Recent Advances in Chemical Engineering, Biochemistry and Computational Chemistry

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1 Themal Conductivity of Oganic Liquids: a New Equation DI NICOLA GIOVANNI*, CIARROCCHI ELEONORA, PIERANTOZZI ARIANO, STRYJEK ROAN 1 DIIS, Univesità Politecnica delle ache, Ancona, ITALY *coesponding autho tel , fax Institute of Physical Chemisty, Polish Academy of Sciences, Wasaw, Poland. g.dinicola@univpm.it, Abstact: The main goal of the pesent wok is to build an empiical and eliable model fo each family of compounds based on few easily accessible physical constants. Fo this pupose, expeimental data fo efigeants, alkanes, alkenes, aomatics, cycloalkanes, cycloalkenes, ethes, estes, ketones, caboxylic acids and alcohols wee collected and selected. To minimize the deviation between the pedictions and the expeimental data and to find the optimal coefficients fo each family of a ecently poposed equation, a non-linea statistical analysis was pefomed. Finally, optimal coefficients and diffeent vesions of the poposed equation wee poposed fo each family. The esulting equations ae simple and ae able to pedict the themal conductivity with vey low deviations fo all the studied families. Keywods: oganic liquids, liteatue suvey, pue fluids, themal conductivity. 1. Intoduction The themal conductivity as defined by Fouie s equation, is a mateial s ability to tansmit heat by means of conduction. Fo this eason, themal conductivity is essential fo heat tansfe knowledge and its estimation has been the subject of many studies. The value of themal conductivity is a mateial elated popety which is dependent on pessue and tempeatue. In ode to povide a eliable database of the themal conductivity fo pue compounds, data wee ecently collected by us at atmospheic pessue fo tempeatues below nomal boiling point and at satuation pessue fo tempeatues above the nomal boiling point [1]. Fo many compounds, themal conductivity data could be found in eviews [2]. A complete and updated souce of data could be found in the DIPPR 801 database [3]. Fo ou data elaboation, we used data fom both of these souces. In addition, a citical analysis and a selection of the published expeimental data was pefomed. The main goal of the pesent wok was to find the optimal coefficients fo each family fo the ecently poposed equation [1] that minimizes the deviation between the pedicted and the expeimental data. Fo the coefficients optimization, the Levenbeg-aquadt cuvefitting method was adopted [4]. The method is actually a combination of two minimization methods: the gadient descent method and the Gauss-Newton method. The Levenbeg-aquadt method acts moe like a gadient-descent method when the paametes ae fa fom thei optimal value, and acts moe like the Gauss-Newton method when the paametes ae close to thei optimal value and the solution typically conveges apidly to the local minimum. In this way, it was possible to identify the paametes of the poposed equation, that guaantee the lowest deviation of the pedicted themal conductivity. In this pape, afte having poposed a geneal equation fo the themal conductivity calculation of oganic liquids [1], optimal coefficients and diffeent vesions of the poposed equation wee poposed fo each specific family of compounds. Finally, to compae the new equation efficiency, the mostly applied simple geneal semiempiical coelations fo the themal conductivity calculation of liquids [5-10] wee analyzed. 2. Developing the new model As a fist step, a citical analysis and a selection of the published expeimental data was pefomed, as epoted in a ecent pape [1]. The main pat of the expeimental data was found to be distibuted fom 0.03 to 0.18 W/mK and the maximum numbe of expeimental data was obtained at aound λ= W/mK. Fo ou model, only oiginal expeimental data wee ISBN:

2 adopted. In addition, fo a tenth of the compounds, data they come fom one souce only and when diffeent souces wee found, sometimes stong diffeences amongst the data fom vaious souces wee obseved. Fo this eason, a fluid by fluid analysis was pefomed and data showing deviations highe than thee times the standad deviation wee ejected. As a second step, we stated fom the consideation that expeimental data could be geneally well descibed adopting a linea dependence with the educed tempeatue. Following the obsevation, we wee seaching fo some specific fluid popety which could be involved in the model impoving the expeimental data epesentation fo all studied species epesenting vaious chemical stuctues. Then, consideing the typically adopted coesponding states pinciple paametes, the statistical analysis suggested that, besides the citical tempeatue and the expeimental tempeatue, an impotant paamete with good statistical effect is the molecula mass, as expected also fom the fact that molecula mass is well elated to the movement of molecules, being based on kinetic enegy of molecules. In addition, a good statistical effect was also found fo the acentic facto, an impotant paamete chaacteizing the shapes of molecules. In ode to obtain lowe deviations, othe additional paametes wee tested. The best esults in tems of deviations wee obtained adopting a tem with enthalpy of fusion, even if this popety is geneally significant fo tansition fom cystal to fluid phase. Afte the egession, the obtained equation was: λ f 10 e = a + b T + c 10 h fus + d ω + (1) λ0 whee a= , b= , c= [kmol J -1 ], d= , e=1 [kg/kmol], f= , λ 0 =1 [W m -1 K -1 ]. The poposed equation, in spite of its simplicity, showed an high quality of data epesentation. The only families that showed athe high deviations wee caboxylic acids, estes, alcohols and efigeants. In this pape, stating fom equation 1, a moe geneal vesion of the equation is poposed: λ f g e = a + b T + c hfus + d ω zc + (2) λ0 In this new vesion, a tem containing the compessibility facto was added. This tem was found to be athe not elevant fo almost all the families of compounds, but it was athe effective on the caboxylic acids and efigeants themal conductivity calculation. In addition, all the coefficients a, b, c, d and f wee ecalculated fo each family, accoding to the Levenbeg- aquadt cuve-fitting method [4]. Finally, the new coefficients wee epoted in Table Compaison with the liteatue equations Fom the liteatue analysis, fo compaison fou diffeent equations wee consideed. The Sato-Riedel equation [5] it is a athe simple equation that needs the knowledge of the expeimental tempeatue, the nomal boiling point tempeatue, the molecula mass, the citical tempeatue as follows: 2 / (1 T ) λ = (3) 1/ 2 2 / (1 Tb ) The Sheffy and Johnson equation [6] is also a vey simple equation, containing only the expeimental tempeatue, the melting tempeatue and the molecula mass as physical paametes: (T T ) m λ = (4) Tm Howeve, the Sato-Riedel equation and the Sheffy and Johnson equation, pobably because of thei simplicity, showed athe high deviations fo almost all the analyzed families, as shown in Table 2. The Latini equation is pobably the most commonly known and adopted equation fo oganic liquids: 0.3 ( T 0.1) λ = A (5) 1/ 6 (1.1 T ) whee the A values wee studied and tabulated fo each family [5]. The Latini equation is geneally ecommended and it was poposed fo seveal chemical families of compounds including olefins, satuated hydocabons, cyclopaaffins, aomatics, alcohols, ketones, caboxylic acids, efigeants and estes and its main dawback is that it may be inaccuate fo educed tempeatues above It is impotant to state that none of the pesented methods is able to pedict in a eliable way the themal conductivity behaviou nea the citical point. In ode to ovecome this point and to cove a significantly wide numbe of chemical families, a ecent equation was poposed by Ghaagheizi et al. [10] adopting a GEP [11] mathematical stategy: λ = 1 10 whee B 10 ω + 2Pc 2T ( Tb + ) A B B (6) ISBN:

