Computing single-phase transport (Time-of-flight) in fractured media using a discontinuous Galerkin method

Recent numerical results show that the discontinuous Galerkin method is efficient and accurate in solving the time-of-flight equation and the stationary tracer distribution for single-phase transport in porous-media reservoirs; see [Natvig et al., 2006]. The efficiency is obtained by taking advantage of prior knowledge of the direction of flow in solving the resulting system of unknowns. In this work, we investigate the methodology presented in [Natvig et al., 2006] for computing time-of-flight in media with fractures. In particular, we examine the discretisation of the transport model in the fractured regions of the reservoir. Comparing the numerical results of the discontinuous Galerkin approximation with those from a streamline simulator, we demonstrate the importance of a sufficient grid-resolution across the fractures even though they are modelled as one- dimensional lines in the two-dimensional reservoir model.