Pure Component Equations Fitting of Pure Component Equation Parameters DDBSP – Dortmund Data Bank Software Package DDBST - Dortmund Data Bank Software & Separation Technology GmbH Marie-Curie-Straße 10 D-26129 Oldenburg Tel.: +49 441 361819 0 [email protected] www.ddbst.com DDBSP – Dortmund Data Bank Software Package 2020 Contents 1 Introduction.........................................................................................................................................................3 2 List of Equations.................................................................................................................................................4 3 Using the program.............................................................................................................................................10 3.1 Initial Dialog.............................................................................................................................................10 3.2 File Menu..................................................................................................................................................11 3.3 Help Menu.................................................................................................................................................12 3.4 Component Selection.................................................................................................................................12 3.5 Check Data Availability............................................................................................................................13 3.6 Fit..............................................................................................................................................................14 3.6.1 Input by Hand....................................................................................................................................16 3.6.2 Fit Results..........................................................................................................................................17 3.6.3 Plot....................................................................................................................................................17 4 Understanding the ParameterDDB Data Set Display........................................................................................22 5 Working with a Parameter Data Set..................................................................................................................23 5.1 Copy..........................................................................................................................................................23 5.2 Edit............................................................................................................................................................24 5.3 Plot............................................................................................................................................................24 5.4 Details.......................................................................................................................................................25 5.5 Calculate....................................................................................................................................................26 6 Fit Archive.........................................................................................................................................................27 7 Tc/Pc Evaluation.................................................................................................................................................29 8 Density Prediction by Equation of State............................................................................................................31 9 Virial Coefficients.............................................................................................................................................32 9.1 Isotherms...................................................................................................................................................32 9.1.1 Rationale...........................................................................................................................................32 9.1.2 Application Flow...............................................................................................................................32 9.1.3 Description of the Graphics Output...................................................................................................32 9.1.4 Mathematical and Physical Relations................................................................................................33 