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Supercritical_indiv2.m
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function [] = Supercritical_indiv2(temp_indiv, press_indiv)
%% Specific Pressure and Temperature
%%Global Variables
%Structural/Geometric (cm)
ID_LSM = 20/10; %cm
ID_YSZ = ID_LSM + 2/10;
ID_NIYSZ = ID_YSZ + 0.040/10;
OD_NIYSZ = ID_NIYSZ + 0.150/10;
LENGTH_TUBE = 1800/10;
LSM_T = ID_YSZ - ID_LSM ;
YSZ_T = ID_NIYSZ - ID_YSZ ;
NIYSZ_T = OD_NIYSZ - ID_NIYSZ;
N_TUBES = 500;
VOLUME_TANK = 200*200*200; %cm3
VOLUME_OD_TUBE = ((OD_NIYSZ/2)^2)*3.14159*LENGTH_TUBE + 2*3.14159*((OD_NIYSZ/2)^2);
TOTAL_OD_VOL_TUBE = N_TUBES*VOLUME_OD_TUBE;
VOLUME_ID_TUBE = ((ID_LSM/2)^2)*3.14159*LENGTH_TUBE + 2*3.14159*((ID_LSM/2)^2);
TOTAL_ID_VOL_TUBE = N_TUBES*VOLUME_ID_TUBE;
VOLUME_CATHODIC = VOLUME_TANK - TOTAL_OD_VOL_TUBE;
VOLUME_ANODIC = TOTAL_ID_VOL_TUBE;
AREA_OD_TUBE = OD_NIYSZ*3.14159*LENGTH_TUBE + 2*3.14159*((OD_NIYSZ/2)^2);
TOTAL_OD_AREA_TUBE = N_TUBES*AREA_OD_TUBE;
%molar fractions of constituents
OXYGEN_ANODE = 0.9;
OXYGEN_CATHODE = 0.0; %assumption is that oxygen will be consumed immediately
%after formation therefore oxygen percentage would be negligible
M_water = 18.01528; %g/mol
M_hydro = 1.00794*2; %g/mol
load('workspace.mat')
membrane_characteristics
%temp_indiv %K
%press_indiv %MPa
filename = "Temp" + string(temp_indiv) + "_C_Press" + string(press_indiv) + "MPa";
B_Dissociation_indiv = zeros(999,1);
B_Ionic_indiv = zeros(999,1);
KINETIC_P_indiv = zeros(999,1);
P_O2c_indiv = zeros(999,1);
J_indiv = zeros(999,1);
NONIDEAL_P_indiv = zeros(999,1);
IDEAL_P_indiv = zeros(999,1);
nohmic_a = zeros(999,1);
nact_a = zeros(999,1);
nconH2_a = zeros(999,1);
nconO2_a = zeros(999,1);
%Setting Variables
%===============================================================================
row = round((temp_indiv - 20 - 273.15)/5);
col = round(press_indiv - 22);
P_indiv = POTENTIAL(col, row);
%Calculating K Factor
%===============================================================================
K_indiv = exp(GIBBS_FORMATION(col,row)*1000/(8.314*temp_indiv));
%Electronic Region Check
%===============================================================================
Min_950 = 10^(-16);
Max_950 = 10^7;
Min_650 = 10^(-31);
Max_650 = 10^12;
Min_l = Min_650 + ((Min_950 - Min_650)/(950-650))*(temp_indiv - (650 + 273.15));
Max_l = Max_650 + ((Max_950 - Max_650)/(950-650))*(temp_indiv - (650 + 273.15));
E_Dissoc_indiv = -(-2.84215 + 5.02487*10^(-4)*temp_indiv -1.23698*10^(-8)*temp_indiv^2); %negative because supplying voltage
for rxn_index = 1:1:999
rxn = rxn_index/1000;
%Mapping Thermodynamic Potential
%===============================================================================
[pot_ideal, non_ideal] = thermo__potentialb(rxn,OXYGEN_ANODE,temp_indiv,press_indiv,K_indiv);
IDEAL_P_indiv (rxn_index) = -pot_ideal; %negative because supplying voltage
NONIDEAL_P_indiv(rxn_index) = -non_ideal;
%Electronic Region Check
%===============================================================================
P_O2c_indiv(rxn_index) = sqrt(K_indiv)*(1 - rxn)/rxn;
if(P_O2c_indiv(rxn_index) < Min_l || P_O2c_indiv(rxn_index) > Max_l)
B_Ionic_indiv (rxn_index) = 0;
else
B_Ionic_indiv (rxn_index) = 1;
end
%Zirconia Dissociation Check
%===============================================================================
if(E_Dissoc_indiv < NONIDEAL_P_indiv(rxn_index))
B_Dissociation_indiv (rxn_index) = 1;
else
B_Dissociation_indiv (rxn_index) = 0;
end
J_indiv(rxn_index) = 2.50; %A/cm2 current density intitial convergence value
Pre_kinetic = NONIDEAL_P_indiv(rxn_index);
KINETIC_P_indiv(rxn_index) = -100; %just putting a case that would initiate the while loop.
