Thermodynamic behaviour of mixtures containing CO 2. A molecular simulation study

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1 Thermodynamic behaviour of mixtures containing. A molecular simulation study V. Lachet, C. Nieto-Draghi, B. Creton (IFPEN) Å. Ervik, G. Skaugen, Ø. Wilhelmsen, M. Hammer (SINTEF)

2 Introduction quality issues in transport operations Impact of associated gases? H 2 O H 2 S O 2 N 2 Ar SO 2 CO N 2 O NO NO 2... Impure may have significantly different thermo-physical properties compared to pure. Needs for accurate knowledge of the thermodynamic and transport properties of + associated gas mixtures in order to develop optimized transport solutions. Molecular simulation 2

3 Outline Simulation methods Monte Carlo and Molecular Dynamics Application to the calculation of pure properties Thermodynamic study of CO + N 2 2 O mixtures Intermolecular potential for nitrous oxide Vapor-liquid phase diagrams Densities and viscosities Thermodynamic study of + NO mixtures Intermolecular potential for nitric oxide Vapor-liquid phase diagrams Densities and viscosities Thermal conductivity of mixtures Intermolecular potentials for O 2, N 2, and H 2 S Application to + N 2, + O 2, and + H 2 S 3

4 Simulation methods Molecular simulation methodologies Two ways of generating a statistical ensemble Initial Configuration Monte Carlo: Statistical method (Markov chain + Metropolis algorithm) ensuring occurrence of configuration i ~ exp(-u i /kt) Molecular Dynamics: Integration of Newton s equations of motion t = 1 to 2 fs m t = 4 to 5 ns t 1 t 1 + t t = t 1 +m t X MD 1 = t t t1 X ( t) dt Representative array of n configurations ( n > 5.x1 7 ) n 1 X = ( ) X MC i n i= 1 averages for property X = V, U,... Ergodicity theorem: X = MD X MC 4

5 Simulation methods Molecular simulation methodologies Non-Equilibrium Molecular Dynamics x Select particle 4 with highest kinetic energy 35 T (K) 3 25 old v c Cold region Hypothetical elastic collision Select particle Hot regionwith lowest Cold region kinetic energy old v h y J q (W/m 2 ) z new v c new v h z (A) t (ps) 5

6 Simulation methods Intermolecular potential used for Harris and Yung (1995) Lennard-Jones potentiel U disp rep ij Energy ε σ Electrostatic energy U σ = 4ε rij el ij qi q j = 4πε r o 6 σ 6 r distance ij ij Rigid molecule Three 6-12 Lennard-Jones centers + three point charges q = e 3 Lennard-Jones centers (σ Ο = 3.3 Å and ε O = 8.57 K) (σ C = 2.76 Å and ε C = K) O C q =.6512 e O q = e J. Harris and K. Yung, J. Phys. Chem. 99, 1221 (1995). 6

7 Simulation methods Pure properties Thermodynamic and transport properties Temperature (K) Simulation results Experimental data ln Psat (Pa) Simulation results Experimental data ρ (kg.m -3 ) /T (K -1 ) H vap (kj.mol -1 ) Simulation results Experimental data η (mpa.s) Simulation results / Liq. Simulation results / Vap. Experimental data Temperature (K) /T (K -1 ) 7

8 -N 2 O mixtures Study of -N 2 O mixtures Intermolecular potential for nitrous oxide Two sets of parameters are available in the literature: Costa Gomes et al. (26) Hansen et al. (27) Rigid molecule (geometry taken from Chase, 1985) Three 6-12 Lennard-Jones centers + three point charges 3 Lennard-Jones centers (Ν 1, Ν 2, Ο) q N1 N N Ǻ Ǻ O q O q N2 M.W. Chase, C.A. Davies et al., J. Phys. Chem. Ref. Data 14 (Suppl. 1) (1985). M.F. Costa Gomes, J. Deschamps, A.A.H. Padua, J. Phys. Chem. B 11, (26). N. Hansen, F.A.B. Agbor, F.J. Keil, Fluid Phase Equil. 259, (27). 8

9 -N 2 O mixtures Intermolecular potential for N 2 O Optimization of force field parameters Minimization of the error function (Ungerer et al., JCP, 112, 5499, 2): F = 1 n n calc exp ( fi fi ) 2 i= 1 s i where s i = statistical uncertainty on f i = ρ l, H vap, ln(p sat ) Searching for the minimum using the gradient method Calculation of partial derivatives of F from statistical fluctuations (NVT ensemble): 2 f i σ calc j = f i calc σ j β f i calc U σ j f i calc U σ j Bourasseau et al., JCP, 118, 32 (23) Use of two temperatures in the error criterion (19 K and 27 K) Results: σ N1 = Å; ε N1 = K; q N1 = -.34 e σ N2 = Å; ε N2 = K; q N1 =+.68 e σ O = 3.44 Å; ε O = K; q O = -.34 e N N O 9

