Formula to Generate Which week of the year it is based on date entered in ""Process Date"" Field.

This will work. 

The formula Ending Saturday of First Week of Year is

var date TodaysDate= [test today];

LastDayOfWeek(FirstDayOfYear($TodaysDate))

You would set up a field called test today to test various dates.  Then once you are satisfied, change the first formula variable to


var date TodaysDate= Today();


The there would be a separate field for the week number


var date TodaysDate= [test today];

var number WeeksSinceFirstWeek = 
(ToDays(LastDayOfWeek($TodaysDate)-[Ending Saturday of First Week of Year]))/7;

$WeeksSinceFirstWeek+1