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Please imagine you are at the airport and waiting for your plane to get ready so that the airport's announcer would call your flight number and you could board the plane.
Your flight is on 6:00 p.m. It is 5:45 and they have not announced your flight number yet. You go to the information desk and notice that due to some technical issues you have to wait for about an hour and your flight would be at 7:05 p.m.
Finally, you fly and when you arrive, you are talking to your friend who has come to the airport to give you a ride to a hotel. Now you are in his car and talking to him about the pick-up process at the source airport.

How would you normally describe that situation and how would you casually (not in an impolite way) imply that you waited there?

• I was __________ at the X airport for almost one hour.

I know three verbs that can encapsulate this meaning, but I have no idea what verb would a native speaker use in an informal situation like this. Also, I need to know if my provided options work properly here. (I need the most common term in everyday conversation.)

1- I was kept waiting at the X airport. (This choice, although, can make my point across, but it has a connotation of "something forced", though dictionary definition, approves my feelings too. I don't know how to explain that, but I think there should be a better option too.)

2- I was left hanging at the X airport. (I don't know why, but I have an intuition that this is not a correct option here.)

3- I was detained at the X airport. (to me "detain" sounds a bit stilted.)

However, despite all my opinions, I wonder if you could let me know about your own choice either in my options or of there is any other and better choice.

Also, if they all are correct, then please let me know what is the nuance between these three verbs.

As a simple one word answer "I was delayed at the airport for one hour".

"Kept waiting" is fine. "Left hanging" suggest that there was a lack of information about what the reason for the delay is. ("left hanging comes from hanging on the telephone while the other person is doing something else)

"Detained" doesn't work, that means, roughly, that you were arrested by the police.

(BTW "at Heathrow airport" or "at the airport" but not "At the Heathrow Airport".)

"My flight was delayed by almost an hour at the X airport"

or

"I was delayed by almost an hour at the X airport"

Would be my preferences.

1) Is OK, and you were forced to wait, but specifically mentioning the flight gives more information.

2) I agree this is not right "left hanging" is more like abandoned, which you were not, just delayed.

3) "Was detained" is more associated with forcibly held, such as arrested by the police.

I was delayed at the airport for an hour (because my flight was late).

My flight was delayed for an hour.

"Kept waiting" implies some kind of specific action that created an unintentional, or sometimes intentional, delay. It's not used for flights by default, because it's not the intention of the airline to run late. A more common circumstance is where there is something to hold up the flight during which everyone must wait:

We were kept waiting at the airport for an hour while they inspected our plane. They said there was some kind of warning light, but it turned out to be nothing serious I guess.

As I said, it can be intentional:

Even if she wasn't doing anything important, the regional manager liked to keep salespeople waiting in her outer office for fifteen minutes before seeing them, as she liked to see them a little annoyed.

"Left hanging" is a little more colloquial, and also suggests some kind of broken promise or at least misleading expectation, in which you presume things should happen in some defined way, and are inconvenienced when they go a different way:

The tour company left us hanging around the hotel lobby for an hour after breakfast before they came to pick us up. It seemed very unprofessional and not a good start to the holiday.

"Detained" is a little ambiguous. It suggests that you were delayed against your will, although this can be by circumstance not force -- that is, you don't have to be "detained" by the police. It would not normally be used for airlines unless there really was some authority involved:

The flight was delayed when the entire flight crew were detained by the local police. We didn't know why but we guessed maybe one of them was suspected of smuggling drugs.

"Detained" can be used as a polite excuse for being late to an appointment, as it suggests involuntary delay.

I apologize for being later to dinner, folks. I was unavoidably detained at work.