In a 1996 article, Angel Manuel Rodriguez offers a close structural analysis of the day of coverings rite in Leviticus 16.
Overall, he finds that the chapter is a chiasm:
“Yahweh said to Moses”
A. Aaron should not go into most holy place any time he wishes 16:2
B. Aaron’s sacrificial victims and special vestment 16:3-4
C. Sacrificial victims provided by the people 16:5
D. Aaron’s bull, goat for Yahweh, goat for Azazel 16:6-10
E. Aaron sacrifices his bull as a sin-offering 16:11-14
F. Community’s goat is sacrificed as a sin-offering 16: 15
G. Make atonement 16:16-19
G’. Atonement is finished 16:20a
F’. Community’s goat for Azazel sent to the wilderness 16:20b-22
E’. Aaron’s closing activities 16:23-25
D’. Goat for Azazel, Aaron’s bull, goat for sin-offering 16:26-28
C’. People rest and humble themselves 16:29-31
B’. Anointed priest officiates wearing special garments 16:32-33
A’. Anointed priest makes atonement once a year 16:34
“As the Lord commanded Moses”
He also notes the oddly fragmented way that the offerings are describes in the chapter: “It is interesting to notice how a circle of activity is introduced and then, at a rather slow pace, reaches its closure, taking us through a process in which each one of its parts is very significant. For instance, the circle of the burnt-offerings is initiated in 16:3, 5 and closed in 16:24, without any mention of it in between. The goat for Azazel is introduced in 16:5; the selection of the specific goat is recorded in v. 10. The laying on of hands, the transfer of sin to it, and the act of sending it away to the wilderness are found in 16:20b-22. But perhaps the most significant circle is that of Aaron’s sin-offering. It is introduced in 16:3; the sacrificial victim is presented in 16:6, slaughtered in 16:11; the blood manipulation is described in 16:14, the burning of the fat in 16:25, and the circle is closed with the disposal of the flesh of the victim in 16:27. We find a similar situation with respect to the people’s sin-offering, which is introduced (16:5), then presented to the Lord (16:9), slaughtered, the blood manipulation performed (16:15), its fat burned (16:25), and finally the disposal of the flesh brings the circle to an end (16:27).14 What was in the regular sin-offering a series of consecutive steps in the sacrificial process (Lev 4) is intentionally separated in the ritual of the day of atonement in order to make room for new details in this sophisticated and complex ritual unit. Thus, the unity of the chapter is emphasized.”
The article is available at: (available at http://faculty.gordon.edu/hu/bi/Ted_Hildebrandt/OTeSources/03-Leviticus/Text/Articles/Rodriguez-Lev16.pdf ).