Laboratory experiments were performed to investigate if water can leak through the pore network of a water wet seal while oil stays in the reservoir below. The experimental setup consisted of a low-permeability membrane disk attached to the outlet side of a cylindrical sandstone core plug. The core plug and the seal were water wet, and the core plug was saturated with oil to irreducible water saturation (Swi). Water was injected at the inlet side of the core, and the fluid flow through the core and the membrane was monitored. The experimental results from three samples with permeabilities ranging from 0.06 to 1900 mD and with capillary pressure ranging from 1.5 to 10 bars confirmed that water at "irreducible" water saturation moved through the core samples, while the membrane retained the oil by capillary sealing. The experiments demonstrated that the relative permeability to the residual water could be approximated by log krw @ Swi = -1.75 log(Pc √(k/$phi$)) - 1.95, where krw @ Swi is the calculated relative wetting-phase water permeability, k is total reservoir permeability (mD), $phi$ is total reservoir porosity (in fraction), and Pc is capillary pressure (bar). Application of this formula to subsurface conditions suggests that the residual water permeability is generally sufficiently small to result in overpressure gradients in the residual water across the hydrocarbon columns. The magnitudes of these overpressures are typically below 5 bars for oil columns of 200 m or less, but may exceed 50 bars in low porosity and permeability reservoirs with large oil columns. Such overpressures are not large enough to result in capillary leakage through good caprocks but may significantly reduce the sealing capacity of marginal seals.