Prediction of molar volumes, vapor pressures and supercritical solubilities of alkanes by equations of state

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1 Preprt Checal Egeerg Coucatos Volue 173, Issue 1, pp , 1999 Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Ratawat Hartoo *, G.Al Masoor ** Therodacs Research Laborator, Uverst of Illos at Chcago (M/C 063) Chcago, IL USA ad Arad Suwoo Therodacs Research Laborator, Iter Uverst Ceter for Egeerg Scece, Badug Isttute of Techolog, Jl. Taasar No. 126 Badug, Idoesa, arad@tero.paur.tb.ac.d ABSTRACT A geeralzed cubc equato of state whch ca represet all the cubc equatos s troduced ad therodac propert relatos for t are preseted. Fve cubc equatos of states wth respectve xg rules are used to predct olar volues ad vapor pressures of pure alkaes (fro ethae tll -trtracotae) ad solubltes of sold wax copoets (hgh olecular weght alkaes) supercrtcal solvets. The are the RK (Redlch-Kwog), MMM (Mohsea- Modarress-Masoor), RM (Raz-Masoor), PR (Peg-Robso), ad SRK (Soave-Redlch- Kwo) equatos of state. The experetal data ecessar to copare the equatos of state are take fro the lterature. It s deostrated that the SRK equato of state s ore accurate for predctg vapor pressures of alkaes. The RM equato of state s show to be ore accurate for predctg olar volues of saturated ad sub-cooled lqud alkaes as well as olar volues of alkaes ther supercrtcal codto. For the solublt of wax copoets supercrtcal solvets t s show that the MMM equato of state gves the least AAD% for the 270 data pots of 10 bar sstes studed cosstg of a hgh olecular weght alkae ad supercrtcal ethae ad carbo doxde. * Peraet address: Checal Egeerg Departet, Dpoegoro Uverst, Kapus Tebalag, Searag, Idoesa, ratadh@dosat.et.d ** Correspodg author, eal: asoor@uc.edu

2 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state INTRODUCTION Petroleu wax cotas hudreds to thousads of copoets hgher tha C 16 (Hra et al., 1994). These copoets ca be classfed to two aor classes,.e., acrocrstalle or paraffc ad crocrstalle or aphthec waxes. The acrocrstalle wax s coposed of al straght-cha paraffs ad crocrstalle or aorphous wax cotas soparaffs ad aphthees. Macrocrstalle wax s ore valuable tha crocrstalle or crude wax. I order to characterze the petroleu wax ad perfor varous operatos o wax xtures, such as wax fractoato, t s ecessar to be able to predct therodac propertes of wax. I ths report we exae the accurac of three well-kow equatos of state RK (Redlch-Kwog), SRK (Soave-Redlch-Kwog), PR (Peg-Robso) as the are reported uerous textbooks (Walas, 1985) ad two ewl developed equatos of state ael RM (due to Raz ad Masoor, 1993) ad MMM (due to Mohsea, et al. (1995) for predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes. It should poted out that all these fve equatos of state are cubc. CUBIC EQUATIONS OF STATE AND THEIR GENERALIZATION Cubc equatos of state are wdel used phase equlbru calculato because of ther splct ad, geeral, good perforace. The splest ad oe of the wdel kow equatos of state s that of va der Waals. The va der Waals equato of state s a sple odel that corporates soe correctos to the deal gas law for attracto ad repulso betwee olecules. However, ths equato of state s ot accurate eough to predct therodac propertes of ost flud. Ispred b the va der Waals odel, vestgators have proposed several equatos of state through the ears. Alost ever equato of state has bee claed to be superor soe respects 1

