Molecular Modeling and Simulation of Phase Equilibria for Chemical Engineering

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1 InPROMT 2012, Berlin, 16. November 2012 DFG Transregio CRC 63 Molecular Modeling and Simulation of Phase Equilibria for Chemical Engineering Hans Hasse 1, Martin Horsch 1, Jadran Vrabec 2 1 Laboratory of University of Kaiserslautern 2 Thermodynamics and Energy Technology University of Paderborn

2 Modeling and Simulation in Chemical Engineering Bottom up Top down 2

(MC) Statistical method Energetic acceptance criteria Static properties only Reactive

3 Molecular Simulation with Force Fields Molecular Dynamics (MD) Numerical solution of Newtonian equations of motion Deterministic Static and dynamic properties Monte-Carlo (MC) Statistical method Energetic acceptance criteria Static properties only Reactive MC MD/MC Code: S. Deublein et al.: Comput. Phys. Commun. 182 (2011)

electrostatic sites United atom approach All properties

4 Molecular Model Type Example: Ethylene Oxide Rigid, non-polarizable Multicenter Lennard-Jones (LJ) + electrostatic sites United atom approach All properties from one model B. Eckl et al. Fluid Phase Equilib. 274 (2008)

5 Molecular Model Development Geometry: bond lengths bond angles QM Electrostatics: partial charges dipoles quadrupoles QM / VLE Dispersion, Repulsion: Lennard-Jones (LJ) potentials VLE B. Eckl et al. J. Phys. Chem. B 112 (2008)

6 Parameterizing of Molecular Models with VLE Data Multi-Objective Optimization Vapor-pressure Saturated liquid density Enthalpy of vaporization 6

CAPEX Laboratory of Molecular Models from Multi-Objective Optimization: Pareto-based Approach Introduction by well known example Not feasible Pareto frontier Feasible Pareto

7 CAPEX Laboratory of Molecular Models from Multi-Objective Optimization: Pareto-based Approach Introduction by well known example Not feasible Pareto frontier Feasible Pareto optimality Improvement in any chosen objective leads inevitably to a decline in at least one other objective. Pareto frontier: best compromises Design by navigation on Pareto frontier OPEX 7

8 Lennard-Jones (LJ) Pair Potential r U 4 kb r r 12 6 Repulsion r / Attraction Radial symmetry Accounts for: Repulsion Dispersion Two parameters: Size Energy 8

9 Pareto-based Lennard-Jones Modeling of Argon Parameter space Objective space / K δδh v σ / Å δp δρ' 9

10 Pareto-based Lennard-Jones Modeling of Argon Parameter space Objective space / K δδh v σ / Å δp δρ' Model from J. Vrabec et al. J. Phys. Chem. B 105 (2001)

11 / K Laboratory of Pareto-based Lennard-Jones Modeling of Methane Parameter space Objective space δδh v δp δρ' σ / Å Model from J. Vrabec et al. J. Phys. Chem. B 105 (2001)

12 Molecular Models of Fluids: Examples Phosgene Group CCl 2 O HCl C 6 H 6 C 6 H 5 -CH 3 C 6 H 5 -Cl o-c 6 H 4 -Cl 2 Ethylene Oxide Group C 2 H 4 O H 2 O HO(CH 2 ) 2 OH high economic interest difficult experiments few reliable data need for predictive modeling and simulation Excellent test cases for molecular modeling and simulation Y. L. Huang et al. AIChE J. 57 (2011) Y. L. Huang, et al. Ind. Eng. Chem. Res. 51 (2012)

13 Vapor Pressures 0 HCl ln(p / MPa) ocl 2 -Benzene Benzene Phosgene Cl-Benzene Toluene -15 Symbols: Simulation Lines: Reference DIPPR T / K 1 (1/ T ) / K Y. L. Huang et al. AIChE J. 57 (2011)

14 Saturated Densities T / K ocl 2 -Benzene Cl-Benzene Toluene Benzene Phosgene Symbols: Simulation Lines: Reference DIPPR 300 HCl / mol/l Y. L. Huang et al. AIChE J. 57 (2011)

Predictions: Transport Properties of Liquid HCl 20 6 Laboratory of D i / 10-9 m 2 s -1 15 10 5 / 10-4 Pa s 5 4 3 2 1 0 0.5 150 200 250 T / K 0 160 200 240 280 T / K / W m -1 K -1 0.4 0.3 0.2 0.

15 Predictions: Transport Properties of Liquid HCl 20 6 Laboratory of D i / 10-9 m 2 s / 10-4 Pa s T / K T / K / W m -1 K Prediction EMD Simulation Prediction NEMD Simulation Experiment (Literature) DIPPR Correlation p = 0.1 MPa T / K G. Guevara-Carrion et al. Fluid Phase Equilib. 316 (2012)

16 Molecular Modelling of Mixtures A σ A, ε A A Predictions ξ = 1 or B σ AB, ε AB B State-independent parameter ξ fitted to one experimental data point p(t,x) oder H(T) σ B, ε B Unlike interaction A-B: Electrostatics fully predictive Lennard-Jones parameters from combination rules Modified Lorentz-Berthelot σ σ σ ε = + / 2 AB A B = ε ε AB A B T. Schnabel et al. J. Mol. Liq. 135 (2007)