9.1.5 Practical Tips.....................................................................................................................................35 9.1.6 Gas Constant, Molar Mass, Critical Density.....................................................................................35 9.2 All Data Simultaneously............................................................................................................................35 9.2.1 Rationale...........................................................................................................................................35 9.2.2 Problem Description..........................................................................................................................35 9.2.3 Regression.........................................................................................................................................35 9.2.4 Short Tutorial....................................................................................................................................37 10 Volume Translation.........................................................................................................................................40 11 Simultaneous Regression of α Function Parameters........................................................................................42 DDB Pure Component Equations Page 2 of 43 DDBSP – Dortmund Data Bank Software Package 2020 1 Introduction PCPEquationFit fits parameters for a large variety of equations for pure component properties. Parameters can be stored in and retrieved from a parameter database, they can be plotted, and they can be used for calculations. PCPEquationFit normally uses the pure component properties data bank which is a part of the Dortmund Data Bank. It can also be used to fit data from other data sources since tables can be pasted from the clipboard or loaded from files. DDB Pure Component Equations Page 3 of 43 DDBSP – Dortmund Data Bank Software Package 2020 2 List of Equations Property Equation Liquid Viscosity B A 1. Andrade T T [K] =e η [mPa s] B A 2. Vogel T C =e B A C lnT DT E 3. DIPPR 101 T =e 1 4 C−T 3 C−T 3 4. PPDS 9 =E exp A B [ T −D T −D ] B 2 3 A+ + CT + DT + ET 5. Extended Andrade T η=e B C D E 6. Polynomial in 1/T η= A+ + + + T T 2 T 3 T 4 Vapor Viscosity A T B = T[K] 1. DIPPR 102 C D 1 η [mPa s] T T 2 2. Polynomial η=A+ B⋅T + CT 2+ DT 3+ ET 4 DDB Pure Component Equations Page 4 of 43 DDBSP – Dortmund Data Bank Software Package 2020 Property Equation Saturated Vapor Pressure B A− 1. Antoine T C (►Other Units: T [°C], P [mmHg]) T [K] P=10 P [kPa] 2. Wagner 2.5,5 A1−T B1−T 1.5C 1−T 2.5D1−T 5 P=exp ln P r r r r c T r 3. Wagner 3,6 1.5 3 6 A1−T rB 1−T r C 1−T r D 1−T r P=exp ln P c T r T T 2 AB C 4. Cox T T T B P=exp ln 101.325e B B 1− [ T ] B A C lnT DT E 5. DIPPR 101 T P=e (►Other Units: P [Pa]) B 2 6. Extended Antoine (Lonza) P=exp A+ +DT +ET +F ln(T) ( T +C ) (►Other Units: P [bar]) B G 7. Extended Antoine (Aspen) P=exp A+ +DT +E ln(T )+F T ( T+C ) G=1 or G=2 B F 8. Extended Antoine (Hysys) P=exp A+ +D ln(T )+E T ( T +C ) F=1 or F=2 T− B 4.1012 A B B≈T b 9. Rarey2P T− [ 8 ] −1A1 P=Patm 10 10. Xiang/Tan P P exp ln T A A 1 T 1.89 A 1 T 5.67 = c⋅ ( R⋅( 1+ 2( − R) + 3⋅( − R) )) B 2 F 6 H 11. PVExpansion: P=exp A+ +C ln(T )+DT+E T + +G T + ( T T2 T 4 ) 12. Hoffman/Florin: 1 P=exp A+B −7.9151⋅10−3+2.6726⋅10−3⋅log (T )−0.8625⋅10−6⋅T ( ( T 10 )) (►Other Units: P [Pa]) DDB Pure Component Equations Page 5 of 43 DDBSP – Dortmund Data Bank Software Package 2020 Property Equation Saturated Vapor Pressure 1. Mathias-Copeman Constants for EOS by EOS 2 1 m 1 T T [K] = ⋅ − r 2 P [kPa] m=c1c2⋅1− T r c3⋅1−T r 2. Twu-Bluck-Cunningham-Coon Constants for EOS c c 1 3⋅ 2− c2⋅c3 T exp c 1 T (c1, c2, c3 used in DDB programs) = r ⋅ 1⋅ − r N M 1 T ⋅ − exp L 1 T M⋅N (L, M, N like original authors) = r ⋅ ⋅ − r 3. Melhem-Saini-Goodwin Constants for EOS 2 exp c 1 T c 1 T = 1⋅ − r 2⋅ − r 4. Stryjek-Vera Constants for EOS κ=κ0+κ1(1+√ T r )(0.7−T r ) 2 1 1 T α=( +κ( −√ r)) 5. Stryjek-Vera-2 Constants for EOS T 0.5 1 T 0.5 1 T 0.5 0.7 T κ=κ0+[κ1+κ2(κ3− r )( − r )]( + r )( − r ) 2 1 1 T 0.5 α=( +κ( − r )) 6. Schwartzentruber/Renon/Watanasiri Constant for EOS 2 Prm=0.37464+1.54226⋅ω−0.26992⋅ω 2 1 P 1 T 1 T c c T c T 2 α=( + rm⋅( −√ r )−( −√ r )⋅( 1 + 2⋅ r + 3⋅ r )) Liquid Heat Capacity 2 3 4 1. Polynomial cP=ABT CT DT ET T [K] T A 2 3 4 1 cp [J/mol K] 2. PPDS 15 c p=R C D E F with = − T c DDB Pure Component Equations Page 6 of 43 DDBSP – Dortmund Data Bank Software Package 2020 Property Equation Ideal Gas Heat Capacity 2 3 4 1. Polynomial cP=ABT CT DT ET T [K] 2 2 a2 a4 cp [J/mol K] T T 2. Aly-Lee, DIPPR 107 c =a a a p 0 1 a 3 a sinh 2 cosh 4 T T 3. PPDS 2 2 2 3 with C P=RBC−B