3 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state to the earler oes. The RK equato that s a odfcato of the va der Waals equato, was a cosderable proveet over other equatos of relatvel sple fors at the te of ts troducto. I the SRK equato the teperature-depedet ter of a/t 0.5 of the RK equato s replaced b a fucto deoted b α that depeds o the acetrc factor of the copoud ad teperature. The PR equato s aother cubc equato of state volvg acetrc factor (Walas, 1985). Recetl, Raz ad Masoor (1993) stated that paraeter b of the RK equato s ore effectve for calculatg lqud destes because t represets the volue of the olecule. The odfed the paraeter b of the RK equato b troducg a fucto, deoted b β, that depeds o the refractve dex of the copoud. Also recetl, b aother approach Mohsea et al.(1995) odfed the repulsve part of the RK equato. Ther odfcato was based o the statstcal echacal forato avalable for the repulsve therodac fuctos ad the pheoeologcal kowledge of the attractve terolecular potetal tal cotrbutos to the therodac propertes. It should be poted out that the RK ad MMM equatos are twocostat-paraeter equatos of state, whle the RM, PR ad SRK are three-costat-paraeter equatos. All the above etoed fve equatos of state ca be wrtte the followg geeralzed for: Z v + γ b = v b T ε av RT ( v + ηc)( v + λc) (1) where a = Ω a α R 2 T c (2+ε) / P c ad b = c = Ω b β R T c / P c. 2

4 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Paraeters Ω a, Ω b, γ, η ad λ are copoet-depedet costats, whle α ad β are copoet-depedet costats, ad ther uercal values for varous equatos of states are gve Table I. Paraeters a, b ad c are depedet o crtcal propertes ad ( soe cases) o teperature. I extedg the equatos of state to xtures paraeters a, b, ad c are replaced wth a, b, ad c wth the followg expressos (xg rules): RK, PR, SRK, RM-1: a = a b = c = b MMM: a = a b 3 = b + b 4 c = b For the RM equato there s aother alteratve extedg t to xtures b replacg T c ad P c wth T c ad P c as gve below (Raz ad Masoor, 1993): RM-2: T c 2 = Tc Pc T c P c P c 2 = Tc Pc T c P c 2 R * = R * These above equatos of state are used to calculate the propertes of the pure copoets,.e. vapor pressure, olar volues of lqud at saturated, sub-cooled ad supercrtcal codtos as well as the solublt of wax copoets supercrtcal solvets. 3

5 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state To calculate both the vapor pressure ad the saturated lqud olar volue usg equato of state, we eed to kow the fugact coeffcets for pure copoud. The fugact coeffcet for pure copoud s the followg geeralzed for: l b a v + ηb φ = Z 1 l Z ( 1 + γ ) l ( + ) 1 ε v ( η λ) brt l (2) 1 v + λb To calculate the solublt of sold wax copoets ( ) a gas phase the followg expresso ca be used (Walas, 1985; Schulz, et al., 1988): P = V φ v exp P sub S sub ( P P ) RT (3) The fugact coeffcet of a copoud a xture (φ V ) derved fro the geeralzed equato of state s the followg for: lφ V ( 1+ γ ) ( b ) ( v b v) l Z ( 1 ε ) c RT ( v + ηc )( v + λc ) = l + v b a v ( c ) a + ( ε ) ( η λ) c RT 2 ( a ) 1 ( c ) 1 1 v + ηc l (4) 1 a c v + λc where for RK, PR, SRK, RM-1: 4

6 5 ( ) = a a ( ) ( ) b c b = = for MMM: ( ) = a a ( ) = b b b b ( ) b c = ad for RM-2: ( ) = Ω c c c c c c a P T T P T RT a ( ) ( ) + + = = c c c c P T P T c b β β β 2 I order to test the relatve accurac of varous equatos of state the above geeralzed expressos are used to calculate vapor pressures ad olar volues of saturated, sub-cooled ad supercrtcal pure lqud -alkaes [fro ethae (C 1 ) tll -trtracotae (C 33 )] ad carbo doxde as well as the solubltes of wax copoets supercrtcal solvets. Coparsos are ade betwee the calculated results ad the avalable experetal data. R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state

