Application of the Convective-Dispersive Equation to Estimate Field Scale Dispersivity based on a Field Scale Numerical Model and Tracer Production Data

Abstract

The displacement of a given fluid by another in a porous media can occur either in miscible or immiscible conditions. An immiscible displacement happens, for instance, when water displaces oil in a reservoir. It can also occur when the displacing fluid is a gas, if the interfacial tension with the oil is high enough. These processes are usually described by the fractional flow theory, which assumes isothermal flow of two immiscible and incompressible fluids in an one-dimensional, homogeneous porous media; dissipative effects, such as capillary pressure, compressibility and thermal conductivity, are neglected. Miscible floods, on the other hand, can take place in gas-oil displacements when the interfacial tension approaches zero. Common dissipative effects are fingering and dispersion, the former related to mobility ratio magnitudes and the later related to diffusion and velocity contrast commonly caused by the presence of heterogeneities. In miscible displacements through porous media, dispersion is described as the result of diffusion, local velocity gradients, streamlines dimensions in heterogeneous regions, and mechanical mixing into pores. The present work discuss these concepts and relate them to data from an actual deep offshore field. Estimates of field dispersivity by history matching tracer production profiles are based on the analytical solution for the convection-diffusion equation. Gas tracers injected and produced from wells located in the field area were evaluated assuming miscible displacement. The estimated dispersivity allowed the evaluation of mixing/spreading zones. The solution for intermittent tracer injection was used to history match tracer production data. Results shows the scale dependence of the dispersivity, which depends upon the distance and degree of heterogeneity between wells. The field scale dispersivity obtained by history match was coherent with numerical dispersion observed in a field scale numerical model. They were also compared against literature data (laboratory and field scale) in a log-log plot denoting a good agreement of present data with literature.

CO2 Diffusion and Dispersion in Porous Media: Review of Advances in Experimental Measurements and Mathematical Models

“…When a fluid flows through a porous medium, its velocity distribution is not uniform as a result of boundary effects; i.e., the velocity is zero on the solid surface, which creates a velocity gradient in the fluid phase. , Figure illustrates the factors that control the mechanical dispersion in porous media. The mechanical mixing can be in the direction of bulk flow (longitudinal mechanical mixing) and in the direction orthogonal to the bulk flow (transverse mechanical mixing); however, under most conditions, transverse mechanical mixing is observed to be much less significant than longitudinal mechanical mixing. ,, …”