PREOS

Instructions

Page 1

PREOS.XLS

This workbook will calculate P,V,T and thermodynamic properties using the Peng-Robinson Equation.

PVT This worksheet solves the Peng-Robinson Equation given critical constants, acentric factor,and a pressure and temperature.

Props This worksheet calculates departure functions and fugacities. You will need to enter critical constants and heat capacity constants on this worksheet.Critical properties will be transferred automatically to the "Ref State" worksheet.Heat capacity constants are from the appendix or from Reid, Prausnitz and Poling.

Ref State This worksheet specifies the reference state for the "Props" calculations. Both ideal and real fluid reference states may be chosen, and the user may specify whether to set H = 0 or U = 0 in the reference state. The entropy is arbitrarily set to zero at the reference state.

Crit. Props A copy of the critical properties tabulated in the endflap of the book.

IG Cps A copy of the ideal gas heat capacity constants tabulated in the appendix of the book.

Worksheets are protected. Values in blue may be changed without unlocking the spreadsheet, which willpermit most common calculations. The worksheets may easily be changed to use a different equation of state.

Copyright 1996-97, Carl LiraFor use with "An Introduction to Applied Thermodynamics" by J.R. Elliott, C.T. Lirawww.egr.msu.edu/~lira/thermtxt.htm

PVT

Page 2

Peng-Robinson Equation of State (Pure Fluid) Spreadsheet protected, but no password used.Properties

Gas wMETHANE 190.6 4.604 0.011

Intermediate Calculations

Current State Roots 8.314

T (K) 273 Z V fugacity 1.432319

P (MPa) 0.1 MPa 0.02172 212431

answers for three #NUM! #NUM! #NUM! k 0.391572root region #NUM! #NUM! a 0.851819 26.77659

#NUM! #NUM! #NUM! fugacity ratio A 0.004124& for 1 root region 0.997059 22630.46 0.099706 #NUM! B 0.00118

Stable Root has a lower fugacity To find vapor pressure, or saturation temperature,see cell A28 for instructions

Solution to Cubic 9.87E-08

p q If Negative, three unequal real roots,-0.99882 0.00176 -3.47E-06 -0.330787 -0.07323 If Positive, one real root

Method 1 - For region with one real rootP Q Root to equation in x Solution methods are summarized0.333009 0.33111 0.664119 in the appendix of the text.

Method 2 - For region with three real roots

m 3q/pm Roots to equation in x0.664116 1.000037 #NUM! #NUM! #NUM! #NUM! #NUM!

To find vapor pressure, use solver to vary $B$8 (P)

To find saturation temperature, use solver to vary $B$7 (T)to find where target cell $H$12 = 1, by adjusting $B$7, subject to $B$7 <= $B$4

Tc (K) Pc (MPa)

R(cm3MPa/molK)

Tr a (MPa cm6/gmol2)

cm3/gmol Pr

b (cm3/gmol)

Z3 + a2Z2 + a1Z + a0 =0 R = q2/4 + p3/27 =

a2 a1 a0

3*q1 q1

to find where target cell $H$12 = 1, for any T < Tc.

Props

Page 3

Peng-Robinson Equation of State (Pure Fluid) Spreadsheet protected, but no password used.

Properties Heat Capacity constants from Appendix ideal gas

Gas w A B C D values J/mol J/mol J/molKMethane 190.6 4.604 0.011 19.25 5.21E-02 1.20E-05 -1.13E-08 1924.618 1492.29 -45.72158

Current State Roots Stable Root has a lower fugacity

T (K) 350 Z V fugacity H U S

P (MPa) 50 MPa J/mol J/mol J/molK J/mol J/mol J/molKanswers for three #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

root region #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

& for 1 root region 1.11266032 64.7546051 40.98708 -1201.727 -4439.457 -53.01089 -3144.496 -3472.326 -7.331732fugratio

#NUM! If thermodynamic property calculations give a #NUM! error for both root regions in the table above, fix the "reference state index indentifier" on "Ref State" page.