SF_Dissociation = .8;
tol_C = .01; %in amps
tol_V = .1;
Top_J = 5.00;
Bot_J = 0.00;
criteria_kinetic_C = Top_J - Bot_J;
criteria_kinetic_V = abs((abs(Pre_kinetic + KINETIC_P_indiv(rxn_index)) - abs(E_Dissoc_indiv*(SF_Dissociation))));
while ((criteria_kinetic_C > tol_C) || (criteria_kinetic_V > tol_V))
%Mapping Kinetic Potential
%===============================================================================
[nohmic, nact, nconH2, nconO2, kinetic_pot] = kinetics(-J_indiv(rxn_index), ...
temp_indiv, press_indiv, rxn, ...
YSZ_T*10000, NIYSZ_T, LSM_T, ...
NIYSZ_Porosity, NIYSZ_Torosity, NIYSZ_radius, ...
LSM_Porosity, LSM_Torosity, LSM_radius, OXYGEN_ANODE);
if(isnan(kinetic_pot))
kinetic_pot = 100;
end
KINETIC_P_indiv(rxn_index) = kinetic_pot;
nohmic_a(rxn_index) = nohmic;
nact_a(rxn_index) = nact;
nconH2_a(rxn_index) = nconH2;
nconO2_a(rxn_index) = nconO2;
criteria_kinetic_C = (Top_J - Bot_J);
criteria_kinetic_V = abs((abs(Pre_kinetic + KINETIC_P_indiv(rxn_index)) - abs(E_Dissoc_indiv*(SF_Dissociation))));
if((criteria_kinetic_C > tol_C) || (criteria_kinetic_V > tol_V))
if(abs(Pre_kinetic + KINETIC_P_indiv(rxn_index)) > abs(E_Dissoc_indiv*(SF_Dissociation)))
Top_J = J_indiv(rxn_index);
else
Bot_J = J_indiv(rxn_index);
end
else
break
end
J_indiv(rxn_index) = (Bot_J + Top_J)/2;
end
end
%% Illustration of current + voltage subcomponents
figure(20)
pause(0.00001);
frame_h = get(handle(gcf),'JavaFrame');
set(frame_h,'Maximized',1);
X_rxn = 1/10:1/10:999/10;
Pot = zeros(999,1);
Zir = zeros(999,1);
for i = 1:length(Pot)
% set each element to 0
Pot(i) = P_indiv;
Zir(i) = E_Dissoc_indiv;
end
yyaxis left
title(['Voltage + Current at ' , num2str(temp_indiv), ' K & ' , num2str(press_indiv) , ' MPa'])
plot(X_rxn, Pot,'-g');
hold on
plot(X_rxn, NONIDEAL_P_indiv, '-r');
hold on
plot(X_rxn, NONIDEAL_P_indiv + KINETIC_P_indiv, '-b');
hold on
plot(X_rxn, NONIDEAL_P_indiv + nohmic_a, '--r');
hold on
plot(X_rxn, NONIDEAL_P_indiv + nohmic_a + nact_a, '--b');
hold on
plot(X_rxn, NONIDEAL_P_indiv + nohmic_a + nact_a + nconH2_a, '--m');
hold on
plot(X_rxn, NONIDEAL_P_indiv + nohmic_a + nact_a + nconH2_a + nconO2_a, '--c');
hold on
l2 = plot(X_rxn,Zir, ':r');
set(l2,'linewidth',2);
hold on
xlabel('Reaction Completion [%]') % x-axis label
ylabel('Potential [V]') % y-axis label
set(gca,'XLim',[0 100])
set(gca,'XTick',(0:10:100))
set(gca,'YLim',[0 3.5])
set(gca,'YTick',(0:.5:(-3.5)))
yyaxis right
l1 = plot(X_rxn,J_indiv,'-b');
set(l1,'linewidth',2);
ylabel('Current [A/cm^2]') % y-axis label
set(gca,'YLim',[0 max(J_indiv)*1.5])
set(gca,'YTick',(0:.5:max(J_indiv)*1.5))
legend('Thermodynamic','Non-Ideal Thermo Addition', 'Kinetic Addition',...
