Just now in the chat room we came across a reading of the kanji 閉 that seems to be either rare or erroneous.
In the English Wiktionary's entry for 閉 there is the following "Readings section":
None of us in the chat room at the time could come up with anywhere the へつ is used?
Is it a correct reading? What is/was it used for?
I found this in a kanji dictionary from 1920s.
http://kindai.ndl.go.jp/info:ndljp/pid/936724 (set コマ番号 to 866 and you see the page)
It lists four sounds for 閉, but none of the following 熟語 has a sound other than ヘイ. I guess this kind of description (ヘツ、ヘチ。方結切。屑。) originally originates in classical Chinese hanzi dictionaries like 廣韻 or 康煕字典.
This is not an error, as some of the other answers may suggest.
The Kangxi Dictionary records the following additional definition under「閉」:
《廣韻》方結切《集韻》《韻會》必結切《正韻》必列切，𠀤音鼈。義同。
Guangyun, Fanqie rime [方]{ほう}[結]{けつ}; Jiyun and Yunhui, Fanqie rime [必]{ひつ}[結]{けつ}; Zhengyun, Fanqie rime [必]{ひつ}[列]{れつ}. Same sound and meaning as「[鼈]{へつ}」.
What's going on here is that「閉」, in some Chinese texts, was used as a phonetic loan for「[鼈]{へつ}」, and this usage was recorded in Middle Chinese rime dictionaries like Guangyun and Jiyun. Japanese on'yomi largely corresponds to the phonology in these dictionaries and thus may inherit these rare readings/usages.
The readings are there for advanced Chinese literature study if you consult a dictionary, for completeness purposes. There are a lot of obscure on'yomi that you may find in dictionaries which come from this kind of phonetic borrowing in characters (this is practically the Chinese version of ateji), and most of the time you can safely ignore them.
On'yomi given are for Kan'on readings.
As others have noted, the reading へつ is not listed in other dictionaries, such as デジタル大辞泉. But that could be a measure of the lexicographer's rigor. So at this point, maybe it's an error, maybe it's not.
Additional evidence is found in the corresponding Chinese reading of 閉. The coda /-tu/ typically corresponds to Middle Chinese coda /-t/, which would be preserved in modern Cantonese. However, 閉 in Cantonese is /bai3/. So へつ is likely an error.
But looking at Baxter & Sagart's Old Chinese reconstruction (2011), 閉 has the following forms (bearing in mind the well-documented /p/ to /h/ lenition in Japanese):
MC: pejH
OC: *pˁit-s {*pˁi[t]-s}
An important note on time periods: Old Chinese (OC) was around 1200 ~ 300 BC, which makes for an extremely unlikely candidate for borrowing into Japanese. (音読み are generally borrowed from around 700 AD and later.)
My e-dictionary lists the commmon 漢音 reading of へい, and a rarer (and older) 呉音 reading of はい. No 唐音 reading listed.
So we can say with some degree of confidence that へつ is unlikely to be an 音読み for 閉. Although, I guess it's always possible that 閉 was anachronistically used as ateji for へつ in some obscure piece of literature.
The 『デジタル大辞泉』 does not list the reading へつ, so I'd call it an error.
http://dictionary.goo.ne.jp/leaf/jn2/197949/m1u/%e9%96%89/
The dictionary 学研漢和大辞典 does not list any words with this reading either.
kJapaneseOnfield: unicode.org/cgi-bin/GetUnihanData.pl?codepoint=%E9%96%89 (I don't know anything about the readings data in Unicode, but others here might.)