This is a brief diary which is more of a pictorial explanation than anything else.
To me, not an engineer but with a science background, the top kill idea didn't make any sense, with that riser kinked and leaking where it comes out of the BOP. The idea initially shown below is that under very high pressure a dense and viscous substance ("mud") would be injected into the "kill" and "choke" ports, and that this pressurized substance would force the oil back down the well, and then would be cemented over. However, it seemed to me that firstly, the mud could not be injected very rapidly through the small hoses, and, secondly, the mud would just come flying out the top and rip the already leaking riser pipe into shreds.
Now I have run across an animation/explanation which makes the scheme seem more reasonable.
This animation (Flash Player required) shows that there is a plan to remove the leaking riser and seal off the top of the BOP, prior to injecting the mud.
The idea is to set up a sort of drill press over the top of the BOP, and ream it out, and make a seat for a seal which would then be forced down on top of the BOP. I'm not so sure how they can put a cap down on top of the huge gusher that will be coming out at that point. Most likely this cap will actually be a valved pipe, and the valve will be initially open. If this pipe can be seated successfully, then the valve will be closed.
If this capping procedure is successful, and the BOP and the wellhead hold together, this would stop the flow. This would also in theory allow for successful injection of mud through the "choke" and "kill" lines at high pressure. Now this latter assumes that these two lines in the BOP are in continuity with the well, and that BP engineers can successfully jack into these lines and force mud down them. Obviously the whole thing depends on their ability to set up this giant drill press thingy over the BOP. Not easy at a mile under the ocean. It really reminds me of "The Right Stuff."
It seems obvious that this top kill runs the risk of completely opening up the well. I'm wondering if BP is going this route because it is becoming increasingly clear that the leak is already just about as big as it could get, and is getting worse all the time, because of erosion of the riser and/or other parts of the train. If my hunch is right, the chances of success might actually be rather low, but since the consequences are no worse than the status quo, BP is going ahead. If it fails, they will just say, the flow was already huge. If it succeeds, obviously they will be "heroes."
I welcome comments from those who have real expertise, and apologize for any inaccuracies in the diary.
Update: the top kill attempt has been "delayed". There are indications (see comment by taonow, below) that conditions may be changing down there, but one expert, at least, is confident that the well can be capped.