'Ohmic Resistance', 'Activation Polarization', 'Hydrogen Concentration Polar.',...
'Oxygen Concentration Polar.','Zirconia Dissociation','Current Density')
hold off
saveas(gcf,'Current&Voltage_Rxn_' + filename,'fig')
saveas(gcf,'Current&Voltage_Rxn_' + filename,'png')
%% I-V CURVES
KINETIC_P_indiv2 = zeros(100,3);
P_O2c_indiv2 = zeros(100,3);
J_indiv2 = zeros(100,3);
NONIDEAL_P_indiv2 = zeros(100,3);
IDEAL_P_indiv2 = zeros(100,3);
nohmic_a2 = zeros(100,3);
nact_a2 = zeros(100,3);
nconH2_a2 = zeros(100,3);
nconO2_a2 = zeros(100,3);
for J_index = 1:1:100
for rxn_index2 = 1:1:3
J2 = (-49+(J_index-1));
rxn2 = ((rxn_index2-1)*49 + 1)/100;
J_indiv2(J_index, rxn_index2) = J2;
[pot_ideal, non_ideal] = thermo__potentialb(rxn2,OXYGEN_ANODE,temp_indiv,press_indiv,K_indiv);
IDEAL_P_indiv2 (J_index, rxn_index2) = pot_ideal;
NONIDEAL_P_indiv2(J_index, rxn_index2) = non_ideal;
%Mapping Kinetic Potential
%===============================================================================
[nohmic, nact, nconH2, nconO2, kinetic_pot] = kinetics(J2, temp_indiv, press_indiv, rxn2, ...
YSZ_T*10000, NIYSZ_T, LSM_T, ...
NIYSZ_Porosity, NIYSZ_Torosity, NIYSZ_radius, ...
LSM_Porosity, LSM_Torosity, LSM_radius, OXYGEN_ANODE);
KINETIC_P_indiv2(J_index, rxn_index2) = kinetic_pot;
nohmic_a2(J_index, rxn_index2) = nohmic;
nact_a2 (J_index, rxn_index2) = nact;
nconH2_a2(J_index, rxn_index2) = nconH2;
nconO2_a2(J_index, rxn_index2) = nconO2;
end
end
%%
figure (997)
pause(0.00001);
frame_h = get(handle(gcf),'JavaFrame');
set(frame_h,'Maximized',1);
Pot2 = zeros(100,1);
Zir2 = zeros(100,1);
for i = 1:length(Pot2)
% set each element to 0
Pot2(i) = P_indiv;
Zir2(i) = E_Dissoc_indiv;
end
title(['Voltage vs Current at ' , num2str(temp_indiv), ' K & ' , num2str(press_indiv) , ' MPa'])
plot(Pot2, J_indiv2(:,2),'-g');
hold on
plot(NONIDEAL_P_indiv2(:,2), J_indiv2(:,2), '-r');
hold on
plot(NONIDEAL_P_indiv2(:,2) + KINETIC_P_indiv2(:,2), J_indiv2(:,2), '-b');
hold on
plot(NONIDEAL_P_indiv2(:,2) + nohmic_a2(:,2), J_indiv2(:,2), '--r');
hold on
plot(NONIDEAL_P_indiv2(:,2) + nohmic_a2(:,2) + nact_a2(:,2), J_indiv2(:,2),'--b');
hold on
plot(NONIDEAL_P_indiv2(:,2) + nohmic_a2(:,2) + nact_a2(:,2) + nconH2_a2(:,2), J_indiv2(:,2), '--m');
hold on
plot(NONIDEAL_P_indiv2(:,2) + nohmic_a2(:,2) + nact_a2(:,2) + nconH2_a2(:,2) + nconO2_a2(:,2), J_indiv2(:,2),'--c');
hold on
l2 = plot(Zir2, J_indiv2(:,2), ':r');
%set(l2,'linewidth',2);
%set(gca,'XLim',[-5 5])
%set(gca,'XTick',((-5):.25:5))
%set(gca,'YLim',[-5 5])
%set(gca,'YTick',((-5):.25:5))
hold on
line(xlim(), [0,0], 'LineWidth', .5, 'Color', 'k');
hold on
line(ylim(), [0,0], 'LineWidth', .5, 'Color', 'k');
hold on
xlabel('Potential [V]') % x-axis label
ylabel('Current [A/cm^2]') % y-axis label
legend('Thermodynamic','Non-Ideal Thermo Addition', 'Kinetic Addition',...
