The conceptual framework developed in Dagan & Cvetkovic (1996) is applied to specific cases of flow and reactive transport in geological media. Two types of reactions are considered: Langmuir sorption and mineral dissolution. Two-phase immiscible displacement of oil by water (Buckley-Leverett flow) is also analysed. Both reactions and heterogeneity enhance the field-scale dispersive effects. The relative influence of the heterogeneity and reactions on the field-scale dispersion depends on the scale of the transport problem relative to the heterogeneity integral scale on the one hand, and the reaction parameters on the other. The dispersive effect due to sorption nonlinearity may dominate over the effects of heterogeneity. Similarly, for heavier oil, i.e. for small water to oil viscosity ratio, the effect of nonlinearity in the two-phase immiscible dynamics will generally dominate over the heterogeneity for large transport times. If the characteristic transport time, defined as the ratio between the reservoir scale and the flow velocity, is comparable to the heterogeneity characteristic time I/U, heterogeneous fingering and nonlinear two-phase dynamics yield comparable rates of dispersion.
|Number of pages||26|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|State||Published - 1996|