Shell variables in sed script

Use double quotes for the sed expression.

new_db_name=$(echo "$new_db_name" | sed "s/$replace_string/$replace_with/")

This worked for me in using env arguments.

export a=foo
export b=bar

echo a/b | sed 's/a/'$b'/'

bar/b

If you use bash, this should work:

new_db_name=${new_db_name/$replace_string/$replace_with}