World Academy o cece, Egeerg ad echology Iteratoal Joural o Chemcal ad Molecular Egeerg New Mult-old hermodyamc Model or the Predcto o Wax Formato Ehsa Ghaae, Ferdu Esmaelzadeh, ad Jamshd Fath Kalah Iteratoal cece Idex, Chemcal ad Molecular Egeerg waset.org/publcato/7848 Absact I the prevous mult-sold models,ϕ approach s used or the calculato o ugacty the lqud phase. For the rst tme, the proposed mult-sold thermodyamc model,γ approach has bee used or calculato o ugacty the lqud mxture. hereore, some actvty coecet models have bee studed that the results show that the predctve Wlso model s more approprate tha others. he results demosate γ approach usg the predctve Wlso model s more agreemet wth expermetal data tha the prevous mult-sold models. Also, by ths method, geerates a ew approach or presetg stablty aalyss phase equlbrum calculatos. Meawhle, the ru tme γ approach s less tha the prevous methods used ϕ approach. he results o the ew model preset 0.75 AAD % (Average Absolute Devato) rom the expermetal data whch s less tha the results error o the prevous mult-sold models obvously. Keywords Mult-sold thermodyamc model, Predctve Wlso model, Wax ormato. I. INRODUCION N the mult-sold model, t s assumed the sold phase (wax) I cosst o several pure compoet. he studes show two ma models apply the cocept o mult-sold model, cludg ra-galeaa et al. [1] ad Nchta et al. [] models. he other mult-sold models are smlar to them approxmately. I 1996, ra-galeaa et al. [1] preseted a approach based o mult-sold model or the predcto o wax ormato. I ths model, a correlato was preseted or estmatg the meltg pot o pure compoets cludg ormal parac (C 6 -C 30 ), aphthec (C 6 -C 30 alkylcycloalkaes) ad aromatc (C 6 -C 30 alkylbezees) hydrocarbos. Also, they suggested a correlato or the estmatg o the ethalpy o uso. hey used the Pederse et al. correlato [3] to estmate the specc heat capacty derece betwee sold ad lqud phase. Also, the term o sold-sold phase asto was gored the calculato o Mauscrpt receved Jue 9, 007. Ehsa Ghaae s wth the Chemcal ad Peoleum Egeerg Departmet, hraz Uversty, hraz, Ira (e-mal: e-ghaae@spemal.org). Ferdu Esmaelzadeh s wth the Chemcal ad Peoleum Egeerg Departmet, hraz Uversty, hraz, Ira (correspodg author to provde phoe: +98-711-34-3833; ax: +98-711-68-794; e-mal: esmael@shrazu.ac.r). Jamshd Fath Kalah s wth the Chemcal ad Peoleum Egeerg Departmet, hraz Uversty, hraz, Ira (e-mal: zeglda@shrazu.ac.r ). ugacty rato o the sold ad lqud phase or a pure compoet. he PR Eo [4, 5] was used or the ugacty calculato the lud phases. I 001, Nchta et al. [] suggested a mult-sold model. I ths model, the meltg pot temperature o ormal alkaes was estmated rom the correlato proposed by Wo [6]. Also, they appled sold-sold phase asto term or the calculato o the ugacty rato o sold ad lqud phase or a pure compoet. hey suggested correlatos or estmatg o temperature ad ethalpy o sold-sold phase asto. he PR Eo [4, 5] was appled or calculatg ugacty the lud phases. I ths work, or the rst tme, a mult-sold model based oγ approach has bee preseted or the predcto o wax ormato pheomea. ome actvty coecet models cludg the regular soluto [3, 