Modelagem matemática de curvas de ruptura com comportamento duplo sigmoide

Abstract

Fixed-bed adsorption columns are widely used tools in industry, with applications across a variety of fields. Due to the mathematical complexity of the partial differential equations that describe these processes and the lack of an analytical solution that describes the outlet concentration as a function of time (breakthrough curve), empirical models are developed to simplify calculations related to column design. Breakthrough curves typically exhibit sigmoidal behavior, and empirical models often take the form of logistic functions. However, in some cases, columns display more complex behavior, such as the double-sigmoid breakthrough curve experimentally observed by Kruger (2023). This study aims to develop an empirical model for the breakthrough curve capable of describing the double-sigmoid behavior. Models based on functions found in the literature were constructed and fitted to Kruger’s (2023) data using the software Mathematica. The models were then analyzed using adjusted R², Akaike Information Criterion (AIC), and the distribution of residuals. The models that best fit the data were the Double Logistic (adjusted R² = 0.9980), Double Inverse Tangent (adjusted R² = 0.9981), Double Error (adjusted R² = 0.9979), and Double Hyperbolic (adjusted R² = 0.9980). These models successfully described the double-sigmoid behavior and fit the data well. The adsorption capacity of the column was also calculated for each model and compared with the adsorption capacity initially calculated by Kruger (2023) using simple sigmoid models, resulting in a significantly lower value.