Knowledge about the phase equilibrium in the system is essential for a better understanding of the process and improvement of the reaction rate, the selectivity of the desired product, and the separation process for the product mixture. Many researchers have investigated multicomponent systems in order to understand and provide further information about the phase behaviour and the thermodynamic properties of such systems.
After the experimental data is obtained, it is possible to convert the data into a phase diagram. The phase diagram is unique in that they show all components of a system on one plot. There are many ways to plot the data using a diagram.
According to Tizvar et al. (2008) the liquid-liquid phase diagram of quaternary systems of methyl oleate-glycerol-hexane-methanol can be displayed graphically by plotting the data in a pyramid, where each of the corners represents the estimated three-dimensional surface of the two-phase region. Every point inside the two-phase region represents a mixture of the four components and will be separated into two liquid phases at physical equilibria. As a conclusion, this simulation is consistent with the results obtained in the LLE experiments of this system, which showed separation of the mixtures into two liquid phases: one is rich in methyl oleate and hexane, and the other is rich in glycerol and methanol.
Figure 2.1.1: Schematic image of the quaternary phase diagram on a molar basis, using the UNIFAC model for the methyl oleate-glycerol-hexane-methanol system at 20 °C (the methanol vertex is above the plane of the paper, and the dark surface indicates the boundary of the one-phase and two-phase regions). Straight lines with data points on either end represent experimental tielines.
In other work (Kim and Park, 2005), the quaternary systems of toluene-water-propionic acid-ethyl acetate were separated into three ternary systems. After the ternary diagrams were constructed, those diagrams were combined to form pyramid. As a conclusion, the model prediction for the ternary system it is slightly deviate with the experimental data. For the quaternary system, it was shown that the model prediction was capable of predicting the composition with a small deviation value.
Figure 2.1.2 (a): Binodal curves and tielines of three ternary mixtures making up toluene (1)-water (2)-propionic acid (3), ethyl acetate (1)-water (2)-propionic acid (3), and toluene (1)-ethyl acetate (2)-water (3).
Figure 2.1.2 (b): Phase equilibrium of toluene (1)-water (2)-propionic acid (3)-ethyl acetate (4). R1, R2, and R3 denote quaternary sectional planes.
2.2 LLE data for esterification
Many researchers have done their work in developing LLE data for esterification process.
Liu et al. (2009) study the mutual solubility of the esterification process of some free fatty acids (FFAs) with methanol. Ternary diagram were plotted in order to determine the tie lines. The results show that the mutual solubility increases with temperature.
Schmitt and Hasse (2005) study LLE in the systems water + 1-hexanol, water + hexyl acetate, water + acetic acid + 1-hexanol, and water + acetic acid + hexyl acetate at temperatures between (280 and 355)K for the scale-up of reactive distillation. The experimental data obtained was then compared with NRTL. The comparison shows that they give reliable predictions for the conditions encountered in reactive distillation.
Lladosa et al. (2008) study the thermodynamic behaviour of catalytic esteriï¬cation reaction equilibrium and and vapour-liquid equilibria (VLE) of four quaternary system and liquid-liquid equilibria (LLE) of the binary system butan-1-ol + water at 101.3kPa. In this study, p-toluene sulfonic acid was selected as the catalyst to accelerate the chemical reaction. The measured data were correlated by the NRTL and UNIQUAC activity coefficient models. As a conclusion, the data fitted well in both of the models.
Naydenov and Bart (2009) investigated the effect of the alkyl chain on the alcohol and ester on the phase equilibria for thesystems containing reactants and products of esteriï¬cation reactions. The systems were alcohol (1-propanol or 1-butanol) or acetic acid + ester + the ionic liquid 1-ethyl-3-methylimidazolium hydrogen sulphate [EMIM] [HSO4] were studied at (313.2 ± 0.5) K. The result shows that, increase of the alkyl chain length on alcohol and ester leads to bigger immiscibility regions and better solubility of the alcohol in the ester phase. The distribution of the acetic acid between the two phases is almost independent of the esters for the measured systems and is dependent mainly on the ionic liquid.
Grob and Hasse (2005) investigated the reaction equilibrium of the reversible esterification of acetic acid with 1-butanol giving 1-butyl acetate and water. The experiments were carried out in a multiphase batch reactor with online gas chromatography and in a batch reactor with quantitative H NMR spectroscopy, respectively. Thermodynamically consistent models of the reaction equilibrium were developed which predict the concentration dependence of the mass action law pseudo equilibrium constant, Kx. The following different modelling approaches are compared: the GE models NRTL and UNIQUAC as well as the PC-SAFT equation of state and the COSMO-RS model. The results show that all models give good results with regard to reaction equilibrium. Especially the COSMO-RS model seems to be promising for predicting the concentration dependence of the pseudo equilibrium constant, Kx.
