Single- and Two-Phase Flow in Natural Fractures

Abstract

Abstract Understanding and predicting the production behavior of naturally fractured reservoirs requires understanding flow in a single fracture. Individual fractures can be represented as two-dimensional networks of locations of wide and narrow aperture. Percolation theory prohibits two-phase flow in such a network under restricted conditions: that is, the relative-permeability curves cross at a relative permeability of zero. Using the Effective Medium Approximation (EMA), we illustrate the effect of aperture distribution and of gravity on these kri curves. In the absence of gravity effects, as the aperture distribution becomes broader, the cross-over point in the relative-permeability curves approaches zero wetting-phase saturation. On the other hand, straight-line relative-permeability curves obtain if gravity segregation dominates flow. This can occur, however, only if both phases are free to attain gravity equilibrium, which may not be possible given the restriction on local two-phase flow. In fractures, viscous forces become significant at pressure gradients orders of magnitude lower than in rock matrix. Viscous effects would tend to lead to straight-line relative permeability curves, as well. We present also several simple models for non-Newtonian single-phase flow through fractures. Shear-thinning non-Newtonian fluids make the fracture appear to be wider than in Newtonian flow. In addition, plugging a fracture requires a higher fluid yield stress than expected from characterization of fracture aperture from Newtonian flow. Both non-Newtonian effects are greatest for fractures with broad aperture distributions.