Converting portion of residential property to self storage

I bought a duplex about a year ago that produces decent cash flow on its own, but I've always had this idea in the back of my mind to split the double city lot to build a mini storage in the unused lot space. Just thinking that huge space could bring some additional revenue if I already own it. 

I've never done any commercial, and I'm not sure how to go about the rezoning I'm sure would be necessary, but I'm guessing it's doable. Anyone have experience with something this and willing to share?  What would the toughest things to overcome?

TIA,

       -Patrick