Regression of my Experimental data for Ternary mixture into Non-randomness two liquid model (NRTL) thermodynamic model

Question

Ashish Kundaliya 2020-6-6

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/543260-regression-of-my-experimental-data-for-ternary-mixture-into-non-randomness-two-liquid-model-nrtl-t

评论： Roei Shapira 2023-1-1

Dear all,

I am trying to regress my experimental data for ternary mixture using NRTL multicomponent model. can you please help me out with this. I couldn't able to get the good fitting, the reason for this i don't know. hence if you could please change my code and modify it so that i can get the perfect fitting than it would be so gratefulness of yours.

Please note that consider the "Equation" i have written is correct. And if you have time then you can even write whole equation by your logic as well.

clear all;
clc;
alpha=0.3;
%% where, Xd(:,1)= Temperature, xd(:,2)=Mole fraction of 1, xd(:,3)=Mole fraction of 3, xd(:,4)=Psat of component 1, xd(:,5)=Psat of component 2
%% where, Psat of Component 3rd is negligible and hence Activity in below equation
%% yd is Experimental data
%% a is the parameters to be found out by regression
xd(:,1)=[313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15];
length(xd(:,1))
xd(:,2)=[0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182];
length(xd(:,2))
xd(:,3)=[0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818];
length(xd(:,3))
xd(:,4)=[7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36];
length(xd(:,4))
xd(:,5)=[0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316];
length(xd(:,5))
yd=[2.4;2.8;3.2;4.0;4.7;5.5;6.7;8.6;9.9;11.9;13.6;15.6;17.9;19.6;22.2;26.0;27.8;30.7;32.9;2.3;2.7;3.3;4.2;5.0;6.2;7.6;9.4;11.4;13.2;14.9;16.9;19.0;21.1;23.8;26.4;28.9;30.9;33.1;2.7;3.2;4.0;4.9;5.9;7.5;9.2;10.8;12.5;15.7;18.6;20.9;23.9;26.9;30.9;34.1;38.0;41.3;43.9;2.3;2.6;2.9;3.2;3.7;4.3;5.0;6.1;7.2;8.4;9.4;10.1;11.2;11.9;12.6;13.8;15.2;16.4;17.8;2.3;2.5;3.1;3.8;4.8;5.9;7.1;8.6;10.2;12.4;15;17.4;19.7;21.4;24.3;27.8;30.1;32.1;35;2.8;3.2;4.2;5.3;6.6;8.2;10.2;12.4;15.4;17.8;20.4;23.5;27.0;30.0;34.0;37.4;39.6;43.1;47.3;2.1;2.6;3.1;3.8;4.7;5.6;7.2;8.3;9.9;11.7;13.3;14.4;16.7;17.9;19.0;21.0;22.2;23.5;25.0;2.1;2.5;3.0;3.6;4.6;5.9;7.0;8.0;9.0;10.5;12.1;13.6;14.8;16.7;18.6;20.5;21.8;23.8;26.5;2.6;3.5;4.0;5.1;6.6;8.3;9.8;11.4;13.5;14.9;16.9;18.0;20.3;21.8;25.3;27.8;30.1;32.8;35.0;1.9;2.3;2.7;3.2;3.7;4.2;4.8;5.7;6.7;7.7;9.2;10.4;11.1;12.4;14.3;16.3;17.7;19.2;20.1;2.8;3.7;4.9;6.1;7.6;9.0;11.2;13.8;17.0;20.8;25.2;29.7;34.0;37.5;41.0;44.2;47.5;49.8;52.0;2.1;2.6;3.6;4.4;5.6;6.9;8.1;9.0;10.6;12.2;14.2;17.0;20.0;23.3;26.3;29.0;31.0;35.1;38.9];
length(yd)
FitnessFunction = @(a,xd)curvefit_multiobjective_two(a,xd);
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt','MaxFunEvals',2000000,'MaxIter',200000,'TolX',1e-100,'TolFun',1e-100)
lb = [];
ub = [];
A=0.1;
a0=[A A A A A A A A A A A A]; %% Initial guess values of the paramters to be found out
[a,residuals,resnorm]=lsqcurvefit(FitnessFunction,a0,xd,yd,lb,ub,options)
C=[0 a(1) a(2); a(3) 0 a(4); a(5) a(6) 0] %% Parameters to be found out by regression
D=[0 a(7) a(8); a(9) 0 a(10); a(11) a(12) 0] %% Parameters to be found out by regression
p1=[a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) a(11) a(12)]

Below is the other function that i have used in it.

