Excess Gbbs Eergy ad aturato ressure of the Eroetally Fredly Refrgerat Mxture: R365fc ad R152a Dr.-Ig. Mo E. Abdalla Departet of Checal Egeerg, Uersty of Khartou,.O. Box 321, Khartou 11111, uda Abstract- Ths wor presets the saturato pressure of ew eroetally fredly refrgerats 1,1-dfluoroethae (R152a) ad 1,1,1,3,3-etafluorbutae (R365fc), besde ther xture. pecal atteto was ge to eable a hghly accurate predcted saturato pressure ad excess Gbbs eergy data as fucto of coposto a teperature rage of T=260K to T=380K, for the pure flud ad the xture. The sulato data for the saturato pressure were obtaed usg the odfed Ufac ethod, Lee Kesler ad Hoffa Flor odels ad aldated wth the hgh precso fudaetal equatos of state by Outcalt ad McLde fro Natoal Isttute of tadard ad Techology (NIT). Aog all the odel of Lee ad Kesler hae show good results for fttg the lght copoet R152a, axu poste deato less tha 1% was reached. Whereas the odel of Hoffa Flor yelded good results for R365fc, axu poste deato less tha 2.85% was reached. The excess Gbbs eergy fucto for the xture was realzed a teperature rage of T=260K to T=380K by the odfed UNIFAC ethod. Keywords- R152a, R365fc, Excess Gbbs Eergy, Lee Kesler, Hoffa Flor, Ufac. I. INTRODUCTION ce the declarato of the Motreal protocol 1987 the use of the harful aterals of Chlorofluorocarbos (CFCs) ad Hydrochlorofluorocarbos (HCFCs) based refrgerats the atosphere s cosequetly regulated [1]. These aterals hae bee wdely used as solets, foa blowg agets, aerosols ad especally as refrgerats due to ther preeet propertes such as stablty, o-toxcty, o-flaablty ad aalablty. Howeer, these substaces hae a harful effect o the earth s protecte ozoe layer. Moreoer the CFCs had bee recogzed as aterals cotrbutg to the pheoea of the global warg. The teratoal efforts hae legalzed to stop the cosupto of CFCs by replacg the wth ew HFCs [3-5]. Ths paper supports ost portat therodyacs data for those aterals, cludg the pure fluds ad xtures of R152a ad R365fc. The R152a s a HFC type refrgerat. Ths flud has zero OD ad a GW alue of 120. The bolg pot teperature at a pressure of p=1.013 bar s s = 24.0 C, the olecular weght M=66.1 g/ol. R152a s a edu pressure refrgerat for the edu teperature refrgerato rage [2]. The physcal, therodyac ad refrgerato characterstcs are slar to those of the refrgerats R12 ad R134a. Although R152a s a good refrgerat substtute for R12, t s ot used ts pure for because of ts flaablty (flaablty lts 3.7 21.8% by olue ar). For ths reaso, R152a s labeled as hghly flaable. The R365fc s a HFC type refrgerat. Ths flud has zero OD ad a GW alue of 782. The bolg pot teperature at a pressure p=1.013 bar s s =+41.4 C, the olecular weght s at M=148.07 g/ol. R365fc s a ew flud whch s aly used for the producto of rgd polyurethae foas used sulato purposes where a lqud foag aget wth a low theral coductty ad a hgh apor pressure at low teperatures are eeded. Regardg to therodyac propertes ad safety requreets, R365fc s eployed as a a copoet bary bleds wth 7 or 13 ass% wth 1,1,1,2,3,3,3-Heptafluoropropae (R227ea) the producto of lqud foag agets [2]. Besdes the fact that ths flud has o egate pact o the ozoe layer, further eroetal beefts ca be acheed usg R365fc, le the producto of polyurethae foas. To the best of our owledge, oly a ery lted aout of data for the excess Gbbs eergy ad saturated pressure of R365fc ad R152a are aalable the lterature. II. REDICTIVE MODEL The equato type of Hoffa Flor (1), (2) respectely has bee pleeted to detect the saturato pressure. Ths equato 60
