Laminar flow through irregularly-shaped pores in sedimentary rocks

Abstract

Steady-state, laminar flow of an incompressible fluid through prismatic tubes of irregular but constant cross-section is investigated. Several approximations for the hydraulic conductance (Saint-Venant, Aissen, hydraulic radius), some of which were originally proposed for the mathematically analogous problem of torsion of a prismatic elastic bar, are examined and tested for regular geometric shapes for which analytical solutions exist. For such shapes, the Saint-Venant and Aissen approximations are typically within 15% of the exact conductance, whereas the hydraulic radius approximation may be in error by as much as 50%. Conformal mapping and the boundary element method are then used to study the hydraulic conductance of sandstone pores from SEM images of Berea and Massilon sandstone. For these irregular shapes, the hydraulic radius approximation is much more accurate than either the Saint-Venant or Aissen approximation. Moreover, the errors in the hydraulic radius approximation may be of either sign, and thereby partially cancel out when large numbers of pores are considered, whereas the other two methods tend always to overestimate the hydraulic conductance of rock pores.