| We present fluid mixing behavior and mixing zone growth pattern under radially diverging flow conditions, caused by the constant injection of fluid from a source well which is located within a porous medium. In order to study the nature of the fluid flow near the well we consider a flow in a curved geometry. Interfacial fluid mixing induced by heterogeneous porous media will be analyzed in both cylindrical and spherical geometries and compared with the plane geometry case.;To concentrate our study specifically upon the geological difficulty, we perform a tracer flow study, in which only geometrical complexities occur and non-linear flow features are absent. The non-uniform, in the mean, velocity field is formed by the radially diverging fluid from the injection point. This flow feature makes the velocity correlation function non-homogeneous and thus contributes a non-local dispersion term to the governing equation of tracer flow in random porous media.;We derive the functional form of the second moment of the fluctuation of the velocity field and deduce the approximate governing equation by using Corrsin's hypothesis. Our governing equation, a convection-dispersion integro-differential equation with flow history dependence, and the solution we obtain show that the dispersion of fluids should not be considered locally. The stronger the heterogeneity of the porous media, the non-local consideration of the dispersion term is more essential, regardless of the geometry. The finite volume method is successfully utilized as a numerical scheme for our history dependent integro-partial differential equation.;In plane geometry, homogeneity of the velocity correlation gives a further approximation of the dispersivity. It can be approximated by a diffusion term through neglect of the fourth order term with respect to deltaupsilon, when ||deltaupsilon|| " 1. However it is not possible to make the approximation in curved geometry because of the non-homogeneity of the velocity correlation function. The lower order deltaupsilonterm, which is not present in planar case, contributes to the dispersion term in the curved geometry case. It acts as a stress which yields, from the physical point of view, expansion of the zone where the value of concentration is one half of the injected concentration level with increasing time. We perform a qualitative study using frequently employed permeability correlation functions. |
