ASYMPTOTIC-BEHAVIOR OF 2 INTERREACTING CHEMICALS IN A CHROMATOGRAPHY REACTOR

The chromatographic separation of two chemical species (c(1) and c(2)) that transform into each other with first-order kinetics as they pass through a Langmuir isotherm reactor is governed by the following syst em of nonlinear hyperbolic conservation equations: partial derivative c(1)/partial derivative x + partial derivative/partial derivative t (c (1)/1+c(1)+c(2)) = kc(1) + k'c(2) and partial derivative c(2)/partial derivative x + partial derivative/partial derivative t (gamma c(2)/1+c (1)+c(2)) = gamma(kc(1)-k'c(2)), where t is an element of (-infinity, infinity). An analysis is presented of the two species' asymptotic beh avior as they progress down a semiinfinite (i.e., x is an element of [ 0, infinity)) separation reactor with cyclic (periodic) entering feed concentrations. First it is shown that the method of generalized chara cteristics can be extended to describe the above system of equations. Then generalized characteristics are applied to show that the omega-li mit, set for the species concentrations is comprised of a single deter mined point on the curve of chemical equilibrium and that this point i s approached at an exponential rate.