A steady-state mathematical model was developed to analyze the performance of a cascade continuous epoxidation process that was applied to the epoxidation of unsaturated compounds with in-situ-formed performic acid. The model equations were nonlinear, and the model prediction was calculated by solving the model equations using a numerical solution procedure. The experimental results supported the model prediction in that good agreement between the model predictions and experimental results was achieved. The model is necessary for precise operation control, process estimation, and operating parameter optimization and regulation, and will provide a theoretical foundation and research method for automatic control and engineering scale-up.Paper no. J8853 in JAOCS 76, 89-92 (January 1999).The epoxidation of unsaturated fatty acid derivatives, primarily soybean oil and other vegetable oils, is carried out on an industrial scale, producing plasticizers that are compatible with polyvinyl chloride (PVC) and which also act as PVC stabilizers, primarily against heat degradation. In general, the degree of compatibility and stability of an epoxidized oil increases with increasing purity and oxirane number. The iodine value (IV) is a measure of the number of double bonds, while the oxirane value (EPO) is an indication of the percentage content (%, by wt) of epoxide oxygen. The quality of the epoxidized oil is better the higher the oxirane value and the lower the iodine number (1-3). Several processes are available for the preparation of epoxidized oils. The most widely used process is the epoxidation of unsaturated compounds with either pre-or in-situ-formed organic peracids. In-situ epoxidation using hydrogen peroxide with either acetic or formic acid as the peroxygen carrier has achieved commercial importance (4-7). With hydrogen peroxide and acetic acid, however, acid catalysts, such as sulfuric acid or strong cation exchange resins, are needed to speed up peracid formation, whereas performic acid formation requires no strong acid. In our laboratory, the previous study of the kinetics and mechanism of the epoxidation of oils with in-situformed performic acid, as well as the kinetics of oxirane cleavage of epoxidized silkworm pupae oil, showed that formation as well as cleavage of the oxirane ring occurred simultaneously during the epoxidation process. The results indicate that the net yield of epoxides is determined by rates of both reactions, which depend on several factors, such as organic acid concentration and reaction temperature (8,9).Compared with a batch process, a continuous process has three advantages: (i) stable product quality; (ii) convenience, because of use of automatic control; and (iii) lower production costs. Additionally, the continuous process is useful for controlling by-product formation and improving reaction selectivity and yield by changing material contacting time and reaction temperature.Although the epoxidation of unsaturated oils has been extensively investigated, mathematical modeling of a con...