Effect of stress on the hydraulic conductivity of rock pores

We have made a detailed study of the effect of cross-sectional shape on the hydraulic conductance of rock pores. We consider laminar flow through a single tube with an irregular cross-section; constriction effects, and interconnectedness of pores, will be studied in a future work. We employ three approximate methods: the hydraulic radius approximation, which attempts to correlate the conductivity with the perimeter/area ratio, the Aissen approximation, which utilises a mean value of the conductance of the largest (smallest) circles that can be inscribed (circumscribed) inside (outside) the pore, and the Saint-Venant approximation, which is based on the polar moment of inertia of the shape. The Boundary Element Method is used to provide nominally “exact” estimates of the conductivity, but at the expense of large amounts of computational time. All four methods have been tested on pore shapes from SEM (Scanning Electron Microscope) images of thin-sections of Berea and Massilon sandstone. Surprisingly, the hydraulic radius approximation is the most accurate of the three approximate methods, giving, on average, less than 1% error. Finally, we combine these methods with previous results on the effect of stress on pore deformation, to study the stress-dependence of pore conductivity.