I owe an explanation. I said about Session.Clear() to use it whenever the information stored inside the session variables are not needed any more. In this way you might see that you dont need to worry about the closing of the browser.
@JorgeM is absolutelly corect in all he direct you
but how can I guess the period of session timeout ?
In my application when a user open a page I give him the permission to do something, but when he close the browser I have to clear or remove the session.
But the problem when I close the browser and open again the session doesn't remove.
just a guess but i think it can be done in global.asax Session_End event. do call same statements as suggested by @tdrosiadis ..... it will clear session if user closes browser without log-out or any action.