'Ohmic Resistance', 'Activation Polarization', 'Hydrogen Concentration Polar.',...
'Oxygen Concentration Polar.','Zirconia Dissociation')
hold off
saveas(gcf,'VoltagevCurrent_Whole_' + filename,'fig')
saveas(gcf,'VoltagevCurrent_Whole_' + filename,'png')
%%
figure (998)
pause(0.00001);
frame_h = get(handle(gcf),'JavaFrame');
set(frame_h,'Maximized',1);
index_r = 1;
Pot2 = zeros(100,1);
Zir2 = zeros(100,1);
for i = 1:length(Pot2)
% set each element to 0
Pot2(i) = P_indiv;
Zir2(i) = E_Dissoc_indiv;
end
title(['Voltage vs Current at ' , num2str(temp_indiv), ' K & ' , num2str(press_indiv) , ' MPa'])
plot(Pot2, J_indiv2(:,index_r), '-g');
hold on
plot(NONIDEAL_P_indiv2(:,index_r), J_indiv2(:,index_r), '-r');
hold on
plot(KINETIC_P_indiv2(:,index_r), J_indiv2(:,index_r), '-b');
hold on
plot(nohmic_a2(:,index_r), J_indiv2(:,index_r), '--r');
hold on
plot(nact_a2(:,index_r), J_indiv2(:,index_r), '--b');
hold on
plot(nconH2_a2(:,index_r), J_indiv2(:,index_r), '--m');
hold on
plot(nconO2_a2(:,index_r), J_indiv2(:,index_r), '--c');
hold on
l2 = plot(Zir2, J_indiv2(:,index_r), ':r');
set(l2,'linewidth',2);
set(gca,'XLim',[-5 5])
set(gca,'XTick',((-5):.25:5))
set(gca,'YLim',[-5 5])
set(gca,'YTick',((-5):.25:5))
hold on
xlabel('Potential [V]') % x-axis label
ylabel('Current [A/cm^2]') % y-axis label
legend('Thermodynamic','Non-Ideal Thermo Addition', 'Kinetic Addition',...
'Ohmic Resistance', 'Activation Polarization', 'Hydrogen Concentration Polar.',...
