Skip to main content
SpringerLink
Log in

Flowsheet Simulation of Integrated Precipitation Processes

  • Chapter
  • First Online:
Dynamic Flowsheet Simulation of Solids Processes

  • 641 Accesses

Abstract

This work presents the fundamentals and exemplary applications of a generalized model for precipitation, aggregation and ripening processes including the formation of solid phases with two dimensions. The particle formation is governed by a widely applicable population balance approach. Solid formation processes are described via the numerically efficient Direct Quadrature Method of Moments (DQMOM), which can calculate the evolution of multiple solid phases simultaneously. The particle size distribution (PSD) is approximated by a summation of delta functions while the moment source term is approximated by a two-point quadrature. The moments to calculate the multivariate distributions are chosen carefully to represent the second order moments. Solid formation is based on the model of Haderlein et al. (2017) and is extended by a multidimensional aggregation model. Now, the influences of mixing, complex hydrochemistry and particle formation dynamics including nucleation, growth and aggregation on multiphase precipitation processes are modelled and simulated along independent dimensions with high efficiency.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

A:

Fraction of zone in mixing model [–]

A′:

Fraction of zone in mixing model [–]

B:

Fraction of zone in mixing model [–]

B′:

Fraction of zone in mixing model [–]

BHom:

Homogeneous nucleation rate [1/(m3*s)]

BSec:

Secondary nucleation rate [1/(m3*s)]

BHet:

Heterogeneous nucleation rate [1/(m3*s)]

ci:

Concentration of species i [mol/l]

c∞L:

Bulk concentration [mol/l]

Dp:

Diffusion coefficient of phase p [m2/s]

E:

Engulfment factor [1/s]

f:

Particle size distribution density [1/m]

fA,i:

Shape factor of phase i [–]

g:

Residual describing the complex equilibria [–]

Gi:

Diffusion limited growth rate in direction i [m/s]

HA:

Hamaker constant [J]

He:

Adsorption constant [–]

hi,m:

Net particle formation rate of solid phase i in zone m [1/(m*s)]

J:

Jacobian of the residual describing the complex equilibra [–]

I:

Ion activity product of all solid phases [molx/lx]

k:

Order of moment [–]

kB:

Boltzmann constant [J/K]

l:

Oder of mixed moment [–]

ki:

Equilibrium constant of reaction i [molx/lx]

KSP,P:

Solubility product of phase p [molx/lx]

M:

Mixing matrix [–]

Mi:

Molar mass of species i [kg/mol]

N:

Total number of nodes for DQMOM [–]

Ns:

Size of the property vector for node positions [–]

ni,m:

Particle number density of phase i in zone m [1/(m*s)]

n0:

Particle number at the beginning of the simulation [–]

oj:

Logarithmic concentration of species j [–]

R:

Ripening rate [m/s]

Rs:

Reaction stoichiometry matrix [–]

Ri:

Radius of interacting particle [m]

Sp:

Supersaturation of solid phase p [–]

Sξ:

Source term for moment transformation [1/(m*s)]

Sh:

Sherwood number [–]

T:

Temperature [K]

U:

Molar balance stoichiometry matrix [–]

ui:

Mean velocity of internal variable [m/s]

VM:

Molecular volume [m3/mol]

ΔVGrowth:

Volume growth during time step Δt [m3]

wi:

Weighting factor for the Nelder-Mead optimization [–]

Wij:

Fuchs stability ratio [–]

Wtot:

Total interaction potential [J]

x:

Particle diameter [m]

xcrit:

Critical particle diameter [m]

Y:

Normalized center-to-center distance of interacting particles [–]

zi:

Ion charge of species i [–]

β:

Sum of all sources Si [(m/s)k+l]

βBrown:

Brownian aggregation kernel [m3/s]

βTurb:

Turbulent aggregation kernel [m3/s]

γ:

Interfacial energy [N/m]

γi:

Activity coefficient of species i [–]

ε:

Specific power input [W/kg]

ε0:

Vacuum permittivity [A*s/(V*m)]

εr:

