It’s hard to make a case for an annulment, in some instances, but, if you apply, and provide enough information about the circumstances before and after the wedding day, an annulment is probably going to be granted, in my experience. I have worked on annulment cases in a couple of dioceses and, after about 50 of them, I can say that I only encountered one that had to be denied. It was because the person asking for it gave unresponsive answers to the questions, so there was nothing to build a case on at all.
Perhaps, more on the grounds of mercy than on canonical grounds.
I would also add that the use of contraception and acceptance of divorce and remarriage as unexceptional end of a marriage are so prevalent that it is easy to construe invalidity of any marriage just on the basis of that.
The Vatican is making it much easier for Catholics to annul their marriages following a push by Pope Francis for reformation of a process long criticised for being complicated, costly and out of reach for many.
Rules unveiled on Tuesday speed up the annulment process, with a fast-track procedure now available, and allow for appeals to be judged by a local church official rather than the Vatican in what represents a significant decentralisation of power away from Rome...
He also emphasised that annulment ought to be free of cost. - https://www.theguardian.com/world/2015/sep/08/pope-radically-reforms-catholic-churchs-marriage-annulment-process