  Let $g \colon S \looparrowright N$ be a properly immersed $\pi_1$--injective
surface in a non-geometric $3$--manifold $N$. We compute the distortion of
$\pi_1(S)$ in $\pi_1(N)$ and show that how it is related to separability of
$\pi_1(S)$ in $\pi_1(N)$. The only possibility of the distortion is linear,
quadratic, exponential, and double exponential.
