- Email: [email protected]
Analogic simulation in ion exchange
164
E.E. Graham and J.S. Dranoff, Pennsylvania State University, University Park, PA, U.S.A.; Northwestern University, Evanston, IL, U.S.A.: Application of the Stefan-Maxwell Equations to Diffusion in Ion Exchangers Starting with the Stefan-Maxwell equations, and incorporating activity coefficients into the electrochemical driving force, general expressions for the ionic flux rates for binary exchange in ion-exchange resins have been developed. These equations have been shown to reduce to the Nernst-Planck equations exactly only as the concentration of either exchanging ion approaches unity. Furthermore, the single ion diffusion coefficients used in the Nernst-Planck equations are shown to be certain combinations of the Stefan-Maxweli interaction coefficients and resin concentrations. Most importantly, these combinations of the Stefan-Maxwell interaction coefficients are shown to reduce to the tracer diffusion coefficient of each exchanging ion measured in ion-exchange resin completely in the competing ion form. As these limiting tracer ion-diffusion coefficients may be very different from the usual pure self-diffusion coefficients, this result may be used to explain existing anomalies resulting from the use of the Nernst-Planck equations to describe diffusion in ion-exchange resins as well as many related ion-exchange systems, such as glasses and porous solids or crystals. As a test of the theory, the Stefan-Maxwell relations were used to analyze the ion exchange of Na ÷ and Cs ÷ in Dowex 50-X8. Tracer diffusion coefficients for both ions were measured as a function of composition. This allowed the necessary combinations of the Stefan-Maxwell interaction coefficients to be determined, which in turn allowed limiting single-ion tracer coefficients (Na ÷ diffusion in Cs ÷ form resin only and Cs ÷ diffusing in Na ÷ form resin only) to be estimated. The use of these limiting tracer coefficients in the Nernst-Planck equations gave much improved prediction of ion exchange than did the use of the usual self-diffusion coefficients. The improved results were attributed to the fact that the Stefan-Maxwell relations take into account important ion-ion interactions. Finally it can be shown that for ternary ion exchange the Stefan-Maxwell relations do not reduce to the Nernst-Planck equations, and it is suggested that the Stefan-Maxwell relations will provide a much improved basis for describing the kinetics of multicomponent ion exchange.
J. Loureiro, C. Costa, M. Dias, J. Lopes, and A. Rodrigues, University of Porto, Porto, Portugal: Design Methods for Ion Exchange Equipment The methods for designing ion exchange equipment, namely batch, continuous perfectly mixed and fixed beds, are discussed. For each type of equipment we get, either analytically or numerically, the solution concentration (and resin concentration) as a function of time by using three different models: • equilibrium model; • film diffusion model; • homogeneous particle diffusion model. In all cases the ion exchange equilibrium isotherm is nonlinear. The numerical solutions were obtained using the method of lines with a finite element collocation technique for the spatial coordinate.
N. Marignetti, University of Ferrara, Ferrara, Italy: Analogic Simulation in Ion Exchange From the operational point of view, ion exchange technology is based on the resin bed composition at the end of operation, under specified conditions of permissible leakage or concentration level in the effluent. An analogue simulation has been set up in which the effluent composition is programmed as a function of various parameters accessible to measurement (temperature, pressure drop across the bed, flow rate, exhaustion cycle time, and a constant characterizing operating conditions). Simulation data are compared with pilot plant performance. To be published with additional material in VignevinL Riv. Vitic. EnoL, X (6) (1983).
E.E. Graham and J.S. Dranoff, Pennsylvania State University, University Park, PA, U.S.A.; Northwestern University, Evanston, IL, U.S.A.: Application of the Stefan-Maxwell Equations to Diffusion in Ion Exchangers Starting with the Stefan-Maxwell equations, and incorporating activity coefficients into the electrochemical driving force, general expressions for the ionic flux rates for binary exchange in ion-exchange resins have been developed. These equations have been shown to reduce to the Nernst-Planck equations exactly only as the concentration of either exchanging ion approaches unity. Furthermore, the single ion diffusion coefficients used in the Nernst-Planck equations are shown to be certain combinations of the Stefan-Maxweli interaction coefficients and resin concentrations. Most importantly, these combinations of the Stefan-Maxwell interaction coefficients are shown to reduce to the tracer diffusion coefficient of each exchanging ion measured in ion-exchange resin completely in the competing ion form. As these limiting tracer ion-diffusion coefficients may be very different from the usual pure self-diffusion coefficients, this result may be used to explain existing anomalies resulting from the use of the Nernst-Planck equations to describe diffusion in ion-exchange resins as well as many related ion-exchange systems, such as glasses and porous solids or crystals. As a test of the theory, the Stefan-Maxwell relations were used to analyze the ion exchange of Na ÷ and Cs ÷ in Dowex 50-X8. Tracer diffusion coefficients for both ions were measured as a function of composition. This allowed the necessary combinations of the Stefan-Maxwell interaction coefficients to be determined, which in turn allowed limiting single-ion tracer coefficients (Na ÷ diffusion in Cs ÷ form resin only and Cs ÷ diffusing in Na ÷ form resin only) to be estimated. The use of these limiting tracer coefficients in the Nernst-Planck equations gave much improved prediction of ion exchange than did the use of the usual self-diffusion coefficients. The improved results were attributed to the fact that the Stefan-Maxwell relations take into account important ion-ion interactions. Finally it can be shown that for ternary ion exchange the Stefan-Maxwell relations do not reduce to the Nernst-Planck equations, and it is suggested that the Stefan-Maxwell relations will provide a much improved basis for describing the kinetics of multicomponent ion exchange.
J. Loureiro, C. Costa, M. Dias, J. Lopes, and A. Rodrigues, University of Porto, Porto, Portugal: Design Methods for Ion Exchange Equipment The methods for designing ion exchange equipment, namely batch, continuous perfectly mixed and fixed beds, are discussed. For each type of equipment we get, either analytically or numerically, the solution concentration (and resin concentration) as a function of time by using three different models: • equilibrium model; • film diffusion model; • homogeneous particle diffusion model. In all cases the ion exchange equilibrium isotherm is nonlinear. The numerical solutions were obtained using the method of lines with a finite element collocation technique for the spatial coordinate.
N. Marignetti, University of Ferrara, Ferrara, Italy: Analogic Simulation in Ion Exchange From the operational point of view, ion exchange technology is based on the resin bed composition at the end of operation, under specified conditions of permissible leakage or concentration level in the effluent. An analogue simulation has been set up in which the effluent composition is programmed as a function of various parameters accessible to measurement (temperature, pressure drop across the bed, flow rate, exhaustion cycle time, and a constant characterizing operating conditions). Simulation data are compared with pilot plant performance. To be published with additional material in VignevinL Riv. Vitic. EnoL, X (6) (1983).