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Error_analysis.m
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clear all, clc
close all
load('datamix.mat')
set(groot,'defaultLineMarkerSize', 10, ...
'defaultLineLineWidth', 2, ...
'defaultAxesFontName', 'Times');
global R
R = 0.0831446261815324; % L bar / K mol
T_data = [230, 250, 270]; % K
% CH4: species 1
Tc1 = 190.564; % K
Pc1 = 45.992; % bar
Dc1 = 10.139; % mol/L
Vc1 = 1/Dc1; % L/mol
w1 = 0.01142;
% CO2: species 2
Tc2 = 304.21;
Pc2 = 73.829955;
Dc2 = 10.6249;
Vc2 = 1/Dc2;
w2 = 0.22394;
VLE = figure('Position',[0 10000 500 1000]);
plotsettings = {'interpreter','latex','fontsize',14};
% dataset{3,1} = dataset{3,1}([1:7,9:10],:);
n_point = [14,10,9];
% k12_me_SRK = [0.1523, 0.1294, 0.1321];
% k12_me_SRK = [0.1523, 0.1294, 0.11];
% k12_me_PR = [0.1670, 0.1459, 0.1462];
k12_me_PR = [0.1670, 0.1459, 0.13];
for Ti = 1:3
clear P_res y1_res
T = T_data(Ti);
Tr1 = T/Tc1;
Tr2 = T/Tc2;
Tr = (Tr1+Tr2)/2;
fprintf('\n< T = %d K >',T)
% [Omega, Ksi, eps, sig, alpha1, alpha2] = vdW;
[Omega, Ksi, eps, sig, alpha1, alpha2] = PR(Tr1,Tr2,w1,w2);
% [Omega, Ksi, eps, sig, alpha1, alpha2] = SRK(Tr1,Tr2,w1,w2);
% k12 = k12_me_SRK(Ti);
% k12 = 0.0919;
% k12 = 0.05818 + 0.04117*Tr
% k12 = 0.5219 - 0.8254*Tr + 0.4494*Tr^3;
k12 = k12_me_PR(Ti);
% k12 = 0;
a1 = Ksi*alpha1*R^2*Tc1^2/Pc1;
a2 = Ksi*alpha2*R^2*Tc2^2/Pc2;
a12 = (1-k12)*a1^(1/2)*a2*(1/2);
b1 = Omega*R*Tc1/Pc1;
b2 = Omega*R*Tc2/Pc2;
for k = 1:n_point(Ti)
x1 = dataset{Ti}(k+1,1);
x2 = 1 - x1;
if k == 1
P_new(1) = 5;
y1_new(1) = 0.1;
else
P_new(1) = P_res(k-1);
y1_new(1) = y1_res(k-1);
end
power = -0.5;
for j = 1:10000
P = P_new(j);
y1 = y1_new(j);
parameters = [a1, a2, a12, b1, b2, eps, sig];
[K(j), y1_new(j+1)] = K_converge(T, x1, P, y1, parameters);
% fprintf('%.10f\n',K(j))
if j > 1
if ( K(j) -1 )*( K(j-1) -1 ) < 0
power = power - 0.5;
end
end
if abs( K(j) - 1 ) < 10^(-10)
P_res(k) = P_new(j);
y1_res(k) = y1_new(j+1);
break
elseif K(j) > 1
P_new(j + 1) = P + 10^power;
elseif K(j) < 1
P_new(j + 1) = P - 10^power;
end
if j == 10000
fprintf('shit\n')
end
end
end
subplot(3,1,Ti)
plot(dataset{Ti}(:,1),dataset{Ti}(:,3),'.'); hold on
plot(dataset{Ti}(:,2),dataset{Ti}(:,3),'.');
plot(dataset{Ti}(2:1+n_point(Ti),1),P_res,'-');
plot(y1_res,P_res);
axis([0 1 0 100])
pbaspect([1 1 1])
xlabel('$x_{\mathrm{CH_4}}$, $y_{\mathrm{CH_4}}$','Interpreter','latex')
ylabel('$P$ ${\mathrm {[bar]}}$','Interpreter','latex')
P_error{Ti} = 100 * abs( (P_res' - dataset{Ti}(2:1+n_point(Ti),3)) ./dataset{Ti}(2:1+n_point(Ti),3) );
y1_error{Ti} = 100 * abs( (y1_res' - dataset{Ti}(2:1+n_point(Ti),2)) ./dataset{Ti}(2:1+n_point(Ti),2) );
error{Ti} = sqrt(P_error{Ti}.^2 + y1_error{Ti}.^2);
end
error{3}
fprintf('\n 230K: y1 AARD = %5.2f %%', mean(y1_error{1}))
fprintf('\n 250K: y1 AARD = %5.2f %%', mean(y1_error{2}))
fprintf('\n 270K: y1 AARD = %5.2f %%\n', mean(y1_error{3}))
fprintf('\n 230K: P AARD = %5.2f %%', mean(P_error{1}))
fprintf('\n 250K: p AARD = %5.2f %%', mean(P_error{2}))
fprintf('\n 270K: P AARD = %5.2f %%\n', mean(P_error{3}))
fprintf('\n 230K: RMSE = %5.2f %%', mean(error{1}))
fprintf('\n 250K: RMSE = %5.2f %%', mean(error{2}))
fprintf('\n 270K: RMSE = %5.2f %%\n', mean(error{3}))
function [Omega, Ksi, eps, sig, alpha1, alpha2] = vdW
eps = 0;
sig = 0;
alpha1 = 1;
alpha2 = 1;
Omega = 1/8;
Ksi = 27/64;
end
function [Omega, Ksi, eps, sig, alpha1, alpha2] = SRK(Tr1,Tr2,w1,w2)
eps = 0;
sig = 1;
alpha1 = ( 1 + (0.480 + 1.574*w1 - 0.176*w1^2) * (1 - Tr1^(0.5)) )^2;
alpha2 = ( 1 + (0.480 + 1.574*w2 - 0.176*w2^2) * (1 - Tr2^(0.5)) )^2;
Omega = 0.08664;
Ksi = 0.42748;
end
function [Omega, Ksi, eps, sig, alpha1, alpha2] = PR(Tr1,Tr2,w1,w2)
eps = 1-sqrt(2);
sig = 1+sqrt(2);
alpha1 = (1+(0.37464+1.57226*w1-0.26992*w1^2)*(1-Tr1^(1/2)))^2;
alpha2 = (1+(0.37464+1.57226*w2-0.26992*w2^2)*(1-Tr2^(1/2)))^2;
Omega = 0.07780;
Ksi = 0.45724;
end
function Z_out = Zv_CEOS(eps,sig,beta,q)
Z = roots([1 ...
