XXXXXXX,
Could you explain your situation a little more and what you are planning to do?
Hello XXXXXXX,
Welcome to Just Answer.
I have never seen a 7 inch cavity.....that is extremely wide. I wouldn't recommend installing any type of insulation in the cavity at this point, because it will create more problems.
A cavity behind brick is intended to collect any water that penetrates the brick and allow it to flow downwards to weep holes at the bottom, and drain out. Filling the cavity will prevent this from happening and water will get stuck in the cavity, causing moisture problems such as decay, mold, etc.
In todays cavity walls, rigid insulation is installed on the backup wall prior to brick installation and a 1-2 inch space is left between the the rigid insulation and brick to maintain a drainage plain for water. I'm afraid your only option is to insulate the backup wall.
If you need further help or clarification on this answer, please do not hesitate to reply to this post.
Thanks for asking your question at Just Answer.
Best of Luck, Brian
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Architect
Licensed Architect- 12 years, L.E.E.D. AP, Former Remodeling Contractor- 10 years