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This paper examines a numerical modeling approach for two-phase flow and considers the contribution of a simple network of fracture intersections to the whole discrete fracture-matrix flow system; it develops a benchmark problem for a non-wetting, dense, non-aqueous phase liquid invading a water-saturated, discretely fractured, porous medium near a fracture intersection under cases of invader fluid redirection at the intersection, breakthrough to a constricted fracture branch, or breakthrough into the rock matrix using capillary entry pressures. Numerical simulation is performed with a multiphase, compositional DFM software, using a finite difference discretization of the governing equations. In these simulation cases, the "star-delta" method for eliminating line- and point-control volumes at fracture intersections is contrasted to retaining all control volumes, the goal being to test the efficacy of the star-delta simplification. Flux over the domain's boundaries and mass storage are comparison metrics. Results indicate that conduits (or lack thereof) have a strong effect on NAPL architecture with an accompanying change in efflux in the case of redirection; they have some early-time effects on architecture and efflux in constricted fracture cases. The scenario presented herein leads to multiphase flow forecasts in intersection conduits which can serve as an experimentally testable hypothesis and as a benchmark for comparisons of simulator forecasts.