Selecting an optimum kinetic model for gas–solid adsorption based on statistical approaches and a model selection criterion

Abstract

Adsorption heat transformation (AHT) techniques can help to safeguard the environment by reducing the use of fossil fuels. When constructing an adsorption-based dynamic heat pump system, analyzing the kinetic characteristics of the adsorbate–adsorbent pair is important. The recently established time-adapted linear driving force (LDF) and commonly used models such as LDF, modified LDF, and Fickian diffusion (FD) models are available in the literature for analyzing the kinetic characteristics, making it challenging for researchers to select the optimum one for simulating the complete real system. This study applies a non-parametric statistical approach known as bootstrapping for simulating the replica of experimental kinetics data for all studied pairs. The kinetics models mentioned above are used to correlate the bootstrap samples. The estimated values of the statistical parameters are compared, and the optimum kinetics model for gas–solid physical adsorption is proposed. The parameters of the model are estimated using the generalized reduced gradient (GRG) non-linear optimization method. For each bootstrap sample, the optimum model is selected based on the minimum values, which means less information loss, of a set of information-based model selection criteria (ICs). The time-adapted LDF incurs smaller values of IC compared to other kinetics models. The p-value of the proportion test for water adsorption onto AQSOA-Z01, RD silica gel, and Al-Fum is very small, which is less than 0.01. So, the test is significant at a 1% level, which implies that time adapted LDF model is significantly optimum. This is the first time that a rigorous statistical optimization technique has been used to identify the optimum kinetic model for gas–solid adsorption. The current findings are critical for a comprehensive analysis of an adsorption system and its design.