A recently proposed technique for postcombustion CO2 capture in fixed-bed reactors is based on an adsorption procedure carried out by amine supported on pelleted solid substrates. This technology is less energy intensive than adsorption by amines in aqueous solutions. With reference to a laboratory diabatic tubular reactor, two partial differential equation models are produced (and from them, two ordinary differential equation models). The former (two-dimensional, 2-D) model takes into account the mass and energy exchanges along the gas bulk flow longitudinal direction as well as along the reactor radial direction. The latter (one-dimensional, 1-D) model contains a simplified description of the radial effects. The associated ordinary differential equation models are characterized by 840 state variables in the 2-D case and by 280 state variables in the 1-D case. In the models there are two fundamental parameters which are uncertain: the CO2 adsorption and desorption kinetic coefficients. Data for their estimation have been collected in a series of experiments performed in the laboratory plant. The data associated with the steady-state conditions are used to identify the ratio of the kinetic parameters. With the transient data, the two parameters are then separately estimated. The obtained models have been validated with fairly satisfactory results. A problem in the industrial use and control of the reactor for CO2 adsorption desorption is that during its operating life, the kinetic parameters may drift. For this reason, we also propose a method to automatically update their estimate.