• membrane modules;
  • desalination;
  • mathematical modeling;
  • scaling

Modeling the operation of spiral-wound membrane modules is essential for their successful design and optimization. Such models must include the main types of membrane fouling, degrading desalination plant performance, including scaling due to sparingly soluble salts. Unfortunately, the complexity of underlying physicochemical processes and the coexistence of several spatial and temporal scales render intractable modeling of membrane scaling based on first principles. Therefore, a suitable (albeit simplified) framework is developed for incorporating scaling dynamics into a fluid flow model formulated at an intermediate (i.e., mesoscopic) length scale of membrane operation. The general mesoscopic approach involves integration of spatially distributed submodels, thereby allowing predictions at the large (entire membrane sheet) scale; these submodels comprise constitutive laws and kinetic rate expressions derived at fine scales. A submodel for the effect of pre-existing bulk particles on scale formation is developed herein. Several numerical results are presented to exemplify the potential of the proposed framework. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2917–2927, 2013