I'm currently applying for PhD places and one University is advertising three projects that I'm interested in. Is there usually any problem in applying for more than one PhD at the same University, within the same department?

No this isn't a problem.

No it is no problem, I applied for one PhD and then was offered two PhDs in the same department to choose from.

i need to pursue my phd in environmental microbiology and i need a good university where i can register moreso that casn assist me with scholarship