( (eps+sig)*beta - 1 - beta ) ...
( eps*sig*beta^2 - (eps+sig)*beta - (eps+sig)*beta^2 + q*beta) ...
( - eps*sig*beta^2 - eps*sig*beta^3 - q*beta^2) ]);
Zi = Z==real(Z);
Z_real = Z(Zi);
Z_out = max(Z_real);
end
function Z_out = Zl_CEOS(eps,sig,beta,q)
Z = roots([1 ...
( (eps+sig)*beta - 1 - beta ) ...
( eps*sig*beta^2 - (eps+sig)*beta - (eps+sig)*beta^2 + q*beta) ...
( - eps*sig*beta^2 - eps*sig*beta^3 - q*beta^2) ]);
Zi = Z==real(Z);
Z_real = Z(Zi);
Z_out = min(Z_real);
end
function [K_res, y1_res] = K_converge(T, x1, P, y1_in, parameters)
global R
y1_new(1) = y1_in;
x2 = 1 - x1;
a1 = parameters(1);
a2 = parameters(2);
a12 = parameters(3);
b1 = parameters(4);
b2 = parameters(5);
eps = parameters(6);
sig = parameters(7);
for i = 1:100
y1 = y1_new(i);
y2 = 1 - y1;
% fprintf('with y1 = %.4f:\n', y1)
a_l = x1^2*a1 + 2*x1*x2*a12 + x2^2*a2;
a_v = y1^2*a1 + 2*y1*y2*a12 + y2^2*a2;
b_l = x1*b1 + x2*b2;
b_v = y1*b1 + y2*b2;
beta_l = b_l*P/(R*T);
beta_v = b_v*P/(R*T);
q_l = a_l/(b_l*R*T);
q_v = a_v/(b_v*R*T);
qbar1_l = q_l*( (2*x1*a1 + 2*x2*a12)/a_l - b1/b_l );
qbar2_l = q_l*( (2*x2*a2 + 2*x1*a12)/a_l - b2/b_l );
qbar1_v = q_v*( (2*y1*a1 + 2*y2*a12)/a_v - b1/b_v );
qbar2_v = q_v*( (2*y2*a2 + 2*y1*a12)/a_v - b2/b_v );
Z_l = Zl_CEOS(eps, sig, beta_l, q_l);
Z_v = Zv_CEOS(eps, sig, beta_v, q_v);
I_l = I_calc(eps, sig, beta_l, Z_l);
I_v = I_calc(eps, sig, beta_v, Z_v);
phi1_l = exp( (b1/b_l)*(Z_l - 1) - log(Z_l - beta_l) - qbar1_l*I_l);
phi2_l = exp( (b2/b_l)*(Z_l - 1) - log(Z_l - beta_l) - qbar2_l*I_l);
phi1_v = exp( (b1/b_v)*(Z_v - 1) - log(Z_v - beta_v) - qbar1_v*I_v);
phi2_v = exp( (b2/b_v)*(Z_v - 1) - log(Z_v - beta_v) - qbar2_v*I_v);
K1 = phi1_l/phi1_v;
K2 = phi2_l/phi2_v;
K(i) = K1*x1 + K2*x2;
y1_new(i + 1) = (K1*x1) / (K1*x1 + K2*x2);
% fprintf('%.5f %.5f, %d\n', y1_new(i), K(i), i);
if i > 1
if abs ( (K(i)-K(i-1)) / K(i-1)) < 10^(-10)
% fprintf('%d\n',i)
break
end
end
end
K_res = K(i);
y1_res = y1_new(i);
function I = I_calc(eps, sig, beta, Z)
if sig == eps
I = beta/(Z+eps*beta);
else
I = (1/(sig - eps)) * (log((Z + sig*beta)/(Z + eps*beta)));
end
end
end