2.3 Thermodynamic model (UNIQUAC, UNIFAC, NRTL)
Thermodynamic modelling including the selection of the best models for use with process simulation is a recognized topic is chemical engineering that is held in the same regard as process simulation.
A classical chemical plant can be roughly divided in a preparation, reaction, and separation step. Although the reactor can be considered as the heart or core of the chemical plant, often 60-80 % of the total costs are caused by the separation step, where the various thermal separation processes (in particular distillation processes) are applied to obtain the products with the desired purity, to recycle the unconverted reactants, and to remove the undesired side-products (Gmehling, 2003).
Proper selection of thermodynamic models during process simulation is absolutely necessary as a starting point for accurate process simulation. A process that is otherwise fully optimized in terms of equipment selection, configuration, and operation can be rendered essentially worthless if the process simulation is based on inaccurate thermodynamic models. Because of this, good heuristics and appropriate priority should be placed on both selecting thermodynamic models and reporting the selections in process reports.
During process simulation, thermodynamic model selection should be performed in at least two steps. Firstly, as with initial process configurations, the thermodynamic model should be chosen based on heuristics (heuristics) that provide for a good base case but may or may not provide the desired level of accuracy. Secondly, based on the results of the base case simulation (complete with cost estimate), improving the accuracy of the thermodynamic models should be prioritized relative to optimizing other design parameters such as the configuration of unit operations, optimization of specific unit operations, heat integration, and other degrees of freedom used to optimize processes. Optimization includes both economic and simulation accuracy aspects. Thermodynamic model definition should be revisited as often as necessary during process optimization (Suppes, Uni. Missouri-Columbia).
The better-known solution models include equations Margules, van Laar, Wilson, NRTL, and UNIQUAC models. Of these, based on frequencies of best fits, the following choices are best when only one liquid is anticipated:
Table 2.2: Thermodynamic model selection
Aqueous organics
NRTL
Alcohols
Wilson
Alcohols and Phenols
Wilson
Alcohols, Ketones, and Ethers
Wilson or Margules (Wilson is preferred due to its improved ability to correct for changes in temperature)
C4-C18 hydrocarbons
Wilson
Aromatics
Wilson or Margules (Wilson is preferred due to its improved ability to correct for changes in temperature)
When performing simulation that involves LLE, do not use the Wilson equation since the Wilson equation is not capable of performing LLE calculations. Alternative to the Wilson equation use the TK Wilson equation or the NRTL equation. Apply this rule under the assumption that binary interaction coefficients are available or can be estimated.
If the simulation package does not provide the ability to estimate binary interaction coefficients with the Wilson, NRTL, or TK Wilson equations and does offer this ability with the UNIQUAC equation, then use the UNIQUAC solution model with UNIFAC estimation of binary interaction parameters.
2.4 UNIQUAC
UNIQUAC (short for UNIversal QUAsiChemical) is an activity coefficient model used in description of phase equilibria (Abram and Prausnitz, 1975). The model is known as lattice model and has been derived from a first order approximation of interacting molecule surfaces in statistical thermodynamics. The model is however not fully thermodynamically consistent due to its two liquid mixture approach. The UNIQUAC model is frequently applied in the description of phase equilibria (liquid-solid, liquid-liquid or liquid-vapour equilibrium).
The UNIQUAC model also serves as the basis of the development of the group contribution method UNIFAC, where molecules are subdivided in atomic groups. In fact, UNIQUAC is equal to UNIFAC for mixtures of molecules, which are not subdivided. Activity coefficients can be used to predict simple phase equilibria (vapour-liquid, liquid-liquid, solid-liquid), or to estimate other physical properties (viscosity of mixtures).
Models such as UNIQUAC allow chemical engineers to predict the phase behavior of multicomponent chemical mixtures. They are commonly used in process simulation programs to calculate the mass balance in and around separation units.
Tamura et al. (2000) using the UNIQUAC model with binary and ternary parameters and further compared with those reproduced by using additional quaternary parameters for water-cyclohexane-ethyl acetate-acetic acid systems. As a conclusion, the experimental results and calculated values gave a good agreement.
The UNIQUAC model:
(2.4.1)
where; γC = combinatorial contribution
γR= residual contribution
For combinatorial contribution,
(2.4.2)
with;
(2.4.3)
(2.4.4)
Vi = volume fraction per mixture mole fraction
Fi = surface area fraction per mixture molar fraction
ri = relative Van der Waals volumes of the pure chemicals
qi = relative Van der Waals surface areas of the pure chemicals
xj = mole fraction of component i
For residual contribution,
(2.4.5)
with;
(2.4.6)
τij = empirical parameter
Δuij = binary interaction energy parameter
2.5 UNIFAC
UNIFAC (UNIversal Functional Activity Coefficient) is a group contribution method that combines the solution of functional groups concept and the UNIQUAC model. The latter is a model for calculating activity coefficients. The idea of the group contribution method is that a molecule consists of different functional groups and that the thermodynamic properties of a solution can be correlated in terms of the functional groups.
