Statistics of concentration gradients in porous media
Abstract
In subsurface environments, concentration gradients develop at interfaces between surface water and groundwater
bodies, such as hyporheic zones, saline wedges or recharge areas, as well as around contaminant plumes and fluids
injected in subsurface operations. These areas generally represent hotspots of biogeochemical reactions, such as
redox, dissolution and precipitation reactions, as concentration gradients create opportunities for reactive agents
to mix and generate chemical disequilibrium. While macrodispersion theories predict smooth gradients, decaying
in time due to dispersive dissipation, we show that concentration gradients can be broadly distributed since they
are enhanced by velocity gradients induced by medium heterogeneity. We thus present a stochastic theory linking
the Probability Density Function (PDF) of concentration gradients to flow heterogeneity (Le Borgne et al., 2017).
Analytical predictions are validated from high resolution simulations of transport in heterogeneous Darcy fields
ranging from small to large permeability variances and low to high Peclet numbers. This modelling framework
hence opens new perspectives for quantifying the dynamics of chemical gradient distributions and the kinetics of
associated biogeochemical reactions in a stochastic framework.
References:
Le Borgne T., P.D. Huck, M. Dentz and E. Villermaux (2017) Scalar gradients in stirred mixtures and the
deconstruction of random fields, J. of Fluid Mech. 812, pp. 578–610. doi: 10.1017/jfm.2016.799