Analytical Modeling of Calcium Carbonate Deposition for Laminar Falling Films and Turbulent Flow in Annuli: Part I—Formulation and Single-Species Model

This is a two-part series to model scaling of heat transfer surfaces by calcium carbonate based on the first conservation principle approach. In Part I, general physical and chemical processes in CaCO₃ fouling are described and a single-species model is proposed whereby only Ca⁺² species transport needs to be of concern. The deposition process is assumed to be controlled by the two processes of mass transport to and crystallization reaction on the heat transfer surface. The model is then used to solve for CaCo₃ scaling in a laminar falling film system and to assess which of the two types of prevailing reaction rate expressions is more appropriate for the CaCO₃ fouling analysis. The predicted deposition rate, scale thickness, and its profile are compared with experimental data. The comparison shows that the single-species model yields satisfactory predictions only for a limited range of concentrations. It reveals that the type of reaction rate expression used in the single-species model is less accurate than the other type used in the multispecies model. The latter is described in Part II of the series.