Hi.
I’ve been through this process.
The
Pauline Privilege (along with a similar process called the Petrine Privilege) are special dispensations for marriage done “in favor of the faith”–that is, a process for those who were not Christian prior to a previous marriage who want to marry a Catholic after themselves have become Catholic.
While the Church has no authority to dissolve a sacramental marriage (one between two baptized persons), the Church can declare (per
St. Paul in 1 Corinthians 7:12) that one who wants to excuse themselves from a spouse (who does not want to become a Christian) in order for themselves to become a Christian, and thus marry another Christian, may do so.
The key to the Pauline Privilege is that this is not an annulment in the normal sense. The Pauline Privilege simply gives favor in the dissolution of a *natural *marriage (no baptized in the party) in favor of one who has entered the faith to join with another in the faith. That is, both husband and wife of the first marriage must have never been baptized. There are other conditions that must be met from a standpoint of avoiding scandal, but that’s the heart of it.
The Petrine process is similar but more complicated as one of the two members have been baptized. Such decrees are rarer and must have the Holy See’s approval. The Pauline process can be done at the diocesan level.
The process can be quick. I sent in my case to my diocese in late November of 2008. I received a reply four months later, on Good Friday of 2009. It was a very good day for more than one blessed reason for me.