Relative permittivity [–]

ζ:

Target functional of the Nelder-Mead optimization [–]

η:

Dynamic viscosity [Pa*s]

θ:

Contact angle for heterogeneous nucleation [–]

Θ:

Heaviside function [–]

κ:

Debye length [1/m]

µij:

Stoichiometric coefficient of component i in species j [–]

ν:

Kinematic viscosity [m2/s]

νij:

Stoichiometric coefficient of species j in reaction i [–]

ξN,α:

Node position of property N of node α [m]

π:

Archimedes constant [–]

ρ:

Solid density [kg/m3]

σ:

Standard deviation of particle size distribution [m]

σi,p:

Stoichiometric coefficient of species i in solid phase p [–]

Φ:

Solution of implicit equation [–]

Ψi:

Surface potential of face i [C/m2]

ωN,α:

Node weight of property N of node α [–]

References

  1. Segets, D., Hartig, M.A.J., Gradl, J., Peukert, W.: A population balance model of quantum dot formation: oriented growth and ripening of ZnO. Chem. Eng. Sci. 70, 4–13 (2012)

    Article  CAS  Google Scholar 

  2. Voigt, M., Klaumünzer, M., Thiem, H., Peukert, W.: Detailed analysis of the growth kinetics of ZnO nanorods in methanol. J. Phys. Chem. C 114, 6243–6249 (2010)

    Article  CAS  Google Scholar 

  3. Encina, E.R., Distaso, M., Klupp Taylor, R.N., Peukert, W.: Synthesis of goethite α-FeOOH particles by air oxidation of ferrous hydroxide Fe(OH) 2 suspensions: insight on the formation mechanism. Crystal Growth Des. 15, 194–203 (2015)

    Article  CAS  Google Scholar 

  4. Haderlein, M., Güldenpfennig, A., Segets, D., Peukert, W.: A widely applicable tool for modeling precipitation processes. Comput. Chem. Eng. 98, 197–208 (2017)

    Article  CAS  Google Scholar 

  5. Hartig, M.A.J., Jacobsen, N., Peukert, W.: Multi-component and multi-phase population balance model: the case of georgeite formation as methanol catalyst precursor phase. Chem. Eng. Sci. 109, 158–170 (2014)

    Article  CAS  Google Scholar 

  6. Gradl, J., Peukert, W.: Simultaneous 3D observation of different kinetic subprocesses for precipitation in a T-mixer. Chem. Eng. Sci. 64, 709–720 (2009)

    Article  CAS  Google Scholar 

  7. Schikarski, T., Trzenschiok, H., Avila, M., Peukert, W.: Influence of mixing on the precipitation of organic nanoparticles: a lagrangian perspective on scale-up based on self-similar distributions. Chem. Eng. Technol. 23, 1635–1642 (2019)

    Google Scholar 

  8. Rollié, S., Briesen, H., Sundmacher, K.: Discrete bivariate population balance modelling of heteroaggregation processes. J. Colloid Interface Sci. 336, 551–564 (2009)

    Article  Google Scholar 

  9. Haderlein, M., Segets, D., Gröschel, M., Pflug, L., Leugering, G., Peukert, W.: FIMOR: an efficient simulation for ZnO quantum dot ripening applied to the optimization of nanoparticle synthesis. Chem. Eng. J. 260, 706–715 (2015)

    Article  CAS  Google Scholar 

  10. Skorych, V., Dosta, M., Hartge, E.-U., Heinrich, S.: Novel system for dynamic flowsheet simulation of solids processes. Powder Technol. 314, 665–679 (2017)

    Article  CAS  Google Scholar 

  11. Bogacki, P., Shampine, L.F.: A 3(2) pair of Runge—Kutta formulas. Appl. Math. Lett. 2, 321–325 (1989)

    Article  Google Scholar 

  12. Marchisio, D.L., Fox, R.O.: Solution of population balance equations using the direct quadrature method of moments. J. Aerosol Sci. 36, 43–73 (2005)

