Why do we have $\overline{\operatorname{Mov}(X)}\subset \overline{\operatorname{Eff}(X)}$ for any normal variety $X$?

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I am trying to understand why $\overline{\operatorname{Mov}(X)}\subset \overline{\operatorname{Eff}(X)}$, where $X$ is any normal variety.

Here $\operatorname{Mov}(X)$ is the convex cone generated by movable divisors in $N^1(X)$, and $\operatorname{Eff}(X)$ is the cone generated by effective divisors on $X$. A divisor is movable if $\operatorname{Codim}(B(D))\geq 2,$ where $$B(D)=\cap_{m\geq 1}Bs(|mD|).$$ So essentially, I am trying to prove that any movable divisor is a limit of effective divisors. But I do not have any alternate description of movable divisors, which is making the task more difficult and non-intuitive.