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Thermodynamic Modeling of Multi-phase Solid–Liquid Equilibria in Industrial-Grade Oils and Fats

  • Original Paper
  • Published:
Journal of the American Oil Chemists' Society

Abstract

Compositional thermodynamic phase separation is investigated for industrial-grade vegetable oils with complex compositions. Solid–liquid equilibria have been calculated by utilizing the Margules 2-suffix activity-coefficient model in combination with minimization of the Gibb’s free energy of the system. On the basis of quasi-equilibrium solid-fat content (SFC) measurements, a new approach to the estimation of the interaction parameters, needed for the activity-coefficient model, has been developed. The parameters are fitted by matching the SFC of two oils at various degrees of dilution and isothermal temperatures. Subsequently, the parameters are successfully validated against three oils, rich in asymmetric and symmetric triacylglycerols (TAG), respectively. The new approach developed is shown to be very flexible, allowing incorporation of additional TAG and polymorphic states. It thereby provides a simple way to dealing with multi-component, multi-phase TAG mixtures without having the required binary interaction parameters at hand a priori. This ultimately provides a powerful, predictive tool which may serve as a starting point for laboratory screening and creation of tailor-made products because many different oil mixtures can be evaluated quickly with respect to specific properties, prior to more time-consuming experimental evaluation.

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Abbreviations

α :

Polymorphic form, least stable

β :

Polymorphic form, most stable

β′ :

Polymorphic form, intermediate stability

γ j i :

Activity coefficient of TAG i in the solid phase, j

γ l i :

Activity coefficient of TAG i in the liquid phase, l

μ j i (J/mol):

Chemical potential of component in the solid phase, j

μ l i (J/mol):

Chemical potential of component i in the liquid phase, l

θ :

Interaction parameter matrix

A ik :

Interaction parameter between TAG i and k

G (J/mol):

Gibb’s free energy of the system

g E (J/mol):

Gibb’s excess energy

ΔH sl i (J/mol):

Heat of fusion of TAG i

M i (g/mol):

Molar mass of TAG i

m :

Number of evaluated data points

N :

Number of components in the system

n j i (mol):

Number of moles of TAG i in the solid phase, j

n j (mol):

Number of moles in the solid phase, j

n l (mol):

Number of moles in the liquid phase, l

n l i (mol):

Number of moles of TAG i in the liquid phase, l (mol)

n l,eq i :

Number of moles of TAG i in the liquid phase at equilibrium

n i,tot (mol):

Total amount of component i in the system

P :

Number of phases in the system

R [J/(mol K)]:

Gas constant (8.314)

T (K):

Temperature

\(T_{m, i} (K)\) :

Melting temperature of TAG i

x i :

Mole fraction of TAG i in the liquid phase, l

y i :

Mole fraction of component i in the trial phase

Y i :

Phase stability evaluation parameter

z j i :

Mole fraction of TAG i in the solid phase, j

d :

dth adjustable parameter

i :

ith triacylglycerol

j :

jth solid phase

k :

kth triacylglycerol

l :

Liquid phase

s :

sth data point

y :

Trial phase

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Acknowledgments

We gratefully acknowledge the financial support received from The Danish Agency for Science, Technology and Innovation (Forsknings-og Innovationsstyrelsen) and InSPIRe (Project no. III-4).

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Authors and Affiliations

  1. AAK Denmark A/S, Slipvej 4, 8000, Aarhus C, Denmark

    Jeppe L. Hjorth & Rasmus L. Miller

  2. Department of Chemical and Biochemical Engineering, Technical University of Denmark, DTU, Building 229, 2800, Kongens Lyngby, Denmark

    John M. Woodley & Søren Kiil

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  1. Jeppe L. Hjorth
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Correspondence to Jeppe L. Hjorth.

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Hjorth, J.L., Miller, R.L., Woodley, J.M. et al. Thermodynamic Modeling of Multi-phase Solid–Liquid Equilibria in Industrial-Grade Oils and Fats. J Am Oil Chem Soc 92, 17–28 (2015). https://doi.org/10.1007/s11746-014-2577-0

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