diff --git a/autodiff/compositional/examples/equilbrium/exampleVLECO2H2O.m b/autodiff/compositional/examples/equilbrium/exampleVLECO2H2O.m
new file mode 100644
index 000000000..539d05743
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+++ b/autodiff/compositional/examples/equilbrium/exampleVLECO2H2O.m
@@ -0,0 +1,118 @@
+%% C02-H2O Vapor-Liquid Equilibrium Calculations
+% This MRST example calculates the vapor-liquid equilibrium (VLE) for a CO2-water
+% mixture under varying conditions using a thermodynamic equation of state.
+% Two EoS models are used: Peng-Robinson and Soreide-Whitson.
+% Then we compare the Solubility of CO2 in water and NaCl brine obtained
+% with both EoS models.
+% Author: [Stéphanie Delage Santacreu]
+% Date: [16/09/2025]
+% Organization: [Université de Pau et des Pays de l'Adour, E2S UPPA, CNRS, LFCR, UMR5150, Pau, France]
+% ---------------------------------------------------------------------------
+
+clear; clc;
+
+% Add necessary MRST modules
+mrstModule add h2-biochem compositional ad-blackoil ad-core ad-props mrst-gui
+
+%% Define Composition Mixture
+% Create a compositional mixture with water and carbon dioxide components
+compFluid = TableCompositionalMixture({'Water', 'CarbonDioxide'}, {'H2O', 'CO2'});
+disp(compFluid);
+%% Initialize Thermodynamic Model
+% Choose an equation of state model for the calculations
+eosNamesw = 'sw'; % Soreide-Whitson (SW) model
+eosModelsw = EquationOfStateModel([], compFluid, eosNamesw);
+
+eosNamepr = 'pr'; % Peng Robinson (PR) model
+eosModelpr = EquationOfStateModel([], compFluid, eosNamepr);
+
+%% Define Test Case Parameters
+% Set the test case for different pressures, temperatures, and salinity levels
+z0 = [0.8, 0.2]; % Initial composition
+caseTest = 4; % Choose the test case here
+
+switch caseTest %Source: Thermodynamic study of the CO2-H2O system, S.Chabab (https://hal.science/hal-02310963v1,2019)
+    case 1
+        eosModel.msalt=1.13;
+        Temp=[323.02, 322.97, 323.03, 323.04, 372.33, 372.31, 372.29, 372.29, 372.25]*Kelvin;
+        pres=[53.450, 75.550, 100.350, 145.080, 31.148, 60.500, 108.840, 151.920, 191.980]*barsa;
+        xliqCO2Exp=[0.01030, 0.01290, 0.01510, 0.01700,0.00390, 0.00750, 0.01130, 0.01360, 0.01570];
+
+
+    case 2
+        eosModel.msalt=1;
+        Temp=[373.38, 373.37, 373.41]*Kelvin;
+        pres=[16.983, 32.527, 68.182]*barsa;
+        xliqCO2Exp=[0.00237, 0.00426, 0.00833];
+
+    case 3
+        eosModel.msalt=3.01;
+        Temp=[342.82, 342.81, 342.82, 372.39, 372.42, 372.41 , 372.43, 372.45, 372.45]*Kelvin;
+        pres=[30.391, 72.559, 100.910, 25.556, 71.417, 100.517, 152.433, 199.597, 229.817]*barsa;
+        xliqCO2Exp=[0.00441, 0.00880, 0.01057, 0.00292, 0.00707, 0.00878, 0.01141, 0.01258, 0.01337];
+
+    case 4
+        eosModel.msalt=0;
+        Temp=[323.2, 323.2, 323.2, 323.2, 323.2, 323.2, 333.2, 333.2, 333.2,...
+            333.2, 333.2, 333.2, 353.1, 353.1, 353.1, 353.1, 353.1, 353.1]*Kelvin;
+        pres=[40.5, 60.6, 80.8, 100.9, 121, 141.1, 40.5, 60.6, 80.8, 100.9,...
+            121, 141.1, 40.5, 60.6, 80.8, 100.9, 121, 131]*barsa;
+        xliqCO2Exp=[0.0109, 0.0161, 0.019, 0.0205, 0.0214, 0.0217, 0.0096,...
+            0.0138, 0.0166, 0.0186, 0.0201, 0.0208, 0.008, 0.0114, 0.014, ...
