How to wrap image tag into div for post only?

You have the global WP_Post object available so you can look the post type like this:

function wrap_post_images_to_div( $content ) {
    if ( get_post()->post_type === 'post' ) {
        $pattern = '/(<img([^>]*)>)/i';   
        $replacement="<div class="well text-center">$1</div>";    
        $content = preg_replace( $pattern, $replacement, $content );
    }
    return $content;
}
add_filter( 'the_content', 'wrap_post_images_to_div' );

You can use the preg_replace_callback instead to filter the matches with certain ids from the matches.