I applied on February 7 for the Shell Graduate Program (United States).
On February 27, I was contacted for a phone interview for the next morning.
Today, March 5, I was told I'd attend Shell Recruitment Day (SRD) on April 19.

Hopefully this gives people some idea of the timelines involved.

Background details: Ph.D., 4.0 GPA, referred to by Shell employee.

The Shell employee that referred me was a new graduate technical hire from 2011. She gave my resume to her department's recruiter, and they referred me to HR.

By the way, in the US, the math assessment is 16 questions in 18 minutes. Each question, without a doubt, takes at least 2 minutes to do comfortably. Unfortunately, Shell's expectations are wildly overestimated. In my case, I could only finish 11 out of the 16 questions. I still passed. Don't worry too much about the math assessment. At this stage in the game, they are mainly looking at your application and at no red flags in your online assessments.

Best of luck.

A Shell employee who is a friend of mine offered a small glimpse into this question:

1) The candidates are NOT in competition with each other
2) You are chosen based on your CAR(T) performance; if you score well, you will most likely be made an offer
3) Historically, only about 50% of people who attend SRD are offered a position
4) You will be paired with candidates who are either technical or commercial based on your background; Ph.D.'s are assessed slightly differently and have an additional technical requirement they must pass before being hired
5) If you pass SRD, you will not be given a specific position. You will become part of a graduate training program. You will, however, be considered "high potential" for the rest of your career at Shell, which puts you at a great advantage, as Shell uses potential as a measurand for layoffs, raises, and promotions.