Non-Fickian Diffusion Affects the Relation between the Salinity and Hydrate Capacity Profiles in Marine Sediments

On-site measurements of water salinity (which can be directly evaluated from the electrical conductivity) in deep-sea sediments is technically the primary source of indirect information on the capacity of the marine deposits of methane hydrates. We show the relation between the salinity (chlorinity) profile and the hydrate volume in pores to be significantly affected by non-Fickian contributions to the diffusion flux—the thermal diffusion and the gravitational segregation—which have been previously ignored in the literature on the subject and the analysis of surveys data. We provide amended relations and utilize them for an analysis of field measurements for a real hydrate deposit.

💡 Research Summary

The paper addresses a fundamental problem in marine geoscience: how to infer the volume of methane hydrate stored in deep‑sea sediments from measurements of pore‑water salinity, which is readily obtained from electrical conductivity logs. Historically, the relationship between salinity (or chlorinity) profiles and hydrate saturation has been derived under the assumption that solute transport is governed solely by Fickian diffusion. The authors demonstrate that this assumption is inadequate for realistic subsea conditions because two non‑Fickian processes—thermal diffusion (the Soret effect) and gravitational segregation—can contribute significantly to the net solute flux.

The authors begin by reviewing the physical setting of hydrate‑bearing sediments. Geothermal gradients of several tens of degrees Celsius per kilometer and hydrostatic pressure gradients of up to 0.1 MPa m⁻¹ create strong temperature and gravitational fields. In such an environment, dissolved ions (primarily Na⁺ and Cl⁻) experience a thermophoretic drift toward warmer regions and a buoyancy‑driven segregation that tends to concentrate heavier ions at depth. Both mechanisms modify the salinity gradient independently of the hydrate dissolution/formation process.

To capture these effects, the authors augment the classic one‑dimensional mass‑conservation equation with additional flux terms:

 J = – D ∇C – D_T ∇T – D_g ∇Φ,

where D is the ordinary Fickian diffusion coefficient, D_T is the thermal diffusion coefficient, D_g is the gravitational segregation coefficient, C is the solute concentration, T is temperature, and Φ is the gravitational potential. By linking concentration C to electrical conductivity σ through the empirically calibrated linear relation σ = a C + b, they derive an explicit expression for hydrate saturation φ_h as a function of depth z:

 φ_h(z) = (1/β)