7 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state RESULTS AND DISCUSSION To calculate lqud olar volue ad vapor pressure usg equatos of state, the data of crtcal teperature ad pressure, acetrc factor, ad olar refracto are eeded. The experetal crtcal propertes of carbo doxde ad -alkaes up to C 24 are take fro the lterature (Nkt t al., 1994; Frekel et al., 1997a&b), whle those of -alkaes hgher tha C 24 are predcted usg a correlato developed b Twu (1984). The acetrc factors are calculated usg Ptzer correlato. The olar refractos of all copouds are take fro the lterature (Frekel et al., 1997a&b). The olar volues of saturated lquds calculated usg varous equatos of state are copared to those usg a accurate correlato proposed b Hakso ad Thoso (1979). The percetage of average absolute devatos (AAD%) of the equatos are preseted Table II. Accordg to ths table, the RM equato of state s better tha the other equatos copared. The RM equato s actuall oe order of agtude ore accurate tha the other equatos. It ust be also poted out that the two-costat-paraeter MMM equato s ore accurate tha the twocostat-paraeter RK equato ad the three-costat-paraeter SRK equato. The AAD% of varous equatos of state predctg olar volues of lqud subcooled ad supercrtcal codtos are preseted Table III. Accordg to ths table also the RM equato s oe order of agtude ore accurate tha the other equatos. It ust be also poted out that the two-costat-paraeter MMM equato s ore accurate tha the two-costatparaeter RK equato ad three-costat-paraeter PR ad SRK equatos. The AAD% of varous equatos of state predctg vapor pressures of carbo doxde ad -alkaes are preseted Table IV. Accordg to ths table predcto b the SRK equato s oe order of agtude superor to the other three-costat equatos (RM ad PR) ad t s two orders 6

8 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state of agtude better tha the two-costat-paraeter equatos (RK ad MMM). However, t ust be poted out that the PR ad SRK equatos are developed b fttg to the vapor pressure data. To calculate the solublt of sold wax copoets supercrtcal solvet, the data of olar volue ad sublato pressure of the sold wax copoets are eeded, as well as the crtcal propertes, acetrc factors, ad olar refractos of all copouds volved. The olar volues of the sold are take fro the lterature, ad the sublato pressures are calculated usg correlatos developed b Morada ad Tea (1986 & 1988) The solublt of -trtracotae (-C 33 H 68 ) supercrtcal ethae s depcted Fgure 1 alog wth the predctos obtaed fro varous equatos of state. Accordg to ths fgure, aog the two-costat-paraeter equatos, the MMM equato s ore accurate tha the RK equato. The SRK equato of state s closer to the experetal data tha the other equatos are. It s show fgure 1 that there s a cross over rego; at P r ~ 1.33 the experetal solublt at 308 K s hgher tha that at 318 K s, whle at P r > 2 the solubltes at 318 K are hgher tha those at 308 K are. The equatos of state also show cross over regos. Fgure 2 depcts the solublt of - trtracotae supercrtcal carbo doxde. It s show that the MMM equato s better tha the RK equato, ad the RM-1 equato s better tha the MMM, RM-2 ad the SRK equatos. The PR equato of state s closer to the experetal data tha the other equatos are. I both fgures we assue that the teracto paraeter k = 0. The solubltes of sold wax copoets supercrtcal solvets are also calculated wth k best ftted to experetal data. Table V shows the teracto paraeters of varous equatos of state for a uber of sstes at varous teperatures alog wth the AAD%. Accordg to ths table, the MMM equato of state gves the least value of AAD%. For 270 data pots of 10 sstes, ths equato gves the AAD% of A aor advatage of the MMM equato s that t 7

