Solute transport in heterogeneous compressible aquifers under transient forcing

Transient forcing, such as tidal fluctuations, enhances mixing within aquifers [1, 2]. This study focuses on two pivotal characteristics of typical aquifers—heterogeneity in hydraulic conductivity (K) and compressible properties, represented by the log-hydraulic conductivity variance (σ_f²) and specific storage (S_s), respectively. Previous research has individually addressed the influence of these parameters on solute dynamics [3, 4, 5], yet their combined effects remain inadequately understood. Here, we explore how heterogeneity and compressibility (finite storage) in combination governs solute transport in aquifers under transient forcing. To this end, this study employs Monte Carlo particle tracking simulations, providing a comprehensive representation of K heterogeneity. The simulations yield temporal evolutions of the centre of mass and spatial concentration variance. These results are compared with those derived from analytical solutions applicable to homogeneous compressive porous media (σ_f² = 0, S_s ≠ 0)  [5]. Our findings reveal that increasing values of σ_f² and S_s result in a delayed temporal evolution of the centre of mass compared to the predictions of the homogeneous analytical solution. In addition, the homogeneous analytical solution with zero local dispersion predicts a consistently zero concentration variance, whereas our heterogeneous simulations demonstrate an increasing concentration variance over time. The simulations also show that the higher σ_f² and S_s, the faster the temporal evolution of the concentration variance. These insights offer a deeper understanding of transport dynamics under transient forcing conditions, providing valuable information for accurate assessments of tidal impacts on salinity distributions in coastal aquifers.

 

References

[1] Oberdorfer, J. A., Hogan, P. J., and Buddemeier, R. W. (1990). Atoll island hydrogeology: flow and freshwater occurrence in a tidally dominated system. Journal of Hydrology 120, 327-340.

[2] Inouchi, K., Kishi, Y., and Kakinuma, T. (1990). The motion of coastal groundwater in response to the tide. Journal of Hydrology 115, 165-191.

[3] Dagan, G., Bellin, A., and Rubin, Y. (1996). Lagrangian analysis of transport in heterogeneous formations under transient flow conditions. Water Resources Research 32, 891-899.

[4] Dentz, M., and Carrera, J. (2003). Effective dispersion in temporally fluctuating flow through a heterogeneous medium. Physical Review E 68, 036310.

[5] Pool, M., Dentz, M., and Post, V. E. A. (2016). Transient forcing effects on mixing of two fluids for a stable stratification. Water Resources Research 52, 7178-7197.