From "UNIVERSI DOMINICI GREGIS," Apostolic Constitution on the Vacancy of the Apostolic See and the Election of the Roman Pontiff, by John Paul II, February 1996:
"...from the moment when the Apostolic See is lawfully vacant, the Cardinal electors who are present must wait fifteen full days for those who are absent, the College of Cardinals is also granted the faculty to defer, for serious reasons, the beginning of the election for a few days more. But when a maximum of twenty days have elapsed from the beginning of the vacancy of the See, all the Cardinal electors present are obliged to proceed to the election."
April 18 is right in the ballpark.
Although I'm certain any Cardinal physically able will be at the Pope's funeral on Friday, this document places great emphasis on secrecy and non-interference from outside sources in the election. To that end, once the election process begins, no Cardinal is allowed contact with anyone or anything outside the Vatican compound. As a result, I'm sure many of the Cardinals will have unfinished business to attend to before the election -- hence the 15 to 20 day period.
The Apostolic Procedures for electing a new pope
"The Apostolic Constitution Universi Dominici gregis, promulgated by John Paul II on February 22, 1996 have been activated." Read the entire directive...
It will be a blast to watch all CNNABCNBCFOXCBS bunch try to figure out how to break through the veil of secrecy.