There is only one file. And it is written simultaneously as web app copies run.
How do you filter only one session log messages from other log lines?
Here is a page that sets up an MDC filter for web-app -> http://rtner.de/software/MDCUserServletFilter.html
Being a servlet filter it will free you from managing MDC/NDC in each of your servlets.
Of course, you should modify it to save information more pertinent to your web-app.