Twitter says "Could not authenticate you" when space inside a parameter - twitter

Question

The code below works perfectly fine if, $searchterm = "Chinmay", but doesn't work correct, when the $searchterm has a space in it. I have tried many encoding and have no luck with it.
Section 1 - Getting the URL and Parameters
$searchterm = "Chinmay+Patel";
$params = array( "q" => $searchterm );
$url = 'https://api.twitter.com/1.1/users/search.json';
Section 2 - Building the Signature
$oauth = array(
'oauth_consumer_key' => \Config::get("oauth-4-laravel::consumers.Twitter.client_id"),
'oauth_nonce' => hash('SHA1', time()),
'oauth_signature' => '',
'oauth_signature_method' => 'HMAC-SHA1',
'oauth_timestamp' => time(),
'oauth_token' => $this->twitter_user->access_token,
'oauth_version' => '1.0'
);
foreach ($oauth as $key => $value)
{
if (empty($value)) continue;
$oauth_vals[] = "{$key}={$value}";
}
if( !empty( $params ) ){
foreach ($params as $key => $value) {
if(empty($value)) continue;
$oauth_vals[] = "{$key}={$value}";
}
}
$base = 'GET&' . rawurlencode($url) . '&' . rawurlencode(implode('&', $oauth_vals) );// . '&'. implode( '&', $params);
$composite_key = rawurlencode(\Config::get("oauth-4-laravel::consumers.Twitter.client_secret")) . '&' . rawurlencode($this->twitter_user->secret);
$oauth_signature = base64_encode(hash_hmac('sha1', $base, $composite_key, true));
$oauth['oauth_signature'] = rawurlencode($oauth_signature);
Section 3 - Building the request header
foreach ($oauth as $key => $value)
{
$auth_header[] = "{$key}=\"{$value}\"";
}
$auth_header = implode(', ', $auth_header);
Section 4 - Building the url and making the request
if( !empty( $params ) ){
$url .= "?" . http_build_query( $params );
}
$verbose = fopen('php://temp', 'rw+');
$options = array(
CURLOPT_HTTPHEADER => array("Authorization: OAuth {$auth_header}"),
CURLOPT_HEADER => false,
CURLOPT_URL => $url,
CURLOPT_RETURNTRANSFER => true,
CURLOPT_SSL_VERIFYPEER => false,
CURLOPT_HTTPGET => true,
// DEBUGGING
CURLOPT_VERBOSE => TRUE,
CURLOPT_STDERR => $verbose
);
$feed = curl_init();
curl_setopt_array($feed, $options);
$json = curl_exec($feed);
curl_close($feed);
$twitter_data = json_decode($json, true);
rewind($verbose);
Section 5 - Outputting the data
$verboseLog = stream_get_contents($verbose);
echo "Verbose information:\n<pre>", htmlspecialchars($verboseLog), "</pre>\n";
var_dump( $twitter_data );
What could be the issue? A little bit out of scope for the question, but this code doesn't work with multiple parameters either. For example, if I add the count parameter, it gives me the same error.