John, don't know specifics about typical Converse Co well, but yes weather can be a factor along with several other things. All wells produce their most initially, then have a natural decline curve which is steepest within the first couple of years... 200 bbls per day, 100 bbls per day, to 40 bbls per day, etc... Yet after that drastic drop a typical well may produce at a relative stable level for another 20 or even 40 years.
There are multiple reasons a well might have a rise in production after an initial decline; Possibly weather, the switch from a flowing well to one on a pump, increased production after addressing a lack of transportation (hooking into pipeline), and water disposal issues as you mentioned... Well I'd better get back to work. Hope this helps some.