Kansas is a prior appropriation state as far as water law goes, which means basically that the first in time is the first in right. This system of water appropriation also means that every water right is in a seniority system. It is only when the supply becomes insufficient to satisfy all the uses that the seniority system comes into play seriously.
Many people are confused a bit about prior appropriation and water right seniority. Most think that a low number is a senior water right - just because it has a low number.
In Kansas, seniority is more accurately relative to the area of concern (where the supply is insufficient) and to all the water rights in that specific area of concern.
The picture provided is two different cases where seniority would come into play in Kansas. Area 1 is representative of an 8,042 acre area (2-mile radial area) with 11 water rights included - each for 100 AF - and each with its priority number. The priority number actually relates to the date and time that the application was received in the office of the chief engineer. The number itself, for example water right number 5,852 shown, is the 5,852nd water right filed in the state under the 1945 Kansas Water Appropriation Act. It may have reached DWR's office on July 22, 1956 at 2:45 P.M.
If DWR (or in some cases it could be the court) decides that 300 AF is all the supply that can be used in this area, then water rights 3,276; 3,499 and 5,852 are the senior rights in this specific case. If the decision is that 400 AF can be withdrawn, then water right 7,934 becomes a senior right as well. It is entirely possible that water right 3,275 in a different area ends up being the most junior right. Again, its all relative to the specific circumstances in the designated area and the water rights included.
Area 2 is a section of land with only two water rights. If these two wells impair each other, the senior well in this case is 31,234.
Just to be a tad more complete, Kansas also has Vested Water Rights, which are all the recognized water uses that pre-existed the Kansas Water Appropriation Act. Vested rights all have the same priority, and all are senior to every appropriation right - even water right number 1.
There you have it - a cursory look at the meaning of seniority in the Kansas priority system. For more information, visit the DWR website here. There is not a specific rendering of this issue on the DWR website, but these concepts are embodied in the Kansas Water Appropriation Act. You may want to talk to a DWR representative for additional insights.