The fictional forces acting on a drill string in a borehole can be lar
ge if the drill string is embedded in a pastelike filter cake formed a
t the borehole wall by the drilling fluid. In extreme conditions, the
drill string can become stuck, leading to expensive delays in the dril
ling process. The hydraulic pressure within the wellbore is usually hi
gher than the pore pressure within the rock. This excess pressure is r
esponsible both for the growth of the filter cake, and for the normal
force that can hold the drill string against the borehole wall. We obt
ain estimates of the normal and frictional forces acting on the drill
string, based on an analysis of the pressure and concentration profile
within the filter cake. The forces can be minimized by ensuring that
the cake is highly compressible, so that the bulk of the pressure drop
between the borehole and porous rock occurs across a thin boundary la
yer at the base of the cake. The forces acting on a sphere (rather tha
n a cylindrical drill string) are also modeled, and are compared again
st experiment. The predicted frictional force is smaller than observed
experimentally, but the predicted t(3/4) growth of the force with tim
e t agrees with experiment.