Solution to Cubic 0.014236

p q If Negative, three unequal real roots,-0.53990531 -0.46370626 -0.1931306 -0.5608722 -0.288241 If Positive, one real root


8.314

Method 1 - For region with one real root 1.836306

P Q Root to equation in x 10.86012 184853.5

0.64104896 0.29164292 0.93269188 k 0.391572a 0.741237 26.77659

Method 2 - For region with three real roots A 1.091544

m 3q/pm Roots to equation in x B 0.4600950.864771392 1.78283729 #NUM! #NUM! #NUM! #NUM! #NUM!

Reference State Info from 'Ref State' (enter data on Worksheet 'Ref State')T= 298 igrflag= 1P= 0.1 uhflag= 1index= 3

Hig - HRig Uig - UR

ig Sig -SRig

Tc (K) Pc (MPa)

H-Hig U-Uig S-Sig

cm3/gmol

Z3 + a2Z2 + a1Z + a0 =0 R = q2/4 + p3/27 =

a2 a1 a0

R(cm3MPa/molK)


Pr

b (cm3/gmol)

3*q1 q1

Ref State

Page 4

Peng-Robinson Equation of State (Pure Fluid) Spreadsheet protected, but no password used.Properties

Gas w Enter Name and CriticalMethane 190.6 4.604 0.011 Properities on "Props"

Worksheet.Reference State For real fluid Roots

T (K) 298 reference state Z V fugacity

P (MPa) 0.1 identifier index MPa J/mol J/mol J/molK

1 #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! answers for three0 #NUM! #NUM! root region

0 for ig, 1 for real fluid ref 2 #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!1 3 0.997779 24720.69 0.099778 -18.15084 -12.64823 -0.04243 & for 1 root region

Identifier Index for reference state row to use from Row 9 - Row 12 (Enter 1, 2, or 3)YOU MUST CHOOSE A ROW WITH CALCULABLE NUMBERS, NOT ONE WITH #NUM!

3

Z H(J/mol) U(J/mol) S(J/molK)Reference State Values 0.997779 0 -2472.069 0Ref State Departures -18.15084 -12.64823 -0.04243

Solution to Cubic 7.63E-08

p q If Negative, three unequal real roots,-0.99891924 0.001140085 -2.4E-06 -0.331473 -0.073457 If Positive, one real root


8.314

Method 1 - For region with one real root 1.563484

P Q Root to equation in x 0.02172 202879.5

0.333236253 0.331569699 0.664806 k 0.391572a 0.813519 26.77659

Method 2 - For region with three real roots A 0.003305

m 3q/pm Roots to equation in x B 0.0010810.664803862 1.000028279 #NUM! #NUM! #NUM! #NUM! #NUM!

Tc (K) Pc (MPa)

H-Hig U-Uig S-Sig

cm3/gmol

0 for HR = 0, 1 for UR = 0

Z3 + a2Z2 + a1Z + a0 =0 R = q2/4 + p3/27 =

a2 a1 a0

R(cm3MPa/molK)


Pr

b (cm3/gmol)

3*q1 q1

Crit. Props

Page 5

Critical properties from the endflap.PROPERTIES OF SELECTED COMPOUNDSHeat capacities are values for vapor at 298 K and should be used for order of magnitude calculations only. See appendices for temperature dependent formulas and constants.

Hint: To transfer values to the other worksheets, copy the desired cells, then use Paste Special... Values....in order to preserve the formats of the cells.

Compound Tc(K) Pc(MPa) w Zc CP/RParaffins

1 METHANE 190.6 4.604 0.011 0.288 4.2982 ETHANE 305.4 4.88 0.099 0.284 6.3123 PROPANE 369.8 4.249 0.152 0.281 8.8514 n-BUTANE 425.2 3.797 0.193 0.274 11.895 ISOBUTANE 408.1 3.648 0.177 0.282 11.6957 n-PENTANE 469.7 3.369 0.249 0.269 14.4468 ISOPENTANE 460.4 3.381 0.228 0.279 NEOPENTANE 433.8 3.199 0.196 0.269

