Physical dispersion, comprising molecular diffusion and mechanical dispersion, is one of the primary fluid mixing mechanisms in reservoir processes dominated by compositional change. Its effect controls the characteristics and magnitude of oil recovery by miscible displacement. Standard compositional simulators used to model miscible displacement generally do not include physical dispersion effects and solve the governing equations by first order finite-difference scheme with single-point upstream weighting of mobilities. This approach leads to unphysical smearing of fronts (known as numerical dispersion), which is assumed to compensate for the physical dispersion. Unfortunately, this assumption is valid only for one-dimensional problems under very restrictive conditions and can lead to erroneous results in multiple dimensions. The incorporation of physical dispersion in geologically complex models, such as the ones described by non-orthogonal corner-point grids, requires the use of advanced techniques of flux approximation to retain bith physical and numerical accuracy. The use if the tensorial form of the permeability or dispersion coefficient becomes a necessity for convective or dispersive transport when flows are not aligned to the principal coordinate axes, which is almost always the case in practical reservoir simulation. In this paper, a new dispersive flux-continuous scheme based on a multi-point control volume procedure is developed to allow the inclusion of the full tensor form of physical dispersion into compositional simulation of miscible displacement on 3-dimensional hexahedron structured corner point grids.