On the older tractors you need the SN of the tractor and then a listing of the engine used in that SN tractor.Later tractors have a different SN on the engine from the tractor. The first older D311 as you mentioned was used in the D2 tractor and early 11A 933 loader for example and say the early 7J D4s used the D4400 and little later D4s like the 6U & 7U used the D315 and the D6 U series in that era used the D318.I worked for Cat dealer for 36 yrs. so I grew up with all the engines and what they were in but I understand your question.
also check the serial # plate on the engine behind the pony clutch lever--the engine might have been changed as i found out on my 4u7412--the engine serial# was 7S8119 and was still a D311---i believe there are more different models of the D311
Dan, what that engine is is a D311 industrial engine so someone has either used a whole industrial engine and installed it in place of the original engine or could have been just the block and they left the industrial serial number plate on it.All the D2 engines till they went out of production would have the tractor serial number on them that they installed into. In later years after that then the tractor engines all had their own model serial number on them and not the tractor serial number on the back or wherever it was on the tractor.