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# Model calculation on repetitious recycling

Aug 11,2020
Model calculation on repetitious recycling

As a reference, model calculation of recycled material ratio and physicality degradation on repetitious
recycling is indicated. If the recycled material mix rate is a constant value "r", recycled material ratio on
repetitious recycling will be as following.
Number of recycle Virgin material Once recycled material Twice recycled material Three times
recycled material Four times recycled material Five times recycled material ...
0 １
1 1－ｒ ｒ
2 １－ｒ ｒ（１－ｒ） ｒ２
3 １－ｒ ｒ（１－ｒ） ｒ２（１－ｒ） ｒ３
4 １－ｒ ｒ（１－ｒ） ｒ２（１－ｒ） ｒ3
（１－ｒ） ｒ4
5 １－ｒ ｒ（１－ｒ） ｒ２（１－ｒ） ｒ3
（１－ｒ） ｒ4
（１－ｒ） ｒ5
Ex） If ｒ＝0.3（30% recycled）, image will be like Figure 4-9
Figure 4-9 Recycled material mixed image when 30% recycled
Furthermore, considering the physicality degradation by heat history from one molding, and replacing that
physicality retention rate with "α", physicality retention rate in each recycled time will be shown as below.
Number of recycle Physicality retention rate
Figure 4-10 indicates relation between number of recycle and physicality retention rate in the case that
recycled material ratio ｒ＝0.1，0.3，0.5, and physicality retention rate α＝0.98，0.95. In each case,
physicality retention rate will be close to attainable retention rate if the recycling have been done about five
times, so recycling should be considered about five times in recycling discussion of the product. If the recycling
material ratio is too high, attainable retention rate will decrease, and recycling number tend to increase to get
close to the attainable retention rate and get stabilized (Figure 4-11). Generally, recycled material ratio should
be below 30%.
If recycling number cannot be increased, consideration can be made on recycled material ratio thinking about
attainable retention rate. For example, if the actual recycled material ratio is 30%, substitution method can be
made by testing once in recycled material ratio of 50%. However, recycling will be influenced greatly by
pulverization shape and water control, so sufficient confirmation is required.