9 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state s a two-costat-paraeter equato of state; t does ot eed the acetrc factor or olar refracto data whch are rare for heav olecular weght copouds. As t was etoed above for all the wax copoets experetal crtcal propertes ad acetrc factor data are ot avalable ad estato ethods are used for ther calculatos. The olar volue ad vapor pressure of lquds calculated usg equatos of state are flueced b the crtcal propertes ad acetrc factor used. To test the effect of these propertes o such calculatos, we perfored error calculato for olar volues ad vapor pressures of varous wax copoets. As a exaple, Table VI we report the errors whch wll be caused due to accuraces crtcal propertes ad acetrc factor o saturated lqud olar volue ad vapor pressure of -octacosae at 583 K. Accordg to ths table a error of 0.7% T c, a error of 5% P c ad a error of 1% ω wll result 10% axu error saturated lqud olar volue calculato regardless of the equato of state used. For vapor pressure calculato the percetage error b varous equatos of state are dfferet ad vares fro 18 to 35 %. To evaluate the effect of the put data (crtcal propertes, acetrc factor ad sublato pressure of the sold) o the supercrtcal solublt calculato, the solublt of -trtracotae supercrtcal carbo doxde at 308 K are calculated for four cases usg four dfferet sets of put data. I case 1, the crtcal propertes of the sold are predcted usg Twu (1984) ethod ad the sublato pressure s predcted usg Morada-Tea (1988) ethod. I case 2 the crtcal propertes are calculated usg Twu ethod ad the sublato pressure s calculated usg Poullot et al. (1996) ethod. I case 3 the crtcal propertes are calculated usg Costatou- Ga (1994) ethod ad the sublato pressure s calculated usg Morada-Tea ethod. I case 4 the crtcal propertes are calculated usg Costatou-Ga ethod ad the sublato pressure s calculated usg Poullot et al. ethod. I all cases the teracto paraeter k are best 8

10 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state ftted to the experetal data. The results of the above etoed four cases for dfferet equatos of state are reported b Fgures 3-8. Accordg to Fgures 3, 6 ad 7 the supercrtcal solublt calculatos b RK, PR ad SRK equatos are qute sestve to the put data ad the do ot ft well to the experetal data. Accordg to Fgures 4, 5 ad 8 the supercrtcal solublt calculatos b MMM, RM-1 ad RM-2 are less sestve to the varatos of the put data ad the ft well to the experetal data. The lqud olar volues ad vapor pressures of carbo doxde ad -alkaes as well as the solublt of sold wax copoets supercrtcal solvets have bee calculated usg varous equatos of state. The RM equato of state s ore accurate for predctg olar volue, whle the SRK equato of state s ore accurate for predctg vapor pressure. Usg k = 0, the SRK EOS s closer to the experetal solublt of wax copoets supercrtcal ethae data tha the other equatos, whle for carbo doxde-wax copoet sstes, the PR EOS s closer to the experetal data tha the others. The MMM EOS gves the least value of AAD% whe k s best ftted to the experetal data. ACKNOWLEDGEMENT Ths research s supported b the Drectorate Geeral of Hgher Educato, Mstr of Educato ad Culture, Idoesa, through URGE proect, uder grat No. 019/HTPP- II/URGE/

11 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Sbols ad Noeclature MMM Mohsea-Moddaress-Masoor P PR R R * RK RM SRK T v Z uber of ole the sste pressure [bar] Peg-Robso uversal gas costat rato of olar refracto of a copoud to that of a referece (ethae) Redlch-Kwog Raz-Masoor Soave-Redlch-Kwog teperature [K] olar volue [l/ol] ole fracto copressblt factor Greek Letters φ ω fugact coeffcet acetrc factor Subscrpts c crtcal copoet dces xture 10

12 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state r reduced Superscrpts L S sat sub V lqud phase sold phase saturated sublato vapor phase 11