11 n-HEXANE 507.4 3.012 0.305 0.264 17.21217 n-HEPTANE 540.3 2.736 0.349 0.263 19.95427 n-OCTANE 568.8 2.486 0.396 0.259 22.69746 n-NONANE 595.7 2.306 0.437 0.255 25.45156 n-DECANE 618.5 2.123 0.484 0.249 28.21764 n-DODECANE 658.2 1.824 0.575 0.23866 n-TETRADECANE 696.9 1.438 0.57 0.20368 n-HEXADECANE 720.6 1.419 0.747 0.22 44.539

Naphthenes104 CYCLOPENTANE 511.8 4.502 0.194 0.273 9.974105 METHYLCYCLOPENTAN 532.8 3.785 0.23 0.272137 CYCLOHEXANE 553.5 4.075 0.215 0.273 12.738138 METHYLCYCLOHEXANE 572.2 3.471 0.235 0.269 16.25

Olefins and Acetylene201 ETHYLENE 282.4 5.032 0.085 0.277 5.26202 PROPYLENE 364.8 4.613 0.142 0.275 7.688204 1-BUTENE 419.6 4.02 0.187 0.276 10.306207 ISOBUTENE 417.9 3.999 0.189 0.275 10.724209 1-PENTENE 464.8 3.529 0.233 0.27401 ACETYLENE 308.3 6.139 0.187 0.271 5.32303 1,3-BUTADIENE 425.4 4.33 0.193 0.27 9.56309 ISOPRENE 484 3.85 0.158 0.264

Aromatics501 BENZENE 562.2 4.898 0.211 0.271 9.822502 TOLUENE 591.8 4.109 0.264 0.264 12.485504 ETHYLBENZENE 617.2 3.609 0.304 0.263 15.444505 o-XYLENE 630.4 3.734 0.313 0.263 16.033506 m-XYLENE 617.1 3.541 0.326 0.259 15.348507 p-XYLENE 616.3 3.511 0.326 0.26 15.263510 CUMENE 631.2 3.209 0.338 0.262 18.246558 BIPHENYL 789.3 3.847 0.366 0.294 19.521563 DIPHENYLMETHANE 768 2.92 0.461 0.25701 NAPHTHALENE 748.4 4.051 0.302 0.269 16.033702 1-METHYLNAPHTHALEN 772 3.65 0.292 0.297706 TETRALIN 720.2 3.3 0.286 0.243 18.631

Crit. Props

Page 6

Oxygenated Hydrocarbons1101 METHANOL 512.6 8.096 0.566 0.224 5.2831102 ETHANOL 516.4 6.384 0.637 0.248 7.8791103 PROPANOL 536.7 5.17 0.628 0.253 10.4961104 ISOPROPANOL 508.3 4.764 0.669 0.248 10.691105 1-BUTANOL 562.9 4.412 0.594 0.2591107 ISOBUTANOL 547.7 4.295 0.589 0.2571479 THF 501.1 5.19 0.217 0.259

### DIETHYL ETHER 466.7 3.59 0.281 0.262 13.531# ETHYLENE OXIDE 469 7.1 0.2 0.258### METHYL ETHYL KETON 535.6 4.1 0.329 0.249 12.557Halocarbons

FREON-12(CCl2F2) 385 4.07 0.176 0.28FREON-22(CClF2) 369.8 4.97 0.221 0.268FREON-11(CCl3F) 471.2 4.35 0.188 0.279FREON-113(C2Cl3F3) 487.2 3.37 0.252 0.256METHYL CHLORIDE 416.3 6.59 0.156 0.268CHLOROFORM(CHCl3) 536.4 5.4 0.216 0.293CARBON TETRACHLORI 556.4 4.5 0.194 0.272CHLOROBENZENE 632.4 4.46 0.249 0.265

Gases914 ARGON 150.9 4.898 -0.004 0.291 2.499922 BROMINE 584.2 10.335 0.119 0.287918 CHLORINE 417.2 7.711 0.069 0.275913 HELIUM-4 5.2 0.228 0 0.302 2.501920 KRYPTON 209.4 5.502 0.001 0.288919 NEON 44.4 2.653 -0.041 0.3959 XENON 289.7 5.84 0.012 0.286912 NITRIC OXIDE 180.2 6.485 0.585 0.25 3.588899 NITROUS OXIDE 309.6 7.245 0.142 0.274 4.633910 SULFUR DIOXIDE 430.8 7.884 0.245 0.269 4.796911 SULFUR TRIOXIDE 490.9 8.207 0.422 0.256 6.111901 OXYGEN 154.6 5.043 0.022 0.288 3.529902 HYDROGEN 33.3 1.297 -0.215 0.3 3.507905 NITROGEN 126.1 3.394 0.04 0.292 3.5908 CARBON MONOXIDE 132.9 3.499 0.066 0.295 3.505909 CARBON DIOXIDE 304.2 7.382 0.228 0.274 4.456

