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Getting closer to a fully predictive equation of state for rigoroussimulation of chemical processes: COSMO-SAC-Phi

Rafael de Pelegrini Soares

FED. UNIV. OF RIO GRANDE DO SULCHEMICAL ENGINEERING DEPARTMENTVirtual Laboratory for Properties Prediction

http://ufrgs.br/lvpp

October, 2018

IntroductionCOSMO-SAC-Phi

Conclusions

Process SimulationCOSMO-RS or COSMO-SACSigma profile

Rigorous process simulation of chemical processes

Typical chemical process forhigh purity propyleneseparation∗

Distillation column with morethan 150 stages

iiSE† equation-orientedsimulation with around 9000variables

∗Diego F. Mendoza et al. In: Ind. Eng. Chem. Res. 52.16 (2013), pp. 5735–5746†iiSE equation oriented simulator. http://iise.ltd. Accessed: 2019

Rafael de Pelegrini Soares COSMO-SAC-Phi - PSE-BR 2019 2 / 24

http://iise.ltd


Conclusions


Rigorous process simulation: need for thermo-physical properties

9000 variables require 9000equations to solve

In rigorous simulators theseequations are mass balances,energy balances, phaseequilibrium relations,themo-physical properties,etc.

For simple hydrocarbons,cubic equations of state(CEoS) are usually enough



Conclusions


Rigorous process simulation: more complex mixtures

It is difficult to separate benzene from otherhydrocarbons of similar boiling point

benzene cyclohexane

NFM

353.24 K 353.88 K

512 K

Extractive distillation with NFM∗

∗L. B. Brondani, G. B. Flores, and R. P. Soares. In: Braz. J. Chem. Eng. 32 (2015), pp. 283–291Rafael de Pelegrini Soares COSMO-SAC-Phi - PSE-BR 2019 4 / 24


Conclusions



It is difficult to separate benzene from otherhydrocarbons of similar boiling point

benzene cyclohexane NFM353.24 K 353.88 K 512 K

Extractive distillation with NFM∗



Conclusions



benzene (BZ) cyclohexane (CH) NFM

For these cases, CEoS are usually notenough (even with adjusted kij)

NRTL could be used∗, it requirescorrelated parameters for every pair ofsubstances (experimental data)


Even worse if we consider other emerging technologies

Bio-based platforms∗ Ionic Liquids† Deep Eutectic Solvents‡ . . .

GVL EMIM choline

glycerol PF6 urea

......

...It will be very difficult to rely on CEoS, NRTL, UNIFAC, etc. for these applications...

∗Hans Heeres et al. In: Green Chem. 11 (8 2009), pp. 1247–1255†Thomas Welton. In: Chemical Reviews 99.8 (1999), pp. 2071–2084‡Andrew P. Abbott et al. In: J. A. Chem. Society 126.29 (2004), pp. 9142–9147

COSMO method (solutes alone) vs COSMO-RS/SAC

The COSMO∗ method was originally developed for thecomputation of solvation effects

Belongs to the class of dielectric continuum models

, the cavitiesare discretized into segments or patches

Induced charges are computed by quantum chemistry packages(time consuming) and then stored in a database (e.g. LVPPsigma-profile database† http://github.com/lvpp/sigma)

∗A Klamt and G Schuurmann. In: J. Chem. Soc., Perkin Trans. 2 (1993), pp. 799–805†F. Ferrarini et al. In: AIChE Journal 64.9 (2018), pp. 3443–3455

http://github.com/lvpp/sigma

COSMO method (solutes alone) vs COSMO-RS/SAC

The COSMO∗ method was originally developed for thecomputation of solvation effects

Belongs to the class of dielectric continuum models, the cavitiesare discretized into segments or patches

Induced charges are computed by quantum chemistry packages(time consuming) and then stored in a database (e.g. LVPPsigma-profile database† http://github.com/lvpp/sigma)

∗A Klamt and G Schuurmann. In: J. Chem. Soc., Perkin Trans. 2 (1993), pp. 799–805†F. Ferrarini et al. In: AIChE Journal 64.9 (2018), pp. 3443–3455


COSMO-RS – Surface contacting theory (mixtures)

In the COSMO-RS∗ methods we rely on COSMOcomputations with the molecules surrounded by aperfect conductor

Based on these pure substance computations, themixture behavior is predicted (γi , µi )