The advantage of this method is that a very large number of mixtures can be described by a relatively small number of functional groups. The UNIFAC model defines two different groups; subgroups and main groups. Subgroups are the smallest ``building blocks'' and the main groups are used to group subgroups together. The reason for this is that though the subgroups have different volume and surface area parameters, the interaction parameters are the same for all subgroups within a main group.
Tizvar et al. (2008) using UNIFAC and modified UNIFAC activity coefficient models to predict the properties of the coexisting phases at equilibrium of methyl oleate-glycerol-hexane-methanol. As a result, the predicted tie lines showed no significant lack of fit when compared to the experimental tie lines for both models.
The UNIFAC model:
(2.5.1)
where; γC = combinatorial component
γR= residual component
For combinatorial component,
(2.5.2)
with;
(2.5.3)
(2.5.4)
; z = 10 (2.5.5)
where;
(2.5.6)
(2.5.7)
θi = molar weighted segment components for the ith molecule in the total system
φi = area fractional components for the ith molecule in the total system
Li = compound parameter of r, z and q
z = coordination number of the system
ri=calculated from the volume contributions R
qi = calculated from the group surface area contributions Q
νk= number of occurrences of the functional group on each molecule
For residual component,
(2.5.8)
with;
(2.5.9)
where;
(2.5.10)
(2.5.11)
(2.5.12)
Гk(i) = activity of an isolated group in a solution consisting only of molecules of type i
Θm = summation of the area fraction of group m
Ψmn= group interaction parameter and is a measure of the interaction energy between groups
Xn= group mole fraction, which is the number of groups n in the solution divided by the total number of groups
Umn = energy of interaction between groups m and n
2.6 NRTL
The Non-Random Two Liquid model (NRTL) is an activity coefficient model that correlates the activity coefficients of a compound with its mole fractions in the concerning liquid phase. The energy difference introduces also non-randomness at the local molecular level. The NRTL model belongs to the so-called local composition models. The NRTL parameters are fitted to activity coefficients that have been derived from experimentally determined phase equilibrium data (vapour-liquid, liquid-liquid, solid-liquid) as well as from heats of mixing.
Other options are direct experimental work and predicted activity coefficients with UNIFAC and similar models. Noteworthy is that for the same liquid mixture there might exist several NRTL parameter sets. It depends from the kind of phase equilibrium (i.e. solid-liquid, liquid-liquid, vapour-liquid) which NRTL parameter set is going to be used. In the case of the description of a vapour liquid equilibria it is necessary to know which saturated vapour pressure of the pure components was used and whether the gas phases was treated as an ideal or a real gas. Accurate saturated vapour pressure values are important in the determination or the description of an azeotrope. The gas fugacity coefficients are mostly set to unity (ideal gas assumption), but vapour-liquid equilibria at high pressures (i.e. > 10 bar) need an equation of state to calculate the gas fugacity coefficient for a real gas description.
Pence and Gu (1996) study the LLE at atmospheric pressure for the binary acetonitrile-water system at temperatures ranging from -1.3 to -18.6oC. Data points were taken using two methods, the cloud point method and the analysis of phase compositions using gas chromatography. Both methods show excellent agreement in their representation of the phase envelope. Temperature dependent NRTL (non-random two liquid) parameters were calculated from the binary data. The result shows the NRTL model with temperature-dependent parameters correlated from experimental data gives a good representation of this system.
The NRTL model:
For binary mixture:
(2.6.1)
(2.6.2)
with;
(2.6.3)
(2.6.4)
(2.6.5)
(2.6.6)
τ12 and τ21= dimensionless interaction parameters
Δg12 and Δg21= interaction energy parameters
α12 and α21 = non-randomness parameter
For a liquid, in which the local distribution is random around the center molecule, the parameter α12 = 0. In that case the equations reduce to the one-parameter Margules activity model:
(2.6.7)
(2.6.8)
In practice α12 is set to 0.2, 0.3 or 0.48. The latter value is frequently used for aqueous systems. The high value reflects the ordered structure caused by hydrogen bonds.
In some cases a better phase equilibria description is obtained by setting α12 = − 1. However this mathematical solution is impossible from a physical point of view, since no system can be more random than random.
The limiting activity coefficients, aka the activity coefficients at infinite dilution, are calculated by:
(2.6.9)
(2.6.10)
To describe phase equilibria over a large temperature regime, i.e. larger than 50 K, the interaction parameter has to be made temperature dependent. Two formats are frequenty used. The extended Antoine equation format:
(2.6.11)
In here the logarithmic term is mainly used in the description of liquid-liquid equilibria (miscibility gap).
The other format is a third order polynomial format:
(2.6.12)
