I'm pretty sure you (your company) has to be a member of the AGA. From there your company leverages for a seat on a committee. Though I do see a lot of ASME influence throughout 582. CWI7611 was co-chair of 1104 for a long time...basically when GOD created dirt. IF you can contact him on here, he should probably have much better info to offer you than this.

My suggestion.
1. Get to know who's the President of API 582 Committee. I suppose that the committees, together with the names of their Presidents, are listed on API's site. If not, make a telephone call to API's offices in Washington DC and ask. Don't send e-mails. That kind of e-mails are seldom, if ever, answered.
2. Write a letter on your own letterhead (if don't have your own letterhead, use a first quality paper) saying that you wish to become a member of the Committee, and telling him (her) how you can contribute to the Committee's work. Attach your resumé to show that you're qualified to become a member. Don't send e-mails, a letter has more importance than an e-mail and is treated much better.

Tell me how you got along. Good luck.
Giovanni S. Crisi
Sao Paulo - Brazil

Go to the API web site. There is a section where you can volunteer for being on a committee.
http://www.api.org/publications-standards-and-statistics/committee-information
http://www.api.org/publications-standards-and-statistics/standards-committee-application
You will need a background in the area you want to serve with. It helps to have some API certifications such as 510, 570 or 653, or an engineering background in the petroleum industry.