How session is managed in HTML5 session storage, if same user login into multiple tabs / browsers

How session is managed in HTML5 session storage, if same user login into multiple tabs / browsers?

Will old session be invalidated? If yes then how?

Requirement:- Session per tab but if same user tries to login into system (having HTML5 session storage) then the person should be allowed to proceed ahead with new tab/browser window and invalidate old tab/browser session.

Any idea?