6, 7], UNIFAC [8-10], predctve UNIQUAC [11-13] ad predctve Wlso [14] models ad deal soluto approach have bee employed ad compared. For valdatg the proposed model some expermetal data have bee used whch are or 56 equlbrum data pots. II. EXPERIMENA DAA I ths work, our terary systems cludg C 14 -C 15 -C 16 (terary 1), C 16 -C 17 -C 18 (terary ), C 18 -C 19 -C 0 (terary 3) ad C 19 -C 0 -C 1 (terary 4) have bee used [15]. hese systems cota 56 mxtures that the amout o WD (Wax Dsappearace emperature) Kelv (K) at atmospherc pressure ad compostos o mxtures have bee reported ables I-IV. ABE I EXPERIMENA WD (K) DAA FOR C 14 -C 15 -C 16 ERNARY YEM 1 Mxture Composto (molar %) C 14 C 15 C 16 Exp. WD (K) 1 6 57 37 83.4 14 6 63 84.6 3 17 6 77 85.5 4 4 33 43 8. 5 1 56 3 81. 6 7 66 7 80.4 7 37 5 58 8.6 8 3 4 44 81.5 9 43 33 4 79. 10 57 17 6 78.0 11 73 14 13 76.3 Iteratoal cholarly ad cetc Research & Iovato 1(5) 007 48
World Academy o cece, Egeerg ad echology Iteratoal Joural o Chemcal ad Molecular Egeerg Iteratoal cece Idex, Chemcal ad Molecular Egeerg waset.org/publcato/7848 ABE II EXPERIMENA WD (K) DAA FOR C 16 -C 17 -C 18 ERNARY YEM Mxture Composto (molar %) C 16 C 17 C 18 Exp. WD (K) 1 10 10 80 97.8 10 75 15 94.3 3 10 80 10 94.6 4 11 39 50 95.8 5 0 0 60 95.8 6 0 60 0 93.7 7 33 33 34 93.3 8 40 10 50 93.6 9 40 40 0 91.9 10 60 0 0 90.8 11 80 10 10 89.5 ABE III EXPERIMENA WD (K) DAA FOR C 18-C 19-C 0 ERNARY YEM 3 Mxture Composto (molar %) C 18 C 19 C 0 Exp. WD (K) 1 96 309.0 5 5 90 308.5 3 5 90 5 304.7 4 10 10 80 307.5 5 10 40 50 306.3 6 10 55 35 305.9 7 14 73 13 304.4 8 15 15 70 307.3 9 0 0 60 306.3 10 0 60 0 304.9 11 6 6 48 305.5 1 33 33 34 304.3 13 40 10 50 304.6 14 43 43 14 30.8 15 48 15 37 303.8 16 60 0 0 30.3 17 79 11 10 301.4 18 90 5 5 300.6 ABE IV EXPERIMENA WD (K) DAA FOR C 19-C 0-C 1 ERNARY YEM 4 Mxture Composto (molar %) C 19 C 0 C 1 Exp. WD (K) 1 5 5 90 31.9 5 89 6 309.4 3 10 40 50 310.9 4 10 80 10 309.5 5 1 10 78 31.1 6 19 50 31 309.9 7 0 1 59 310.9 8 0 60 0 309.3 9 9 8 43 309.7 10 39 10 51 309.5 11 39 50 11 307.8 1 49 0 31 308.1 13 50 40 10 307.4 14 60 0 0 307.3 15 80 10 10 306.0 16 90 5 5 305.5 III. HE MUI-OID MODE BAED ONγ APPROACH I the mult-sold model, the umber o compoets precptate should be obtaed by stablty aalyss codto. he compouds cover ths codto precptates as a pure sold phase. he deto o stablty aalyss s the ollowg expresso [16]:, Pure, ) ) > 0 1,..., C (1) where,, ), s the compoet ugacty the mxture at pressure P, temperature ad wth mxture composto. I (1),C, s the umber o compoets. I all correlatos ths paper, subscrpts, ad superscrpt are reerred to the sold ad lqud phase ad the umber o compoets, respectvely. By the deto o ugacty γ approach, compoet ugacty the mxture,, ), ca be calculated as ollows: thus: ad, ) ) γ x (), Pure, Pure, Pure ) γ x ) > 0 (3), Pure ) γ x > 0 (4), Pure ) I (4), γ ca be calculated usg the actvty coecet models. o obta a sutable actvty coecet model, the regular soluto [3, 6, 7], UNIFAC [8-10], predctve UNIQUAC [11-13] ad predctve Wlso [14] models have bee appled reported the Appedx. he deal soluto approach ( γ 1 ) has bee also cosdered. he ugacty rato ca be calculated as ollows []: (, ) Δ pure P H exp[ 1 + (, ) pure P R Δ H 1 + R 1 1 ΔC d R p R he uso temperature ( ΔC p d ] (5) ) o ormal alkaes s estmated rom the ollowg correlato proposed by Wo [6]. 017 374.5 + 0.617MW (6) MW Iteratoal cholarly ad cetc Research & Iovato 1(5) 007 49