The COSMO-SAC† formulation follows the sameidea

For every contact between segments m and n thereis an energy change ∆Wm,n

There are many possible contacts in solution

∗Andreas Klamt. In: The J. of Phys. Chem. 99.7 (1995), pp. 2224–2235†ST Lin and S.I. Sandler. In: Ind. Eng. Chem. Res. 41.5 (2002), pp. 899–913


Conclusions


Sigma profile – p(σ)

For a statistical thermodynamicstreatment (without using MD or MC),the 3D apparent surface charges areprojected into a simple histogram

These pure compound distributions,known as sigma profiles – p(σ), are thebasis for computing γi or µi in mixture

“It is always desirable to express the properties of a solution in terms that can be calculated completelyfrom the properties of the pure components.” – J. M. Prausnitz. Molecular thermodynamics offluid-phase equilibria. Third. Prentice-Hall, 1999.



Conclusions

Model developmentResults

Model for liquid phases only?

The real solution should not contain theperfect conductor surrounding themolecules

For every contact between molecules, theconductor is partially excluded

Thus, all surface segments should be inpairwise contact

Hence there is no free volume andV = nibi


EOS combined with COSMO-RS/SAC

NRCOSMO∗: combination of COSMO with the so called non-randomhydrogen-bonding (NRHB) equation of state

σ-MTC†: an extension of the Mattedi-Tavares-Castier equation which combinesthe sigma-profile from COSMO computations with the generalized van der Waalstheory

Cubic EOS + MR + COSMO-SAC:

PR+WS+COSMO-SAC‡

PR+SCMR+COSMO-SAC§

PR+mSCMR+COSMO-SAC¶

. . .

All methods need some bridge to couple COSMO with the EOS

∗C. Panayiotou. In: Pure and Appl. Chem. 83.6 (2011), pp. 1221–1242†C.T.O.G. Costa, F.W. Tavares, and A.R. Secchi. In: Fluid Phase Equilib. 409 (2016), pp. 472–481‡MT Lee and ST Lin. In: Fluid Phase Equilib. 254.1-2 (2007), pp. 28–34§P.B. Staudt and R.P. Soares. In: Fluid Phase Equilib. 334 (2012), pp. 76–88¶LH Wang, CM Hsieh, and ST Lin. In: Ind. Eng. Chem. Res. 57.31 (2018), pp. 10628–10639


Conclusions


COSMO-SAC-Phi: seamless extension∗

By this pseudo-mixture, COSMO-RS, COSMO-SAC, or F-SAC can be used tocompute µi and µh as long as we know the number of molecules and holes

∗R. de P. Soares, L. F. Baladao, and P. B. Staudt. In: Fluid Phase Equilib. 488 (2019), pp. 13–26Rafael de Pelegrini Soares COSMO-SAC-Phi - PSE-BR 2019 12 / 24


Conclusions


COSMO-SAC-Phi: seamless extension



Conclusions


COSMO-SAC-Phi: current status

Repulsive pressure by a simple hard spheremodel

σ-profiles from the open source LVPPsigma-profile

GMHB1808 COSMO-SAC parametrization

Freely availabe athttp://github.com/lvpp/sigma

Per compound parameters:bi , δ

0i , δTi , and bh,i



Pure compound saturation pressure and liquid volume

COSMOSAC-PHI SRK-MCPressure Volume Pressure Volume

Average deviation (%) 1.15 1.63 1.64 15.48

100 150 200 250 300 350 400 450 500 550 600T [K]

9.0

9.5

10.0

10.5

11.0

11.5

12.0

12.5

13.0

13.5

14.0

14.5

15.0

15.5

16.0

16.5

ln P

[P

a]

METHANE

CARBON DIOXIDE

AMMONIA

WATER

COSMO-SAC-Phi

SRK-MC

100 150 200 250 300 350 400 450 500 550 600T [K]

2 0

2 5

3 0

3 5

4 0

4 5

5 0

5 5

6 0

6 5

v [

cm

3/m

ol]

METHANE

CARBON DIOXIDE

AMMONIA

WATER

COSMO-SAC-Phi

SRK-MC

Pure compound saturation pressure and liquid volume

COSMOSAC-PHI SRK-MCPressure Volume Pressure Volume

Average deviation (%) 1.15 1.63 1.64 15.48

250 300 350 400 450 500 550T [K]

