Changing Keywords

Hi guys,

I have a hypothetic scenario. Say my website originally ranked for a more niche keyword, but the site has since grown and I wanted to change my keywords. If it's a suitable keyword for the size of the site, how long would it take for the changes to propagate and for it to list properly under the new keyword? Would this happen upon Google crawling the site, or would it take a few weeks?

Cheers.