World Academy o cece, Egeerg ad echology Iteratoal Joural o Chemcal ad Molecular Egeerg Iteratoal cece Idex, Chemcal ad Molecular Egeerg waset.org/publcato/7848 For the estmato o sold state asto temperature ( ), Nchta et al. proposed the ollowg correlato []: 0879 366.39775 + 0.03609MW (7) MW I (6) ad (7), s K, ad MW s the compoet molecular weght. For the calculato o uso ad the soldsold asto ethalpy o ormal alkaes, Nchta et al. suggested the ollowg correlatos or MW > 8 (gr/mol) []: Δ H 0. 1186MW (8) Δ H 0. 0577MW (9) ad or MW < 8 (gr/mol), Nchta et al. expressed the total ethalpy (uso+ sold state asto) by the ollowg correlato []: Δ H 0. 1777MW (10) t I (8) to (10), ΔH s cal/mol. For calculato o heat capacty derece betwee sold ad lqud phase, Δ C, the ollowg correlato proposed by Pederse et al. have bee appled [3]: that ΔC 4 Δ C 0.3033MW 4.635 10 MW (11) P p ad are cal/mol.k ad K, respectvely. For precptatg compoets the thermodyamc equlbrum ca be wrtte as ollows [1,, 16]:, x ) ) 1,..., C (1), Pure where, C s s the umber o precptatg compoets. By usg the stablty aalyss correlato, (4), ad materal balace or precptatg ad o-precptatg compoets, the mole racto ad composto o sold phase ca be obtaed. he algorthm ad materal balace equatos have bee reported the lterature [16]. IV. REU AND DICUION he results o calculatos have bee reported able V. hs table shows the ew mult-sold model usg predctve Wlso model gves better results comparso wth other actvty coecet models ad deal soluto approach ad the prevous mult-sold models. Fgs. 1-4 show the results o calculatos wth ew mult-sold model by usg the predctve Wlso model. s p ABE V HE REU OF CACUAION erary systems 1 3 4 otal No. o data pots 11 11 18 16 56 Models AAD % a ra-galeaa et al. (1996) [ ] 16.6 13.11 10.85 10.66 1.30 Nchta et al. (001) [ ] 1.17 1.00 1.07 1.63 1.4 New Model γ 1 1.17 1.00 1.08 1.63 1.4 New M model Regular soluto 1.17 1.00 1.08 1.63 1.4 New M model UNIFAC 1.18 1.00 1.08 1.63 1.4 New M Model P. UNIQUAC 0.91 0.7 0.87 1.37 0.99 New M model P. Wlso 0.51 0.49 0.66 1.19 0.75 a Cal Exp %AAD Exp WD (K) WD (K) 90 88 86 84 8 80 78 76 Expermetal data New mult-sold model ad usg predctve Wlso 74 1 3 5 7 9 11 Number o mxture Fg. 1 he results o calculato by ew mult-sold model ad predctve Wlso model terary 1 (C 14 -C 15 -C 16 ) 300 98 96 94 9 90 88 Expermetal data New mult-sold model ad usg predctve Wlso 86 1 3 5 7 9 11 Number o mxture Fg. he results o calculato by ew mult-sold model ad predctve Wlso model terary (C 16 -C 17 -C 18 ) Iteratoal cholarly ad cetc Research & Iovato 1(5) 007 50
