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)
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
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
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
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.6.5.4.3 new v c new v h 2 4 6 8 1 z (A) 1 2 3 4 t (ps) 5
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 12 12 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 = -.3256 e 3 Lennard-Jones centers (σ Ο = 3.3 Å and ε O = 8.57 K) (σ C = 2.76 Å and ε C = 28.129 K) O C q =.6512 e O q = -.3256 e J. Harris and K. Yung, J. Phys. Chem. 99, 1221 (1995). 6
Simulation methods Pure properties Thermodynamic and transport properties 3 15.5 Temperature (K) 28 26 24 Simulation results Experimental data ln Psat (Pa) 15 14.5 14 Simulation results Experimental data 22 13.5 2 2 4 6 8 1 12 ρ (kg.m -3 ) 13.33.36.39.42.45 1/T (K -1 ) 14.25 H vap (kj.mol -1 ) 12 1 8 6 4 2 Simulation results Experimental data η (mpa.s).2.15.1.5 Simulation results / Liq. Simulation results / Vap. Experimental data 2 22 24 26 28 3 Temperature (K).33.36.39.42.45 1/T (K -1 ) 7
-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 1.1282 Ǻ 1.1842 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, 18566-18572 (26). N. Hansen, F.A.B. Agbor, F.J. Keil, Fluid Phase Equil. 259, 18-188 (27). 8
-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 = 3.116 Å; ε N1 = 78.17 K; q N1 = -.34 e σ N2 = 2.927 Å; ε N2 = 34.647 K; q N1 =+.68 e σ O = 3.44 Å; ε O = 65.891 K; q O = -.34 e N N O 9
-N 2 O mixtures Intermolecular potential for N 2 O Accuracy of different force-fields Liquid-vapor coexisting densities Temperature (K) 3 25 2 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 2 4 6 8 1 12 ρ (kg.m -3 ) Exp data: DIPPR data bank and Quinn (1929) 1
-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.35.4.45.5.55 1/T (K -1 ) AAD Costa Gomes 24.7 % Hansen 6.7 % New force field 5.8 % Exp data: DIPPR data bank 11
-N 2 O mixtures Intermolecular potential for N 2 O Accuracy of different force-fields Vaporization enthalpies 18 H vap (kj.mol -1 ) 16 14 12 1 8 6 4 2 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 % 18 2 22 24 26 28 3 32 Temperature (K) Exp data: DIPPR data bank 12
-N 2 O mixtures Intermolecular potential for N 2 O Accuracy of different force-fields Viscosities along the saturation curve.25 η (mpa.s).2.15.1.5 New force field / Vap. Costa Gomes / Vap. Hansen / Vap. New force field / Liq. Costa Gomes / Liq. Hansen / Liq. Experimental data.36.38.4.42.44.46 1/T (K -1 ) AAD Costa Gomes 22.3 % Hansen 35.2 % New force field 11.8 % Exp data: NIST website 13
-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 7.5 7 6.5 6 Sim. results Exp. / DIPPR Exp. / Rowlinson, 1957 Exp. / Cook, 1953 T = 33.15 K T = 298.15 K P (MPa) 5.5 5 T = 293.15 K 14 Exp data: - D. Cook, Proceedings of the Royal Society of London Series A 219, 245-256 (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 4.5 4 3.5 T = 283.15 K T = 273.15 K 3.2.4.6.8 1 mole fraction