13 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state REFERENCES: Agus, S.; Arstrog, B.; de Reuck, K.M. Carbo Doxde - Iteratoal Tables of Flud State - 3, IUPAC Proect Cotrol, Iperal College, Lodo, Chadler, K.; Poullot, F.L.L.; Eckert, C.A. Phase Equlbra of Alkaes Natural Gas Sstes. 3. Alkaes Carbo Doxde. J. Che. Eg. Data 1996, 41, Costatou, L.; Ga, R. New Group Cotrbuto Method for Estatg Propertes of Pure Copouds. AIChE J. 1994, 40, Doolttle, A.K. Specfc Volues of Noral Alkaes. J. Che. Eg. Data 1964, 9, Frekel, M.; Gadalla, N.M.; Hall, K.R.; Hog, X.; Marsh, K.N.; Wlhot, R.C. (edtors), TRC Therodac Tables-Hdrocarbo; Therodac Research Ceter, The Texas A&M Uverst Sste, 1997a. Frekel, M.; Gadalla, N.M.; Hall, K.R.; Hog, X.; Marsh, K.N.; Wlhot, R.C. (edtors), TRC Therodac Tables-No-Hdrocarbo; Therodac Research Ceter, The Texas A&M Uverst Sste, 1997b. Goodw, R.D.; Haes, W.M. Therophscal Propertes of Propae fro 85 to 700 K at Pressures to 70 MPa; Natoal Bureau of Stadards, NBS Moograph 170, Goodw, R.D.; Roder, H.M., Therophscal Propertes of Ethae fro 90 to 600 K at Pressures to 700 Bar; Natoal Bureau of Stadards, NBS Tech. Note 684, Goodw, R.D. The Therophscal Propertes of Methae fro 90 to 500 K at Pressures to 700 Bar; Natoal Bureau of Stadards, NBS Tech. Note 653, Hakso, R.W.; Thoso, G.H. A New Correlato for Saturated Destes of Lquds ad Ther Mxtures. AIChE J. 1979, 25,

14 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Haes, W.M.; Goodw, R.D. Therophscal Propertes of Noral Butae fro 135 to 700 K at Pressures to 70 MPa; Natoal Bureau of Stadards, NBS Moograph 169, Hra, S.; Suwoo, A.; Masoor, G.A. Characterzato of Alkaes ad Paraff Waxes for Applcatos as Chage Eerg Storage Medu. Eerg Source 1994, 16, Kalaga, A.; Trebble, M. Solubltes of Tetracosae, Octacosae, ad Dotracotae Supercrtcal Ethae. J. Che. Eg. Data 1997, 42, McHugh, M.A.; Secker, A.J.; Yoga, T.J. Hgh Pressure Phase Behavor of Bar Mxtures of Octacosae ad Carbo Doxde. Id. Eg. Che. Fuda. 1984, 23, Mohsea, M.; Moddaress, H.; Masoor, G.A. A Cubc Equato of State Based o a Splfed Hard-core Model. Che. Eg. Co. 1995, 131, Morada, I.; Tea, A.S. Solubltes of Sold -Octacosae, -Tracotae ad -Dotracotae Supercrtcal Ethae. Flud Phase Equlb. 1986, 28, Morada, I.; Tea, A.S. Solubltes of -Noacosae ad -Trtracotae Supercrtcal Ethae. J. Che. Eg. Data 1988, 33, Morga, D.L.; Kobaash, R. Drect Vapor Pressure Measureets of Te -Alkaes the C 10 -C 28 Rage. Flud Phase Equlb. 1994, 97, Nkt E.D.; Pavlov, P.A.; Bessaova, N.V. Crtcal Costats of -Alkaes wth fro 17 to 24 Carbo Atos. J. Che. Therod. 1994, 26, Poullot, F.L.L.; Chadle, K.; Eckert, C.A. Sublato Pressure of -Alkaes fro C 20 H 42 to C 35 H 72 the Teperature rage K. Id. Eg. Che. Res. 1996, 35, Revercho, E.; Russo, P.; Stass, A. Solubltes of Sold Octacosae ad Tracotae Supercrtcal Carbo Doxde. J. Che. Eg. Data, 1993, 38,

15 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Raz, M.R.; Masoor, G.A. Sple Equato of State Accuratel Predcts Hdrocarbo Destes. Ol & Gas Joural 1993, Jul 12, Salero, S.; Cascella, M.; Ma, D.; Watso, P.; Tassos, D. Predcto of Vapor Pressures ad Saturated Volues wth a Sple Cubc Equato of State: Part I: A Relable Data Base. Flud Phase Equlb. 1986, 27, Schulz, K.; Martell, E.E.; Masoor, G.A. Supercrtcal Flud Extracto ad Retrograde Codesato (SFE/RC) Applcatos Botecholog, I Supercrtcal Flud Techolog: Revews Moder Theor ad Applcatos; Bruo, T.J., El, J.F., Ed.; CRC Press: Boca Rato, Sulea, D.; Eckert, C.A. Phase Equlbra of Alkaes Natural gas Sstes. 2. Alkaes Ethae. J. Che. Eg. Data 1995, 40, Twu, C.H. A Iterall Cosstet Correlato for Predctg the Crtcal Propertes ad Molecular Weghts of Petroleu ad Coal-Tar Lquds. Flud Phase Equlb. 1984, 16, Walas, S.M. Phase Equlbra Checal Egeerg; Butterworth-Heea: Bosto,

