Well, the problem with the write limits is that they need to vary / be adaptive based on our antispam system (Botmaker), and on overall traffic on Twitter.
So, you can look at the “1,000 messages per day” limit, and divide that down into 15 minute segments - but that’s not the exact science, as you’ve found, because with DMs you may want to post a bunch in quick succession, and then none for hours. If your app was detected as behaving in a spammy manner, then the Botmaker might mark it as suspicious and it might be rate-limited or suspended.
What I’m saying is that unfortunately I cannot give you a specific, hard-and-fast number for this action (and I cannot do so for regular Tweets or other write actions either).
Be reasonable about the rate at which you hit the API. You might also want to take a look at our rules on DMs and automation, because automated DMs are generally a bad experience for users.
I hope that helps a little more!
