Mathematical Modeling of Ion Exchange Columns with Emphasis on Hydrous Crystalline Silico-Titanates, Molecular Sieves and Non Ideal Solutions (fef025ea-7007-41d7-9897-1882c90a0444)

"In this paper, we review the equations needed to construct an ion exchange column model. These models contain three major components: 1) a differential material balance around the column, 2) a differential material balance around an ion exchange particle, and 3) a constitutive equation for diffusive flux. We then examine the ability of a fairly simple mathematical model to predict ion exchange column experimental data. This model contains the traditional absorption theory equations and is used to predict the behavior of a column filled with a hydrous crystalline silico-titanate and which is removing trace amounts of Cs+ from a high pH, complex electrolyte solution. Finally, we propose replacing Fick's law with the Nemst-Planck equation as the constitutive equation for diffusive flux. We use a NemstPlanck type model to predict batch experimental data, then evaluate it by comparing it's ability to predict experimental data to that of a more traditional Fick's law type model. The data from this comparison suggests that the Nemst-Planck type model yields better results.IntroductionMillions of gallons of strongly basic, radioactive waste are currently stored in underground storage tanks at Hanford and Savannah River and several locations within the United States. Due to the limited life expectancy of the tanks, there is a pressing need to remediate these wastes. This need has prompted the recent development of new ion-exchange materials for removing radioactive elements from aqueous solutions. A novel material called TAM-5 has been developed jointly by Texas A&M University and Sandia National Laboratories. TAM- 5, a crystalline silico-titanate, is highly selective for Cs + in the complex electrolytic solutions typical of these wastes. It is stable in very basic solutions and in radioactive environments [1, 2 ,3]. In laboratory testing to determine the selectivity of various materials, TAM-5 was superior to other candidate ion exchangers [4, 5]. The selectivities were determined by measuring a distribution coefficient, Kd, which is defined as the concentration, gig or mmols/g of Cs in the solid phase divided by the concentration, mg/L or mmols/mL, of Cs in the liquid phase. The units of Kd are ml/g or L/kg. Table 1 shows Kd values for TAM-5 compared to 9 other candidate materials in a typical waste solution [6]."