16 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Table I. Paraeters of the geeralzed equato of state Eq. of State RK MMM RM PR SRK Paraeters γ η λ ε Ω a Ω b α α PR α SRK β 1 1 β RM 1 1 α PR = [1+( ω ω 2 )(1-T r 0.5 )] 2 α SRK = [1+( ω ω 2 )(1-T r 0.5 )] 2 (β RM ) -1 = 1+{0.02[ exp(-1,000 T r -1 )] (T r -1)} (R * -1) 15

17 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Table II. The Average Devatos of Varous Equatos of State Predctg Saturated Lqud Molar Volues of Pure Copouds Copared wth Those Calculated Usg the Hakso ad Thoso (1979) Correlato. AAD % Copoud T r rage RK MMM RM PR SRK CO CH C 2 H C 3 H C 4 H C 5 H C 6 H C 7 H C 8 H C 9 H C 10 H C 11 H C 12 H C 13 H C 14 H C 15 H C 16 H C 17 H C 18 H C 19 H C 20 H C 22 H C 24 H C 28 H Overall

18 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Table III. The Average Devatos of Varous Equato of State Predctg Molar Volues of Lquds Sub-cooled ad Supercrtcal Codtos Copared wth Experetal Data AAD % Experetal data Copoud T r rage P r rage RK MMM RM PR SRK No. of data pts. ref CO a CH b C 2 H c C 3 H d -C 4 H e -C 5 H f -C 6 H f -C 7 H f,g -C 9 H g -C 11 H g -C 13 H g -C 17 H g -C 20 H g -C 30 H g Overall a Agus et al., b Goodw, c Goodw ad Roder, d Goodw ad Haes, e Haes ad Goodw, f Frekel et al., 1997a. g Doolttle,

19 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Table IV. The Average Devatos of Varous Equatos of State Predctg Vapor Pressures of Pure Copouds Copared wth the Experetal Data Copoud T r rage AAD % Experetal data RK MMM RM PR SRK No. of data pts. ref CO a CH b,c C 2 H b,d C 3 H b,e -C 4 H b,f -C 5 H b,h -C 6 H > b,h -C 7 H > b,h -C 8 H > b,h -C 9 H > c,h -C 10 H > b,g,h -C 11 H > b -C 12 H > b,g,h -C 13 H >100 > b -C 14 H >100 > b,g,h -C 15 H >100 > b -C 16 H >100 > b,g,h -C 17 H >100 > b -C 18 H >100 > b,g -C 19 H >100 > b,g -C 20 H >100 > b,g -C 22 H >100 > b,g -C 24 H >100 > b,g -C 28 H >100 > b,g -C 29 H >100 > b -C 30 H >100 > b -C 32 H >100 > b -C 33 H >100 > b Overall ~ 2,100 ~ a Agus et al., b Frekel at al., 1997a. c Goodw, d Goodw ad Roder, e Goodw ad Haes, f Haes ad Goodw, g Morga ad Kobaash, h Salero et al.,

