Inverse analysis applying the Levenberg-Marquardt method for simultaneously estimating parameters of the adsorption of CO2 on activated carbon in a fixed-bed adsorber

An inverse approach (IA) was used to estimate unknown physical parameters selected of a mathematical model built up (MMB) for the adsorption process of CO2 on an activated carbon (AC) bed in a fixed-bed adsorber (FBA). The MMB was reported as the direct problem (DP) for the FBA and is used as the working model of this article. The DP is defined for mass balance equations of CO2 in gaseous and solid phases inside the FBA. The implicit finite volume method and explicit finite difference method were used to solve the DP of this work. These methods were used to test the better method regarding to processing time of the DP. The IA has been applied to the DP to adjust the axial dispersion coefficient of CO2, gas-solid mass transfer coefficient, and adsorption constant of CO2 on the AC bed of the FBA using the Levenberg-Marquardt (LM) method. The solution procedures applied in this work for direct and inverse problems have increased the reliability of the estimation of the chosen parameters from the DP. The results of this work show that the LM method was successfully applied to an adsorption problem to estimate the parameters chosen of the MMB. The numerical simulations have reported that the MMB predicts concentration distribution of CO2 in the gaseous and solid phases, and therefore, the simulated results enable us further generalization of the MMB to adsorption of CO2 on the AC inside the FBA.