Theoretical Investigation of Thermal Effects in an Adiabatic Chromatographic Column Using a Lumped Kinetic Model Incorporating Heat Transfer Resistances

Abstract

A non-equilibrium non-isothermal lumped kinetic model (LKM) is analytically and numerically investigated to evaluate the effects of inherent temperature fluctuations in an adiabatic chromatographic column. The model comprises of convectiondiffusion partial differential equations quantifying mass and energy balances in the mobile phase coupled with differential and algebraic equations for mass and energy in the stationary phase. Besides two mass transfer coefficients, two heat transfer coefficients are involved in the model equations. The properties of the considered model are investigated for linear concentration and temperature dependencies of the equilibrium loadings. The Laplace transformation and eigen-decomposition techniques are utilized to solve the set of equations. These solutions are helpful for understanding,

A linearized non-isothermal general rate model for studying thermal effects in liquid chromatographic columns

“…The equilibrium relation between the solid and liquid-phase concentrations in Eq. (5) can be linearized by using first order Taylor-expansion considering small variations in the temperature and concentration [25,26]. The Taylors expansion is defined as…”

“…Other contributions regarding temperature variations inside liquid chromatographic columns can be found in the articles of [17][18][19][20][21]. Moreover, [22][23][24][25][26][27] have theoretically investigated the effects of temperature changes by using non-isothermal dispersive equilibrium model (DEM) and kinetic lumped model (KLM). The modeling of chromatographic procedures is usually carried out with mass-balance based macroscopic or deterministic models.…”

“…This article extends our previous analysis (c.f. [25,26,28]) by formulating and solving analytically the non-isothermal general rate model (GRM) of liquid chromatography, which is one of the most detailed kinetic model that accounts for many of the factors influencing the process of chromatography.…”

“…To obtain the analytical solution of governing model equations, the Laplace transformation and the eigenvalue-decomposition technique are employed. Here, an accurate and efficient numerical Laplace inversion is applied to acquire back the solution in the time domain, see [26,29]. To determine ranges in which our analytical solutions are useful and valid, a second order finite volume scheme is also implemented to approximate the model equations.…”

Simulation of nonisothermal reactive liquid chromatography using two‐dimensional lumped kinetic model

“…The corresponding energy balance equations in the bulk and solid phases are demonstrated as 19,35,44,45…”