3 ( B ) 8 A = (7) and = + (8) B T [2] NB. Vagaftik, LP. Filippov, AA. Tazimanov, EE. Totskii: Handbook of Themal Conductivity of b Liquids and Gases. Boca Raton: CRC Pess; [3] DIPPR-801, Poject 801, Evaluated Pocess Design Data, Public Release Documentation, Design institute fo Physical Popeties (DIPPR), Ameican Institute of Chemical Enginees, AIChE, [4] DW. aquadt, An algoithm fo least-squaes estimation of nonlinea paametes, J Soc Ind Appl ath, Vol. 11, 1963, pp [8] BE. Poling, J. Pausnitz, JP. O Connell. The Popeties of Gases and Liquids, 5 th ed. New Yok: cgaw-hill, [9] WY. Scheffy, EF. Johnson, Themal Conductivities of Liquids at High Tempeatues, J Chem Eng Data, Vol. 6, 1961, pp [10] F. Ghaagheizi, P. Ilani-Kashkouli,. Sattai, - (9) AH. ohammadi, D. Ramjugenath, D. Richon, (9) This equation consideed also amines, silanes/siloxanes, inoganic compounds, sulfides/thiophenes, mecaptanes, epoxides, peoxides, nitiles, elements and aldehydes. On the othe hand, the main dawback of this wok is that it was based on empiical appoach, with a huge numbe of coefficients being coelated. To test the goodness of the existing equation s calculation, deviations between the expeimental themal conductivities and the ones pedicted by equations 1, 3, 4, 5 and 6 wee calculated fo and epoted as aveages in Table 2. Deviations wee calculated accoding to equation 9. n 1 dλ% = [ ( λ exp λ calc ) / λ exp ] 100 n i= 1 In Figue 1, a summay of the deviations fo each family ae epoted fo equation 1 and 2. As a geneal comment, it could be stated that equation 1 is giving the lowe deviations fo almost all the selected families and that equation 2 is impoving the esults fo all families, especially efigeants, alcohols, caboxylic acids and ethes. When compaed with othe equations, paticulaly low deviations wee found fo alkanes, cycloalkanes, alkenes, cycloalkenes and aomatics, confiming the validity of the model. Development of a Geneal odel fo Detemination of Themal Conductivity of Liquid Chemical Compounds at Atmospheic Pessue, AIChE J,. Vol. 59, 2013, pp [11] C. Feeia, Gene expession pogamming: a new adaptive algoithm fo solving poblems, Complex Syst, Vol. 13, 2001, pp Conclusions In this pape a new and simple method was developed fo the themal conductivity calculation. The model does not equie any stuctue knowledge, but it simply needs a vey limited numbe of physical constants. The influence of seveal physical paametes on the themal conductivity pediction was discussed. The pesented genealized equation consideed the influence of the educed tempeatue, acentic facto, molecula mass, compessibility facto and enthalpy of fusion and showed a clea impovement in the themal conductivity calculation with espect to othe existing equations. Refeences [1] G. Di Nicola, E. Ciaocchi,. Pieantozzi, R. Styjek, A New Equation fo the Themal Conductivity of Oganic Compounds, J Them Anal Caloim. In pess. ISBN:

4 Family a b c d e f g Refigeants Cycloalkanes Cycloalkenes Estes Ethes Alkenes Alcohols Alkanes Ketones Aomatic Caboxylic acids Table 1. Coefficients fo equation 2 fo each family. Family N. of points Sato and Riedel Latini Sheffy and Johnson Ghaagheizi et al. eq. 1 eq. 2 Refigeants Cycloalkanes Cycloalkenes Estes Ethes Alkenes Alcohols Alkanes Ketones Aomatic ISBN:

5 Caboxylic acids ALL FAILIES Table 2. Deviations fo each family. Figue 1. Expeimental themal conductivity data vesus educed tempeatue. Figue 2. Deviations vesus educed tempeatue. ISBN: