When is a divorce irrevocable and when is it revocable, and can a woman request an irrevocable divorce if it is the first divorce?

The basic principle regarding divorce is that it is revocable, and it becomes irrevocable in specific cases, such as khul' (divorce at the wife's instance) according to the majority of scholars. This occurs when the wife gives compensation to her husband in return for her release. If the woman has been consummated with, the way to make the divorce irrevocable, so that the husband does not have the right to take her back, is for her to refer her case to the ruler if she has a valid reason for seeking divorce, or for her to seek khul' from him in exchange for property. In this case, she becomes irrevocably divorced from him, and he does not have the right to take her back except with a new marriage contract.