Saving log out time if admin close the browser directly

i want to srore data of login info of  admins. If any admin is login then i am storing his name,email id,  Login Time in database and when he log out i store the logut time. The problem is that if the admin doesn't click on Logout button, he comes out by closing the browser directly then i am unable to save his logout tome. How i will do it. Please suggest me.