This work applied a Bayesian computational technique for parameter estimation of adsorption breakthrough curve models with experimental data of caffeine (CAF) adsorption onto granular activated carbon (GAC). Different operational conditions were evaluated (volumetric flow: Q, adsorbent mass: W, and initial CAF concentration: C 0) by a two-level factorial experimental design (23) to determine the best operational conditions. The models (Thomas, Yoon–Nelson, Yan, Clark, Gompertz, and Log-Gompertz) were fitted to the experimental data, estimating and not estimating the maximum adsorption capacity (q S). For model selection, five statistical metrics were calculated. The results showed that the proposed Bayesian technique, not estimating q S, was effective and all analyzed operational conditions obtained 95% of CAF removal. In the best condition, when q S reached 7.317 mgCAF/gGAC, the model that best adjusted the experimental data was Log-Gompertz, being suitable for practical approaches, and for its mechanisms, the Clark model best predicted the evaluated fixed-bed column.

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approach was able to identify the pre-mixed and diffusive combustion phases, for different engine loads. Results were compared with a simple inversion procedure, showing a good agreement. The combustion ignition delay was also calculated, showing its variation with the engine load. Keywords Rate of heat release • Inverse problems • Bayesian technique List of symbols A Area A/F Air/fuel ratio B Piston bore CA Crankshaft angle f Linear or non-linear function of the state variables g Linear or non-linear function representing the observation model h Heat transfer coefficient LHV Lower heating value m Mass n Engine speed in Hz n Vector of noise associated with the observation model P Pressure Q Heat t Time T Temperature v Average gas velocity within the cylinder v Vector of noise associated with the evolution model V Volume w Weights of particles W Covariance matrix x Mass fraction of burned fuel y Vector of state variables z Vector of observation variables Abstract The rate of heat released during the combustion in Diesel engines is important for many reasons, including performance evaluation, pollutant formation, and control. Combustion in Diesel engines can be generally divided into three phases: pre-mixed, diffusive or mixed-controlled, and late combustion. The objective of this paper is to estimate the rate of heat released by the fuel in a marine Diesel engine, in order to identify the pre-mixed and diffusive phases, using the Sampling Importance Resampling (SIR) Bayesian Particle Filter. Experimental pressure data obtained from a piezoelectric sensor, installed in a research marine diesel engine (MAN Innovator 4c), was used to feed the observation model in such Bayesian approach. The evolution model for the pressure was formulated in terms of a set of ordinary differential equations, coming from the First Law of Thermodynamics, together with a random walk model for the unknown state variable. The proposed

The modeling of complex phenomena such as adsorption often requires the determination of parameters that cannot be directly measured and, therefore, must be estimated. An important point is related to the analysis of the inverse problem as a method of estimating parameters and selecting models. In view of this, this work aims to apply the Monte Carlo method via Markov Chains (MCMC) as a technique for solving the inverse problem of estimating fixed-bed adsorption parameters using analytical models proposed in the literature. In addition, this work aims to select the best model through the statistical metrics Akaike, corrected Akaike and Bayesian Information Criterion. The use of the Bayesian approach allowed the analysis of the convergence of the chains, as well as selected the best model to represent the experimental data obtained from the literature.

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