Experiment Planning in the Simulation of Industrial Processes

In the analysis of complex industrial processes, it is of great importance to select the most significant factors. Factors are usually ranked on the basis of the researchers’ experience or expert opinions in the field, with mathematical appraisal of their consistency. However, that approach cannot be used in the development of a new process. In that case, experimental methods are used to select the most significant factors. However, this approach is expensive, time-consuming, and sometimes not even feasible. In the present work, a different approach is outlined. Thermodynamic modeling permits numerical experiments. By means of mathematical experiment planning, the influence of more than ten factors on the target function may be taken into account in a single calculation. The particular formulas for the process parameters obtained by this means permit the elimination of the least significant factors without the need for physical experiments. Another important benefit is that this approach permits assessment of the variation in phase and elemental composition of the products and the threshold of practicality of the process in terms of the batch and temperature conditions, with monitoring of the reliability of the results by mathematical means. On that basis, a generalized equation for the monitored process parameter as a function of all the relevant factors may be derived. That is not possible in standard modeling. As an illustration, the proposed approach is used in the development of a production technology for ferroboron using local material. In this case, thermodynamic modeling employs factors selected on the basis of prior calculations. These factors are also used in physical modeling of the process in a high-temperature furnace. The physical experiment confirms the significance of the factors selected. By experiment planning, the number of numerical experiments may be decreased by a factor of 25, and the number of physical experiments by a factor of 125, without loss of predictive accuracy. In the proposed approach, the extraction coefficient may be brought closer to the equilibrium value on the basis of the most significant factors, by comparison of the calculation results with the results of the physical experiments..