The drilling insider forum The Oil Drum describes the static top kill process and the risks involved. The two risks involved are: 1) It may not work at all and 2) it may rupture the casing by pumping heavy mud under pressure.
The post describes the top kill process: Heavy mud is pumped into the well through the choke and kill lines on the blowout preventer and allowed to sink to the bottom of the well. The mud retards the flow so that some of the pressure can be bled off by producing oil to the surface for a short period. Then, more heavy mud is pumped into the well, and the process repeated as necessary until the well contains enough mud to kill the well.
The first problem with stopping the flow from the top is that it has to be an annular kill: the flow was coming up the annulus outside the production casing. This is a very narrow space so mud will have to pumped at high pressure to achieve entry. It will initially be working against a full column of gas and oil and the shut-in pressure at the well head. On the positive side, if produced sand has accumulated in the annulus, the operation may not have to contend with the full force of the reservoir pressure in addition to these obstacles. On the negative side, the well head seals might prevent or restrict downward flow, or the pumping pressure could rupture the 22-inch casing, or reach a pressure high enough to call off the operation.