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From UNIQUAC to Modified UNIFAC Dortmund: a Discussion 3rd International Conference on Medical Sciences and Chemical Engineering (ICMSCE'2013) Dec. 25-26, 2013 Bangkok (Thailand) From UNIQUAC to Modified UNIFAC Dortmund: A Discussion Edison Muzenda the excess Helmholtz energy of mixing (at constant Abstract—This paper reviews and discusses the universal quasi – temperature and volume) [1]. This hypothesis leads to the chemical theory and group contribution methods focusing on their generalised excess Gibbs energy UNIQUAC expression as application in phase equilibrium modeling and computation. The defined in (1). historical perspective, algorithm, strength, weaknesses and E E E E limitations are presented. The paper concludes with comparison of a g g g (1) the performance of the various UNIFAC models. RT RT RT RT TV, TP, C R Keywords—Gibbs energy, Group contribution, phase The UNIQUAC equation is described in terms of the equilibrium, quasi –chemical, UNIFAC. combinatorial and residual terms. The combinatorial term is used to describe the dominant entropic contribution. It uses I. UNIVERSAL QUASI-CHEMICAL (UNIQUAC) EQUATION only pure-component data and is determined only by the size, HE UNIQUAC equation was developed by Abrams and shape and composition of the molecules in the mixture [2]. For T Prausnitz in 1975, and is based primarily on binary mixtures the excess Gibbs energy expression of the Guggenheim’s quasi-chemical lattice model developed in 1952 combinatorial term is [1]. Guggenheim postulated that a liquid can be represented by g E a three-dimensional lattice with lattice sites spaced equidistant 1 2 x1 ln x2 ln from each other. A volume, known as a cell, exists in the RT C x1 x2 immediate vicinity of each lattice site. Each molecule in the z liquid is divided into attached segments, and each segment 1 2 (2) q1 x 1 ln q2 x 2 ln occupies one cell. The total number of cells is then considered 2 1 2 to be equal to the total number of segments [1]. In its original The residual term is used to describe the intermolecular form, Guggenheim’s lattice model was restricted to describing forces responsible for the enthalpy of mixing. Thus the two only small molecules which were essentially the same size. adjustable binary interaction parameters appear only in the Abrams and Prausnitz however managed successfully to residual term [2]. For binary mixtures the residual term is extend Guggenheim’s lattice theory to mixtures containing described in terms of excess Gibbs energy as in (3). molecules of different size and shape by incorporating and E adapting Wilson’s local-composition model into g q1 x 1ln 1 2 21 q2 x 2ln 2 1 12 (3) Guggenheim’s lattice model [1]. RT R The average segment fraction (Φi) is only used in the A. Mixing Theory calculation of the combinatorial term. For a binary mixture, it The effects of volume on mixtures of nonelectrolyte liquids is defined mathematically as at constant temperature and constant pressure (remote from x r 1 1 (4) critical conditions) are minimal. However, Scatchard (1937) 1 x1 r 1 x 2 r 2 demonstrated that even minor volume changes can and significantly affect the entropy- and enthalpy of mixing. Fortunately these effects are largely nullified in the excess x2 r 2 2 (5) Gibbs energy. Therefore, for mixtures of non-electrolyte x1 r 1 x 2 r 2 liquids at low or modest pressures, Hildebrand and Scott The average area fraction is used in both the combinatorial (1950) proposed that the excess Gibbs energy of mixing (at and residual terms. When using the empirical adjustment of the constant temperature and pressure) is approximately equal to (q'i) parameters, as defined by Anderson [3], the average area fraction should be similarly depicted as (θ'i). For a binary E. Muzenda is with the Department of Chemical Engineering, Faculty of Engineering and the Built Environment, University of Johannesburg, mixture, the average area fraction is defined as in (6) Doornfontein, Johannesburg 2028; phone: 0027-11-5596817; Fax: 0027-11- 5596430; e-mail: [email protected]). 