molecular modeling and simulation of phase … modeling and simulation of phase equilibria for...

Laboratory of Engineering Thermodynamics Prof. Dr.-Ing. H. Hasse

Molecular Modeling and Simulation of

Phase Equilibria for Chemical Engineering

Hans Hasse1, Martin Horsch1, Jadran Vrabec2

1Laboratory of Engineering Thermodynamics

University of Kaiserslautern 2Thermodynamics and Energy Technology

University of Paderborn

InPROMT 2012, Berlin, 16. November 2012

DFG Transregio CRC 63


Modeling and Simulation in Chemical Engineering

Top down Bottom up

2


Molecular Dynamics (MD)

Numerical solution of

Newtonian equations of motion

Deterministic

Static and dynamic properties

Molecular Simulation with Force Fields

Monte-Carlo (MC)

Statistical method

Energetic acceptance criteria

Static properties only

Reactive MC

S. Deublein et al.: Comput. Phys. Commun. 182 (2011) 2350-2367 MD/MC Code: www.ms-2.de

3


Molecular Model Type

Rigid, non-polarizable

Multicenter Lennard-Jones (LJ) + electrostatic sites

United atom approach

All properties from one model

Example: Ethylene Oxide

B. Eckl et al. Fluid Phase Equilib. 274 (2008) 16-26

4


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) 12710-12721

5


Parameterizing of Molecular Models with VLE Data

www.withfriedship.com

Vapor-pressure

Saturated liquid density

Enthalpy of vaporization

6

Multi-Objective Optimization


OPEX

CA

PE

X

Pareto optimality

Improvement in any chosen

objective leads inevitably to

a decline in at least one

other objective.

Molecular Models from Multi-Objective Optimization:

Pareto-based Approach

Introduction by well known example

Feasible

Not

feasible

Pareto frontier

Pareto frontier: best

compromises

Design by navigation on

Pareto frontier

7


12 6

4B

U

k r r

Lennard-Jones (LJ) Pair Potential

Radial symmetry

Accounts for:

Repulsion

Dispersion

Two parameters:

Size

Energy

Repulsion Attraction

r

8

/r


Pareto-based Lennard-Jones Modeling of Argon

9

σ / Å

/ K

δp

δΔ

hv

δρ'

Parameter space Objective space


Pareto-based Lennard-Jones Modeling of Argon

Model from J. Vrabec et al. J. Phys. Chem. B 105 (2001) 12126-12133

10

σ / Å

/ K


δp

δΔ

hv

δρ'


Pareto-based Lennard-Jones Modeling of Methane

Model from J. Vrabec et al. J. Phys. Chem. B 105 (2001) 12126-12133

11

σ / Å

/ K


δp

δΔ

hv

δρ'


Phosgene Group

C6H5-Cl C6H6 CCl2O o-C6H4-Cl2 HCl C6H5-CH3

Molecular Models of Fluids: Examples

Ethylene Oxide Group

C2H4O H2O HO(CH2)2OH

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. Ind. Eng. Chem. Res. 51 (2012) 7428-7440

Y. L. Huang et al. AIChE J. 57 (2011) 1043-1060

12


T / K0.002 0.003 0.004 0.005 0.006 0.007

ln(p

/ M

Pa)

-15

-10

-5

0HCl

Benzene

Cl-Benzene

Phosgene

Toluene

oCl2-Benzene

Vapor Pressures

Symbols: Simulation

Lines: Reference DIPPR


13

1(1/ ) / KT


/ mol/l0 10 20 30

T /

K

200

300

400

500

600

700

HCl

Phosgene

oCl2-Benzene

Cl-Benzene

Toluene

Benzene

Saturated Densities

Symbols: Simulation

Lines: Reference DIPPR


14


Prediction EMD Simulation

Experiment (Literature) +

T / K150 200 250

Di /

10

-9 m

2 s

-1

0

5

10

15

20

T / K175 200 225 250 275

/

W m

-1 K

-1

0.0

0.1

0.2

0.3

0.4

0.5

T / K160 200 240 280

/ 1

0-4

Pa s

0

1

2

3

4

5

6

Prediction NEMD Simulation

Predictions: Transport Properties of Liquid HCl

p = 0.1 MPa

DIPPR Correlation

G. Guevara-Carrion et al. Fluid Phase Equilib. 316 (2012) 46-54

15


Unlike interaction A-B:

Electrostatics fully predictive

Lennard-Jones parameters from combination rules

Molecular Modelling of Mixtures

AB A B+= / 2σ σ σ

AB A B

=ε ε ε

A A

B B

σA, εA

σB, εB

σAB, εAB

or

State-independent parameter ξ

fitted to one experimental

data point p(T,x) oder H(T)

