If BCH doesn't crash and burn on a technical level, which it very well might, then I think that there will be three stages:

1. For the next 2-4 days, people will have BCH and be trading it inside of exchanges, but will not be able to readily deposit or withdraw it because BCH blocks will be mined very slowly. This will cause a very inflated price on at least some exchanges.
2. Over the course of a few weeks after that, it will be driven absolutely into the ground as people dump their free BCH.
3. Then it will recover somewhat and hover between 0.001 to 0.01 BTC as a maybe slightly-above-average altcoin. Depending on how committed its supporters are, it could continue indefinitely similar to Litecoin or peter out after some time.