Epoxidation of oleic acid by peracetic acid (PAA) was studied in a recycled reactor system under conventional heating and microwave irradiation. This reaction system consists of several steps. Thus, a kinetic modelling strategy to diminish the number of parameters to be estimated was developed by investigating each reaction step: PAA synthesis and decomposition, epoxidation and ring-opening. The energy balance for microwave heating was correlated with the concentration of the microwave-absorbent species and the total input power of the microwaves. The epoxidation reaction was conducted in the vigorously stirred tank reactor under isothermal conditions within a temperature range of 50-70 degrees C. The organic phase content was 32-45% v/v. The interfacial mass transfer was supposed to be faster than the intrinsic reaction kinetics suppressing the use of mass transfer correlations. Nonlinear regression was used to estimate the kinetic parameters. Two models were developed for microwave and conventional heating respectively. The perhydrolysis showed to be the slowest reaction, followed by the epoxidation and the ring-opening. The use of microwave irradiation resulted in considerable process intensification for the epoxidation process. By employing microwave heating, the perhydrolysis step in the aqueous phase was enhanced, and the reaction time was reduced by 50% in best cases, which implies that the reactor size can be diminished by microwave technology. (C) 2019 Elsevier Ltd. All rights reserved.