based o the charts deeloped by Cox [6] ad t has two adustable paraeters ad. It s calculated as follows: f (T) 1 T 7.9151*10 l 0 *f (T) 2.6726 *10 * log T 0.8625*10 3 3 6 * T (1) (2) The equato ca be ftted to two or ore ow data pots for the saturato pressure. The paraeter ad ca the be calculated a: 1 l 0 l 1 2 f (T 1) * f (T ) f (T 1 l 2 f (T ) f (T 1 A ore coeet equato of Lee ad Kesler [10] was also used to estate the saturato pressure as follows: expa wb I ths equato A ad B are fuctos o the crtcal teperature of the flud. c 1 2 ) I 1975, the UNIFAC group cotrbuto ethod was publshed by Fredeslud et al. [7-10]. Le the AOG ethod, the UNIFAC ethod s based o the soluto of groups cocept. Howeer the UNIFAC ethod, the actty coeffcets are calculated fro a cobatoral ad a resdual part exactly le the UNIQUAC odel. I ths ethod the teperature depedet cobatoral part taes to accout the sze ad the for of the olecules, whch cosders the etropc cotrbuto ad the resdual part, cosders the ethalpc teractos as follows: Table I. ropertes of the fluds. 2 ) (3) (4) (5) Copoet M w (g/ol) T c (K) c (bar) 3 (g/ ) c R365fc 148.07 460.0 3266.0 473.84 0.377 R152a 66.051 386.41 4516.8 368.0 0.27521 The cobatoral part Where l l C l R C I ca be calculated usg the followg equato, whch s detcal to the UNIQUAC odel: l C 1 V l V V V 5q 1 l F F V (Volue/ole fracto rato) ad F (surface area/ole fracto rato) ca be calculated for a ge coposto usg the (6) (7) 61
relate a der Waals olue r ad a der Waals surface areas q of the olecules. The relate a der Waals propertes r ad a der Waals group surface areas V F r r x q q x q ca be obtaed usg the relate a der Waals group olues Q,whch ca be dered fro x-ray data. Tabulated alues for R ad Hase et al. [10].They ca also be dered fro the tabulated a der Waals propertes publshed by Bod [11]. where () r R (10) () () q Q (11) s the uber of fuctoal groups of type copoud. The teperature depedet resdual part (8) (9) R ad relate Q ca be foud R l taes to accout the teractos betwee the dfferet copouds. I group cotrbuto ethods, ths part s calculated by the soluto of groups cocept usg group actty coeffcets ad [6]: ad () () R () () l (l l ) (12) are the group actty coeffcets for group the xture, for the pure copoud. The UNIQUAC equato s used to descrbe the ole fracto depedece of the group actty coeffcets as follows [6]: l The surface area fractos The paraeter follows: Q 1 l ad the group ole fractos X of group ca be calculated usg the followg relatos: X Q X (13) Q X (14) ( ) x ( ) x cotas the group teracto paraeter a betwee the fuctoal groups ad whch s descrbed as (15) a exp T (16) 62
For eery a group cobato two teperature depedet group teracto paraeters ( a, a ) are requred, the group teracto paraeters betwee detcal a groups ( a, a ) are equal to zero. All the paraeters were ftted to cosstet experetal apor-lqud equlbru data whch are stored the Dortud Data Ba [12]. To proe ad treat the weaesses of UNIFAC, the odfed UNIFAC ethod was deeloped [13].The a dffereces copared to orgal UNIFAC are [6]: A eprcally odfed cobatoral part was troduced to proe the results for asyetrc systes. Teperature depedet group teracto paraeters are used. Addtoal a groups were added, for exaple for cyclc alaes ad forc acd. The odfcato of the odfed UNIFAC copared to the orgal UNIFAC was establshed frstly