Molecular dynamics simulation of liquid-liquid equilibria ... · PROF.DR.-ING.HABIL. JADRAN VRABEC INSTITUT FÜR VERFAHRENSTECHNIK THERMODYNAMIK UND ENERGIETECHNIK ThEt Molecular

PROF. DR.-ING. HABIL. JADRAN VRABEC

INSTITUT FÜR VERFAHRENSTECHNIK

THERMODYNAMIK UND ENERGIETECHNIK ThEt

Molecular dynamics simulation of liquid-liquid

equilibria using molecular models adjusted to

vapor-liquid equilibrium data

Darmstadt, 27.03.2012

STEFAN ECKELSBACH

ZHONGNING WEI

THORSTEN WINDMANN

JADRAN VRABEC




page 2

Phase equilibrium data needed for thermodynamic processes

• Distillation

• Adsorption

• Extraction

Vapor-liquid equilibria (VLE)

Liquid-liquid equilibria (LLE)

→ Classical approach:

Properties determined by experiments

Data correlated by empirical models

Introduction




page 3

Models for VLE and LLE are inconsistent

• Different models

• Different parameters

* E. Hendriks, G. M. Kontogeorgis, R. Dohrn, et al., Ind. Eng. Chem. Res. 49 (2010), 11131.

Difficulties of classical approach

Large effort for measurements required

• Multicomponents sytems

• Multiple phases (e.g. VLLE)

Need for predictive approach*




page 4

Molecular simulation

• Predictive method for consistent description of VLE and LLE?

A

a

B

b ijab

ab

ijab

ababij

rru

1 1

612

4

• All thermodynamic data can be determined from molecular

interactions

• Interactions can be described by force fields, e. g.

Lennard-Jones potential




page 5

Numerical solution of Newton’s equations of motion

ir

i

ir

velocity

acceleration

ircoordinate

ij ij

uFr

i ijj i

F F

i

i

i

m

Fr

Force between two molecules

Resulting force on one molecule

Acceleration of one molecule ir

ir

<time averaging>

Molecular dynamics




• Models for molecular interaction

page 6

Molecular models

* T. Merker, J. Vrabec and H. Hasse: Soft Materials 10 (2012) 3.

• Parameters physically interpretable

Based on quantum mechanical

calculations

• Adjusted to VLE data*

Transition from pure substances to mixtures straightforward

Good reliability

High predictive power




mole fraction (N2)

0,0 0,2 0,4 0,6 0,8 1,0

pre

ssure

[M

Pa]

0

5

10

15

simulation

equation of state

experimental data

200 K

290 K

page 7

Molecular models adjusted to VLE data

mixture parameter

ξ = 0.974

Good results compared

to equation of state

(Peng-Robinson) and

experiments

Nitrogen and ethane




• Every day example: mixture

of water and oil

page 8

Liquid-liquid equilibria

• Water dominated by hydrogen bonding

• Oil dominated by van der Waals interactions

Separation in two phases

Surface tension at interface




page 9

Liquid-liquid equilibria

mole fraction (component 1)0,0 0,2 0,4 0,6 0,8 1,0

tem

pera

ture

critical point

miscibility gap

Temperature dependence of LLE (example)




page 10

Molecular dynamics code ls1

• Developed in Stuttgart, Kaiserslautern, Munich and Paderborn

• Language: C++

• Computing time scales linearly with number of molecules

• Capable of dealing with large molecular systems

• Excellent parallelization

• Release of ls1 in 2012




page 11

Molecular dynamics code ls1: parallelization

• Parallelization benchmarks

• Performed on Cray XE6

(Hermit) at Höchstleistungsrechenzentrum Stuttgart (HLRS)

• Peak performance: 1.045 PFLOPS; cores: 113,664

• Three systems (bulk, drop, film)




page 12

cores102 103 104 105

com

puting t

ime [

s]

10

100

1000 bulk

film

drop

Scaling of ls1 on Cray XE6 (Hermit)

Strong scaling

222 = 4,194,304

molecules

Simulation of

1,000 timesteps




page 13

cores102 103 104 105

com

puting tim

e [s]

10

100

1000

bulk

film

drop

Strong scaling

226 = 67,108,864

molecules

Simulation of

1,000 timesteps

Scaling of ls1 on Cray XE6 (Hermit)




page 14

Present simulation

• Mixture of 40 mol-% ethane and 60 mol-% nitrogen

• Canonical ensemble (constant NVT)

• 20,000 molecules

• Starting from random distribution of components




page 15

box length [nm]

0 2 4 6 8 10 12 14 16 18

mole

fra

ction

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

N2

C2H6

Results

LLE phases after 24 Million timesteps

temperature: 128 K

pressure: 11.03 MPa

averaged over

500,000 simulation steps




page 16

Results

simulation steps [106]

0 5 10 15 20 25

mo

le f

ractio

n (

N2)

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

phase 1

phase 2

Mole fraction of N2 in both phases

temperature: 128 K

pressure: 11.03 MPa

averaged over

800,000 simulation

steps




page 17

Im DDB-plot Simulationsergebnisse darstellen

Abweichung angeben?

mole fraction (phase 1; N2)

0,30 0,32 0,34 0,36 0,38 0,40 0,42 0,44

pre

ssure

[M

Pa]

4

6

8

10

12

14

DDB

simulation results

Results in comparison to experimental data

Results

temperature: 128 K




page 18

Computation

All simulations were realized on Cray XE6 (Hermit) at

Höchstleistungsrechenzentrum Stuttgart (HLRS)

• 576 cores

• 18 nodes

• Duration of computing time: ~107 h




page 19

Conclusion

• With molecular modelling and simulation it is possible to

cover VLE and LLE consistently with the same models and

parameters

• Good accuracy

• Needs some computing time

• Particularly interesting for components, which are not

easy to measure (explosive, toxic, …)

• Reduction of simulation time through preparing two phases in

advance




page 20

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Molecular dynamics simulation of liquid-liquid equilibria ... · PROF.DR.-ING.HABIL. JADRAN VRABEC INSTITUT FÜR VERFAHRENSTECHNIK THERMODYNAMIK UND ENERGIETECHNIK ThEt Molecular