Rates of salinization by free convection in high-permeability sediments: insights from numerical modeling and application to the Dutch coastal area

Numerical modeling and dimensional analysis is used to study the salinization of thick, high-permeability aquifers by free convection from a salt source at the surface. Current understanding of this process mainly concerns the initial stages of salinization only (boundary-layer development, break-up into fingers and initial phase of finger descent). In the modeling, special attention is paid to the role of two processes in the long-term salinization rate: (1) the progressive loss of salt from fingers by lateral diffusion, and (2) the coalescence of fingers during their descent. From the numerical simulations a relationship is derived that describes the development of the horizontally averaged salinity with depth and time as a function of permeability and initial-density contrast for aquifer Rayleigh numbers up to Ra =6,000. This relationship is consistent with and provides an extension to previous generalized relationships of the rate of finger descent. Its applicability to real-world aquifers (Ra >10⁵) that include complexities due to anisotropy, heterogeneity, and mechanical dispersion is discussed. Application to the Pleistocene coastal aquifer of the Netherlands (thickness ≈200 m, permeability ≈10^-11 m²) suggests that salinization of the aquifer during historic episodes of inundation by seawater occurred within decades.