Program Ternar2 v.2.16 user manual

Transcription

1 Numercal Processng of Ternary Lqud Expermental Data Vladmír Hanta 1, Lenka Morávková 2 1 Department of Computng and Control Engneerng, Faculty of Chemcal Engneerng, Insttute of Chemcal Technology Prague, Techncká 5, Prague 6, Czech Republc, phone: , fax: , e-mal: hantav@vscht.cz 2 Department of Separaton Processes, Insttute of Chemcal Process Fundamentals, Rozvojová 2/135, Prague 6, Czech Republc, phone: , fax: , e-mal: moravkova@cpf.cas.cz Keywords: excess molar volume; ternary mxture; ternary data fttng; least squares method; Matlab, Optmzaton Toolbox Introducton Matlab program Ternar2, ver. 2.16, carres out fttng of excess volumes values for ternary mxtures. The values of excess volumes were calculated from the expermental data of mxture denstes and denstes of pure components. The modfed Redlch-Kster equaton s used for data fttng. Ths data model can optonally contan dfferent numbers of bnary and ternary constants. The optmzaton s performed usng the least squares method n computatonal envronment of the Matlab system wth help of Optmzaton Toolbox functons. Bref theoretcal fundamentals E The V m values were calculated [2] from the mxtures denstes,, and the denstes,, and molar masses, M, of pure components by usng the general relaton for multcomponent mxture of k component: V E m k 1 x M 1 1 ( where subscrpt refers to component of the mxture and x stands for the mole fracton of the respectve component. For the ternary system, the Redlch Kster equaton was modfed [3] as follows V E m j x x n j k 0 k A( j) k ( x x j) x1x 2x3 ( B0 B1 x1 B2x2 B3x1 B4x1 x2 B5 x2) where A ( j ) k are bnary and B m ternary dsposable parameters. The ternary terms n the equaton are usually used n dfferent forms [1]. It was used here a smple and transparent polynomal. ) 2 1

2 Procedure of dgtal processng of measured data selecton of the language of menus, fgures and nformaton messages enterng the name of the data fle and readng the data structure of mxture components data (worksheet Constants) Mxture components Comp 1 Comp 2 Comp 3 Molar masses M 1 M 2 M 3 114, , , g.mol -1 g.mol -1 g.mol -1 Denstes , , , g.cm -3 g.cm -3 g.cm -3 2

3 readng mxture components data readng measured values of denstes selecton of method of mole fractons normalzaton 3

4 structure of expermental measured densty data (worksheet Data) Comp1 Comp2 Comp3 Temperature 298,15 K Mole fractons Densty wrtng expermental data x 1 x 2 x g.cm -3 0, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,70100 wrtten processed densty and excess molar volume data (part of worksheet Results) Comp1 Comp2 Comp3 Temperature 298,15 Mole fractons Densty Excess volume x1 x2 x3 r VEm g.cm-3 cm3.mol , ,026 0,974 0,808-0, ,133 0,867 0,815-0, ,261 0,739 0,822 0, ,407 0,593 0,831-0, ,541 0,459 0,838 0, ,671 0,329 0,845 0, ,797 0,203 0,851 0, ,933 0,067 0,858 0, , ,02 0,03 0,95 0,804-0, ,021 0,081 0,898 0,807-0, , ,969 0,799 0,

5 wrtng calculated values of excess molar volumes vsualzaton of excess molar volumes 5

6 enterng parameters of modfed Redlch-Kster equaton fttng excess molar volumes usng modfed Redlch-Kster equaton by means of least squares method optmal values of modfed Redlch-Kster equaton coeffcents 6

7 wrtng optmal values of modfed Redlch-Kster equaton coeffcent (worksheet Coeffcents) wrtten optmum values of modfed Redlch-Kster equaton (worksheet Coeffcents) Coeffcents of modfed Redlch-Kster equaton bnary parts degree 2 ternary part degree 2 A(1,2)0 0, A(1,2)1 0, A(1,2)2 1, A(1,3)0 0, A(1,3)1 1, A(1,3)2 0, A(2,3)0 0, A(2,3)1 0, A(2,3)2 0, B(0) 8, B(1) -11, B(2) -18,48257 B(3) -1, B(4) 40, B(5) 6, wrtng ftted values of excess molar volumes 7

8 graphcal comparson of calculated and ftted values of excess molar volumes vsualzaton of ftted values of excess molar volumes 8

9 wrtten values of excess molar volumes calculated from expermental data and ftted usng modfed Redlch-Kster equaton (part of worksheet Results) Excess volume Excess volume VEm exp VEm RKe cm3.mol-1 cm3.mol , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , References [1] Kratochvíla, J., Cbulka, I., Holub, R.: Excess volume of the benzene-methanolacetontrle ternary mxture at temperatures of 25 and 40 C and correlaton of ts concentraton dependence. Collect. Czech. Chem. Commun., 45, 12, , [2] Morávková, L., Wagner, Z., Sedláková, Z., Lnek, J.: Volumetrc behavour of bnary and ternary lqud systems composed of ethanol, sooctane, and toluene at temperatures from ( to ) K. Expermental data and correlaton. J. Chem. Thermodynamcs, 43, 12, , [3] Morávková, L., Wagner, Z., Sedláková, Z., Lnek, J.: Volumetrc behavour of the ternary lqud system composed of methyl tert-butyl ether, toluene, and sooctane at temperatures from ( to ) K: Expermental data and correlaton. J. Chem. Thermodynamcs, 42, 7, ,