Leakage through filtercake into a fluid sampling probe

Pore fluid can be withdrawn from reservoir rock by means of a probe lowered down a well and clamped against the rock surface. The rest of the rock surface is covered by a drilling fluid filtercake which impedes, but does not totally prevent, flow of filtrate from the wellbore into the rock and thence into the probe. The magnitude of this filtrate flow is investigated in an idealized geometry in which the porous rock, with permeability k, occupies the half-space z > O. The probe covers the circular region r < a of the plane z = O, and the rest of the plane is covered by a thin filtercake of permeability k_c and thickness h. The fluid is assumed incompressible and obeys Darcy's law, so that the fluid pressure p in the porous rock satisfies the Laplace equation. The pressure in the probe is p_o < O, and p = O in the wellbore and in the pore fluid at infinity. This mixed boundary value problem depends only on K = k_ca/kh. If K = O the problem is equivalent to that of an electrified disc at constant potential p_o in unbounded space, and pore fluid is drawn from the rock at infinity. If K > 0, fluid leaks from the wellbore into the reservoir, and the volume of fluid withdrawn by the probe is equal to the volume of fluid which passes from the wellbore into the rock. When O < K ≪ 1 fluid streamlines within the rock are similar to those for K = O close to the probe, but emanate from the filtercake on z = O on a length scale r ∼ a/K. Estimates of the hydraulic resistance of filtercakes usually encountered when drilling for petroleum indicate that this leakage flux is sufficiently small to be neglected over typical time scales for fluid sampling.