Introduction to Thermodynamics models for process engineering How to choose a thermodynamic model - Simulation Baptiste Bouillot École Nationale Supérieure des Mines de Saint-Etienne - Centre SPIN 2019-2020 Thermodynamics reminders Phase equilibrium theory Equilibrium equationss, issues of phase equilibrium Thermodynamic models Why study Thermodynamics ? Thermodynamic properties calculation (Hv, Hl, Cp,...) Phase equilibrium prediction 2/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Phase equilibrium theory Equilibrium equationss, issues of phase equilibrium Thermodynamic models Why study Thermodynamics ? Débit sortie P, T Tension vapeur ! Q Thermodynamic properties calculation (Hv, Hl, Cp,...) Phase equilibrium prediction 2/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Phase equilibrium theory Equilibrium equationss, issues of phase equilibrium Thermodynamic models How does it work ? P (bar) 220 C (Point critique) Liquide Solide (s) (T) P 1 point triple 0,006 Gaz 273,15 273,16 373,15 673,16 T (K) Data base Correlations Thermodynamic models (6= correlations) 3/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Phase equilibrium theory Equilibrium equationss, issues of phase equilibrium Thermodynamic models How does it work ? 60 (S) T=50°C P1 50 Liquide 40 courbe de bulle P (kPa) Liquide + Vapeur 30 courbe de rosée 20 Vapeur (S) P2 10 0 x1, y1 1 Data base Correlations Thermodynamic models (6= correlations) 3/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Phase equilibrium theory Equilibrium equationss, issues of phase equilibrium Thermodynamic models How does it work ? A 0 1 xB miscibilité M(x ,x ,x ) α A B C xA x B α α x A D β 1 immiscibilité 0 B 0 α β 1 x C xC x C C Data base Correlations Thermodynamic models (6= correlations) 3/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Phase equilibrium theory Equilibrium equationss, issues of phase equilibrium Thermodynamic models Issues : Thermodynamics and Chemical Engineering Express magnitudes that characterizes phase properties and phase equilibria from measurable quantities (T, P...) ! Thermodynamic Equilibria Pure phases and mixtures properties LV Pure phase : single Thermodynamic LL component potentials : LLV Mixtures : more than 1 H(T; P; :::), component G(T; P), A(T; V) LS Mixing properties S ... Chemical potential Cp calculation Cv Fugacities ... ... 4/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Phase equilibrium theory Equilibrium equationss, issues of phase equilibrium Thermodynamic models Objectives Sensitize the engineer to be to Thermodynamics and its importance, Identify issues and choose the apropriate thermodynamic model, Know the theory and how to use a complex thermodynamic model in a process 5/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Phase equilibrium theory Equilibrium equationss, issues of phase equilibrium Thermodynamic models Outline 1 Thermodynamics reminders 2 Phase equilibrium theory 3 Equilibrium equationss, issues of phase equilibrium 4 Thermodynamic models 6/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Fundamental properties Phase equilibrium theory Phase rule Equilibrium equationss, issues of phase equilibrium Gibbs-Duhem Thermodynamic models Outline 1 Thermodynamics reminders 2 Phase equilibrium theory 3 Equilibrium equationss, issues of phase equilibrium 4 Thermodynamic models 7/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Fundamental properties Phase equilibrium theory Phase rule Equilibrium equationss, issues of phase equilibrium Gibbs-Duhem Thermodynamic models Rappels Magnitude symbol unit Temperature TK Pressure P Pa Volume V m3 Molar composition x - Internal Energy UJ Enthalpy HJ Entropy SJ=K Gibbs “Free Energy” (Potential) GJ Helmoltz “Free Energy” (Potential) AJ Chemical Potential µ J=mol 8/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Fundamental properties Phase equilibrium theory Phase rule Equilibrium equationss, issues of phase equilibrium Gibbs-Duhem Thermodynamic models Potentials and Fundamental relations Fundamental relation A thermodynamic system can be perfectly defined by its fundamental relation : - S = f (U; V; N) - U = f (S; V; N) How to do without it ? 2 “equations of state”, OR : 0 Mechanic equation under the form f (P; Vm; T) = 0 Thermal relation under the form Cpm = T=N:(@S=@T)p = Cp(T) These equations are usually unknown ! 9/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Fundamental properties Phase equilibrium theory Phase rule Equilibrium equationss, issues of phase equilibrium Gibbs-Duhem Thermodynamic models Usuall Thermodynamic quantities Quantity symbol differential expression P ∗ Internal Energy U dU = TdS − PdV (+ i µidNi ) P ∗ Enthalpy H dH = TdS + VdP (+ i µidNi ) P ∗ Gibbs “Free Energy” (Potential) G dG = −SdT + VdP (+ i µidNi ) P ∗ Helmoltz “Free Energy” (Potential) A dA = −SdT − PdV (+ i µidNi ) ! Which one to use ? ? ? !