Close browser,insert record in database

Question

My issue is 
 

As user login i insert data in datbase to track the record of user's login
 
And in same way when user logout .Record is inserted in database to track 
the logout record
 
thats why there is button to logout on the top of my site (that is Master page)
 
My issue is if user directly close the browser so how to insert the record in Database
 
My " Logout " button is on master page
 

when user close the browser so i want to update logout field in db(sql server)
 
thanks in advance