You will need to know the name for your “portfolio_tags” taxonomy. Check where it is defined as a custom taxonomy, and it will need to be added to the portfolio custom post type.
The register_taxonomy() function would be your theme like this:
register_taxonomy('portfolio_tags',
array('portfolio'),
array('hierarchical' => false, 'show_ui' => true, 'query_var' => true,
'rewrite' => array( 'slug' => 'portfolio-tags' )));
Or you could be using a custom post / custom taxonomy plugin — then you would need to check what id was given (for example, it could be “portfolio_tag” instead)
Once you have confirmed this, you should use get_the_terms() instead, since it is part of the WordPress API (wp_get_object_terms() isn’t using the object cache so it would be less efficient)
$post_cat = get_the_terms( $post->ID, 'portfolio_tags' );
Finally, in order to use $post-ID, make sure you are in The Loop or you have referenced the global $post object.