Miscible displacements with concentration-dependent diffusion and velocity-induced dispersion in porous media

Diffusion and dispersion play significant roles in miscible displacements. In the present study, the frontal instabilities in miscible displacements incorporating both concentration-dependent diffusion coefficient (CDDC) and velocity-induced dispersion (VID) are investigated in homogeneous porous media through nonlinear numerical simulation. Special characteristics have been presented and analyzed for such CDDC-VID case by examining the frontal instabilities. In particular, the VID has more important influence on stabilizing displacements than CDDC. While with CDDC considered, the displacements are more unstable compared with the ConstD-VID case with constant diffusion coefficient (ConstD) and velocity-induced dispersion (VID). Parametric analysis is conducted to study the effects of longitudinal dispersion strength, transverse dispersion, mobility ratio, and Peclet number for the CDDC-VID case. They all affect the development of frontal instabilities, while their roles are different with those of ConstD-VID case. Furthermore, the relative importance of these parameters is analyzed. It is found that the same parameter plays different roles in affecting breakthrough time and sweep efficiency. The correlated equations are obtained to predict breakthrough time and sweep efficiency which agree quite well with the simulated values. It is therefore capable of predicting breakthrough time and sweep efficiency with high accuracy for the CDDC-VID cases in miscible displacements.