It doesn’t look like a valid syllogism to me, because “some students study well in privacy” doesn’t imply that those students don’t study well without privacy. So the fact that some small dorms don’t provide privacy only means that some students might not study well in those dorms; it doesn’t follow that they will not study well.
Pulling over my logic textbook (I hate this class) the syllogism is of the form IOO-2, which is an invalid form from both the Boolean and Aristotelian viewpoints.
It is possible to do a “partial syllogism”, which is what you have constructed. Your syllogism leads to the conclusion that “some students study well in some dorms”. Nowhere in your premises do you state what conditions prevent them from studying well.
Actually Dogface, that conclusion would require the assumed premise “Some small dorms provide enough privacy.” Even then, there is no guarantee that those students who study well in privacy would ever encounter those dorms.