    Article  CAS  Google Scholar 

  13. Bourne, J.R.: Mixing and the selectivity of chemical reactions. Org. Process Res. Dev. 7, 471–508 (2003)

    Article  CAS  Google Scholar 

  14. Schwarzer, H.-C., Peukert, W.: Combined experimental/numerical study on the precipitation of nanoparticles. AIChE J. 50, 3234–3247 (2004)

    Article  CAS  Google Scholar 

  15. Gradl, J., Schwarzer, H.-C., Schwertfirm, F., Manhart, M., Peukert, W.: Precipitation of nanoparticles in a T-mixer: coupling the particle population dynamics with hydrodynamics through direct numerical simulation. Chem. Eng. Process. 45, 908–916 (2006)

    Article  CAS  Google Scholar 

  16. Baldyga, J., Bourne, J.R.: Simplification of micromixing calculations. I. Derivation and application of new model. Chem. Eng. J. 42, 83–92 (1989)

    Article  CAS  Google Scholar 

  17. Bałdyga, J., Bourne, J.R.: Turbulent Mixing and Chemical Reactions. Wiley, Chichester (1999)

    Google Scholar 

  18. Schwarzer, H.-C.: Nanoparticle Precipitation: An Experimental and Numerical Investigation Including Mixing. Logos-Verl, Berlin (2005)

    Google Scholar 

  19. Guichardon, P., Falk, L., Villermaux, J.: Characterisation of micromixing efficiency by the iodide–iodate reaction system. Part II: kinetic study. Chem. Eng. Sci. 55, 4245–4253 (2000)

    Article  CAS  Google Scholar 

  20. Commenge, J.-M., Falk, L.: Villermaux-Dushman protocol for experimental characterization of micromixers. Chem. Eng. Process. 50, 979–990 (2011)

    Article  CAS  Google Scholar 

  21. Davies, C.W.: 397. The extent of dissociation of salts in water. Part VIII. An equation for the mean ionic activity coefficient of an electrolyte in water, and a revision of the dissociation constants of some sulphates. J. Chem. Soc. 2093–2098 (1938)

    Google Scholar 

  22. Lifshitz, I.M., Slyozov, V.V.: The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids 19, 35–50 (1961)

    Article  Google Scholar 

  23. Zur, Fuchs N., der Koagulation, Theorie: Z. Phys. Chem. 171A, 199–208 (1934)

    Google Scholar 

  24. Monnin, C.: A thermodynamic model for the solubility of barite and celestite in electrolyte solutions and seawater to 200 °C and to 1 kbar. Chem. Geol. 153, 187–209 (1999)

    Article  CAS  Google Scholar 

  25. Powell, K.J., Brown, P.L., Byrne, R.H., Gajda, T., Hefter, G., Sjöberg, S., Wanner, H.: Chemical speciation of environmentally significant metals with inorganic ligands Part 2: The Cu2+, OH−Cl−, CO32−, SO42−, and PO43− systems (IUPAC Technical Report). Pure Appl. Chem. 79, 95–950 (2007)

    Article  Google Scholar 

  26. Reichle, R.A., McCurdy, K.G., Hepler, L.G.: Zinc hydroxide: solubility product and hydroxy-complex stability constants from 12.5–75 ℃. Can. J. Chem. 53, 841–3845 (1975)

    Article  Google Scholar 

  27. Martell, E., Smith, R.M.: NIST Standard Reference Database 46. NIST Critically Selected Stability Constants of Metal Complexes: Version 8.0 (2016)

    Google Scholar 

  28. Alwan, A.K., Thomas, J.H., Williams, P.A.: Mineral formation from aqueous solution. Part III. The stability of aurichalcite, (Zn, Cu)5(CO3)2(OH)6, and rosasite (Cu, Zn)2(CO3)(OH)2. Transition Met. Chem. 5, 3–5 (1980)

    Article  CAS  Google Scholar 

  29. Leussing, D.L., Kolthoff, I.M.: The solubility product of ferrous hydroxide and the ionization of the aquo-ferrous ion. J. Am. Chem. Soc. 75, 2476–2479 (1953)

