Looking at the Sydney Sands Directory, there are entries for A D WELLS in 1892 at 8 Elizabeth St, Paddington ; and in 1893 both at the Elizabeth St address and at Old South Head Rd, Waverley. I can't see any entries after this time.
There is also an item on trove for the A D WELLS of Elizabeth St - helping at an accident site in 1891.
http://nla.gov.au/nla.news-article228182982These addresses, and the Edgecliffe Rd one are all in the same general area of Sydney.