10 -N 2 O mixtures Intermolecular potential for N 2 O Accuracy of different force-fields Liquid-vapor coexisting densities Temperature (K) New force field Costa Gomes force field Hansen force field Experimental data AAD Costa Gomes 2.6 % Hansen.9 % New force field 1. % + good estimate of the critical coordinates ρ (kg.m -3 ) Exp data: DIPPR data bank and Quinn (1929) 1

11 -N 2 O mixtures Intermolecular potential for N 2 O Accuracy of different force-fields Vapor pressures Psat (MPa) 1.1 New force field Costa Gomes force field Hansen force field Experimental data /T (K -1 ) AAD Costa Gomes 24.7 % Hansen 6.7 % New force field 5.8 % Exp data: DIPPR data bank 11

12 -N 2 O mixtures Intermolecular potential for N 2 O Accuracy of different force-fields Vaporization enthalpies 18 H vap (kj.mol -1 ) New force field Costa Gomes force field Hansen force field Experimental data AAD Costa Gomes 9.5 % Hansen 7.4 % New force field 3.5 % Temperature (K) Exp data: DIPPR data bank 12

13 -N 2 O mixtures Intermolecular potential for N 2 O Accuracy of different force-fields Viscosities along the saturation curve.25 η (mpa.s) New force field / Vap. Costa Gomes / Vap. Hansen / Vap. New force field / Liq. Costa Gomes / Liq. Hansen / Liq. Experimental data /T (K -1 ) AAD Costa Gomes 22.3 % Hansen 35.2 % New force field 11.8 % Exp data: NIST website 13

14 -N 2 O mixtures Study of -N 2 O mixtures Vapor-liquid phase diagrams Good agreement between experimental and simulated data at 283 K and 293 K Strong similarities between and N 2 O (in terms of molecular weights, vapor pressures, critical coordinates...) => quasi-azeotropic system over the full range of compositions Sim. results Exp. / DIPPR Exp. / Rowlinson, 1957 Exp. / Cook, 1953 T = K T = K P (MPa) T = K 14 Exp data: - D. Cook, Proceedings of the Royal Society of London Series A 219, (1953): 293 K -> 37 K - J.S. Rowlinson, J.R. Sutton, F. Weston, Proceedings, International Conference Thermodynamics and Transport Properties Fluids (1957): 277 K -> 293 K T = K T = K mole fraction

15 -N 2 O mixtures Study of -N 2 O mixtures Densities and viscosities Pressure-density and pressure-viscosity diagram at 283 K and 293 K of a -N 2 O mixture with 1 mol% of N 2 O. 8.8 ρ (kg.m -3 ) N 2 O / Sim. / K / Sim. / K / Experimental data -N 2 O / Sim. / K / Sim. / K / Experimental data η (mpa.s) N 2 O / Sim. / K / Sim. / K / Experimental data -N 2 O / Sim. / K / Sim. / K / Experimental data P (MPa) P (MPa) Excellent agreement between experimental and simulated data for pure No significant impact of N 2 O on both densities and viscosities Exp data for : NIST website 15

16 -NO mixtures Study of NO Equilibrium between monomers and dimers Nitric oxide: 2 NO N 2 O 2 Monte Carlo in the Reactive Ensemble Constraints Fixed T and V, or fixed T and P Mass conservation Equilibrium condition Monte Carlo moves Usual moves performed in the NVT or NPT ensembles Reaction move s i= 1 ν µ = i i example: µ(n 2 O 2 ) = 2µ(NO) M. Lisal, J.K. Brennan, W.R. Smith, J. Chem. Phys. 124 (26) W.R. Smith and B. Triska, J. Chem. Phys. 1 (1994) J. K. Johnson, A.Z. Panagiotopoulos, and K.E. Gubbins, Mol. Phys. 81 (1994) 16

17 -NO mixtures Study of the -NO mixtures Intermolecular potential for NO and N 2 O 2 Rigid molecules No account of the polarity of the molecule (µ ( =.159 D for NO) NO: a unique 6-12 Lennard-Jones center N 2 O 2 : two NO 6-12 Lennard-Jones centers separated by Å Several sets of parameters are available in the literature: σ (Å) ε/k (K) Kohler et al. (1987) Hirshfelder (1954) Hirshfelder (1954) one IFPEN force field Lennard-Jones center 2 Lennard-Jones center NO NO Å NO 17

