  In this short note, we extend the results of [Alexeev-Orlov, 2012] about
Picard groups of Burniat surfaces with $K^2=6$ to the cases of $2\le K^2\le 5$.
We also compute the semigroup of effective divisors on Burniat surfaces with
$K^2=6$. Finally, we construct an exceptional collection on a nonnormal
semistable degeneration of a 1-parameter family of Burniat surfaces with
$K^2=6$.
