Molecular Thermodynamics of Adsorption Using a 2D- SAFT-VR-Mie Approach

Transcription

1 Molecular Thermodynamics of Adsorption Using a 2D- SAFT-VR-Mie Approach Gerardo Campos, Jonatan Suaste, Andrew Haslam, George Jackson and Alejandro Gil-Villegas

2 Outline Adsorption Statistical Associating Fluid Theory (SAFT-VR) Adsorption Model: The quasi-two dimensional fluid approach 2D SAFT-VR-Mie EOS Running the Machinery: Modelling of Adsorption of Carbon Dioxide on Dry Coal Conclusions and Outlook 1

3 Adsorption Theoretical Modelling More accurate platforms are available, e.g.: Molecular Simulation at different length-scales Quasi-two dimensional approach via SAFT θ = KP g 1 + KP g Langmuir, I., J. Am. Chem. Soc., 37, (1915). 2

4 Surface coverage SAFT-VR SW on adsorption Model and predicts asphaltene precipitation and adsorption Bedford limestone at 298K Bulk packing fraction (reduced density) Castro et al., Fluid Phase Equilibria, 286, (2009). 3

5 SAFT-VR SW on adsorption Adsorption of hydrogen on activated carbon (semiclassical approach) Trejos et al., Mol. Phys., 112, (2014). 4

6 SAFT-VR Free-energy Equation of State based on Statistical Mechanical Perturbation Theory a = a IDEAL + a MONO + a CHAIN + a ASSOC a = A NkT Gil-Villegas et al., J. Chem. Phys., 106, 4168 (1997). 5

7 SAFT-VR Free-energy Equation of State based on Statistical Mechanical Perturbation Theory a = a IDEAL 6

8 SAFT-VR Free-energy Equation of State based on Statistical Mechanical Perturbation Theory a = a IDEAL + a MONO 7

9 SAFT-VR Free-energy Equation of State based on Statistical Mechanical Perturbation Theory a = a IDEAL + a MONO + a CHAIN 8

10 SAFT-VR Free-energy Equation of State based on Statistical Mechanical Perturbation Theory a = a IDEAL + a MONO + a CHAIN + a ASSOC 9

11 SAFT-VR Free-energy Equation of State based on Statistical Mechanical Perturbation Theory In this work we restrict our description to only monomeric fluids a = a IDEAL + a MONO 10

12 Solid Wall Adsorption Model ADSORBED PHASE The adsorption isotherms are calculated by solving the thermodynamic equilibrium between the two phases BULK PHASE λ w σ z Martinez et al., J. Chem. Phys., 126, (2007). 11

13 Adsorption Model BULK PHASE : Described with SAFT-VR-Mie u Mie = Cε σ r λ r σ r λ a a bulk = a IDEAL + a MONO Lafitte et al., J. Chem. Phys., 139, (2013). 12

14 Solid Wall Adsorption Model u 1D wall ADSORBED PHASE : Treated as a quasi-2d system u ads = u 2D Mie x, y + u 1D wall z u 2D Mie u 1D wall z = ε w 0 z 0 0 < z λ w σ z > λ w σ λ w σ z 13

15 Solid Wall Adsorption Model u 1D wall ADSORBED PHASE : Treated as a quasi-2d system u 2D Mie To guarantee the 2D approach (monolayer formation): < λ w < λ w σ z del Rio and Gil Villegas., J. Phys. Chem., 95, (1991). 14

16 Solid Wall Adsorption Model u 1D wall ADSORBED PHASE : Treated as a quasi-2d system u 2D Mie a ads = a 2D Mie + a 1D wall = a 2D IDEAL + a 2D MONO + a 1D wall λ w σ z 15

17 Solid Wall Adsorption Model u 1D wall ADSORBED PHASE : Treated as a quasi-2d system u 2D Mie a ads = a 2D Mie + a 1D wall = a 2D IDEAL + a 2D MONO + a 1D wall 2D-SAFT-VR-Mie EOS (This work) λ w σ z 16