18 -NO mixtures Simulation of the NO + N 2 O 2 system Liquid-vapor equilibrium properties Simultaneous use of the ReMC and GEMC methods N 2 O 2 mole fraction New force field Kohler force field Hirschfelder 1 force field Hirschfelder 2 force field Exp. data / Smith, Temperature (K) 18

19 -NO mixtures Simulation of the NO + N 2 O 2 system LVE properties: use of the ReMC and GEMC methods 18 Temperature (K) New force field Kohler force field Hirschfelder 1 force field Hirschfelder 2 force field Experimental data ρ (kg.m -3 ) Psat (MPa) 1.1 New force field Kohler force field Kohler force field (Lísal et al.) Hirschfelder 1 force field Hirschfelder 2 force field Experimental data H vap (kj.mol -1 ) New force field Kohler force field Hirschfelder 1 force field Hirschfelder 2 force field Experimental data /T (K -1 ) Temperature (K) 19

20 -NO mixtures Study of -NO mixtures Pressure-composition and pressure-density diagrams P (MPa) Sim. / K Sim. / K Sim. / K P (MPa) Sim. / K Sim. / K Sim. / K x,y (NO) ρ (kg.m -3 ) 2

21 -NO mixtures Study of -NO mixtures Densities and viscosities Pressure-density and pressure-viscosity diagram at 263 K and 273 K of a -NO mixture with 1 mol% of NO ρ (kg.m -3 ) NO / Sim. / K / Sim. / K / Experimental data -NO / Sim. / K / Sim. / K / Experimental data η (mpa.s).8.4 -NO / Sim. / K / Sim. / K / Experimental data -NO / Sim. / K / Sim. / K / Experimental data P (MPa) P (MPa) Excellent agreement between experimental and simulated data for pure Significant impact of NO on both liquid densities and viscosities Exp data for : NIST website 21

22 Thermal conductivities Intermolecular potentials for O 2, N 2, and H 2 S Rigid molecules O 2 N 2 H 2 S [1] [2] [3] 2 Lennard-Jones centers (σ Ο = 3.11 Å and ε O = 43.2 K) 2 Lennard-Jones centers (σ Ν = 3.33 Å and ε N = 36. K) 1 Lennard-Jones center (σ S = 3.73 Å and ε S = 25. K) O O N N q = -.9 e S q = e q = 4.2 e q = e q = e q = 1.15 e q = e H H q =.25 e q =.25 e q = -.9 e [1] Boutard et al., Fluid Phase Equilibria 236, (25). [2] Delhommelle, PhD Thesis, France (2). [3] Kristof T., Liszi J., J. Phys. Chem. B 11, 548 (1997). 22

23 Thermal conductivities Study of + N 2 systems bar, 288K 15 bar, 288K.1 McLoughlin NEMD λ (W/m*K) λ (W/m*K) McLaughlin NEMD X N2 13 bar, 293K 15 bar, 293K X N2 λ (W/m*K) McLaughlin NEMD λ (W/m*K) McLaughlin NEMD X N2 X N2 23

24 Thermal conductivities Study of + O 2 systems 13 bar, 288K 13 bar, 293K λ (W/m*K) McLaughlin NEMD λ (W/m*K) McLaughlin NEMD X O2 X O2 24

25 Thermal conductivities Study of + H 2 S systems 13 bar, 288K 13 bar, 293K Li NEMD.21 Li NEMD λ (W/m*K) λ (W/m*K) φ H2S φ H2S 25

26 Conclusion and perspectives Development of new force fields and prediction of some property values for CO + N 2 2 O and + NO mixtures. All results have been published: V. Lachet,, B. Creton, T. de Bruin,, E. Bourasseau,, N. Desbiens, Ø. Wilhelmsen,, M. Hammer, Equilibrium and transport properties of CO +N 2 2 O and +NO mixtures: molecular simulation and equation of state modelling study, Fluid Phase Equilibria , (212). Calculation of thermal conductivities for binary mixtures such as + N, 2 + O 2 and + H 2 S. A publication is currently in preparation in collaboration with SINTEF. 26

CE 530 Molecular Simulation

1 CE 530 Molecular Simulation Lecture 1 David A. Kofke Department of Chemical Engineering SUNY Buffalo kofke@eng.buffalo.edu 2 Time/s Multi-Scale Modeling Based on SDSC Blue Horizon (SP3) 1.728 Tflops