Herein disclosed is a method for hydrodesulfurization, hydrodenitrogenation, hydrofinishing, amine production or a combination thereof. The method comprises forming a dispersion comprising hydrogen-containing gas bubbles dispersed in a liquid feedstock, wherein the bubbles have a mean diameter of less than about 5 μm and wherein the feedstock comprises a mixture of petroleum-derived hydrocarbons and a naturally derived renewable oil. The feedstock comprises hydrocarbons selected from the group consisting of liquid natural gas, crude oil, crude oil fractions, gasoline, diesel, naphtha, kerosene, jet fuel, fuel oils, and combinations thereof. The method further comprises contacting the dispersion with a catalyst that is active for hydrodesulfurization, hydrodenitrogenation, hydrofinishing, amine production, or a combination thereof. The catalyst comprises homogeneous catalysts and heterogeneous catalysts. The catalyst may be utilized in fixed-bed or slurry applications.