7317cade-1a39-42fc-9fb0-20c132997765 59 4 5 decimal

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Peng-Robinson EOS [Propane]

Construct the mtp Isotherms

PR-EOS  ... propane project data pa 100 : base pressure to v ≡ K 273.15 : base Kelvin to T °C ≡ Tc 369.89 : critical temperature °K ≡ Pc 42.512 : critical pressure bar ≡ ω 0.1521 : acentric factor ≡ R 83.1472 : universal gas constant ≡ b 0.0778 R Tc * Pc / (* : m 0.37464 1.54226 ω * + 0.26992 ω 2^* - : T a 0.45724 R Tc * (2^Pc / * 1 m 1 T K + (Tc / sqrt - (* + (2^* : 91 line

v T P R T K + (* v b - (/ T a v v b + (* b v b - (* + / - :

T 409050 range : (°C ≡ v pa 1024 pa 2 + range : 21 line

bar r 1 : ii 1 v rows range c 1 : j 1 T rows range M r c el v ii el T j el P eval : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

PREOS v bar 1 col augment v bar 2 col augment v bar 3 col augment v bar 4 col augment v bar 5 col augment v bar 6 col augment 24256 32.36 + 15 black 15 mat 81 sys :

bar 1 :

sanity 25680 P : bar 32.36

Solving for 'v [cm³/mol]' on selected °C x 60 P 24 ≡ x 1001000 solve 103.4 299.4 695.1 31 mat

Peng-Robinson Equation of State [PR EOS] Isotherms Propane @ °K [313.15 ... 363.15] Y = |bar|absolute, X = cm³/mol

PREOS pa 100 pa 50 - 2 2 mat 2 1 sys

P bar absolute ≡ v cm³/mol ≡ T °C ≡ 31 line

0 x ≤ ( x 96 ≤ ( & x a N/A if

0 a 96 a 21 mat 1107^* 1107^* 21 mat

----- cm³/mol -----

Solving for 'v' on the triplet P(v,T) x 60 P 24 ≡ x 1001000 solve 103.4 299.4 695.1 31 mat

critical Pc[bar], Tc[°C] Tc K - Pc 21 mat 96.74 42.512 21 mat

@ critical for 'z'

Tc 96.74 :

T 25 : P 1.01 : 21 line

α 1 m 1 T 0 + Tc / sqrt - (* + (2^:

a 0.45724 R Tc * (2^Pc / * : b 0.07780 R Tc * Pc / * : 12 mat

A 0.45724 R Tc * α * (2^Pc / * 1 * P * R T 0 + (* (2^/ : B 0.07780 R Tc * Pc / * P * R T 0 + (* / : 12 mat

m α A B 41 mat 0.602973 1.68078 0.459524 0.007152 41 mat

clear complex polyroots p B 3^B 2^+ A B * - A 3 B 2^* - 2 B * - B 1 - 1 stack polyroots : k 1 p rows range Z k el p k el abs p k el ≡ (p k el * : for z Z sum : 41 line

z 0.007

B 3^B 2^+ A B * - A 3 B 2^* - 2 B * - B 1 - 1 stack polyroots 0.00739 0.492729 0.441589 i * + 0.492729 0.441589 i * - 31 mat

Critical Values

T.c 96.74 °C * : P.c 4251.2 kPa * : ω 0.1521 : 13 mat

Ref State

T.o 25 °C * : P.o 101 kPa * : 12 mat

T P PR κ 0.37464 1.54226 ω * + 0.26992 ω 2^* - : α 1 κ 1 T T.c / sqrt - (* + : 12 mat a 0.45724 R.m T.c * α * (2^P.c / * : b 0.07780 R.m T.c * P.c / * : 12 mat A a P * R.m T * (2^/ : B 0.07780 R.m T.c * P.c / * P * R.m T * / : 12 mat A B 21 mat 41 line :

κ 0.37464 1.54226 ω * + 0.26992 ω 2^* - : α 1 κ 1 T T.c / sqrt - (* + : 12 mat a 0.45724 R.m T.c * α * (2^P.c / * : b 0.07780 R.m T.c * P.c / * : 12 mat A a P * R.m T * (2^/ : B b P * R.m T * / : 12 mat Z B 3^B 2^+ A B * - A 3 B 2^* - 2 B * - B 1 - 1 stack polyroots : ZR 0 : 12 mat Z 51 line

T.o P.o PR 0.018844 0.002293 21 mat

R.m T * (2^

T Psat 52.3785 3490.551 T / - 6.10875 T ln * - 1.11869 105 -^* T 2^* + exp 100 / :

x Ps x Psat :

Psat[T °K] ... Psat[bar], T[°K]

369.9 42.512 + 15 blue 1 5 mat 42.2 - x ≤ ( x 370 ≤ ( & x Psat N/A if 2 1 sys

Saturation pressure was obtained from "Genfit" non-linear model fit

Matlab paper http://cache.org/files/site/news_stand/summer09/ summer09%20Binous%20applic%20of%20equation.pdf

Propane: C3H8 Molecular Weight 44.097 Specific Gravity of gas (air = 1.00) 1.52 Specific Volume (ft3/lb, m3/kg) 8.84, 0.552 Density of liquid at atmospheric pressure (lb/ft3, kg/m3) 36.2, 580 Vapor pressure at 25oC (psia, MN/m2) 135.7, 0.936 Absolute Viscosity (lbm/ft s, centipoises) 5.38 10-6, 0.0074 Sound velocity in gas (m/s) 253 Specific Heat - cp - (Btu/lboF or cal/goC, J/kgK) 0.39, 1630 Specific Heat Ratio - cp/cv 1.13 Gas constant - R - (ft lb/lboR, J/kgoC) 35.0, 188 Thermal Conductivity (Btu/hr ft oF, W/moC) 0.010, 0.017 Boiling Point - saturation pressure 14.7 psia and 760 mm Hg - (oF, oC) -44, -42.2 Latent Heat of Evaporation at boiling point (Btu/lb, J/kg) 184, 428000 Freezing or Melting Point at 1 atm (oF, oC) -309.8, -189.9 Latent Heat of Fusion (Btu/lb, J/kg) 19.1, 44400 Critical Temperature (oF, oC) 205, 96 Critical Pressure (psia, MN/m2) 618, 4.26 Critical Volume (ft3/lb, m3/kg) 0.073, 0.0045 Flammable yes Heat of combustion (Btu/ft3, Btu/lb, kJ/kg) 2450, 21660, 50340