+            0.016, 0.0176, 0.0184];
+
+end
+
+
+%% Perform Flash Calculations
+% Determine the liquid-phase hydrogen fraction (xliqH2) for each condition
+nc = numel(pres);
+namecp = eosModelsw.getComponentNames();
+indCO2=find(strcmp(namecp,'CO2'));
+indH2O= find(strcmp(namecp,'H2O'));
+
+[Lsw, xsw, ~] = standaloneFlash(pres, Temp, z0, eosModelsw);
+[Lpr, xpr, ~] = standaloneFlash(pres, Temp, z0, eosModelpr);
+xliqCO2sw=xsw(:,indCO2);
+xliqCO2pr=xpr(:,indCO2);
+
+
+
+%% calculate and display the errors models vs experiments
+errorSWexp=abs(xliqCO2sw-xliqCO2Exp')./xliqCO2Exp';
+errorPRexp=abs(xliqCO2pr-xliqCO2Exp')./xliqCO2Exp';
+
+fprintf('Errormax SW-Experiment: %12.8f, Errormax PR-Experiment: %12.8f\n', max(errorSWexp), max(errorPRexp));
+fprintf('Errormin SW-Experiment: %12.8f, Errormin PR-Experiment: %12.8f\n', min(errorSWexp), min(errorPRexp));
+fprintf('Errormean SW-Experiment: %12.8f, Errormean PR-Experiment: %12.8f\n', mean(errorSWexp), mean(errorPRexp));
+
+%% plot the results
+plotEosPRSW(pres,xliqCO2Exp,xliqCO2sw,xliqCO2pr)
+
+%% Copyright notice
+
+% <html>
+% <p><font size="-1">
+% Copyright 2009-2025 SINTEF Digital, Mathematics & Cybernetics.
+% </font></p>
+% <p><font size="-1">
+% This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).
+% </font></p>
+% <p><font size="-1">
+% MRST is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% </font></p>
+% <p><font size="-1">
+% MRST is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% </font></p>
+% <p><font size="-1">
+% You should have received a copy of the GNU General Public License
+% along with MRST.  If not, see
+% <a href="http://www.gnu.org/licenses/">http://www.gnu.org/licenses</a>.
+% </font></p>
+% </html>
\ No newline at end of file
diff --git a/autodiff/compositional/examples/equilbrium/exampleVLEH2H2O.m b/autodiff/compositional/examples/equilbrium/exampleVLEH2H2O.m
new file mode 100644
index 000000000..50f896637
--- /dev/null
+++ b/autodiff/compositional/examples/equilbrium/exampleVLEH2H2O.m
@@ -0,0 +1,123 @@
+%% H2-H2O Vapor-Liquid Equilibrium Calculations
+% This MRST example calculates the vapor-liquid equilibrium (VLE) for a hydrogen-water
+% mixture under varying conditions using a thermodynamic equation of state.
+% Two EoS models are used: Peng-Robinson and Soreide-Whitson.
+% Then we compare the Solubility of H2 in water and NaCl brine obtained
+% with both EoS models
+% Author: [Stéphanie Delage Santacreu]
+% Date: [16/09/2025]
+% Organization: [Université de Pau et des Pays de l'Adour, E2S UPPA, CNRS, LFCR, UMR5150, Pau, France]
+% ---------------------------------------------------------------------------
+
+clear; clc;
+
+% Add necessary MRST modules
+mrstModule add h2-biochem compositional ad-blackoil ad-core ad-props mrst-gui
+
+%% Define Composition Mixture
+% Create a compositional mixture with water and hydrogen components
+compFluid = TableCompositionalMixture({'Water', 'Hydrogen'}, {'H2O', 'H2'});
+disp(compFluid);
+
+%% Initialize Thermodynamic Model
+% Choose an equation of state model for the calculations
+eosNamesw = 'sw'; % Soreide-Whitson (SW) model
+eosModelsw = EquationOfStateModel([], compFluid, eosNamesw);
+
+eosNamepr = 'pr'; % Peng Robinson (PR) model
+eosModelpr = EquationOfStateModel([], compFluid, eosNamepr);
+
+%% Define Test Case Parameters
+% Set the test case for different pressures, temperatures, and salinity levels
+z0 = [0.8, 0.2]; % Initial composition
+caseTest = 1; % Choose the test case here
+
+switch caseTest
+    case 1 %sources: Solubility of H2 in water and NaCl brine under subsurface
+        % storage conditions (https://hal.science/hal-04623907v1, 2023)
+        eosModelsw.msalt=0;
+        pres=[100.01, 150.01, 200.01, 200.01, 101.11, 101.31, 130.01,...
+            165.01, 199.91, 200.11, 100.01, 100.01, 100.01, 175.11]*barsa;
+        Temp=[298.20,298.05,298.15,298.15,323.55,323.50,323.85,323.55,...
