NON-NEWTONIAN FLOW IN A VARIABLE APERTURE FRACTURE

The transmissivity of a variable aperture fracture for flow of a non-N ewtonian, purely viscous power-law fluid with behavior index n is stud ied. The natural logarithm of the fracture aperture is considered to b e a two-dimensional, spatially homogeneous and correlated Gaussian ran dom field. We derive an equivalent fracture aperture for three flow ge ometries: (1) flow perpendicular to aperture variation; (2) flow paral lel to aperture variation; (3) flow in an isotropic aperture field. Un der ergodicity, results are obtained for cases 1 and 2 by discretizing the fracture into elements of equal aperture and assuming that the re sistances due to each aperture element are, respectively, in parallel and in series; for case 3, the equivalent aperture is derived as the g eometric mean of cases 1 and 2. When n = 1, all our expressions for th e equivalent aperture reduce to those derived in the past for Newtonia n flow and lognormal aperture distribution. As log-aperture variance i ncreases, the equivalent aperture is found to increase for case 1, to decrease for case 2, and to be a function of flow behavior index n for case 3.