dynamic shortcode not working

I am trying to add a dynamic shortode using:
echo do_shortcode('[user_profile_avatar user_id="<?php $user->id ?>" size="original" align="aligncenter" link="image" target="_blank"]'. $user->display_name .'[/user_profile_avatar]');

but it is not working.

I have tested that $user-id is returning the correct user ID, but I just get a default image.