New approach to a general nonlinear multicomponent chromatography model

✍ Scribed by Tingyue Gu; Gow-Jen Tsai; George T. Tsao

• Publisher: American Institute of Chemical Engineers
• Year: 1990
• Tongue: English
• Weight: 327 KB
• Volume: 36
• Category: Article
• ISSN: 0001-1541
• DOI: 10.1002/aic.690360517

✦ Synopsis

Mathematical modeling and numerical analysis of multicomponent fixed-bed adsorption/desorption operations, such as frontal, displacement and elution, have received considerable attention since the late 1960s. Various mathematical models with different complexities have been proposed and a comprehensive review was given by Ruthven (1984). Basically, they can be classified into the following three major categories: 1. staged equilibrium models, 2. interference theory (Helfferich and Klein, 1970), and 3. rate equation models. Among them, the general nonlinear multicomponent rate equation model is the most "realistic" model for all kinds of multicomponent adsorption/desorption column processes. The model is formulated according to mass balance of each species in bulk fluid and particle phases. It considers axial dispersion, external mass transfer, intraparticle diffusion and multicomponent nonlinear isotherms. Due to the complexity and nonlinearity of the model, analytic solution is impossible and numerical computation can be very time-consuming because the system equations are stiff in many cases. Hence, an efficient algorithm is essential.

So far three different algorithms have been proposed to solve models similar to ours. Liapis and coworkers (1978a, b, 1980) used orthogonal collocation (OC) method for the discretization of both bulk-and particle-phase equations. The resulting ordinary differential equations (ODE's) were solved using a fifth-order Runge-Kutta method. Their model was applied to frontal adsorption. Yu and Wang (1989) tried OC on finite element for bulk-phase equations and OC method for particlephase equations. The resulting ODE's and algebraic equations were solved using a differential algebraic equation solver.