Mathematical modeling in chemical engineering: a tool to analyse complex systems

Mathematical modeling is an attempt to describe a slice of reality in mathematical terms. In Chemical Engineering, mathematical modeling is used for simulation, control and optimization of a process and it is also a tool to design the industrial devices. Mathematical modeling is a technique commonly in place also in both theoretical and experimental studies of chemical processes. In the present chapter mathematical modelling applications to complex systems as a consequence of structure heterogeneity and involved various physical-chemical phenomena are presented. Particular attention will be focused on improving the quantitative understanding of the basic phenomena of a process that can come from the use of mathematical models. Specific task is also demonstrating how, through the use of information coming from experimental investigations and simulations, it is possible checking on the validity of the assumptions made and fine tuning the predictive mathematical model capability. The possibility of analyzing and quantifying the role played by each single step of the process is examined in order to define the relevant mathematical expressions. The latter allows getting useful indications about the impact of different operating conditions on the role of each single step and at the very end it gives indication about the efficiency of the process itself. Next step focuses on the estimation of the significant parameters of the process. In complex systems the determination “a priori” of some parameters is not always feasible and they are therefore determined as a comparison of experimental and simulation data. The final result is therefore the availability of a tool, the verified and validated (V&V) mathematical model, that can be used for simulation, process analysis, process control, optimization, design. Specific reference will be made to the use of the proposed methodology on a system whose behaviour, on varying the agitation level, was quantified and validated against the results of an experimental investigation in a pilot plant. A second application will allow to analyse the effect of transport phenomena in multi-phase heterogeneous systems in order to detect the conditions at which production plant efficiency is improved.