Simple Inequality 1

Given that $a,b,c$ are non-negative real numbers satisfying $abc=2$ , then $a\left(b^2+\dfrac{1}{b}\right)+b\left(c^2+\dfrac{1}{c}\right)+c\left(a^2+\dfrac{1}{a}\right)\ge k$ for some integer $k$ . What is $k$ ?