Speaker
Description
Solute transport in porous media is a fundamental process in various applications, yet the influence of fluid characteristics is often overlooked. When the viscosity ratio, defined as $M=\mu_{\text{displaced}}/\mu_{\text{displacing}}$, exceeds unity, the displacement becomes hydrodynamically unstable and gives rise to viscous fingering. Under such adverse viscosity ratio conditions ($M>1$), the observed solute dispersion deviates systematically from the classical behaviour associated with viscosity-matched flows ($M=1$). To quantify this deviation, a correction factor $\delta$ is introduced, defined as the ratio between the effective dispersion coefficient in a viscosity-contrasted system and that obtained for the corresponding unit-viscosity case.
Analysis reveals that $\delta$ is not an independent function of viscosity ratio and geological heterogeneity, but instead collapses onto a single dimensionless control parameter,
\begin{equation}
\Gamma=\frac{\ln M}{\sqrt[4]{\sigma^2_{\ln K}}}
\end{equation}
where $\sigma^2_{\ln K}$ denotes the variance of the logarithm of permeability and characterizes the degree of medium heterogeneity. This parameter governs a continuous transition between two distinct transport regimes. For small $\Gamma$, dispersion is primarily controlled by the pore-scale heterogeneity of the medium, and the influence of viscosity contrast is weak. In contrast, for sufficiently large $\Gamma$, the system enters a viscosity-ratio-dominated regime in which the enhanced dispersion observed for $M>1$ can be rescaled using $\Gamma$ to recover the behaviour of the reference $M=1$ case.
These results demonstrate that solute dispersion at the Darcy scale is a property of the coupled interaction between fluid viscosity contrast and porous medium structure. Consequently, the common practice of assigning a single, constant dispersivity to represent a given formation is inadequate when viscosity contrasts are present. Accurate prediction of solute transport therefore requires explicit incorporation of fluid properties alongside geological heterogeneity, particularly in applications involving multiphase displacements and mobility-unstable flows.
| Country | United Kingdom |
|---|---|
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