Exact limits of mixture properties and excess thermodynamic functions

2006

Neural Computation

A modified version of the single hidden-layer perceptron architecture is proposed for modeling mixtures. A particular flexible mixture model is obtained by implementing the Box-Cox transformation as transfer function. In this case, the network response can be expressed in closed form as a weighted power mean. The quadratic Scheffé K-polynomial and the exponential Wilson equation turn out to be special forms of this general mixture model. Advantages of the proposed network architecture are that binary data sets suffice for "training" and that it is readily extended to incorporate additional mixture components while retaining all previously determined weights.

Section: Model Consistencymentioning

confidence: 94%

“…A common conjecture in chemical engineering is that only binary interactions between species need to be considered in mixtures (Hamad, 1998;Prausnitz et al, 1999). This is a strong assumption but is accepted here for the simplicity and convenience it introduces.…”

Section: Introductionmentioning

confidence: 99%

Mixture Models Based on Neural Network Averaging

2006

Neural Computation

“…The selection of the functional form is crucial because statistical tests and formulas for quantifying uncertainties of parameter estimates and model predictions are valid only under the assumption that the postulated model adequately represents the underlying structure of the data. 15 Mixture models, and excess thermodynamic functions in particular, must satisfy the following elementary consistency requirements: 16,17 • Parameter values should not change when additional components are added to the mixture • The mixture property should reduce to the pure component value when any mole or mass fraction approaches unity • The relation for an n-component mixture should reduce to the corresponding (n − 1)-component form in the limit of infinite dilution of one of the components • Predicted properties should be independent of how the component indices are assigned • The model must be invariant with respect to dividing one component into two or more identical subcomponents. Models that fail this consistency criterion are said to suffer from the Michelsen−Kistenmacher syndrome.…”

Section: Mixture Modelsmentioning

confidence: 99%

“…The behavior of multicomponent mixtures is naturally affected by the interactions of unlike molecules . It is expedient to assume that only binary interactions between components need to be considered in mixtures. , The implications of this assumption are two-fold: First, it leads to a major reduction in the required experimental data gathering effort. Second, beyond the pure component data, the multicomponent mixture model only needs to incorporate information on the constituent binary systems .…”

Section: Mixture Modelsmentioning

confidence: 99%

Revisiting the Classic Activity Coefficient Models

Endres

Toit

et al. 2021

Ind. Eng. Chem. Res.

A link, established between the classic excess Gibbs free energy expressions and conventional mixture models, allowed the extension of the Margules and van Laar models to multicomponent mixtures. It is shown that the multicomponent form of the classic van Laar model features only one parameter per component in the mixture. It is also a special case of several other models including those due to Wassiljewa and Scatchard. This means that the latter can be seen to be a more general Scatchard–van Laar expression. It is also proven that the composition dependence of the Porter, Margules, van Laar, NRTL, and Wilson are all obtainable as special cases of the weighted double power mean mixture model. The ability of the models to accurately predict ternary performance from knowledge of binary behavior was tested using nine isothermal vapor–liquid data sets. The Wilson-type models performed best in this regard. The extended Scatchard–van Laar model also proved to be effective despite being particularly parameter-sparse.

“…Therefore, for illustrating D s -optimal designs, we consider model (14) and specifically we assume that the parameters a kk , k = 1, 2, 3 are not of interest for estimation. This assumption is sensible in analytical chemistry because the behavior of multicomponent Table 5: D-optimal design for model (16) mixtures is naturally affected by the interactions of unlike molecules (Hamad, 1998;Prausnitz et al, 1999;Walas, 1985). Focke et al (2007) also assumed the pure component properties to be known and only estimated the binary interaction parameters.…”

Section: Continuous D S -Optimal Designsmentioning

confidence: 99%

Optimal designs for estimating the parameters in weighted power‐mean‐mixture models

Coetzer

Journal of Chemometrics

2009

In the mixing of fluids, a mixture may be viewed conceptually as a hypothetical collection of fluid clusters. In this context a mixture model is defined by prescriptions for (a) estimating fluid cluster properties and (b) combining them to yield an overall mixture property. A particular flexible form is obtained from using generalized weighted-power-means with the weighting based on global mole fractions x i , 0 ≤ x i ≤ 1, i x i = 1, i = 1, 2, . . . , q. Optimal designs for estimating the parameters in Scheffé S-and K-polynomials are well known. In this paper we present optimal designs for estimating the parameters in the generalized weighted-power-mean mixture models, which may be nonlinear in the pure and binary interaction parameters. We illustrate the practical value of applying optimal designs for mixture variables through design efficiencies. The designs are derived for modeling viscosity from three-component mixtures.