Nasty gases1922 HYDROGEN SULFIDE 373.5 8.937 0.081 0.283

### CARBON DISULFIDE 552 7.8 0.115 0.293 4.109### HYDRAZINE(N2H4) 653 14.5 0.328 0.26 5.47### HYDROGEN CHLORIDE 324.6 8.2 0.12 0.249### HYDROGEN CYANIDE 456.8 5.32 0.407 0.197Miscellaneous Compounds

1051 ACETONE 508.2 4.701 0.306 0.233 8.961772 ACETONITRILE 545.5 4.833 0.353 0.1841251 ACETIC ACID 592.7 5.786 0.462 0.2 15.0111911 AMMONIA 406.6 11.27 0.252 0.242 4.2891921 WATER 647.3 22.12 0.344 0.233 4.041

References: API Technical Data Book (extant 1988), and Reid,R.C., Prausnitz,J.M., and Sherwood, T.K., The Properties of Liquids and Gases , 3rd Edition,Mcgraw-Hill, New York (1977)

Crit. Props

Page 7

Hint: To transfer values to the other worksheets, copy the desired cells, then use Paste Special... Values....

Crit. Props

Page 8

References: API Technical Data Book (extant 1988), and Reid,R.C., Prausnitz,J.M., and Sherwood, T.K., The Properties of Liquids and Gases , 3rd Edition,Mcgraw-Hill, New York (1977)

IG Cps

Page 9

Heat Capacity constants from the Appendix Ideal gas heat capacity constants are tabulated below as selected from The Properties of Gases and Liquids, 4th ed. R.C. Reid, J.M. Prausnitz, B.E. Poling, McGraw-Hill, 1987, p 656-732. The heat capacities tabulated in the endflap are only suitable for quick order of magnitude calculations. The full form of the heat capacity should be used when possible.

Hint: To transfer values to the other worksheets, copy the desired cells, then use Paste Special... Values....in order to preserve the formats of the cells.

Caution: Note that the value of the heat capacity at room temperature is not given by the firstcoefficient A. The polynomial should not be truncated.

Compound A B C DParaffins

1 METHANE 19.25 5.21E-02 1.20E-05 -1.13E-082 ETHANE 5.409 1.78E-01 -6.94E-05 8.71E-093 PROPANE -4.224 3.06E-01 -1.59E-04 3.22E-084 n-BUTANE 9.487 3.31E-01 -1.11E-04 -2.82E-095 ISOBUTANE -1.39 3.85E-01 -1.85E-04 2.90E-087 n-PENTANE -3.626 4.87E-01 -2.58E-04 5.31E-088 ISOPENTANE -9.525 5.07E-01 -2.73E-04 5.72E-089 NEOPENTANE (2,2-Dimethylpropane) -16.59 5.55E-01 -3.31E-04 7.63E-08

11 n-HEXANE -4.413 5.28E-01 -3.12E-04 6.49E-0817 n-HEPTANE -5.146 6.76E-01 -3.65E-04 7.66E-0827 n-OCTANE -6.096 7.71E-01 -4.20E-04 8.86E-0841 ISOOCTANE46 n-NONANE -8.374 8.73E-01 -4.82E-04 1.03E-0756 n-DECANE -7.913 9.61E-01 -5.29E-04 1.13E-0764 n-DODECANE -9.328 1.149 -6.35E-04 1.36E-0766 n-TETRADECANE -1.10E+01 1.338 -7.42E-04 1.60E-0768 n-HEXADECANE -1.30E+01 1.529 -8.54E-04 1.85E-07

