Fluid flow and solute transport through three-dimensional networks of variably saturated discrete fractures

Abstract

Methodologies for estimating hydraulic and solute transport properties of unsaturated, fractured rock are developed. The methodologies are applied to networks of discrete fractures for the purpose of estimating steady fluid flow rates and breakthrough curves of entrained solutes. The formulations employ the boundary integral method to discretize the outer rim of each fracture and to solve a two dimensional flow equation within fracture planes. A three dimensional variant of the two dimensional boundary integral method is used to calculate flow through a permeable matrix with embedded permeable fractures. Exterior and interior surfaces are discretized using boundary elements to account for flow between fractures and the matrix, and between the matrix and fractures and the exterior boundaries. Synthetic fracture networks are created using planar fractures of finite areal extent embedded within a three dimensional rock matrix for the purpose of performing sensitivity studies of network hydraulic conductivity with respect to geometric parameters, such as fracture orientation and density. Results of the sensitivity studies show that: (1) The global hydraulic conductivity is linearly dependent on the product of fracture transmissivity and density for fractures of which fully penetrate the rock volume; (2) The effect of correlation between fracture length and transmissivity is to increase the global hydraulic conductivity; and (3) Results using a three dimensional coupled fracture— matrix flow regime compare favorably with analytic results. Flow through variably saturated fracture networks is modeled by assuming a constant capillary head within individual fractures. A free surface is found using an iterative procedure which locates nodal points at the intersection of constant total head and pressure head contours. The simulated free surface compares favorably with an approximate analytic solution and with laboratory results. Simulations indicate the presence of zones of water under both positive and negative pressure, as well as regions of air—filled voids. Travel times and breakthrough curves are determined by integrating the inverse velocity over a streamline, and then summing over all streamlines. For the fracture network examined, travel times decrease with decreasing fracture saturation. The effects of retardation and matrix diffusion are also examined.