Answer
I say, and with God's success: Istinja (cleaning oneself after relieving oneself) is obligatory if the impurity is the size of a dirham. If there is impurity the size of a dirham on him and he prays with it, his prayer is valid, although he is required to remove it; for the size of a dirham is excused, because one who performs istinja with stones instead of water, his prayer is valid by consensus, and stones do not completely eliminate the impurity. Therefore, if he sits in a small amount of water and it becomes impure, it indicates that it is excused and is measured by the dirham. See: Bada'i' al-Sana'i, 1/80, and Tabyin al-Haqaiq, 1/73, and God knows best.