What is the ruling on a man marrying three women, with the condition that the marriage be secret and unofficial, along with the intention of divorce in the future should he move to another area, and without procreation?

Polygyny is permissible within the bounds of Islamic law. If the marriage is conducted according to its regulations and pillars, then it is valid.

As for the mentioned conditions: 1. The condition that the marriage be secret does not invalidate the marriage as long as witnesses were present. 2. The lack of official documentation for the marriage does not invalidate it. 3. The intention to divorce upon leaving the area or explicitly stating it is merely a promise and does not invalidate the marriage; the contract is valid and the divorce within it is not temporary. 4. The condition of not having children is invalid, but it does not invalidate the contract. Rather, the contract remains valid and the condition becomes void.

Based on this, the conditions mentioned do not affect the validity of the marriage.