17 17 Laboratory of Vapor-Liquid Equilibrium HCl + Chlorobenzene K p / MPa K K Symbols: simulation (full) experiment (cross) Lines: Peng-Robinson EOS x HCl / mol mol -1 Y. L. Huang et al. AIChE J. 57 (2011)

18 Application to Reaction Studies Phosgeneation, Liquid Mixture (110 C, 1 bar) Phosgene + Cl-Benzene + HCl + 2,4-Diaminetoluene 50 mol% 40 mol% 7 mol% 3 mol% Local concentration Overall concentration Study of radial pair correlation functions g ij () r local concentration c ji, overall concentration c j 18

19 8 7 g ij (r) g ij (r) Radial Pair Correlation Functions: Amine Groups HCl Important for Formation of Undesired Hydrochlorides 6 d H Cl Amine group N2 DAT.N2--HCl.Cl DAT.N2--HCl.H N Amine group N4 DAT.N4--HCl.Cl DAT.N4--HCl.H NH 2 (H in HCl) NH 2 (Cl in HCl) g(r) [-] 5 4 g(r) [-] 5 4 d H Cl 3 2 N r r /Å [Å] r /Å r [Å] 0 Deviations between overall and local concentration up to a factor of 8 HCl strongly prefers amine group N2 over N4 HCl docks preferentially with the proton at amine group N2 19

20 Proton Catalyzed Reaction Ethylene Oxide + Water 20

21 Proton Catalyzed Reaction Ethylene Oxide + Water + 21

22 Radial Pair Correlation Functions 22

23 Transient Radial Pair Correlation Functions Laboratory of 23

24 H EO / MPa H EO / MPa Henry s Law Constants of Ethylene Oxide EO in Water Laboratory of EO in (Water + Ethylene glycole) K K 0 Molecular Simulation Guide for eye Physical solubility No chemical reactions * T / K x EG / mol mol -1 Y. L. Huang, et al. Ind. Eng. Chem. Res. 51 (2012)

25 Spherical Vapor-Liquid Interfaces Droplet + metastable vapor liq Δp 2γ R γ Spinodal limit: For the external phase, metastability breaks down. gas 25

26 Spherical Vapor-Liquid Interfaces Droplet + metastable vapor Bubble + metastable liquid liq Δp 2γ R γ Spinodal limit: For the external phase, metastability breaks down. gas Planar limit: The curvature changes its sign and the radius R γ diverges. 26

27 Curvature Dependence of Surface Tension Equimolar radius (from density profile) R 0 R dr 0 R 2 2 R R R dr Laplace radius R 2 p Capillarity radius R 2 0 p density / ρ 0 LJTS fluid T = 0.75 /k equimolar radius R capillarity radius R = 2 0 / p distance from the centre of mass / ρ M. Horsch et al. Phys. Rev. E 85 (2012)

28 Curvature Dependence of Surface Tension No evidence for curvature dependence of surface tension of small droplets M. Horsch et al. Phys. Rev. E 85 (2012)

29 Planar Vapor-Liquid Interfaces Surface tension: Abundant studies on small droplets, i.e. simultaneous variation of curvature & size No previous studies on thin slabs with planar surfaces, i.e. variation of size only 29

30 Planar Vapor-Liquid Interfaces Lennard-Jones fluid Surface tension Density in center * T * T S / S / Evidence for finite size effects for very thin slabs S. Werth Physica A submitted (2012) 30

Wetting and Dispersive Fuid-Wall Interactions contact angle in degrees 180 150 120 90 60 30 0 Symbols: Simulation (LJTS) Lines: correlations Curve parameter: reduced temperature Reduced wall density

31 Wetting and Dispersive Fuid-Wall Interactions contact angle in degrees Symbols: Simulation (LJTS) Lines: correlations Curve parameter: reduced temperature Reduced wall density σ -3 three phase contact vapor (V) 1 /k contact angle Θ solid (S) liquid (L) 0.88 /k 0.73 /k reduced fluid-wall dispersive energy Young s equation SV = SL + LV cos Θ M. Horsch et al., Langmuir 26 (2010)

32 Wetting and Dispersive Fuid-Wall Interactions y / σ Density in droplet ρ / σ -3 Density profile center LJTS Simulation Correlation ρ / σ y / σ x / σ 32

33 Wetting, Adsorption and Surface Diffusion Laboratory of Molecular dynamics LJTS Model 33

34 Summary Molecular modeling and simulation in chemical engineering Atomistic force fields Molecular simulations of real systems are feasible Wide range of applications Fluid properties (static, dynamic, ) Surfaces (nucleation, wetting, adsorption, ) Reactions Challenges Complex molecules, electrolytes Fluid-wall interactions Bridging scales (long times, large systems, ) Computational efficiency, massive parallelization High potential (to be exploited ) 34

35 Acknowledgment People Stefan Becker Bernhard Eckl Manfred Heilig (BASF) Yow-Lin Huang Peter Klein (ITWM) Karl-Heinz Küfer (ITWM) Thorsten Merker Thorsten Schnabel Katrin Stöbener (ITWM) Stephan Werth Thorsten Windmann Funding DFG SPP 1155 DFG TFB 66 DFG SFB 706 DFG SFB 926 BMBF IMEMO RLP Research Center CM 2 35

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