For any automatic kick done by the chat software, the ban is for 30 minutes.

In the case of the profanity filter, if you use a profanity more than 10 times, it will kick you out. You are warned prior to the kicking, however, giving you a chance to bring your behavior back into compliance with our community guidelines.

The chat system cannot differentiate between private and public chat for these filters, so I'm sorry to say, it applies to private chats as well.

DocJohn