'Oxygen Concentration Polar.','Zirconia Dissociation')
hold off
saveas(gcf,'VoltagevCurrent_Comp_' + filename,'fig')
saveas(gcf,'VoltagevCurrent_Comp_' + filename,'png')
%% Reaction Completion Dependency
figure (999)
pause(0.00001);
frame_h = get(handle(gcf),'JavaFrame');
set(frame_h,'Maximized',1);
Pot2 = zeros(100,1);
Zir2 = zeros(100,1);
for i = 1:length(Pot2)
% set each element to 0
Pot2(i) = P_indiv;
Zir2(i) = E_Dissoc_indiv;
end
title(['Voltage vs Current at ' , num2str(temp_indiv), ' K & ' , num2str(press_indiv) , ' MPa'])
plot(NONIDEAL_P_indiv2(:,1) + nohmic_a2(:,1) + nact_a2(:,1) + nconH2_a2(:,1) + nconO2_a2(:,1), J_indiv2(:,1),'--r');
hold on
plot(NONIDEAL_P_indiv2(:,2) + nohmic_a2(:,2) + nact_a2(:,2) + nconH2_a2(:,2) + nconO2_a2(:,2), J_indiv2(:,2),'--b');
hold on
plot(NONIDEAL_P_indiv2(:,3) + nohmic_a2(:,3) + nact_a2(:,3) + nconH2_a2(:,3) + nconO2_a2(:,3), J_indiv2(:,3),'--m');
hold on
l2 = plot(Zir2, J_indiv2(:,2), ':r');
set(l2,'linewidth',2);
set(gca,'XLim',[-3 3])
set(gca,'XTick',((-3):.25:3))
hold on
line(xlim(), [0,0], 'LineWidth', .5, 'Color', 'k');
hold on
line(ylim(), [0,0], 'LineWidth', .5, 'Color', 'k');
hold on
xlabel('Potential [V]') % x-axis label
ylabel('Current [A/cm^2]') % y-axis label
legend('0.1% Reaction', '50.0% Reaction', '99.9% Reaction','Zirconia Dissociation')
hold off
saveas(gcf,'VoltagevCurrent_RxnV_' + filename,'fig')
saveas(gcf,'VoltagevCurrent_RxnV_' + filename,'png')
%% Energy Post Processing
%Start of Reaction
rxn_initial = .05;
rxn_final = .999;
%Calculation of Energy Produced by Reaction
Final_Voltage = Pot + NONIDEAL_P_indiv + KINETIC_P_indiv;
Final_Current = J_indiv*TOTAL_OD_AREA_TUBE;
Final_Power = -Final_Current.*Final_Voltage;
figure(23)
pause(0.00001);
frame_h = get(handle(gcf),'JavaFrame');
set(frame_h,'Maximized',1);
title(['Power at ' , num2str(temp_indiv), ' K & ' , num2str(press_indiv) , ' MPa'])
plot(X_rxn,Final_Power, '-r');
xlabel('Reaction Completion [%]') % x-axis label
ylabel('Power [J]') % y-axis label
hold on
density_indiv_w = W_DENSITY(col, row);
density_indiv_h = H_DENSITY(col, row); %mol/L
i_moles_water = (VOLUME_CATHODIC*(rxn_final-rxn_initial)/1000)*density_indiv_w;
%starting moles of water at the beginning of the reaction
Reduced_Scope_Power = Final_Power((rxn_initial*1000):(rxn_final*1000));
Reduced_Scope_Rxn = X_rxn((rxn_initial*1000):(rxn_final*1000));
Reduced_Scope_Current = Final_Current((rxn_initial*1000):(rxn_final*1000));
Averaged_Power = trapz(Reduced_Scope_Rxn,Reduced_Scope_Power)/(rxn_final-rxn_initial);
Averaged_Current = trapz(Reduced_Scope_Rxn, Reduced_Scope_Current)/(rxn_final-rxn_initial);
%1 Ampere = 1 Coloumb/second
charge_e = 1.60217662*10^(-19); %coloumbs/electron
Time_Compl = (i_moles_water*6.022*10^23*2)/(Averaged_Current/charge_e);%seconds
Total_Energy = Averaged_Power*Time_Compl; %Joule
Normalized_Energy = Total_Energy/i_moles_water;
resultant_bottling_pressure = bottling_benefit(temp_indiv,press_indiv);
%MPa
txt = {'Time to Completion: ' + string(round(Time_Compl,3,'significant')) + ' secs',...
'Total Energy: ' + string(round(Total_Energy,3,'significant'))+ ' Joule',...
'Noramalized Energy: ' + string(round(Normalized_Energy,3,'significant')) + ' Joule/mol'};
text(10,.2*max(Final_Power),txt,'FontSize',12)
hold off
saveas(gcf,'Power_Rxn_' + filename,'fig')
saveas(gcf,'Power_Rxn_' + filename,'png')
%% Calculate How Much Energy Required From Bringing Hydrogen Gas to Required Pressure
%====================================================================================
Energy_Compression = -8.314*(273.15 + 25)*ln(0.101325/resultant_bottling_pressure);
%Results are in Joules
%This is the ideal amount of energy required to pressure hydrogen gas to
%its bottled form. If the conclusions to
%% Calculate Heat Transfer Loss from Tank (basic heat transfer model)
%====================================================================================
%this will assume that the tank is a sphere assuming basic effeciencies
%expected from that size
save(filename)
end