Numerical comparison between relaxation and nonlinear equilibrium models. Application to chemical engineering

A model to take into account the finite exchange kinetic for the equilibrium between phases in the chromatography experiment is studied. The resulting hyperbolic system with a nonlinear relaxation term is then formally treated with a Chapman–Enskog type expansion. A first order correction to the classical quasilinear hyperbolic model is derived which consists of a nonlinear diffusion term. Numerical schemes for both models — relaxed and parabolic — are then tested and compared for different initial and boundary values. A range of validity for the first order approximation is obtained through numerical simulations where its computational performance indicates that it should be advantageously used.