Rule number 1 when working with forms:
All Form Processing MUST occur on the page specified as the action in the form tag.
<form action="send_email.php" method="post" name="BAP_form" id="BAP_form">
specifies the send_email.php page as the action.
the server validation behavior to validate the captcha element must be added to the send_email.php page.
see this tutorial for detail on working with validation on forms that post to another page: