In temperate climate without NewGRFs, the wells are soon closing down. OpenTTD keeps the behaviour of the original Transport Tycoon Deluxe, where temperate oil wells never increase production. They only decrease production until they run dry and close. New wells never spawn after year 1950, so wells continue to close until they're all gone. Because of this, some players ignore Oil Wells and wait for Oil Rigs to appear.
In sub-arctic and sub-tropical climates, the wells increase and decrease production like other primary industries. New wells never spawn after year 1950.