EntityFieldQuery gives error on adding propertyCondition
Fields have columns. Properties do not. You want:

$query-&gt;entityCondition('entity_type', 'taxonomy_term')
  -&gt;propertyCondition( 'tid',  $tid, '&gt;=')
  -&gt;propertyCondition('vid', 3)
  -&gt;propertyOrderBy('tid', 'ASC')
  -&gt;range(0, 1000);