Hi Kimberly

If they are a client [and not an employer] then you don't need to ask for a raise, but rather, iinform them of a change in your fee structure.
I'd send them a letter informing them of the change, although I do think three weeks notice is maybe not enough - I always give two months. In any case, draft a letter, thank them for the working relationship, offer a few examples of how you've improved your skill set and service offerings [to the benefit of your clientele] and then let them know how much the increase is, when it will take effect, and any other relative items that might come into play. Close the letter with a note about how much you're looking forward to working with them in the new year and voila!
No excuses, no apologies. If you know that you're worth more and you feel they've outgrown their current hourly rate then be kind but straightforward.
I'll look forward to hearing how this goes for you, please keep us posted.