A New Formulation For Decoupling of Large and Small Scale Heterogeneities in Multi Layered Reservoirs

Abstract

Abstract This paper examines decoupling of the small-scale heterogeneity and permeability variation in multi-layered reservoirs. Here, the growth of vertically averaged concentration is formulated through incorporating dispersivity and the permeability variation; hence, unrealistic large dispersivity values, needed otherwise, are avoided to match the concentration distribution in time-distance domain. A simulation approach is used to verify the analytical solution derived in this study. The simulation models consist of a vertical injection well and a producer located at the ends of two-dimensional (2D) heterogeneous reservoirs. The vertically averaged concentration from simulation is compared with the average concentration obtained from the analytical solution. The simulation results match the analytical solution. It is concluded that scale-dependent dispersivity in the field-scale represents the lack of knowledge about the heterogeneity involved in the system. The results suggest that the effects of permeability heterogeneity that are ignored while using the one-dimensional (1D) solution of the convection-diffusion (CD) equation manifest themselves as an apparent scale-dependent dispersivity. Furthermore, the impact of heterogeneity and dispersivity on the length of the mixing zone within each layer of 2D reservoirs is evaluated in this study. From that, I determine the fraction of layers in which the mixing zone grows faster than that 1D dispersive flow as a function of the Koval factor and input dispersivity. The transition between channeling and dispersive flow regimes is clearly shown in the examples studied here.