  In this paper, we consider a finite, torsion-free module $E$ over a
Gorenstein local ring. We provide sufficient conditions for $E$ to be of linear
type and for the Rees algebra $\mathcal{R}(E)$ of $E$ to be Cohen-Macaulay. Our
results are obtained by constructing a generic Bourbaki $I$ ideal of $E$ and
exploiting properties of the residual intersections of $I$.