You can take below equation granted and move ahead for regressoin and if you suspect something in equation than please look into below equation as well. This below screenshot shows you the equation for your reference purpose.

function yd=curvefit_multiobjective_two(a,xd)
alpha=0.3;
tow11=0;
tow12=(a(1)+(a(7)./(xd(:,1))));
tow13=(a(2)+(a(8)./(xd(:,1))));
tow21=(a(3)+(a(9)./(xd(:,1))));
tow22=0;
tow23=(a(4)+(a(10)./(xd(:,1))));
tow31=(a(5)+(a(11)./(xd(:,1))));
tow32=(a(6)+(a(12)./(xd(:,1))));
tow33=0;
G11=exp(-alpha.*tow11);
G12=exp(-alpha.*tow12);
G13=exp(-alpha.*tow13);
G21=exp(-alpha.*tow21);
G22=exp(-alpha.*tow22);
G23=exp(-alpha.*tow23);
G31=exp(-alpha.*tow31);
G32=exp(-alpha.*tow32);
G33=exp(-alpha.*tow33);
%%%% this a1, a2, ....., a8 are the breaked parts of the NRTL equation (Above shown in screenshot). 
a1=((xd(:,2).*tow11.*G11)+(xd(:,3).*tow21.*G21)+((1-xd(:,2)-xd(:,3)).*tow31.*G31))./((xd(:,2).*G11)+(xd(:,3).*G21)+((1-xd(:,2)-xd(:,3)).*G31));
a2=((xd(:,2).*G11)./((xd(:,2).*G11)+(xd(:,3).*G21)+((1-xd(:,2)-xd(:,3)).*G31))).*(tow11-(((xd(:,2).*tow11.*G11)+(xd(:,3).*tow21.*G21)+((1-xd(:,2)-xd(:,3)).*tow31.*G31))./((xd(:,2).*G11)+(xd(:,3).*G21)+((1-xd(:,2)-xd(:,3)).*G31))));
a3=((xd(:,3).*G12)./((xd(:,2).*G12)+(xd(:,3).*G22)+((1-xd(:,2)-xd(:,3)).*G32))).*(tow12-(((xd(:,2).*tow12.*G12)+(xd(:,3).*tow22.*G22)+((1-xd(:,2)-xd(:,3)).*tow32.*G32))./((xd(:,2).*G12)+(xd(:,3).*G22)+((1-xd(:,2)-xd(:,3)).*G32))));
a4=(((1-xd(:,2)-xd(:,3)).*G13)./((xd(:,2).*G13)+(xd(:,3).*G23)+((1-xd(:,2)-xd(:,3)).*G33))).*(tow13-(((xd(:,2).*tow13.*G13)+(xd(:,3).*tow23.*G23)+((1-xd(:,2)-xd(:,3)).*tow33.*G33))./((xd(:,2).*G13)+(xd(:,3).*G23)+((1-xd(:,2)-xd(:,3)).*G33))));
a5=((xd(:,2).*tow12.*G12)+(xd(:,3).*tow22.*G22)+((1-xd(:,2)-xd(:,3)).*tow32.*G32))./((xd(:,2).*G12)+(xd(:,3).*G22)+((1-xd(:,2)-xd(:,3)).*G32));
a6=((xd(:,2).*G21)./((xd(:,2).*G11)+(xd(:,3).*G21)+((1-xd(:,2)-xd(:,3)).*G31))).*(tow21-(((xd(:,2).*tow11.*G11)+(xd(:,3).*tow21.*G21)+((1-xd(:,2)-xd(:,3)).*tow31.*G31))./((xd(:,2).*G11)+(xd(:,3).*G21)+((1-xd(:,2)-xd(:,3)).*G31))));
a7=((xd(:,3).*G22)./((xd(:,2).*G12)+(xd(:,3).*G22)+((1-xd(:,2)-xd(:,3)).*G32))).*(tow22-(((xd(:,2).*tow12.*G12)+(xd(:,3).*tow22.*G22)+((1-xd(:,2)-xd(:,3)).*tow32.*G32))./((xd(:,2).*G12)+(xd(:,3).*G22)+((1-xd(:,2)-xd(:,3)).*G32))));
a8=(((1-xd(:,2)-xd(:,3)).*G23)./((xd(:,2).*G13)+(xd(:,3).*G23)+((1-xd(:,2)-xd(:,3)).*G33))).*(tow23-(((xd(:,2).*tow13.*G13)+(xd(:,3).*tow23.*G23)+((1-xd(:,2)-xd(:,3)).*tow33.*G33))./((xd(:,2).*G13)+(xd(:,3).*G23)+((1-xd(:,2)-xd(:,3)).*G33))));
gamma_one=exp(a1+a2+a3+a4);
gamma_two=exp(a5+a6+a7+a8);
yd=(xd(:,2).*gamma_one.*xd(:,4))+(xd(:,3).*gamma_two.*xd(:,5));
end

