Scaling of transport coefficients of porous media under compaction

Abstract

-Fluid flow through porous media PACS 92.40.Kf -Groundwater: aquifers PACS 91.50.Hc -Marine geology: gas and hydrate systemsAbstract. -Porous sediments in geological systems are exposed to stress by the above-laying mass and consequent compaction, which may be significantly nonuniform across the massif. We derive scaling laws for the compaction of sediments of similar geological origin. With these laws, we evaluate the dependence of the transport properties of a fluid-saturated porous medium (permeability, effective molecular diffusivity, hydrodynamic dispersion, electrical and thermal conductivities) on its porosity. In particular, we demonstrate that the assumption of a uniform geothermal gradient is not adequate for systems with nonuniform compaction and show the importance of the derived scaling laws for mathematical modelling of methane hydrate deposits; these deposits are believed to have potential for impact on global climate change and Glacial-Interglacial cycles.Introduction. -The reconstruction of properties of grounds is an important problem related to geological surveys for extraction of minerals and hydrocarbons, construction of buildings, forecasting geological hazards (seismic, erosion-related, anomalous impact on the climate, etc.) [1][2][3]. Dealing with this problem one faces challenges, some of which hardly may be overcome. These challenges are related to the impossibility of direct measurements of required parameters across large massifs. Even making boreholes provides limited information about the narrow vicinity of the borehole; for instance, measurements of the electrical conductivity and the porosity of the porous medium are generally not enough to reconstruct its permeability, which practically can not be measured directly. Thus, the problem actually turns into one of the recovery of relations between different (transport) parameters of the porous media. Generally, this problem is nonresolvable, because it requires thorough knowledge of the composition of the massif, its geological and seismic history, etc. Meanwhile, many recent studies deal with systems where the massif possesses a homogenous geological origin on the field scale [4][5][6][7][8][9]. Opportunities for an advance in the problem of reconstruction of relations between parameters for such kinds of systems might lay in the field of mathematical physics. In this study we wish to approach this problem in application to some important

Diffusive counter dispersion of mass in bubbly media

“…Nonlinearity of the temperature profile [21] is neglected in our study because it is system specific and not a principal ingredient for the phenomenon we consider. The assumption of a linear temperature profile is typical for studies on physical processes in marine sediments [5,6].…”

“…Here P 0 is the atmospheric pressure, H is the height of the pure-water layer above the bubble-bearing porous medium, T sf is the temperature of the seafloor and G is the geothermal gradient. Nonlinearity of the temperature profile [21] is neglected in our study because it is system specific and not a principal ingredient for the phenomenon we consider. The assumption of a linear temperature profile is typical for studies on physical processes in marine sediments [5,6].…”

Non-Fickian diffusion and the accumulation of methane bubbles in deep-water sediments

“…The solubility profiles and thus transport processes depend on the pressure and temperature profiles. The system is essentially characterized by the hydrostatic pressure P and geothermal temperature gradient G. Although the role of porosity nonuniformity for the geothermal gradient was demonstrated in [23], we follow the conventional approximation of a linear temperature profile [2,15,14]. Therefore,…”

The Influence of Water Storage in Marine Sediment on Sea‐Level Change

“…If marine sedimentary water storage were neglected, this flux combined with a mean sediment deposit density of 1,500 kg m −3 (e.g., Brain et al, ) would imply a displacement of ~1.4 · 10 15 m 3 of water over the ~10 5 year timespan between interglacials, equivalent to ~4.5 m of global mean sea level (GMSL). Field measurements show that marine sediments gradually compact after being deposited with a high porosity (50–90%), such that a sediment column several kilometers thick retains a vertically averaged mean porosity of ~20–40% after compaction (e.g., Bahr et al, ; Goldobin, ; Mondol et al, ; Spinelli et al, ; Spinelli & Underwood, ). This implies a significant influx of water into deposited sediment, and a commensurately smaller displacement of water by the deposited sediment.…”