by Kc et al. [14]. The cobatoral part s calculated usg the followg slghtly odfed eprcal equato: For whch V s: C V V l 1 V l V 5q 1 l. F F (17) r 2 / 3 2 / 3 r V. Wedlch [15-16] has recoeded usg the alue 3/4 for the olue fracto expoetal ter as follows: x (18) r 3/ 4 3 / 4 r V. x To descrbe the teperature depedece, lear or quadratc teperature depedet paraeters were troduced as follows: (19) a exp III. 2 b T c T T REULT AND DICUION. (20) Fg.1. Excess Gbbs eergy predcted for the syste R152a (1) ad R365fc (2) by odfed UNIFAC. 63
Fg.2. -T-xy dagra fro odfed UNIFAC for the syste R152a (1) ad R365fc(2). As a fudaetal fucto the feld of therodyacs, Fg.1 llustrated the predcto of excess Gbbs eergy for the syste R152 ad R365fc as a fucto of teperature ad coposto relate to ore olatle copoet R152a by odfed UNIFAC ethod. It s to be etoed that fucto s strogly depedet o coposto ad teperature of xture. The fucto probably creases as teperature ad coposto crease a rsg cure utl reachg certa coposto of 0.7, ad the cure the exhbts erted character whle reachg the deal behaor of pure copoet upo whch ts alue turs to a zero. Excess Gbbs eergy fucto ples dfferet effects oled the xg of arous olecules ad ges the eergetc effect to olecules due to the arato of terolecular forces ad also the etropc effect preseted by excess etropy fucto. Ths results fro a lac of coplete radoess dstrbuto of olecule xture. The equlbru state of the syste R152a ad R365fc s preseted a three desoal -T-coposto dagra for teperature rage 263.15K-363.15K Fg.2. Ths fgure shows scheatcally the -T-coposto surfaces whch cota the equlbru states of saturated apor ad saturated lqud for ths bary xture, where R152a s the ore olatle copoet ad R365fc s the less olatle copoet. The lower surface cotas the saturated apor states whch ow as -T-y surface. The upper surface cotas the saturated lqud states whch ow as -T-x surface. Fg.3. aturato pressure teperature dagra of R152a ad R365fc. 64
Fg.4. Relate deato to experetal data [17] [18] for saturato pressure of R152a. Fg.5. Relate deato to experetal data [17] [18] for saturato pressure of R365fc. Fg.6. Bubble pressure teperature dagra of the syste R152a (1) ad R365fc (2) fro odfed UNIFAC ethod. Fg.7. Relate deato saturato pressure easureet of the syste R152a (1) ad R365fc (2), the data copared wth data obtaed fro odfed UNIFAC [19][20] ethod ad the data of Mc Lde, M.O. ad Leo et al. (NIT) [17] [18]. 65
Obously see Fg.3 ad Fg.5, the pure flud data exhbted a u relate deato pressure for the teperature rage of T=263.15K to T=363.15K. The odel of Lee ad Kesler (LK) hae show good results for fttg the lght copoet R152a, axu poste deato less tha 1% was proded by Lee Kesler. Whereas the odel of Hoffa Flor (HF) yelded good results for R365fc, axu poste deato of 2.85% was proded by Hoffa Flor. The relate deato the case of the xture as show Fg.7 has dcated a hgh deato o the way of creasg the xture copostos. Ths xture pressure data were copared wth the pressure obtaed fro odfed UNIFAC as preseted Fg.6 ad the data of Mc Lde, M.O. ad Leo et al (NIT) [17] [18]. IV. CONCLUION The wor has delered arous therodyac data cocetratg o the Excess Gbbs eergy fucto ad the saturato pressure of the eroetally fredly syste of R152a ad R365fc. The lqud phase behaor of the xture was estgated usg the group cotrbuto ethod of odfed UNIFAC, whch proed ts relablty to predct the excess Gbbs free eergy odel. The wor has also explored predcte odels for the saturato pressure, aely the Lee Kesler ad Hoffa-Flor, besde the hgh precso fudaetal equatos of state by Outcalt ad McLde fro Natoal Isttute of tadard ad Techology (NIT). The sulato results acheed good agreeet wth the experetal data by Outcalt ad McLde (NIT). V. ACKNOWLEDGMENT The author greatly apprecated the facal support of Gera Acadec Exchage erce (DAAD) ad the Faculty of Mechacal Egeerg-Isttute of Therodyacs, Haoer Uersty for techcal executo. pecal thas for Dr.