World Academy o cece, Egeerg ad echology Iteratoal Joural o Chemcal ad Molecular Egeerg Iteratoal cece Idex, Chemcal ad Molecular Egeerg waset.org/publcato/7848 Also, able VI dcates the Nchta et al. ad ew multsold models gve better results tha the ra-galeaa model sogly. It proves that the cosderato o sold-sold asto term s requred or the calculato o sold-lqud phase equlbrum based o the cocept o mult-sold model or predcto o wax ormato pheomea. WD (K) WD (K) 31 310 308 306 304 30 300 98 Expermetal data New mult-sold model ad usg predctve Wlso 96 1 3 5 7 9 11 13 15 17 19 Number o mxture Fg. 3 he results o calculato by ew mult-sold model ad predctve Wlso model terary 3 (C 18 -C 19 -C 0 ) 316 314 31 310 308 306 304 30 Expermetal data New mult-sold model ad usg predctve Wlso 300 1 3 5 7 9 11 13 15 17 Number o mxture Fg. 4 he results o calculato by ew mult-sold model ad predctve Wlso model terary 4 (C 19 -C 0 -C 1 ) V. CONCUION I the prevous mult-sold models or the predcto o wax precptato pheomea, the equato o state has bee used or calculato o ugacty the lqud phase. For the rst tme, ths work, actvty coecet models have bee appled or the stablty aalyss ad ugacty calculato. he results show that ths approach s better tha that oe uses the equato o state. Also, the ru tme o ew method s less tha the prevous models. APPENDIX A. Actvty Coecet Models 1) Regular oluto heory [6, 7] V ( δ δ ) lγ (1) R Where,V,δ adδ are the molar volume, solublty parameter ad average solublty parameter, respectvely. δ ϕ δ () As, ϕ ad ϕ are the volume racto o lqud ad sold phases, respectvely. x V ϕ (3) x V x V x V ϕ (4) I ths approach, the lqud ad sold molar volumes are assumed to be equal. hereore, MW V V V (5) d,5 For estmato o the lqud desty o each compoet at 5 c ( d, 5 ), the ollowg correlato depedg o molecular weght s used [3]: 4 13.06 d, 5 0.8155 + 0.67 10 MW (6) MW olublty parameters the lqud ad sold phases ( δ ad δ ) related to carbo umber ( C ) are calculated by (7) ad (8) suggested by Pederse et al. [3]: δ 7.41+ 0.5194(l C l 7) (7) δ 8.5 + 5.763(l C l 7) (8) ) UNIFAC [8] For mxtures cotag alkaes oly, the ollowg correlato s used [8]: Φ Φ Φ Φ l γ + l 1 q l + x x θ 1 (9) θ s the coordato umber. For orthorhombc molecular sucture s set to 6 ad θ, the area racto, adϕ, the segmet racto, are obtaed rom the ollowg correlatos: xq θ (10) x q Iteratoal cholarly ad cetc Research & Iovato 1(5) 007 51
World Academy o cece, Egeerg ad echology Iteratoal Joural o Chemcal ad Molecular Egeerg Iteratoal cece Idex, Chemcal ad Molecular Egeerg waset.org/publcato/7848 Φ x r x r (11) he values o molecular sze parameter, r, ad molecular exteral surace parameter, q, have bee obtaed rom the Esmaelzadeh et al. correlatos [9-10]: r 0.6744 + 0.4534 (1) lγ C.54C q 0 + 0.616 (13) 3) Predctve UNIQUAC [11, 1] Φ l x + q q Φ + 1 x l 1 Φ Φ q l + 1 θ θ θ τ q θ τ m 1 k 1 k θ τ k (14) λ λ τ exp (15) q R I ths equato, the λ s the teracto eergy. mlar to UNFAC, θ ad Φ are calculated by (10) ad (11). he correlatos or the r ad q values wth the -alkae cha legth are [13]: r 0.0148C + 0.00996 (16).0185C q 0 + 0.011 (17) he teracto eergy, λ s estmated rom the heat o sublmato o pure orthorhombc crystal, λ ( ΔH sub R ) (18) wth beg the coordato umber. For the orthorhombc crystals, the value o 6 s cosdered or [11, 14]. he teracto eergy betwee two o-detcal molecules s gve by: λ λ λ (19) where s the -alkae wth the shorter cha o the par. Heat o sublmato ca be calculated by: sub vap Δ H ΔH + ΔH + ΔH (0) where vaporzato ethalpy s assessed usg the PER correlato by Morga ad Kobayash [17]. he crtcal propertes eeded Morga ad Kobayash correlatos ca be calculated by wu correlatos [18]. Δ H, s calculated by the ollowg correlato: Δ H ΔH tot ΔH (1) ΔH 3.7791C 1.654 () tot Λ 4) Predctve Wlso [14] x Λ lγ 1 l x Λ (3) k k x Λ λ λ exp (4) R mlar to the predctve UNIQUAC approach, λ s calculated ad the value o 6 s cosdered or. NOMENCAURE ymbols C umber o compoet C carbo umber C p d H MW P q r R V x specc heat capacty desty ugacty ethalpy couter o compoet molecular weght pressure molecular exteral surace parameter molecular sze parameter gas uversal costat temperature volume mole racto coordato umber eed composto Greek letters Δ varato actvty coecet γ δ δ ϕ Φ θ Λ λ τ uperscrpts lqud sold solublty parameter average solublty parameter volume racto segmet racto area racto teracto parameter teracto eergy characterstc eergy parameter k k Iteratoal cholarly ad cetc Research & Iovato 1(5) 007 5
World Academy o cece, Egeerg ad echology Iteratoal Joural o Chemcal ad Molecular Egeerg Iteratoal cece Idex, Chemcal ad Molecular Egeerg waset.org/publcato/7848 ubscrpts C crtcal F eed uso sub tot vap compoet umber compoet umber compoet umber sublmato total asto vaporzato ACKNOWEDGMEN he authors are grateul to the hraz Uversty or supportg ths research. REFERENCE [1] C. ra-galea, A. Froozabad ad J.M Praustz, hermodyamc o wax precptato peoleum mxtures, AIChE J., vol. 4, pp. 39-48, 1996. [] D.V. Nchta,. Goual ad A. Froozabad, Wax precptato gas codesate mxtures, PE Prod. Facl., vol. 16, pp. 50-59, 001. [3] K.. Pederse, P. kovborg ad H.P. Rogse, Wax precptato rom orth sea crude ols 4. hermodyamc modelg, Eergy ad Fuels, vol. 5, pp. 94-93, 1991. [4] D.Y. Peg ad D.B. Robso, A ew two-costat equato o state, Id. Eg. Chem. Fud., vol. 15, pp. 59-64, 1976. [5] A. Daesh, PV ad Phase Behavor o Peoleum Reservor Fluds, 3rd mpresso, Elsever, Netherlads, 003. [6] K.W. Wo, hermodyamcs or sold soluto-lqud-vapor equlbra: wax phase ormato rom heavy hydrocarbo mxtures, Flud Phase Equlb., vol. 30, pp. 65-79, 1986. [7] J.M. Praustz, R.N. chtethaler ad E.G. de Azevedo, Molecular hermodyamcs o Flud-Phase Equlbra, Pretce-Hall, Eglewood Cls, NJ, 1999. [8] B.. arse, P. Rasmusse ad A. Fredeslud, A moded UNIFAC group-cobuto model or predcto o phase equlbra ad heats o mxg, Id. Eg. Chem. Res., vol. 6, pp. 74-86, 1987. [9] F. Esmaelzadeh, J. Fath Kalah ad E. Ghaae, Ivestgato o deret actvty coecet models thermodyamc modelg o wax precptato, Flud Phase Equlb., vol. 48, pp. 7-18, 006. [10] E. Ghaae, hermodyamc modelg o wax precptato through gas codesate ppeles, M.. thess, Chem. ad Pet. Eg. Dept., hraz Uv., hraz, Ira, 006. [11] J.A.P. Coutho, Predctve UNIQUAC: A ew model or the descrpto o multphase sold-lqud equlbra complex hydrocarbo mxtures, Id. Eg. Chem. Res., vol. 37, pp. 4870-4875, 1998. [1] J.A.P. Coutho, Predctve local composto models: NR ad UNIQUAC ad ther applcato to model sold lqud equlbrum o - alkae, Flud Phase Equlb., vol. 158-160, pp. 447-457, 1999. [13] J.A.P. Coutho, C. Dauph, J.. Dardo, Measuremets ad modellg o wax ormato desel uels, Fuel, vol. 