New form of dispersion tensor for axisymmetric porous media with implementation in particle tracking

A general form of the dispersion tensor is derived for axisymmetric porous media involving four dispersivity coefficients corresponding to longitudinal and transverse dispersion in horizontal and vertical directions, defined as perpendicular and parallel to the axis of symmetry, respectively. The general form of the dispersion tensor provides for distinct vertical and horizontal longitudinal dispersivity values. Transverse dispersion is isotropic for flow parallel to the symmetry axis and anisotropic for flow perpendicular to the symmetry axis with distinct horizontal and vertical transverse dispersivities. The new form of the dispersion tensor is applied to several examples involving axisymmetric media utilizing particle tracking techniques and compared to the tensor proposed by Burnett and Frind [1987]. It is demonstrated that for the case of spatially variable flow the drift term ∇ · (ϕD)/ϕ must generally be included in the particle tracking algorithm to obtain accurate results.