Statistical analysis of randomized pseudo-first/second order kinetic models. Application to study the adsorption on cadmium ions onto tree fern

Abstract

[EN] Adsorption kinetics are commonly modeled using pseudo-first order (PFO) and pseudo-second order (PSO) rate laws. Both models are formulated via differential equations whose coefficients are commonly treated as deterministic quantities, which are calculated from experimental data using regression techniques. In this paper, we propose a full randomization of both models by assuming that all the parameters of the PFO and PSO models are random variables with arbitrary densities. Then, we probabilistically solve both models by determining semi-explicit expressions of the first probability density functions of the corresponding solution stochastic processes, as well as the densities of the time until a fixed adsorbed amount of reactant has been reached for each model too. The analysis is conducted under very general assumptions and is based on extensive application of the so-called Random Variable Transformation (RVT) technique. Finally, we apply all the aforementioned theoretical findings to model the adsorption of cadmium ions onto tree fern, using real data. We compare the results obtained by the randomized PFO and PSO models, using a Bayesian and a randomized version of the least mean square method to assign reasonable densities to model parameters. After comparing the results, the PSO model is selected, and, we then show how the RVT technique can be applied to obtain further key information, such as the second probability density function, of the solution and the covariance function.