If you take as an example 1- 2x10 Cedar with a LL @10 PSF and DL @ 10 PSF you can span that 19' with Deflection Limit @ L/360
I don't think it will be a problem going 18'-20' with a double 2x10 for the beam... But also keep in mind how much shading you want to have, and how will you run your rafters 12",16",18" OC etc. The more lumber you use on top, the more lateral force the structure will take.
With that said, the bigger the span the less points of bracing you will have. On 18' span you will have bracing at 4 corners, everything in between will move and cause friction when wind hits. The best way to go about this is to break up that span and will have a more sound structure that will last a long time and that would be also in the best interest of your clients.
Good luck