Mixture models versus free energy of hydration models for waste glass durability

Abstract

Two approaches for modeling high-level waste glass durability as a function of glass composition are compared. The mixture approach utilizes first-order mixture (FOM) or second-order mixture (SOM) polynomials in composition, whereas the free energy of hydration (FEH) approach assumes durability is linearly related to the FEH of glass. Both approaches fit their models to data using least squares regression. The mixture and FEH approaches are used to model glass durability as a function of glass composition for several simulated waste glass data sets. The resulting FEH and FOM model coefficients and goodness-of-fit statistics are compared, both within and across data sets. The goodness-of-fit statistics show that the FOM model fits/predicts durability in each data set better (sometimes much better) than the FEH model. Considerable differences also exist between some FEH and FOM model component coefficients for each of the data sets. These differences are due to the mixture approach having a greater flexibility to account for the effect of a glass component depending on the level and range of the component and on the levels of other glass components. The mixture approach can also account for higher-order (e.g., curvilinear or interactive) effects of components, whereas the FEH approach cannot. SOM models were developed for three of the data sets, and are shown to improve on the corresponding FOM models. Thus, the mixture approach has much more flexibility than the FEH approach for approximating the relationship between glass composition and durability for various glass composition regions.