Please have a look into this code as i am stucked in this code since 2 months (probably it's hard to believe but it's true).

Hoping for a valuable response from all Dear ones.

Thanking you,

Ashish Kundaliya

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Alex Sha 2020-6-7

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Hello, Ashish, the result above was obtained by another software of 1stOpt, the code looks like below, very simple and easy for understanding, the he most notable advantages are that the guess of initial start-values is no longer required.

Constant alpha=0.3, tow11=0;
ConstStr
tow12=(a1+(a7/(xd1))),
tow13=(a2+(a8/(xd1))),
tow21=(a3+(a9/(xd1))),
tow22=0,
tow23=(a4+(a10/(xd1))),
tow31=(a5+(a11/(xd1))),
tow32=(a6+(a12/(xd1))),
tow33=0,
G11=exp(-alpha*tow11),
G12=exp(-alpha*tow12),
G13=exp(-alpha*tow13),
G21=exp(-alpha*tow21),
G22=exp(-alpha*tow22),
G23=exp(-alpha*tow23),
G31=exp(-alpha*tow31),
G32=exp(-alpha*tow32),
G33=exp(-alpha*tow33),
aa1=((xd2*tow11*G11)+(xd3*tow21*G21)+((1-xd2-xd3)*tow31*G31))/((xd2*G11)+(xd3*G21)+((1-xd2-xd3)*G31)),
aa2=((xd2*G11)/((xd2*G11)+(xd3*G21)+((1-xd2-xd3)*G31)))*(tow11-(((xd2*tow11*G11)+(xd3*tow21*G21)+((1-xd2-xd3)*tow31*G31))/((xd2*G11)+(xd3*G21)+((1-xd2-xd3)*G31)))),
aa3=((xd3*G12)/((xd2*G12)+(xd3*G22)+((1-xd2-xd3)*G32)))*(tow12-(((xd2*tow12*G12)+(xd3*tow22*G22)+((1-xd2-xd3)*tow32*G32))/((xd2*G12)+(xd3*G22)+((1-xd2-xd3)*G32)))),
aa4=(((1-xd2-xd3)*G13)/((xd2*G13)+(xd3*G23)+((1-xd2-xd3)*G33)))*(tow13-(((xd2*tow13*G13)+(xd3*tow23*G23)+((1-xd2-xd3)*tow33*G33))/((xd2*G13)+(xd3*G23)+((1-xd2-xd3)*G33)))),
aa5=((xd2*tow12*G12)+(xd3*tow22*G22)+((1-xd2-xd3)*tow32*G32))/((xd2*G12)+(xd3*G22)+((1-xd2-xd3)*G32)),
aa6=((xd2*G21)/((xd2*G11)+(xd3*G21)+((1-xd2-xd3)*G31)))*(tow21-(((xd2*tow11*G11)+(xd3*tow21*G21)+((1-xd2-xd3)*tow31*G31))/((xd2*G11)+(xd3*G21)+((1-xd2-xd3)*G31)))),
aa7=((xd3*G22)/((xd2*G12)+(xd3*G22)+((1-xd2-xd3)*G32)))*(tow22-(((xd2*tow12*G12)+(xd3*tow22*G22)+((1-xd2-xd3)*tow32*G32))/((xd2*G12)+(xd3*G22)+((1-xd2-xd3)*G32)))),
aa8=(((1-xd2-xd3)*G23)/((xd2*G13)+(xd3*G23)+((1-xd2-xd3)*G33)))*(tow23-(((xd2*tow13*G13)+(xd3*tow23*G23)+((1-xd2-xd3)*tow33*G33))/((xd2*G13)+(xd3*G23)+((1-xd2-xd3)*G33)))),
gamma_one=exp(aa1+aa2+aa3+aa4),
gamma_two=exp(aa5+aa6+aa7+aa8);
Variable xd(5),yd;
Parameter a(12);