20 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Table V. Iteracto Paraeter (k 12 ) of Soe Sstes exp. data T P k 12 AAD % o.of Sste [K] [bar] RK MMM RM-2 PR SRK RM-1 RK MMM RM-2 PR SRK RM-1 data pts. ref. C 2 H 6 - -C 28 H a,b,c C 2 H 6 - -C 29 H c,d C 2 H 6 - -C 30 H b,c b C 2 H 6 - -C 32 H a,b,c b b,c b C 2 H 6 - -C 33 H c,d d c,d CO 2 - -C 28 H e f,g f f,g e e e CO 2 - -C 29 H g g CO 2 - -C 30 H f f CO 2 - -C 32 H g g g CO 2 - -C 33 H g g g Overall a Kalaga ad Trebble, b Morada ad Tea, c Sulea ad Eckert, d Morada ad Tea, e McHugh et al., f Revercho et al., g Chadler et al.,

21 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Table VI. Saturated Lqud Molar Volue ad Vapor Pressure -Octacosae at 583 K Calculated Usg Varous Equatos of State wth T c = (829.2±6.0) K, P c = (7.550±0.358) bar, ω = (1.1772±0.0129) Eq. of state v sat P sat [l/ol] [bar] RK ± ± MMM ± ± RM ± ± PR ± ± SRK ± ± Experetal

22 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state Table VII. Phscal Propertes of -Trtracotae Used Sestvt Test of Varous Equatos of State Predctg Supercrtcal Solublt T c P c ω P sub v S [K] [bar] [-] [bar] [l/ol] Case (a) (a) (a) (c) (c) Case (a) (a) (a) (d) (c) Case (b) (b) (b) (c) (c) Case (b) (b) (b) (d) (c) a Twu (1984). b Costatou ad Ga (1994). c Morada ad Tea (1988). d Poullot et al. (1996). 22

23 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state 0 RM K -2 SRK 318 K RM K RM K SRK 308 K Log () -4-6 RM K PR 318 K PR 308 K MMM 318 K -8 MMM 308 K -10 RK 318 K RK 308 K Pr Fgure 1 Solublt of -trtracotae (-C 33 H 68 ) supercrtcal ethae at varous teperatures. The experetal data are take fro Chadler et al. (1996): (o) 308 K, (x) 318 K. The les are the solublt calculated usg varous equato of state wth k =0 23

24 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state 0-2 RM-2 308K RM K RM K RM K -4 SRK 318K SRK 308K PR 318 K Log() -6 PR 308K MMM 318K -8 MMM 308K -10 RK 318K RK 308K Pr Fgure 2 Solublt of -trtracotae (-C 33 H 68 ) supercrtcal carbo doxde at varous teperatures. The experetal data are take fro Chadler et al. (1996): (o) 308 K, (x) 318 K. The les are the solublt calculated usg varous equato of state wth k =0 24

25 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state -4 RK Eq.ofState Log () Case 1, k= Case 2, k= Case 3, k= Case 4, k= Pr Fgure 3 Sestvt of calculatos of solublt of -trtracotae (-C 33 H 68 ) supercrtcal carbo doxde at 308 K b the RK equato of state to varatos of the put. The put data for varous cases are reported Table 7. The experetal solublt data s take fro Chadler et al.,

26 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state -4 MMM Eq. of State Log () Case 1, k= Case 2, k= Case 3, k= Case 4, k= Pr Fgure 4 The sae as Fgure 3 but for the MMM equato of state. 26

27 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state -4-5 RM-2 Eq. of State -6-7 Log () Case 1, k= Case 2, k= Case 3, k= Case 4, k= Pr Fgure 5 The sae as Fgure 3 but for the RM-2 equato of state 27

28 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state -4 PR Eq. of State Log () Case 1, k= Case 2, k= Case 3, k= Case 4, k= Pr Fgure 6 The sae as Fgure 3 but for the PR equato of state 28

29 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state -4 SRK Eq. of State Log () Case 1, k= Case 2, k= Case 3, k= Case 4, k= Pr Fgure 7 The sae as Fgure 3 but for the SRK equato of state 29

30 R. Hartoo, G.A. Masoor, A. Suwoo Predcto of olar volues, vapor pressures ad supercrtcal solubltes of alkaes b equatos of state -4 RM-1 Eq. of State Log () Case 1, k= Case 2, k= Case 3, k= Case 4, k= Pr Fgure 8 The sae as Fgure 3 but for the RM-1 equato of state 30