-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 ) 6 4 2 -N 2 O / Sim. / 283.15 K / Sim. / 283.15 K / Experimental data -N 2 O / Sim. / 293.15 K / Sim. / 293.15 K / Experimental data η (mpa.s).6.4.2 -N 2 O / Sim. / 283.15 K / Sim. / 283.15 K / Experimental data -N 2 O / Sim. / 293.15 K / Sim. / 293.15 K / Experimental data 4 4.5 5 5.5 6 6.5 7 7.5 4 4.5 5 5.5 6 6.5 7 7.5 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
-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
-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 2.237 Å Several sets of parameters are available in the literature: σ (Å) ε/k (K) Kohler et al. (1987) 3.171 125. Hirshfelder (1954) 3.599 91. Hirshfelder (1954) 3.47 119. + one IFPEN force field 3.4 13. 1 Lennard-Jones center 2 Lennard-Jones center NO NO 2.237 Å NO 17
-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.9.8.7.6.5.4.3.2.1 New force field Kohler force field Hirschfelder 1 force field Hirschfelder 2 force field Exp. data / Smith, 1952 11 12 13 14 15 16 17 Temperature (K) 18
-NO mixtures Simulation of the NO + N 2 O 2 system LVE properties: use of the ReMC and GEMC methods 18 Temperature (K) 16 14 12 New force field Kohler force field Hirschfelder 1 force field Hirschfelder 2 force field Experimental data 2 4 6 8 1 12 14 ρ (kg.m -3 ) 16 14 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 ) 12 1 8 6 4 2 New force field Kohler force field Hirschfelder 1 force field Hirschfelder 2 force field Experimental data.6.7.8.9 1/T (K -1 ) 11 12 13 14 15 16 17 18 Temperature (K) 19
-NO mixtures Study of -NO mixtures Pressure-composition and pressure-density diagrams 12 1 12 1 P (MPa) 8 6 4 Sim. / 253.15 K Sim. / 263.15 K Sim. / 273.15 K P (MPa) 8 6 4 Sim. / 253.15 K Sim. / 263.15 K Sim. / 273.15 K 2 2.1.2.3.4.5.6.7.8.9 1 x,y (NO) 2 4 6 8 1 ρ (kg.m -3 ) 2
-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. 1.12 8 ρ (kg.m -3 ) 6 4 2 -NO / Sim. / 263.15 K / Sim. / 263.15 K / Experimental data -NO / Sim. / 273.15 K / Sim. / 273.15 K / Experimental data η (mpa.s).8.4 -NO / Sim. / 263.15 K / Sim. / 263.15 K / Experimental data -NO / Sim. / 273.15 K / Sim. / 273.15 K / Experimental data 2 3 4 5 6 7 8 P (MPa) 2 3 4 5 6 7 8 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
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 = - 2.1 e q = 4.2 e q = - 2.1 e q = -.575 e q = 1.15 e q = -.575 e H H q =.25 e q =.25 e q = -.9 e [1] Boutard et al., Fluid Phase Equilibria 236, 25-41 (25). [2] Delhommelle, PhD Thesis, France (2). [3] Kristof T., Liszi J., J. Phys. Chem. B 11, 548 (1997). 22
Thermal conductivities Study of + N 2 systems.12 13 bar, 288K 15 bar, 288K.1 McLoughlin NEMD.8.6.4 λ (W/m*K) λ (W/m*K).12.1.8.6.4 McLaughlin NEMD.2.25.5.75 1 X N2 13 bar, 293K 15 bar, 293K.12.2.12.25.5.75 1 X N2 λ (W/m*K).1.8.6.4 McLaughlin NEMD λ (W/m*K).1.8.6.4 McLaughlin NEMD.2.2.25.5.75 1.25.5.75 1 X N2 X N2 23
Thermal conductivities Study of + O 2 systems 13 bar, 288K 13 bar, 293K.12.12 λ (W/m*K).1.8.6.4 McLaughlin NEMD λ (W/m*K).1.8.6.4 McLaughlin NEMD.2.2.25.5.75 1.25.5.75 1 X O2 X O2 24
Thermal conductivities Study of + H 2 S systems 13 bar, 288K 13 bar, 293K.31.26.26 Li NEMD.21 Li NEMD λ (W/m*K).21.16 λ (W/m*K).16.11.11.6.25.5.75 1.6.25.5.75 1 φ H2S φ H2S 25
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 322-323, 66-78 (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