Extension Of CVBEM To Dispersive Flow In ThePresence Of Distributed Fractures

Abstract

This study aims to extend the applicability of the complex variable boundary element method (CVBEM) to convective-dispersive flow in the presence of distributed fractures. It is difficult to model the behavior of detailed flow around thin objects such as fractures, owing to singularity at the object edges. In addition, when tracking streamlines that pass through fractures, one cannot identify the outward streamline corresponding to a specific inward streamline. This article shows how complex variables can be used to remedy these difficulties. It then proposes a numerical scheme for modeling potential flow in the presence of distributed fractures. The singular solution for flow around fractures is coupled with the CVBEM through singularity programming.Streamlines can be tracked through fractures by using the stream function. Another research target is the effect of dispersivity on flow behavior. In order to utilize the analytical solution of convective-dispersive flow obtained for onedimensional (1D) problems, two-dimensional (2D) flow is decomposed into flow along multiple 1D streamlines. Variations in velocity along the streamlines can be taken into account with the aid of a set of coordinate transformations, which the CVBEM accurately evaluates. The complete 2D solution is recovered by combining the individual 1D solutions. The numericalresults of threeexampleproblems:convectiveflow througha single fracture, flow with various dispersivities, and dispersive flow through multiple fractures, confirm that the developed model enables accurate flow computations with dispersivity in the presence of distributed fractures.