Numerical approximation of non-linear chromatographic models considering Bi-Langmuir isotherm

Abstract

In this research article, two standard models of liquid chromatograophy, namely the dispersive equilibrium model (DEM) and the kinetic lumped model (KLM) are approximated numerically. We studied the transport of multi components in a single column of chromatography considering non linear adsorption thermodynamics. The models are analyzed for standard Bi-Langmuir and generalized Bi-Langmuir types adsorption equilibrium isotherms using Danckwert (Robin) boundary conditions. Mathematically, the model equations form a non linear system of partial differential equations accounting for the phenomena of advection and diffusion, paired with an algebraic equation or a differential equation for adsorption isotherm. An extended semi-discrete high-resolution finite volume scheme is employed to obtain the approximate solutions of the governing model equations. The method has second to third order accuracy. Several test case studies are conducted to examine the influence of various critical parameters on the process performance. The contemplated case studies incorporate the elution process of liquid chromatography with an increasing number of components. In particular, single component, two component and three component mixtures are considered for the assessment of process performance. The formulated numerical algorithm provide an efficacious mechanism for investigating the retention behavior and the influence of mass transfer kinetics on the shapes of elution profiles.

Simulation of Fixed-Bed Chromatographic Processes Considering the Nonlinear Adsorption Isotherms

“…Understanding the Henry constant is essential for optimizing the conditions in a system and achieving high-quality separations. In Figure , the already available high-resolution FVM of Koren , of second- to third-order accuracy is used to compare the results of the suggested method. The findings show an amazing level of accuracy and consistency.…”

“…Consequently, the only method for finding a solution is to use a precise, reliable, and effective numerical technique. In general, the finite difference (FD), finite element method (FEM), and finite volume method (FVM) are three well-known numerical techniques that can simulate chromatographic processes. ,,,,− , These techniques are widely recognized and well-established methods for numerical simulations. The FD is based on the discretization of the spatial domain into a grid of discrete points and the approximation of the partial derivatives in the governing equations.…”

Analysis of Liquid Chromatography Considering a Linear Single-Component Heterogeneous-Type Reactive General Rate Model

“…Some other wellknown flux-limiting functions, used to validate the proposed model, are displayed in Table 2. The following flux limiters 16 will be used to examine the chromatogram efficiency for specific case studies.…”

“…This study extends and generalizes our research group’s past studies on nonreactive linear single-component GRM. Koren’s high-resolution finite volume method (HR-FVM) , is extended for heterogeneous-type reactive general rate model (RGRM). The approach approximates the solution with second-order precision.…”

Nanofiber-Textured Organic Semiconductor Films for Field-Effect Ammonia Sensors

“…As the interaction between gas analyte and OTFTs can be regarded as isothermal to avoid the calculation complexity. Langmuir isotherm adsorption model was applied and the gas molecules adsorbed on the surface of the sensing layer are in a dynamic equilibrium [28][29][30].…”