Multiple browser instances - is it possible to determine which browser?

We have an application framework that tidies up application session variables as you traverse from page to page. It works really nicely - until a user opens up 2 instances of a browser. Our code cannot distinguish between different browser instances, so browser instance 2 causes our application session vars for browser instance 1 to be cleared out. We've toyed with many ideas and short of forcing a unique hidden value to be 'POST'ed to every page from every page we don't have an elegant solution. Is there any other way that we could do this? Neil