32 3rd International Conference on Medical Sciences and Chemical Engineering (ICMSCE'2013) Dec. 25-26, 2013 Bangkok (Thailand) x1 q 1 x1 q' 1 ri Vwi 15.17 (14) 1 or 1 (6) x q x q x q'' x q 9 1 1 2 2 1 1 2 2 qi Awi 5.2 10 (15) and x2 q 2 x2 q' 2 2 or 2 C. Binary Adjustable Parameters (τij) x1 q 1 x 2 q 2 x1 q'' 1 x 2 q 2 The binary adjustable parameters (τij) contain the characteristic interaction energy parameters (uij) which represent average intermolecular energies, since in a given B. Pure-component Structural Parameters molecule the segments are not necessarily chemically identical In terms of lattice theory, each molecule of component (i) [1]. These in turn relate to the UNIQUAC binary interaction consists of a set of bonded segments occupying a set volume parameters (aij) as shown in (16). (parameter r1). In terms of component (i), parameter (ri) is the u a exp 12 exp 12 (16) van der Waals molecular volume relative to that of a standard 12 RT T segment [1] and is expressed as and ri Vwi V ws (7) u21 a21 In (7), (Vwi) is the van der Waals volume of molecule (i) as exp exp (17) 21 RT T published by Bondi in 1968, and (Vws) is the van der Waals volume of a standard segment. The volume for a standard The parameters (aij) are determined from binary sphere in terms of its radius (Rws) is as in (8) experimental data [3], sourced mainly from VLE data (P, y, x ) VR 4 3 ³ (8) at constant temperature, VLE data (T, y, x ) at constant ws ws pressure and total pressure data (P, x or y ) at constant The UNIQUAC arbitrarily defines a standard segment as a temperature. The UNIQUAC can be used to calculate activity sphere which satisfies (9) for a linear polymethylene molecule coefficients for a binary mixture according to (18) and (19). of infinite length z r z r q r 1 (9) ln x ln 1 q ln 1 l 1 l 2 1 1 1 2 1 2 x1 2 1 r2 Numerical results are insensitive to the value of the lattice co-ordination number (z) provided a reasonable number q ln q 21 12 (18) between 6 and 12 is selected. The lattice co-ordination number 1 1 2 21 2 1 is thus arbitrarily set equal to 10. Segments differ in terms of 1 2 21 2 1 12 and their external contact area (parameter q1) for example the CH3 molecules of pentane have a larger exposed external area than z r ln x ln 2 q ln 2 l 2 l the CH2 molecules, but the central carbon of neopentane has 2 1 2 2 2 1 x2 2 2 r1 no external contact area at all. Parameter (qi) is referred to as the van der Waals molecular area relative to that of a standard 12 21 segment [1] and is defined as q ln q (19) 2 2 1 12 1 2 q A A (10) 2 1 12 1 2 21 i wi ws The pure-component parameters (l ) and (l ) are determined In (10), (A ) is the van der Waals surface area of molecule 1 2 wi as in (20) and (21) (i) as published by Bondi in 1968, and (Aws) is the van der Waals surface area of a standard segment, described in (9). z l1 r1 q 1 r 1 1 (20) The area of a standard sphere in terms of its radius (Rws) is 2 provided as z l2 r2 q 2 r 2 1 (21) ARws 4 ws ² (11) 2 Bondi stipulated that van der Waals volume and area of an Strengths n-mer of polymethylene are n times the volume and area of a The UNIQUAC model gives reliable estimates of both methylene group: vapour-liquid and liquid-liquid equilibria for binary and multi- component mixtures containing a variety of non-electrolyte Vwi n10.23 cm /³ mole (12) polar or non-polar mixtures [2]. 9 Awi n.1 35 10 cm /² mole (13) The UNIQUAC model uses only two adjustable parameters Substituting (7), (8) and (10), (11) and (12), (13) into (9) per binary. This makes the equation simpler to use for multi- 15 with (Rws) being fixed at 10.95 × 10 cm/mole as n tends to component mixtures [2]. infinity, yields the following expressions for the parameters (ri) The UNIQUAC model can yield adequate results even when and (qi): available experimental data is limited. 33 3rd International Conference on Medical Sciences and Chemical Engineering (ICMSCE'2013) Dec. 25-26, 2013 Bangkok (Thailand) Weaknesses applicable predictive model based on regular solution theory Molecular-dynamic calculations have shown that [7], using pure-component data. However, the greatest UNIQUAC often over-rectifies the deviations for random weakness of regular solution theory was that it could not be mixing because the magnitudes of the arguments of the applied to polar systems and this was addressed with the Boltzmann factors are too large. Thus UNIQUAC is often not introduction of the ASOG model in 1969. as accurate as NRTL for LLE calculations, and Wilson for VLE calculations. B. Solution of Groups Concept Whilst thousands of chemical compounds exist, the number II. GROUP CONTRIBUTION METHODS of functional groups which constitute these compounds is much smaller. It is therefore convenient to correlate the Reliable phase equilibrium data is essential for optimum properties of the large number of chemical compounds in separation process synthesis, design and operation.
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