D&D Next: Lords of Waterdeep?
Page 232 of the pdf has the xp guidelines based on the level of the encounter and the toughness of the encounter.
Characters need 1800 xp to go from 3rd to 4th level.
So, that’s around 180xp/session for very slow progression. 10 adventures for a level.
300xp/session for a slow average. 6 adventures for a level.
600xp/session for the high end of average. 3 adventures for a level.