Date of Award
Doctor of Engineering Science in Chemical Engineering
Chemical Engineering and Chemistry
Edward Charles Roche, Jr.
A model was developed to simulate ion exchange within fixed beds for ternary systems. Models of the fluid phase material balance, phase equilibria, and diffusion of ions through the film and within the resin phase incorporated the latest advances in ion exchange theory. The separate model elements were combined after testing into an overall general model. Non-linear regression support programs were developed to estimate equilibrium parameters and resin phase diffusion coefficients.
A computer program was developed to estimate axial dispersion coefficients from experimental data. General correlations derived from literature sources were tested, and axial dispersion terms were included in the electrolyte phase material balance equations.
The rational thermodynamic equilibrium constant, utilizing resin phase activity coefficients based on the 3 suffix Redlich-Kister equation and the Bromley equation for electrolyte phase activity coefficients, was selected. The Wilson and NRTL equations were tested but were not as good. This model was used to correlate published data on 13 binary systems and to predict ternary compositions for comparison to published data on 4 ternary systems. Average root mean square of % normalized difference was about 3% on the binary systems and 4-12% on data predicted for the ternary systems.
The Nernst-Planck equation was used to model resin phase diffusion. An integrated form of the Nernst-Hartley equation, based on the Bromley equation, was developed and tested to predict the effect of concentration on electrolyte phase diffusion coefficients. These coefficients were used in a pseudo electric field model which was developed and tested to approximate the electric field effect on diffusion of ions in the film.
The overall ternary system model resulted in four coupled non-linear second order parabolic partial differential equations, with appropriate boundary conditions. The equations were reduced to a set of algebraic equations by finite difference approximations and solved by the implicit Crank-Nicholson method. Non-linear terms were quasilinearized. The resulting five diagonal coefficient matrix describing the fluid phase, coupled with the 7 diagonal coefficient matrices describing the resin phase, were inverted with algorithms developed in this work. An iterative procedure resolved all nonlinear terms at each time step. Comparison of concentration histories generated by the model with experimental results obtained by previous researchers showed that the ternary model could be used in practice to optimize process design applications with a bed in a condition of partial presaturation, and for favorable or unfavorable ion exchange.
Resin phase activity coefficients developed in correlation of the equilibrium data were used to test chemical potential as a driving force in the systems simulated. Indication that use of chemical potential would obviate the need for ion pair specific diffusion coefficients in the Nernst-Planck model, or the use of ion pair corrector coefficients (Stefan-Maxwell), is shown by comparison of results on seven binary systems. Implications for industrial application and directions for further research are discussed.
Roth, David W. H., "Ternary ion exchange in fixed beds : equilibrium and dynamics" (1985). Dissertations. 1202.