Hydrologic Mechanisms Governing Fluid Flow in a Partially Saturated, Fractured, Porous Medium

TLDR: In this paper, a general statistical theory is constructed for flow along the fracture and for flow between the matrix blocks to the fractures under partially saturated conditions, and the effects of distortion of flow paths by the air pockets are taken into account by a phaseseparation constriction factor in a generalized cubic law for fracture flow under a partially saturated condition.

Abstract: In contrast to the saturated zone within which fluid moves rapidly along fractures, the fractures (with apertures large relative to the size of matrix pores) will desaturate first during the drainage process, and the bulk of fluid flow would be through interconnected pores in the matrix. Within a partially drained fracture, the presence of a relatively continuous air phase will produce practically an infinite resistance to liquid flow in the direction parallel to the fracture. The residual liquid will be held by capillary force, in regions around fracture contact areas where the apertures are small. Normal to the fracture surfaces, the drained portion of the fractures will reduce the effective area for liquid flow from one matrix block to another matrix block. A general statistical theory is constructed for flow along the fracture and for flow between the matrix blocks to the fractures under partially saturated conditions. Results are obtained from an aperture distribution model for fracture saturation, hydraulic conductivity, and effective matrix-fracture flow areas as functions of pressure. The effects of distortion of flow paths by the air pockets are taken into account by a phase-separation constriction factor in a generalized cubic law for fracture flow under a partially saturated condition. The reduction of matrix-fracture flow area is taken into account by summing the aperture distribution function to a saturation cutoff aperture, which is inversely proportional to the suction head. Drainage from a column of fractured tuff is simulated using available parameters for the densely welded tuff of the Topopah Spring Member at Yucca Mountain, southern Nevada. The column is bounded by discrete vertical fractures and dissected by horizontal fractures with the fracture spacings determined by the frequencies and orientations of fractured cores. The fraction of fracture surfaces with coatings is assumed to correspond to the fraction of in situ fracture contact area. The characteristic curves for the matrix are based on laboratory measurements of tuff samples. From the cases simulated for the fractured, porous columns with discrete vertical and horizontal fractures and porous matrix blocks explicitly taken into account, it is observed that the highly transient changes from fully saturated conditions to partially saturated conditions are extremely sensitive to the fracture properties. However, the quasi-steady changes of the fluid flow of a partially saturated, fractured, porous system could be approximately simulated without taking the fractures into account.