79, pp. 607-616, 000. [14] J.A.P. Coutho, E.H. teby, Predctve local composto models or sold/lqud equlbrum -alkae systems: Wlso equato or multcompoet systems, Id. Eg. Chem. Res., vol. 35, pp. 918-95, 1996. [15] V. Metvaud, F. Raabalee, H.A.J. Ook, D. Modeg, Y. Haget, Complete determato o the sold (RI)-lqud equlbra o our cosecutve -alkae terary systems the rage C 14 H 30 -C 1 H 44 usg oly bary data, Ca. J. Chem., vol. 77, pp.33-339, 1999. [16] A. Froozabad, hermodyamcs o Hydrocarbo Reservors, 1 st edto, McGraw-Hll, New York Cty, 1999. [17] D.. Morga, R. Kobayash, Exteso o Ptzer CP models or vapor pressures ad heats o vaporzato to log-cha hydrocarbos, Flud Phase Equlb., vol. 94, pp. 51-87, 1994. [18] C.H. wu, A terally cosstet correlato or predctg the crtcal propertes ad molecular weghts o peoleum ad coal-tar lquds, Flud Phase Equlb., vol. 16, pp. 137-150, 1984. Ehsa Ghaae was bor 1979 Mashhad, Ira. He has a B.. degree chemcal egeerg rom the Ira Uversty o cece ad echology, ehra, Ira (003) ad a M.. degree Natural Gas Egeerg rom the hraz Uversty, hraz, Ira (006). Hs research terests clude hermodyamc o Peoleum Reservor Fluds such as thermodyamc modelg o wax precptato peoleum luds specally porous meda. He has publshed ad preseted artcles Flud Phase Equlbra oural ad teratoal coereces wth Dr. Esmaelzadeh ad Proessor Fath Kalah. He s a member o ocety o Peoleum Egeers (PE). Ferdu Esmaelzadeh was bor 1963 Abada, Ira. He has a B.. degree rom the Abada Isttute o echology, Abada, Ira (1986), a M.. degree rom the hraz Uversty, hraz, Ira (1990) ad a Ph.D. degree rom the har Uversty o echology, ehra, Ira (001), all chemcal egeerg. He s Assstat Proessor o the hraz Uversty ad Aduct Proessor o the har Uversty o echology sce 00 ad 001, respectvely. He was Vstg Proessor o Peoleum Uversty o echology ad Isaha Uversty o echology 1994-00. He has more tha 10 years' experece the Natoal Iraa Ol Compay (N.I.O.C.) as a admsator o Reservor mulato, Producto Egeerg ad Peophyscs Ahvaz, ehra ad hraz Ira. Hs prmary research terests clude Gas Codesate Reservor, upercrtcal Fluds, Phase Equlbrum (Eo), mulato ad urace Faclty Problems Peoleum Iduses ad publshed artcles related to these subects ourals. He s a member o ocety o Peoleum Egeers (PE) ad Iraa Assocato o Chemcal Egeerg. Jamshd Fath Kalah was bor 1947 abrz, Ira. He has a B.. degree rom the Orego tate Uversty, Corvalls, Orego, UA (1974), a M.. degree rom Vrga Polytechque Isttute ad tate Uversty, Blacksburg Vrga, UA (1976) ad a Ph.D. degree rom Vrga Polytechque Isttute ad tate Uversty, Blacksburg Vrga, UA (1978) all chemcal egeerg. He s Proessor o the hraz Uversty sce 1995. He was vstg Proessor o Oklahoma tate Uversty (Oklahoma, UA) ad akehead Uversty (Otaro, Caada) 1987-1988 ad 1996-1997, respectvely. He was Charma o Chemcal ad Peoleum Egeerg Departmet o hraz Uversty or seve years. He s teachg Chemcal Egeerg hermodyamc, Chemcal Reactor Desg, Mass aser ad Polymer cece ad echology, B.., M.. ad Ph.D. levels ad he has publshed artcles theses subects ourals. He s a member o ocety o Peoleum Egeers (PE) ad Iraa Assocato o Chemcal Egeerg. Iteratoal cholarly ad cetc Research & Iovato 1(5) 007 53