-Ig. Mchael Kleber for perttg to use hs odfed UNIFAC ethod. Noeclature CFCs HCFCs HFCs EO GW OD DDB UNIFAC NIT T c, c T r E g r x q chlorofluorocarbos hydrochlorofluorocarbos hydrofluorocarbos equato of state global warg potetal ozoe depleto potetal dortud data ba uersal quas checal fuctoal group actty atoal sttute of stadard ad techology crtcal teperature ad pressure reduced teperature excess Gbbs eergy relate a der Waals olue of copoet ole fracto of copoet the lqud phase relate a der Waals surface area of copoet () group actty coeffcet of group pure copoet. group actty coeffcet of group the xture. () uber of groups copoet. () uber of groups copoet. 66
() uber of oles of copoet. () () total uber of oles of groups the xture. () () X group ole fracto of group copoud. () () () X () () group ole fracto of group the xture. REFERENCE [1] Uted Natos Eroet rogra: Motreal protocol o substaces that deplete the ozoe layer, 2000. [2] H. Buchwald, F. Flohr, J. Hella, H. Kög, C. Meurer: olae ocet Maual, Refrgerato ad ar codtog techology, olay Fluor ud Derate,2007. [3] B. G. Lee, H. K, H. K,. D. Lee, ad I. eo, J. Id. Eg.Che.,3,160 (1997). [4] H. K, H.. K, B. G. Lee, Y.. Kwo, ad K. Y. ar, J. Id. Eg. Che., 3, 203 (1997). [5] K. H Lee, K.W. eo, Y. I. Mo, K. Y. ar, ad B.. Ah, J. Id. Eg. Che., 6, 305 (2000). [6] Jürge Gehlg, Bärbel Kolbe, Mchael Kleber, Jürge Rarey: Checal therodyacs for process sulato, frst edto, Wley-VCH Verlag, 2012. [7] (a) Ahlers,J.ad Gehlg,J.: Flud hase Equlbra.,191,177-188;2001, (b)ahlers,j.ad Gehlg, J.: Id. Eg.Che. Res.,41,3489-3489; 2002,(c) Ahlers, J.ad Gehlg, J.: Id.Eg.Che.Res.,41,5890-5899,2002. [8] Fredeslud, Aa., Gehlg, J., ad Rasusse,.Vapor -Lqud Equlbra Usg UNIFAC, Elseer,Asterda, (1977). [9] Fredeslud,Aa.,Joes,R.L., ad raustz,j. M. AIChE J.,21,1086-1099,1975. [10] Hase, K.H., chller, M., Fredeslud, Aa., Gehlg,J., ad Rasusse,.: Id. Eg. Che. Res., 30,2352-2355,1991. [11] Bod,A.: Che.Re.,67,565. [12] Dortud Data Ba (DDB), software ad separato techology GbH, Oldeburg, 2006. [13] Wedlch,U. ad Gehlg, J.: Id.Eg. Che.Res., 26,1372-1381,1967. [14] Kc, T., Aless,., Rasusse,., Fredeslud, Aa.: Ca. J. Che. Eg., 58,253, 1980. [15] Wedlch, U., Experetelle ud theoretsche Utersuchuge zur Erweterug der Gruppebetragsethode UNIFAC, Dssertato, Dortud, 1985. [16] Wedlch, U., Gehlg, J., Id. Eg. Che. Res., 26, 1372, 1987. [17] Outcalt,.L. ad McLde, M.O.: A odfed Beedct-Webb-Rub equato of state for the therodyac propertes of R152a (1,1-dfluoroethae), J. hys. Che. Ref. Data, 25(2):605-636, 1996. [18] McLde, M.O. ad Leo, E.W.: Therodyac ropertes of R-227ea, R-365fc, R-115, ad R-131, J. Che. Eg. Data, 2013. [19] Kleber, M.: A exteso to the UNIFAC group assget for predcto of apor lqud equlbra of xtures cotag refrgerats. Flud hase Equlbra 107,161-188,1995. [20] Kleber,M, Axa, J.K.: Eolutoary algorths for the optzato of odfed UNIFAC paraeters, coputer ad checal egeerg 23,63-82,1998. 67