Fracture connectivity and flow path tortuosity elucidated from advective transport to a pumping well in complex 3D networks

Abstract

Conservative, non-sorbing particle arrivals to a pumping well are used to provide high-resolution data to explore network connectivity and flow path tortuosity as a function of scale for a series of complex 3D discrete fracture networks (DFNs). The DFNs are stochastically generated using orientations ranging from random to three orthogonal planes, power-law distributions of length, and a broad range of density ranging from sparse to moderately dense networks. The internal architecture of the DFNs is intensively sampled by distributing conservative particles evenly over all fractures within a large spherical release volume. A non-directional framework featuring a radially convergent flow field, established by applying a weak sink in the center of the model domain and assigning equal-value constant head boundaries to all sides of the model domain, is used to minimize directional dependence on network connectivity. Results indicate particle velocity is significantly influenced by fracture set orientation in the degree to which fracture sets promote fracture connectivity, and that broad distributions of ensemble velocity can arise from networks with constant fracture transmissivity where slower velocities are characteristic of particle placement into fracture elements less connected to the sink, and vice versa. Inverse particle velocity is strongly power-law for all networks tested and indicates persistent and diverse retention characteristics. The degree of retention decreases in the transition from poorly- to well-connected networks and with increasing distance of particle release due to the availability of more fracture pathways with stronger connection to the sink. Tortuosity is exponentially distributed for all networks tested with median values that stabilize over a distance approximately 10 times the minimum fracture length, and is most sensitive to fracture length, followed by orientation and density.