## 1 Introduction  
Industrial growth and the increase in the scale of production in societies have had a major impact on the quality of water available to the population. Several contaminating sources can be cited as causing this threat to the drinkability of water, including contamination by heavy metals through waste effluents from industries such as battery manufacturing, foundry, mining, and electroplating, among others [1; 2; 3]. Such effluents may contain a mixture of heavy metals, such as Pb, Cd, Ni, Cu, etc., which, if disposed of improperly, present a threat to human health [4]. These metal ions, aside from being toxic to humans, are non-biodegradable, meaning they can accumulate in the human body and throughout the entire food chain, potentially causing various health issues such as headaches, stomach pain, and cancer [5; 6; 7; 8]. Various treatment methods have been proposed in the literature to address this issue. Among them are chemical precipitation [9; 10], ion exchange [11; 12; 13], adsorption [14; 15], membrane filtration [16; 17; 18], reverse osmosis [19; 20; 21], and electrochemical treatment [22]. Many of these methods have high capital and operating costs. In this context, adsorption stands out as one of the most widely used methods [23] due to its high efficiency, low cost, and ease of operation. Adsorption is an important tool for treating contaminated effluents, which, as observed by [PERSON] et al. [24], has excellent performance if used in a continuous process in fixed bed columns, where the adsorbent works better. During the bed adsorption process, each adsorbent particle in the column will adsorb the solute until it reaches the saturation state. This process proceeds successively, layer by layer, from the input to the output of the column [25]. Thus, describing the rupture curve of the adsorption processes is of great importance for evaluating the dynamics of the phenomenon, since it contains a lot of information, such as the rupture point and saturation point. Furthermore, mathematical models are used to predict the behavior of the system and relate these to the data and process parameters. The dynamics of adsorption in the column are based on phenomena such as axial dispersion, resistance to diffusion in the outer film, and resistance to intra-particle diffusion [26]. Therefore, it is important that the model manages to account for all the mechanisms that occur within the fixed bed [27]. There are two ways to develop mathematical models: through differential equations obtained through mass balances or through empirical approximations [28]. Several mathematical models used to evaluate adsorbent-adsorbate interactions can be found in the literature, such as the model by [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] [13]. However, the models that are developed from mass balance are less limited than the empirical ones, since they are based on the fundamental principle of the conservation of mass and are not limited by the specific experimental conditions of the process. Therefore, once the model is shown to be reliable, the challenge is to estimate the parameters that are part of it. When we deal with inverse problems and we have some knowledge of the structure of the model, solving these problems involves estimating the parameters that constitute them. Thus, using information from the experimental data and the mathematical structure of the model, it is possible to estimate the values of the parameters that best link the model to the data. There are several approaches to this estimation, including statistics using prior knowledge (Bayesian approach), that is, using the prior knowledge we have about a certain parameter, which proves to provide a great advantage over other estimation techniques [29; 30]. Thus, in this work, a Bayesian statistical approach is used to estimate the parameters involved in the model, obtained through the mass balance in the column, Langmuir isotherm, and LDF hypothesis, for the experimental data of [PERSON] et al. (2021) [14] and [PERSON] et al.