Naphthenes104 CYCLOPENTANE -5.36E+01 5.43E-01 -3.03E-04 6.49E-08105 METHYLCYCLOPENTANE -5.01E+01 6.38E-01 -3.64E-04 8.01E-08137 CYCLOHEXANE -5.45E+01 6.11E-01 -2.52E-04 1.32E-08138 METHYLCYCLOHEXANE -6.19E+01 7.84E-01 -4.44E-04 9.37E-08153 cis-DECALIN154 trans-DECALIN

Olefins and Acetylene201 ETHYLENE 3.806 1.57E-01 -8.35E-05 1.76E-08202 PROPYLENE 3.71 2.35E-01 -1.16E-04 2.21E-08204 1-BUTENE -2.994 3.53E-01 -1.99E-04 4.46E-08205 cis-2-BUTENE206 trans-2-BUTENE207 ISOBUTENE (Isobutylene) 1.61E+01 2.80E-01 -1.09E-04 9.10E-09209 1-PENTENE -1.34E-01 4.33E-01 -2.32E-04 4.68E-08216 1-HEXENE260 1-DECENE270 CYCLOHEXENE303 1,3-BUTADIENE -1.687 3.42E-01 -2.34E-04 6.34E-08

IG Cps

Page 10

309 2-METHYL-1,3-BUTADIENE (Isoprene) -3.412 4.59E-01 -3.34E-04 1.00E-07401 ACETYLENE 2.68E+01 7.58E-02 -5.01E-05 1.41E-08

Aromatics501 BENZENE -3.39E+01 4.74E-01 -3.02E-04 7.13E-08502 TOLUENE -2.44E+01 5.13E-01 -2.77E-04 4.91E-08504 ETHYLBENZENE -4.31E+01 7.07E-01 -4.81E-04 1.30E-07505 1,2-DIMETHYL BENZENE -1.59E+01 5.96E-01 -3.44E-04 7.53E-08506 1,3-DIMETHYL BENZENE -2.92E+01 6.30E-01 -3.75E-04 8.48E-08507 1,4-DIMETHYL BENZENE -1.509 6.04E-01 -3.37E-04 6.82E-08510 ISOPROPYLBENZENE (Cumene) -3.39E+01 7.84E-01 -5.09E-04 1.29E-07558 DIPHENYL -9.71E+01 1.106 -8.86E-04 2.79E-07601 PHENYLETHENE701 NAPHTHALENE -6.88E+01 8.50E-01 -6.51E-04 1.98E-07702 1-METHYLNAPHTHALENE -6.48E+01 9.39E-01 -6.94E-04 2.02E-07706 1,2,3,4-TETRAHYDRONAPHTHALENE (Tetralin)803 INDENE805 PHENANTHRENE

Oxygenated Hydrocarbons1001 FORMALDEHYDE1002 ACETALDEHYDE1052 2-BUTANONE 1.09E+01 3.56E-01 -1.90E-04 3.92E-081051 ACETONE 6.301 2.61E-01 -1.25E-04 2.04E-081101 METHANOL 21.15 7.09E-02 2.59E-05 -2.85E-081102 ETHANOL 9.014 2.14E-01 -8.39E-05 1.37E-091103 PROPANOL 2.47 3.33E-01 -1.86E-04 4.30E-081104 2-PROPANOL 3.24E+01 1.89E-01 6.41E-05 -9.26E-081105 1-BUTANOL 3.266 4.18E-01 -2.24E-04 4.69E-081107 ISOBUTANOL -7.708 4.69E-01 -2.88E-04 7.23E-081114 1-HEXANOL1181 PHENOL1201 ETHYLENE GLYCOL1211 PROPYLENE GLYCOL1251 ACETIC ACID 4.84 2.55E-01 -1.75E-04 4.95E-081256 BUTYRIC ACID1281 BENZOIC ACID1289 TEREPHTHALIC ACID1312 METHYL ACETATE1313 ETHYL ACETATE1381 DIMETHYL TEREPHTHALATE1479 TETRAHYDROFURAN(THF) 1.91E+01 5.16E-01 -4.13E-04 1.45E-071402 DIETHYL ETHER 2.14E+01 3.36E-01 -1.04E-04 -9.36E-091403 ISOPROPYL ETHER