“Best” differential expression ? ? ? 10/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Fundamental properties Phase equilibrium theory Phase rule Equilibrium equationss, issues of phase equilibrium Gibbs-Duhem Thermodynamic models Usuall Thermodynamic quantities Quantity differential expression (T,P) @V @V @V Internal Energy dU = Cp − P j dT − T j + P j dP @T P @T P @P T @V Enthalpy dH = Cp dT + V − T j dP @T P Helmoltz “Free Energy” (Potential) dA = −S − P @V j dT − P @V j dP @T P @P T Gibbs “Free Energy” (Potential) dG = −S dT + V dP C Entropy dS = p dT − @V j dP T @T P Temperature and Pressure are measurable quantities, therefore the “bests”. 10/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Fundamental properties Phase equilibrium theory Phase rule Equilibrium equationss, issues of phase equilibrium Gibbs-Duhem Thermodynamic models Gibbs Phase Rule How many degree of freedom ? : F = N − Φ + 2 − R (1) avec : F degree of freedom, N number of components (molecules), Φ number of phases, R constraints (additional relations such as, constant composition, chemical reaction, azeotropy...). 11/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Fundamental properties Phase equilibrium theory Phase rule Equilibrium equationss, issues of phase equilibrium Gibbs-Duhem Thermodynamic models Gibbs Phase Rule How many degree of freedom ? : F = NP− (bar)Φ + 2 − R (1) 220 C (Point critique) avec : F degree of freedom, Liquide Solide (T) N number of components (molecules), (s) P 1 Φ number of phases, point triple R constraints (additional relations0,006 such as, constant composition, chemical reaction, azeotropy...). Gaz 273,15 273,16 373,15 673,16 T (K) Example : - Single component system/single phase : F = 2 - Single component / two phases : F = 1 - Singel component / three phases : F = 0 11/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Fundamental properties Phase equilibrium theory Phase rule Equilibrium equationss, issues of phase equilibrium Gibbs-Duhem Thermodynamic models Gibbs Phase Rule How many degree of freedom ? : F = N − Φ + 2 − R (1) avec : F degree of freedom, N number of components (molecules), Φ number of phases, R constraints (additional relations such as, constant composition, chemical reaction, azeotropy...). 60 (S) T=50°C P1 50 Liquide 40 courbe de bulle Example : Binary system ? P (kPa) Liquide + Vapeur 30 courbe de rosée 20 Vapeur (S) P2 10 0 x1, y1 1 11/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Fundamental properties Phase equilibrium theory Phase rule Equilibrium equationss, issues of phase equilibrium Gibbs-Duhem Thermodynamic models Gibbs Phase Rule How many degree of freedom ? : F = N − Φ + 2 − R (1) avec : F degree of freedom, N number of components (molecules), Φ number of phases, R constraints (additional relations such as, constant composition, chemical reaction, azeotropy...). 60 (S) T=50°C P1 50 Example : Liquide - 1 phase : F = 3 40 courbe de bulle ( T-P-x for instance), P (kPa) Liquide + Vapeur - two phases : F = 2 30 courbe de rosée ( T-P ou T-x ou P-x for instance) 20 Vapeur (S) P2 10 0 x1, y1 1 11/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Fundamental properties Phase equilibrium theory Phase rule Equilibrium equationss, issues of phase equilibrium Gibbs-Duhem Thermodynamic models Gibbs-Duhem equation Remember that : P dU = TdS − PdV + i µdNi et que : U = f (S; V; Ni) These two equations lead to the standard Gibbs-Duhem equation : l’Équation de Gibbs-Duhem : X SdT − VdP + Nidµi = 0 (2) i Why is this equation essential ? 12/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Fundamental properties Phase equilibrium theory Phase rule Equilibrium equationss, issues of phase equilibrium Gibbs-Duhem Thermodynamic models Gibbs-Duhem equation Remember that : P dU = TdS − PdV + i µdNi et que : U = f (S; V; Ni) These two equations lead to the standard Gibbs-Duhem equation : l’Équation de Gibbs-Duhem : X SdT − VdP + Nidµi = 0 (2) i Why is this equation essential ? It provides the chemical potential variation as a function of measurable quantities, temperature adn pressure 12/85 Baptiste Bouillot Thermodynamics Thermodynamics reminders Chemical equilibrium ? Phase equilibrium theory Residual approach Equilibrium equationss, issues of phase equilibrium Excess approach Thermodynamic models Conclusion - Objectives - Exercise Outline 1 Thermodynamics reminders 2 Phase equilibrium theory 3 Equilibrium equationss, issues of phase equilibrium 4 Thermodynamic models 13/85 Baptiste Bouillot Thermodynamics Thermodynamics