18 2D SAFT-VR-Mie EOS BH perturbation expansion up to first order term a 2D MONO = a HD + βa 1 Mie 2D β = 1 kt J. A. Barker and D. Henderson, Rev. Mod. Phys. 48, 587 (1976). 17

19 2D SAFT-VR-Mie EOS BH perturbation expansion up to first order term a 2D MONO = a HD + βa 1 Mie 2D d HD (T) = σ 1 e βumie (r) dr 0 a HD = 9γ 8 1 γ 7 ln 1 γ 8 Henderson, Mol. Phys., 34, (1977). 18

20 2D SAFT-VR-Mie EOS BH perturbation expansion up to first order term a 2D MONO = a HD + βa 1 Mie 2D a 1 Mie 2D = πρ 2D u Mie r g HD r r σ dr 19

21 2D SAFT-VR-Mie EOS BH perturbation expansion up to first order term a 2D MONO = a HD + βa 1 Mie 2D a 1 Mie 2D = πρ 2D u Mie r g HD r r σ dr = a 1 Mie 2D γ; σ, ε, λ r, λ a 20

22 2D SAFT-VR-Mie EOS BH perturbation expansion up to first order term a 2D MONO = a HD + βa 1 Mie 2D a 1 Mie 2D = πρ 2D u Mie r g HD r r σ dr = a 1 Mie 2D γ; σ, ε, λ r, λ a Validation by comparison with MC simulation results (Suaste) 21

23 2D SAFT-VR-Mie EOS T = kt ε = 1 T = kt ε = 2 The theory accurately reproduces the MC simulation results 22

24 Solid Wall Modelling Adsorption ρ ads ρ b Phase equilibrium criterion μ b ρ b = μ ads ρ ads μ b ρ b = A b N b V,T μ ads ρ ads = A ads N ads s,t λ w σ z 23

25 Adsorption of a LJ (12-6) fluid T = 2 24

26 Adsorption of CO2 on dry coal Single-site CG model of bulk CO2 ε k K σ nm λ r λ a Avendano et al., J. Phys. Chem., 115, (2011). 25

27 Adsorption of CO2 on dry coal The parameters for the pair-potential describing the adsorbed phase can be selected following two distinct routes: Route a: Different parameters respect to those of the bulk phase Classical approach followed in previous SAFT-VR SW models of adsorption λ r ads = λ r bulk λ a ads from Rc = T c ads T c bulk = 0.4 (*) ε ads = 0.8ε bulk (**) (*) Machin and Ross, Proc. R. Soc. London, Ser., 265, (1962). (**) Sinanoğlu and Pitzer, J. Chem. Phys.,32, (1960). 26

28 Adsorption of CO2 on dry coal The parameters for the pair-potential describing the adsorbed phase can be selected following two distinct routes: Route b: Same parameters of the bulk phase λ r ads = λ r bulk λ a ads = λ a bulk ε ads from R c 27

29 Adsorption of CO2 on dry coal SOLID-FLUID INTERACTIONS: < λ w < ε w must be fitted to experimental data The specific surface of the adsorbent is also required 28

30 Adsorption of CO2 on dry coal T = 318K Ottiger et al., Adsorption, 14, (2008). 29

31 Conclusions and Outlook It has been demonstrated that changing the pair potential of the adsorbed phase is not a requisite as it has been argued in previous SAFT-VR (SW) approaches The theoretical framework presented here is suitable for a wide range of applications, however, the particle-wall interactions have to be fitted to experimental data The 2D-SAFT-VR-Mie EOS can still be enhanced by incorporating higher-order terms in the thermal expansion The theory can be extended to model mixtures, reactive systems and phase transitions of confined fluids 30

32 Acknowledgements QCCSRC, Imperial College London and University of Guanajuato for project funding University of Manchester for conference funding 31

33 Thank you Any questions? Contact:

34 SAFT-VR Mie terms S1

35 SAFT-VR Mie terms S2

36 Adsorption model S3

37 Adsorption model S4

38 Analytical expression of a 1 Mie 2D S5