Numerical Results for Nonlinear Systems

Theoretical breakthrough curves for nonlinear systems may be calculated by numerical solution of the model equations using standard finite difference or collocation methods. Such solutions have been obtained by many authors and a brief summary is given in Table 8.4. In all cases plug flow was assumed and the equilibrium relationship was taken to be of cither Langmuir or Freundlich form. As linearity is approached ( - 1.0) the linearized rate models approach the Anzelius model (Table 8.1, model la) while the diffusion models approach the Rosen model (Table 8.1, model la). The conformity of the numerical solution to the exact analytic solution in the linear limit was confirmed by Garg and Ruthven.  

For many zeolitic systems the equilibrium isotherm can jbe represented in an approximate way by the Langmuir model while the intracrystalline diffu-sivity varies with concentration according to Eq. (6.12). Model 2c is intended to describe the dynamic behavior of such systems under conditions of intracrystalline diffusion control. 

FIGURE 8.18. Theoretical breakthrough curves calculated for a nonlinear (Langmuir) system according to the pore diffusion model (model 3i, Table 8.4) showing effect of nonlinearity. In b) the desorption curves of (a) are shown plotted on an inverted concentration scale with 

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