Modeling, parametric sensitivity analysis, and parameter estimation for methanol synthesis in trickle bed reactors

Abstract

Three types of reactor models were developed for simulating the performance of trickle bed reactors for methanol synthesis. These reactor models incorporate plug flow and axial dispersion with: resistance to interparticle and intraparticle diffusion and resistance to mass transfer between gas and liquid phases (the three-phase model); no resistance to interparticle and intraparticle diffusion but resistance to mass transfer between gas and liquid phases (the two-phase model I); no resistance to interparticle and intraparticle diffusion and dynamic equilibrium between gas and liquid phases (the two-phase model II). Mathematical, the model equations are classified as the two-point boundary-value problem and the initial value problem. The former was solved by combination of orthogonal collocation and quasi-linearization, and the latter was treated by Gear's BDF method. Model parameters associated with the reactor models were estimated independently from either published correlations or literature data. The effect of gas space velocity, feed ratio, and temperature on methanol productivity and synthesis gas conversion was discussed. It was indicated that there is a significant difference between model predictions obtained from the three-phase reactor model and ones obtained from the two-phase reactor models. It was also found from a comparison of model predictions between a pilot size trickle bed and slurry reactors that the trickle bed reactor would be more advantageous compared to the slurry reactor for methanol synthesis even with diffusion limitations. For such a large system of two-point boundary-values problem, combination of orthogonal collocation and quasi-linearization is a powerful algorithm. It was further demonstrated from parametric sensitivity analysis of a pilot size trickle bed reactor that rate constants, activation energies, wetting efficiency, solubilities and effective diffusivities of H$sb2,$ CO, and CH$sb3$OH, as well as wall heat transfer coefficients are critical to the reactor design. Finally, a powerful procedure in which the Gauss method combined with an interpolation and extrapolation scheme was used for evaluation of kinetic parameters based on a two-phase reactor model. Model predictions were improved significantly with the optimized parameters.