+            323.30,323.35,373.85,373.80,373.85,373.65]*Kelvin;
+        xliqH2Exp=[0.00135994,0.00199679,0.00264397,0.00263320,0.00125091,...
+            0.00123925,0.00159253,0.00201117,0.00244186,0.00245479,...
+            0.00142471,0.00140332,0.00140893,0.00243347];
+
+    case 2
+        eosModelsw.msalt=1;
+        Temp=[298.20,298.30,298.15,298.30,323.20,323.40,323.35,323.20,...
+            323.30,323.30,323.20,373.25,373.40,373.10,373.15,373.45,373.15,373.00];
+        pres=[100.71,150.01,150.01,200.01,100.31,100.61,101.01,150.06,...
+            175.01,199.91,200.01,100.11,126.01,150.36,150.46,150.71,175.51,200.46]*barsa;
+        xliqH2Exp=[0.00107012,0.00159298,0.00161244,0.00213575,0.00102099,...
+            0.00102078,0.00102426,0.00151377,0.00176728,0.00202590,...
+            0.00204487,0.00119671,0.00148492,0.00175595,0.00179573,...
+            0.00177350,0.00204000,0.00234604];
+    case 3
+        eosModelsw.msalt=2;
+        Temp=[298.15,298.05,298.05,323.20,323.40,323.35,323.40,373.05,373.20,373.40];
+        pres=[100.01,150.01,200.01,100.01,150.01,150.01,200.01,100.01,150.01,200.51]*barsa;
+        xliqH2Exp=[0.00088640,0.00132235,0.00171848,0.00088260,0.00131242,...
+            0.00128912,0.00172402, 0.00099379, 0.00151866, 0.00205031 ];
+    case 4
+        eosModelsw.msalt=4;
+        Temp=[298.20, 298.20, 298.15, 323.30, 323.40, 323.40, 373.25, 373.35, 373.15];
+        pres=[100.01, 150.01, 200.01, 100.01, 150.01, 200.01, 100.01, 150.01, 200.01]*barsa;
+        xliqH2Exp=[0.00059422, 0.00093595, 0.00121838, 0.00061736, ...
+            0.00095752, 0.00129237, 0.00077991, 0.00114509, 0.00157469];
+end
+
+
+%% Perform Flash Calculations
+% Determine the liquid-phase hydrogen fraction (xliqH2) for each condition
+nc = numel(pres);
+namecp = eosModelsw.getComponentNames();
+indH2=find(strcmp(namecp,'H2'));
+indH2O= find(strcmp(namecp,'H2O'));
+
+[Lsw, xsw, ~] = standaloneFlash(pres, Temp, z0, eosModelsw);
+[Lpr, xpr, ~] = standaloneFlash(pres, Temp, z0, eosModelpr);
+xliqH2sw=xsw(:,indH2);
+xliqH2pr=xpr(:,indH2);
+
+
+
+%% calculate and display the errors models vs experiments
+errorSWexp=abs(xliqH2sw-xliqH2Exp')./xliqH2Exp';
+errorPRexp=abs(xliqH2pr-xliqH2Exp')./xliqH2Exp';
+
+fprintf('Errormax SW-Experiment: %12.8f, Errormax PR-Experiment: %12.8f\n', max(errorSWexp), max(errorPRexp));
+fprintf('Errormin SW-Experiment: %12.8f, Errormin PR-Experiment: %12.8f\n', min(errorSWexp), min(errorPRexp));
+fprintf('Errormean SW-Experiment: %12.8f, Errormean PR-Experiment: %12.8f\n', mean(errorSWexp), mean(errorPRexp));
+
+%% plot the results
+plotEosPRSW(pres,xliqH2Exp,xliqH2sw,xliqH2pr)
+
+%% Copyright notice
+
+% <html>
+% <p><font size="-1">
+% Copyright 2009-2025 SINTEF Digital, Mathematics & Cybernetics.
+% </font></p>
+% <p><font size="-1">
+% This file is part of The MATLAB Reservoir Simulation Toolbox (MRST).
+% </font></p>
+% <p><font size="-1">
+% MRST is free software: you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation, either version 3 of the License, or
+% (at your option) any later version.
+% </font></p>
+% <p><font size="-1">
+% MRST is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+% </font></p>
+% <p><font size="-1">
+% You should have received a copy of the GNU General Public License
+% along with MRST.  If not, see
+% <a href="http://www.gnu.org/licenses/">http://www.gnu.org/licenses</a>.
+% </font></p>
+% </html>
\ No newline at end of file