    Article  CAS  Google Scholar 

  30. Güldenpfennig, A., Distaso, M., Klupp Taylor, R.N., Peukert, W.: Modelling the two-dimensional growth and oriented attachment of goethite nanorods synthesized via oxidation of aqueous ferrous hydroxide slurries. Chem. Eng. J. 347, 798–807 (2018)

    Article  Google Scholar 

  31. Russell, B., Payne, M., Ciacchi, L.C.: Density functional theory study of Fe(II) adsorption and oxidation on goethite surfaces. Phys. Rev. B 79, 165101–165114 (2009)

    Article  Google Scholar 

  32. Rustad, J.R., Felmy, A.R., Hay, B.P.: Molecular statics calculations of proton binding to goethite surfaces: a new approach to estimation of stability constants for multisite surface complexation models. Geochim. Cosmochim. Acta 60, 1563–1576 (1996)

    Article  CAS  Google Scholar 

  33. Israelachvili, J.N.: Intermolecular and surface forces. Academic Press, MA, Burlington (2011)

    Google Scholar 

  34. Güldenpfennig, A., Pflug, L., Peukert, W.: How to estimate material parameters for multiphase, multicomponent precipitation modeling. Cryst. Growth Des. 19, 2785–2793 (2019)

    Article  Google Scholar 

  35. Akdas, T., Distaso, M., Kuhri, S., Winter, B., Birajdar, B., Spiecker, E., Guldi, D.M., Peukert, W.: The effects of post-processing on the surface and the optical properties of copper indium sulfide quantum dots. J. Colloid Interface Sci. 445, 337–347 (2015)

    Article  CAS  Google Scholar 

  36. Süß, S., Michaud, V., Amsharov, K., Akhmetov, V., Kaspereit, M., Damm, C., Peukert, W.: Quantitative evaluation of fullerene separation by liquid chromatography. J. Phys. Chem. C 123, 16747–16756 (2019)

    Article  Google Scholar 

  37. Süß, S., Metzger, C., Damm, C., Segets, D., Peukert, W.: Quantitative evaluation of nanoparticle classification by size-exclusion chromatography. Powder Technol. 339, 264–272 (2018)

    Article  Google Scholar 

  38. Khomane, A.S., Hankare, P.P.: Structural, optical and electrical characterization of chemically deposited CdSe thin films. J. Alloys Compd. 489, 605–608 (2010)

    Article  CAS  Google Scholar 

  39. Salaheldin, A.M., Walter, J., Herre, P., Levchuk, I., Jabbari, Y., Kolle, J.M., Brabec, C.J., Peukert, W., Segets, D.: Automated synthesis of quantum dot nanocrystals by hot injection: mixing induced self-focusing. Chem. Eng. J. 320, 232–243 (2017)

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge financial support of Deutsche Forschungsgemeinschaft (DFG) in the scope of SPP 1679 (Dynamic Simulation of Interconnected Solids Processes) coordinated by Prof. S. Heinrich.

Author information

Authors and Affiliations

  1. Institute of Particle Technology, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    Mark Michaud, Michael Haderlein & Wolfgang Peukert

  2. Process Technology for Electrochemical Functional Materials, Institute for Combustion and Gas Dynamics - Reactive Fluids (IVG-RF), and Center for Nanointegration Duisburg-Essen (CENIDE), Essen, Germany

    Doris Segets

Authors
  1. Mark Michaud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Haderlein
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Doris Segets
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wolfgang Peukert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wolfgang Peukert .

Editor information

Editors and Affiliations

  1. Institute of Solids Process Engineering and Particle Technology, Hamburg University of Technology, Hamburg, Germany

    Stefan Heinrich

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Michaud, M., Haderlein, M., Segets, D., Peukert, W. (2020). Flowsheet Simulation of Integrated Precipitation Processes. In: Heinrich, S. (eds) Dynamic Flowsheet Simulation of Solids Processes. Springer, Cham. https://doi.org/10.1007/978-3-030-45168-4_8

Download citation

Publish with us

Policies and ethics

Search

Navigation