Function yd=(xd2*gamma_one*xd4)+(xd3*gamma_two*xd5);
Data;
xd1=[313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15];
xd2=[0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182];
xd3=[0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818];
xd4=[7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36];
xd5=[0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316];
yd=[2.4,2.8,3.2,4.0,4.7,5.5,6.7,8.6,9.9,11.9,13.6,15.6,17.9,19.6,22.2,26.0,27.8,30.7,32.9,2.3,2.7,3.3,4.2,5.0,6.2,7.6,9.4,11.4,13.2,14.9,16.9,19.0,21.1,23.8,26.4,28.9,30.9,33.1,2.7,3.2,4.0,4.9,5.9,7.5,9.2,10.8,12.5,15.7,18.6,20.9,23.9,26.9,30.9,34.1,38.0,41.3,43.9,2.3,2.6,2.9,3.2,3.7,4.3,5.0,6.1,7.2,8.4,9.4,10.1,11.2,11.9,12.6,13.8,15.2,16.4,17.8,2.3,2.5,3.1,3.8,4.8,5.9,7.1,8.6,10.2,12.4,15,17.4,19.7,21.4,24.3,27.8,30.1,32.1,35,2.8,3.2,4.2,5.3,6.6,8.2,10.2,12.4,15.4,17.8,20.4,23.5,27.0,30.0,34.0,37.4,39.6,43.1,47.3,2.1,2.6,3.1,3.8,4.7,5.6,7.2,8.3,9.9,11.7,13.3,14.4,16.7,17.9,19.0,21.0,22.2,23.5,25.0,2.1,2.5,3.0,3.6,4.6,5.9,7.0,8.0,9.0,10.5,12.1,13.6,14.8,16.7,18.6,20.5,21.8,23.8,26.5,2.6,3.5,4.0,5.1,6.6,8.3,9.8,11.4,13.5,14.9,16.9,18.0,20.3,21.8,25.3,27.8,30.1,32.8,35.0,1.9,2.3,2.7,3.2,3.7,4.2,4.8,5.7,6.7,7.7,9.2,10.4,11.1,12.4,14.3,16.3,17.7,19.2,20.1,2.8,3.7,4.9,6.1,7.6,9.0,11.2,13.8,17.0,20.8,25.2,29.7,34.0,37.5,41.0,44.2,47.5,49.8,52.0,2.1,2.6,3.6,4.4,5.6,6.9,8.1,9.0,10.6,12.2,14.2,17.0,20.0,23.3,26.3,29.0,31.0,35.1,38.9];

Ashish Kundaliya 2020-6-7

Thanks for this assistance. But i found that 1stOpt is a paid version not a free version.! so how will i get that. can you have any idea about it.

I mean if you know any free software similar to 1stOpt then please suggest me that software and share appropriate code for that as well.

Sorry for this much inconvinience from you, but i have no choice other than regression.

Roei Shapira 2023-1-1

Hi Did you get an answer? Im facing the same problem

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Regression of my Experimental data for Ternary mixture into Non-randomness two liquid model (NRTL) thermodynamic model

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Regression of my Experimental data for Ternary mixture into Non-randomness two liquid model (NRTL) thermodynamic model

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