How long does take for the women to ask for divorce when she does not stay with her husband because of problems?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Asking divorce without any sound reason is a great sin. The Prophet said: “If any woman asks her husband for divorce without any sound Islamic reason, the smell of Paradise will be forbidden for her.” [Ahmad, Abu Daawood and At-Tirmithi who classified it as sound]

However, if there is any Islamic reason or dire necessity, such as when the wife cannot live in harmony with her husband and there is no hope to live a happy life with him, then it is permissible for her to ask for Khul’ (i.e. divorce in return for monetary compensation to be paid to her husband) or divorce.

Know that one should resort to divorce or Khul’ as a last solution after trying all the other means to bring the conjugal life to its normal channels.

Allah Says (what means): {And if a woman fears from her husband contempt or evasion, there is no sin upon them if they make terms of settlement between them - and settlement is best.} [Quran 4:128]

Allah knows best.