Oil diffusion mathematical model in oily sludge particle under supercritical water environment

Supercritical water (SCW, T > 374.15 °C, P > 22.1 MPa) treatment can achieve volume reduction, harmless disposal, and resource utilization of oily sludge. Herein, we investigated the oil removal efficiency (ORE) and oil diffusion characteristics in oily sludge particles under SCW environment. The experimental results showed that when the treatment duration was extended from 5 min to 60 min, the particle diameter decreased from 4 mm to 2 mm, and the ORE improved considerably; however, the treatment temperature (375 °C ∼ 425 °C) had little influence. Based on these findings, an oil diffusion mechanism in oily sludge particles under SCW environment was proposed. Subsequently, a reasonable mathematical model of diffusion was developed to represent the heat and mass transfer in oily sludge particles characterized by porous, high moisture, and oil content. Finally, by analyzing the oil diffusion process in sludge particles within this model, it was found that the oil concentration in SCW and particle diameter had a considerable influence on ORE, while the effect can be ignored when the diameter < 0.2 mm. This research serves as a guide for effectively using SCW to remove oil from oily sludge.