(0.3228-17.335/PEMe)\times10^{12}/PEMe^{3}\\ MM & = & t_{1}+t_{2}+t_{3} \end{eqnarray} \]

Farah¶

\[ \begin{eqnarray} MM & = & \exp(6.8117+1.3372A-3.6283B)\\ MM & = & \exp(4.0397+0.1362A-0.3406B-0.9988d15+0.0039PEMe), \end{eqnarray} \]

\ where

\(A,B\) Walther-ASTM equation parameters for viscosity calculation

Specific Gravity¶

Riazi e Al Sahhaf¶

\[ SG=1.07-\exp(3.56073-2.93886MM^{0.1}), \]

where

\(SG\) Specific Gravity

\(MM\) Molecular weight (kg/kmol)

Critical Properties¶

Lee-Kesler¶

\[ T_{c}=189.8+450.6SG+(0.4244+0.1174SG)T_{b}+(0.1441-1.0069SG)10^{5}/T_{b} \]

\[ \begin{eqnarray} \ln P_{c} & = & 5.689-0.0566/SG-(0.43639+4.1216/SG+0.21343/SG^{2})\times \\ & & \times10^{-3}T_{b}+(0.47579+1.182/SG+0.15302/SG^{2})\times10^{-6}\times T_{b}^{2}- \\ & & -(2.4505+9.9099/SG^{2})\times10^{-10}\times T_{b}^{3}, \end{eqnarray} \]

where

\(T_{b}\) NBP (K)

\(T_{c}\) Critical temperature (K)

\(P_{c}\) Critical pressure (bar)

Farah¶

\[ \begin{eqnarray} T_{c} & = & 731.968+291.952A-704.998B\\ T_{c} & = & 104.0061+38.75A-41.6097B+0.7831PEMe\\ T_{c} & = & 196.793+90.205A-221.051B+309.534d15+0.524PEMe \end{eqnarray} \]

\[ \begin{eqnarray} P_{c} & = & \exp(20.0056-9.8758\ln(A)+12.2326\ln(B))\\ P_{c} & = & \exp(11.2037-0.5484A+1.9242B+510.1272/PEMe)\\ P_{c} & = & \exp(28.7605+0.7158\ln(A)-0.2796\ln(B)+2.3129\ln(d15)-2.4027\ln(PEMe)) \end{eqnarray} \]

Riazi-Daubert¶

\[ \begin{eqnarray} T_{c} & = & 9.5233\exp(-0.0009314PEMe-0.544442d15+0.00064791\times PEMe\times d15)\times \\ & & \times PEMe^{0.81067}d15^{0.53691} \end{eqnarray} \]

\[ \begin{eqnarray} P_{c} & = & 31958000000\exp(-0.008505PEMe-4.8014d15+0.005749\times PEMe\times d15)\times \\ & & \times PEMe^{-0.4844}d15^{4.0846} \end{eqnarray} \]

Riazi¶

\[ \begin{eqnarray} T_{c} & = & 35.9413\exp(-0.00069PEMe-1.4442d15+0.000491\times PEMe\times d15)\times \\ & & \times PEMe^{0.7293}d15^{1.2771} \end{eqnarray} \]

Acentric Factor¶

Lee-Kesler method¶

\[ \omega=\frac{-\ln\frac{P_{c}}{1.10325}-5.92714+6.09648/T_{br}+1.28862\ln T_{br}-0.169347T_{br}^{6}}{15.2518-15.6875/T_{br}-13.472\ln T_{br}+0.43577T_{br}^{6}} \]

Korsten¶

\[ \omega=0.5899\times((PEMV/T_{c})^{1.3})/(1-(PEMV/T_{c})^{1.3})\times\log(P_{c}/101325)-1 \]

Vapor Pressure¶

Lee-Kesler method¶

\[ \begin{eqnarray} \ln P_{r}^{pv} & = & 5.92714-6.09648/T_{br}-1.28862\ln T_{br}+0.169347T_{br}^{6}+\\ & & +\omega(15.2518-15.6875/T_{br}-13.4721\ln T_{br}+0.43577T_{br}^{6}), \end{eqnarray} \]

where

\(P_{r}^{pv}\) Reduced vapor pressure, \(P^{pv}/P_{c}\)

\(T_{br}\) Reduced NBP, \(T_{b}/T_{c}\)

\(\omega\) Acentric factor

Viscosity¶

Letsou-Stiel¶

\[ \begin{eqnarray} \eta & = & \frac{\xi_{0}+\xi_{1}}{\xi}\\ \xi_{0} & = & 2.648-3.725T_{r}+1.309T_{r}^{2}\\ \xi_{1} & = & 7.425-13.39T_{r}+5.933T_{r}^{2}\\ \xi & = & 176\left(\frac{T_{c}}{MM^{3}{P}_{c}^{4}}\right)^{1/6} \end{eqnarray} \]

where

\(\eta\) Viscosity (Pa.s)

\(P_{c}\) Critical pressure (bar)

\(T_{r}\) Reduced temperature, \(T/T_{c}\)

\(MM\) Molecular weight (kg/kmol)

Abbott¶

\[ \begin{eqnarray} t_{1} & = & 4.39371-1.94733Kw+0.12769Kw^{2}+0.00032629API^{2}-0.0118246KwAPI+ \\ & & +(0.171617Kw^{2}+10.9943API+0.0950663API^{2}-0.869218KwAPI\\ \log v_{100} & = & \frac{t_{1}}{API+50.3642-4.78231Kw}, \end{eqnarray} \]

\[ \begin{eqnarray} t_{2} & = & -0.463634-0.166532API+0.000513447API^{2}-0.00848995APIKw+ \\ & & +(0.080325Kw+1.24899API+0.19768API^{2}\\ \log v_{210} & = & \frac{t_{2}}{API+26.786-2.6296Kw}, \end{eqnarray} \]

\ where

\(v_{100}\) Viscosity at 100 °F (cSt)

\(v_{210}\) Viscosity at 210 °F (cSt)

\(K_{w}\) Watson characterization factor

\(API\) Oil API degree

Hypothetical Components¶

The majority of properties of the hypothetical components is calculated, when necessary, using the group contribution methods, with the UNIFAC structure of the hypo as the basis of calculation. The table 57 lists the properties and their calculation methods.


Property	Symbol	Method
Critical temperature	\(T_{c}\)	Joback
Critical pressure	\(P_{c}\)	Joback
Critical volume	\(V_{c}\)	Joback
Normal boiling point	\(T_{b}\)	Joback
Vapor pressure	\(P^{pv}\)	Lee-Kesler (Eq. [eq:PVAP LK])
Acentric factor	\(\omega\)	Lee-Kesler (Eq. [eq:W LK])
Vaporization enthalpy	\(\Delta H_{vap}\)	Vetere
Ideal gas heat capacity	\(C_{p}^{gi}\)	Harrison-Seaton
Ideal gas enthalpy of formation	\(\Delta H_{f}^{298}\)	Marrero-Gani

Hypo calculation methods.