ETHYLENE OXIDE -7.519 2.22E-01 -1.26E-04 2.59E-08Halocarbons

1501 CARBON TETRACHLORIDE 4.07E+01 2.05E-01 -2.27E-04 8.84E-081502 METHYL CHLORIDE 1.39E+01 1.01E-01 -3.89E-05 2.57E-091503 ETHYL CHLORIDE1511 DICHLOROMETHANE1521 CHLOROFORM(CHCl3) 2.40E+01 1.89E-01 -1.84E-04 6.66E-08

CHLOROBENZENE -3.39E+01 5.63E-01 -4.52E-04 1.43E-07

IG Cps

Page 11

1591 VINYLIDENE CHLORIDE(1,1-C2H2Cl2)1601 FREON-12(CCl2F2) 3.16E+01 1.78E-01 -1.51E-04 4.34E-08

FREON-22(CClF2) 1.73E+01 1.62E-01 -1.17E-04 3.06E-08 FREON-11(CCl3F) 4.10E+01 1.67E-01 -1.42E-04 4.15E-08

FREON-113(C2Cl3F3) 6.11E+01 2.87E-01 -2.42E-04 6.90E-08Gases

899 NITROUS OXIDE 2.16E+01 7.28E-02 -5.78E-05 1.83E-08901 OXYGEN 2.81E+01 -3.68E-06 1.75E-05 -1.07E-08902 HYDROGEN (equilibrium) 2.71E+01 9.27E-03 -1.38E-05 7.65E-09905 NITROGEN 3.12E+01 -1.36E-02 2.68E-05 -1.17E-08908 CARBON MONOXIDE 3.09E+01 -1.29E-02 2.79E-05 -1.27E-08909 CARBON DIOXIDE 1.98E+01 7.34E-02 -5.60E-05 1.72E-08910 SULFUR DIOXIDE 2.39E+01 6.70E-02 -4.96E-05 1.33E-08911 SULFUR TRIOXIDE 1.92E+01 1.37E-01 -1.18E-04 3.70E-08912 NITRIC OXIDE 2.94E+01 -9.38E-04 9.75E-06 -4.19E-09913 HELIUM-4 2.08E+01914 ARGON 2.08E+01917 FLUORINE918 CHLORINE 2.69E+01 3.38E-02 -3.87E-05 1.55E-08919 NEON 2.08E+01920 KRYPTON 2.08E+01922 BROMINE 3.39E+01 1.13E-02 -1.19E-05 4.53E-09959 XENON 2.08E+01

Nitrogen and Sulfur Gases1904 HYDROGEN CHLORIDE 3.07E+01 -7.20E-03 1.25E-05 -3.90E-091922 HYDROGEN SULFIDE 3.19E+01 1.44E-03 2.43E-05 -1.18E-081938 CARBON DISULFIDE 2.74E+01 8.13E-02 -7.67E-05 2.67E-08

HYDRAZINE(N2H4) 9.768 1.90E-01 -1.66E-04 6.03E-08HYDROGEN CYANIDE 2.19E+01 6.06E-02 -4.96E-05 1.82E-08

Miscellaneous Compounds1701 METHYLAMINE1704 ETHYLAMINE1772 ACETONITRILE 2.05E+01 1.20E-01 -4.49E-05 3.20E-091801 METHANETHIOL1802 ETHANETHIOL1820 DIMETHYL SULFIDE1877 UREA1901 SULFURIC ACID1902 PHOSPHORIC ACID1903 NITRIC ACID1911 AMMONIA 2.73E+01 2.38E-02 1.71E-05 -1.19E-081912 SODIUM HYDROXIDE1921 WATER 32.24 1.92E-03 1.06E-05 -3.60E-09

IG Cps

Page 12

Ideal gas heat capacity constants are tabulated below as selected from The Properties of Gases and Liquids, 4th ed. R.C. Reid, J.M. Prausnitz, B.E. Poling, McGraw-Hill, 1987, p 656-732. The heat capacities tabulated in the endflap are only suitable for quick order of magnitude calculations. The full form of the heat capacity

Hint: To transfer values to the other worksheets, copy the desired cells, then use Paste Special... Values....

Documents

PREOS