ξ = 1 Predictions

Modified

Lorentz-Berthelot

T. Schnabel et al. J. Mol. Liq. 135 (2007) 170-178

16


xHCl

/ mol mol-1

0.0 0.2 0.4 0.6 0.8 1.0

p /

MP

a

0

5

10

15

283.15 K

423.15 K

393.15 K

0.05 0.10

0.0

0.1

0.2

0.3

Vapor-Liquid Equilibrium HCl + Chlorobenzene

Symbols: simulation (full)

experiment (cross)

Lines: Peng-Robinson EOS

1.02


17


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%

Study of radial pair correlation functions

,( )

j i

ij

j

local concentration cg r

overall concentration c

18

Local concentration ≠ Overall concentration


r [Å]

0 2 4 6 8

g(r

) [-

]

0

1

2

3

4

5

6

7

8DAT.N2--HCl.Cl

DAT.N2--HCl.H

r [Å]

0 2 4 6 8

g(r

) [-

]0

1

2

3

4

5

6

7

8DAT.N4--HCl.Cl

DAT.N4--HCl.HdH–Cl

dH–Cl

Amine group N2

Radial Pair Correlation Functions: Amine Groups – HCl Important for Formation of Undesired Hydrochlorides

r /Å r /Å

gij(

r)

gij(

r)

Amine group N4

NH2 – (H in HCl)

NH2 – (Cl in HCl)

N4

N2

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


Proton Catalyzed Reaction Ethylene Oxide + Water

20


Proton Catalyzed Reaction Ethylene Oxide + Water

+

21


Radial Pair Correlation Functions

22


Transient Radial Pair Correlation Functions

23


Henry’s Law Constants of Ethylene Oxide

Y. L. Huang, et al. Ind. Eng. Chem. Res. 51 (2012) 7428-7440

EO in Water EO in (Water + Ethylene glycole)

T / K xEG / mol mol-1

350 K

500 K

350 400 450 500

0

10

20

30

HE

O / M

Pa

0

10

20

30

HE

O / M

Pa

Molecular Simulation

Guide for eye

0.00 0.05 0.10 0.15

*

Physical solubility

No chemical reactions

24


Spherical Vapor-Liquid Interfaces

• Droplet + metastable vapor

Spinodal limit: For the external

phase, metastability breaks down.

γR

γpΔ

2

25

liq

gas


Spherical Vapor-Liquid Interfaces

• Droplet + metastable vapor

• Bubble + metastable liquid

Spinodal limit: For the external

phase, metastability breaks down.

Planar limit: The curvature changes

its sign and the radius Rγ diverges.

γR

γpΔ

2

26

liq

gas


Curvature Dependence of Surface Tension

distance from the centre of mass / 0 5 10 15 20

density

/

-3

0.01

0.1

1

T = 0.75 /k

equimolar radius R

LJTS fluid

distance from the centre of mass / 0 5 10 15 20

density

/

-3

0.01

0.1

1

T = 0.75 /k

equimolar radius R

capillarity radius

R = 20/p

LJTS fluid

2R

p

Laplace radius Capillarity radius 02

Rp

Equimolar radius

(from density profile) 2 2

0

0

R

R R

R

R dR R dR

M. Horsch et al. Phys. Rev. E 85 (2012) 031605

27

ρ0

ρ∞


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) 031605

28


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

Planar Vapor-Liquid Interfaces

29


Lennard-Jones fluid

*T*T

/S /S

Evidence for finite size effects for very thin slabs

Surface tension Density in center

S. Werth Physica A submitted (2012)

Planar Vapor-Liquid Interfaces

30


Wetting and Dispersive Fuid-Wall Interactions

reduced fluid-wall dispersive energy 0.05 0.10 0.15 0.20

conta

ct angle

in d

egre

es

0

30

60

90

120

150

180

0.88 /k 0.73 /k1 /k

Young‘s equation

SV SL LV = + cos Θ

solid (S)

liquid (L)vapor (V)

three phase contact

contact angle Θ

Symbols:

Simulation (LJTS)

Lines:

correlations

Curve parameter:

reduced temperature

Reduced wall density

5.876 σ-3

M. Horsch et al., Langmuir 26 (2010) 10913-10917

31


Wetting and Dispersive Fuid-Wall Interactions

Simulation

Correlation

x / σ

y / σ

ρ / σ-3

ρ / σ

-3

y / σ

0

5

10

15

20

25

30

0 5 10 15 20 25

Density profile center Density in droplet

LJTS

32


Wetting, Adsorption and Surface Diffusion

Molecular dynamics

LJTS Model

33


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


Acknowledgment

Funding

DFG SPP 1155

DFG TFB 66

DFG SFB 706

DFG SFB 926

BMBF IMEMO

RLP Research Center CM2

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

35

molecular modeling and simulation of phase … modeling and simulation of phase equilibria for...

Documents