Infiltration of a Liquid Front in an Unsaturated, Fractured Porous Medium

Abstract

We consider liquid infiltrating by gravity flow into a system of parallel, regularly spaced fractures in an unsaturated porous medium. The position of the fracture liquid front as a function of time, under some simplifying assumptions, is shown to obey a nonlinear integrodifferential equation. Approximate analytic solutions are developed, showing that the movement of the liquid front exhibits three major flow periods: (1) at early time, the frontal position is determined by the fracture inlet boundary condition and the gravity‐driven flow behavior of the fracture with negligible influence by the matrix; (2) at intermediate time, matrix imbibition retards the frontal advance against the pull of gravity; (3) at late time, the matrix approaches saturation and the frontal velocity approaches a limiting value. A two‐dimensional numerical model is used to confirm the approximate solutions. Implications of the model for nuclear waste storage are discussed. The analysis is applicable not only to fractured rock but also to lateral infiltration into coarse‐grained sediments lying between layers of fine‐grained soil.

Numerical dual-porosity model with semianalytical treatment of fracture/matrix flow

“…The results of the new method can also be compared to the asymptotic analytical solutions developed by Nitao and Buscheck [1991]. They treated the mathematically analogous problem of linearized capillary-driven flow into an unsaturated, fractured formation, and found the leading-order terms for the flux in each of the three time regimes.…”

“…Following their procedure, we can develop the asymptotic solutions for the present saturated flow problem. At small times the solution corresponds to flow into the fracture network with the matrix blocks assumed to be impermeable, which leads to a mass fiowrate of (38) In the late time regime, Nitao and Buscheck [1991] showed that the problem becomes asymptotically equivalent to one-dimensional flow into a porous formation whose permeability is essentially equal to k 1 (since km « k 1 ), but whose porosity is equal to <l>t +<l>m· Since the compressibility terms (which reflect only cwater) in both the matrix and fractures are equal, the late-time fiowrate is asymptotically wven by (39) J,. ; Nitao and Buscheck [1991, eq.…”

TH{_}PULSE: Program for Calculating Infiltration of Episodic Liquid Fingers in Superheated Rock Fractures - Theory, User's Manual and Sample Applications

“…There are two bounding cases: -A lower bound for flow velocity in the superheated environment is provided by assuming that flow is always fully developed and the saturation in the liquid finger remains at its initial value (i.e., S l = 1). (This scenario was used by Nitao and Buscheck [1991], studying liquid infiltration into a fracture under the influence of matrix imbibition.) Flow velocity in the liquid finger changes linearly with mass flow rate (v(z,t)/v P = m(z,t)/m P = k r ), which gives rise to a significant decrease of v(z,t) as vaporization becomes effective.…”

The Impact of Episodic Nonequilibrium Fracture-Matrix Flow on Repository Performance at the Potential Yucca Mountain Site

“…Under these conditions, the speed of the wetting front in the fracture is governed by the competition between the driving forces in the fracture (gravity and fracture capillarity) and capillary imbibition into the matrix. Fracture-dominated flow can be classified into three physically interpretable flow periods [3,13], conesponding to the degree to which matrix interaction retards the speed of the wetLing front in the fracture, with minimal retardation occurring during flow period I, intermediate retardation during flow period II, and maximal retardation during flow period III (Fig. 2).…”