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

10.5

11.0

11.5

12.0

12.5

13.0

13.5

14.0

14.5

15.0

ln P

[P

a]

N-OCTANE

BENZENE

N-BUTANE

ETHANOL

COSMO-SAC-Phi

SRK-MC

250 300 350 400 450 500 550T [K]

5 0

7 5

100

125

150

175

200

225

250

275

300

325

350

v [

cm

3/m

ol]

N-OCTANE

BENZENE

N-BUTANE

ETHANOL

COSMO-SAC-Phi

SRK-MC


Conclusions


Low pressure VLE predictions (no BIPs)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0x1, y1

0.650

0.675

0.700

0.725

0.750

0.775

0.800

0.825

0.850

0.875

0.900

0.925

0.950

Pre

ssu

re [

ba

r]

Exp. 323.15 KCOSMO-SAC-PhiSRK-MC+vdWCOSMO-SAC

(a) methyl acetate/1-hexene

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0x1, y1

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

Pre

ssu

re [

ba

r]


(b) methanol/waterRafael de Pelegrini Soares COSMO-SAC-Phi - PSE-BR 2019 17 / 24


Conclusions


Low pressure VLE predictions (no BIPs)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0x1, y1

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

Pre

ssu

re [

ba

r]


(c) chloroform/diethyl ether

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0x1, y1

0.27

0.28

0.29

0.30

0.31

0.32

0.33

0.34

0.35

0.36

0.37

0.38

Pre

ssu

re [

ba

r]


(d) chloroform/acetoneRafael de Pelegrini Soares COSMO-SAC-Phi - PSE-BR 2019 18 / 24


Conclusions


High pressure VLE predictions (no BIPs)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0x1, y1

5.0

7.5

10.0

12.5

15.0

17.5

20.0

22.5

25.0

Pre

ssu

re [

ba

r]

Exp. 323.15 KCOSMO-SAC-PhiSRK-MC+vdW

(e) ammonia/n-butane

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0x1, y1

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

100

Pre

ssu

re [

ba

r]

Exp. 399.14 KCOSMO-SAC-PhiSRK-MC+vdW

(f) ammonia/waterRafael de Pelegrini Soares COSMO-SAC-Phi - PSE-BR 2019 19 / 24


Conclusions


LLE predictions

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

x1 (N-PENTANOL)

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

460

470

Te

mp

era

ture

[K

]

Exp.

COSMO-SAC-Phi

UNIFAC-LLE

(g) n-pentanol/water

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

x1 (N-OCTANE)

275

300

325

350

375

400

425

450

475

500

525

550

575

Te

mp

era

ture

[K

]

Exp.

COSMO-SAC-Phi

UNIFAC-LLE

(h) n-octane/waterRafael de Pelegrini Soares COSMO-SAC-Phi - PSE-BR 2019 20 / 24

Gas related systems∗

(i) methane/water, CPA+BIP (solid) andGERG-WATER+T-BIP (dashed)

(j) COSMO-SAC-Phi predictions

∗Michael Frost et al. In: J. of Chem. Eng. Data 59.4 (2014), pp. 961–967

Gas related systems∗

(k) methanol in gas phase, CPA+BIP (solid) (l) COSMO-SAC-Phi predictions

∗Michael Frost et al. In: J. of Chem. Eng. Data 59.4 (2014), pp. 961–967


Conclusions

ConclusionsLinks and more info

Conclusions and Future Work

COSMO-SAC can be seamlessly extended to capture pressure effects by theaddition of free-volume (holes)

There is no need to define a lattice, coordination number, or association scheme

Currently, the model is calibrated with pure compound parameters for volume anddispersion

Pure compound saturation pressure and volume could be correlated with less than2% average error

Mixture VLE and LLE were predicted with a good accuracy for several differentsubstances, kinds of deviations and pressures

Future work:Reduce the number of model parametersReduce the dependence on pure compound data. . .


Thank you!

The LVPP sigma-profile database is freely available athttps://github.com/lvpp/sigma

Our homepage: http://ufrgs.br/lvpp

Contact: [email protected]

CBTERMO 2019 - RJ - Nova Friburgo - nov. 2019:

Cosmo-type models: fundamentals and tools

Special thanks:

https://github.com/lvpp/sigma

http://ufrgs.br/lvpp

[email protected]

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