Immiscible displacement of viscosity-matched fluids in two-dimensional porous media

Abstract

The effect of stabilization has been investigated experimentally when a nonwetting fluid is displacing a wetting fluid with the same viscosity in a two-dimensional porous medium. Experiments were done at different injection rates, with capillary numbers ranging from ${10}^{\mathrm{\ensuremath{-}}7}$ to ${10}^{\mathrm{\ensuremath{-}}4}$. The features of the front between the liquids were analyzed and found similar to those observed from invasion percolation models including a spatial gradient in the average pore threshold value, and gravitationally stabilized experiments. Front and structure of the trapped clusters of the invaded fluid at different capillary numbers are self-similar with the fractal dimensions ${\mathrm{D}}_{\mathrm{b}}$=1.33 and ${\mathrm{D}}_{\mathrm{b}}^{\mathrm{m}}$=1.85, respectively. The dependence of the front width ${\mathrm{w}}_{\mathrm{s}}$ on the capillary ${\mathrm{C}}_{\mathrm{a}}$ was found to be consistent with a power law ${\mathrm{w}}_{\mathrm{s}}$\ensuremath{\sim}${\mathrm{C}}_{\mathrm{a}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$, with \ensuremath{\alpha}=0.6. The dynamic exponent ${\mathrm{\ensuremath{\mathrm{B}}}}_{\mathrm{d}}$\ensuremath{\approx}0.8 describing front width evolution as a function of time was determined by collapsing the density-density correlation function data. An analytical argument is presented to support the stabilization of the front owing to the viscous effects.