Estimating permeability based on grain size -
This chapter illustrates that the porosity, permeability, and grain size distribution of sandstone cores (dry and containing an irreducible minimum of interstitial . This set of prediction curves incorporated only the average size and dispersion, because these parameters best described the relationship between permeability . with porosity, degree of cementation, and a number of grain-size- distribution . cient of r = , whereas d2ghas a correlation coefficient of r =
Stingaciuseem to exhibit a more or less direct sensitivity to permeability e. Amongst the latter, spectral induced polarization SIP measurements seem to offer particularly significant potential with regard to a wide range of practical hydrological applications e. SIP is a low-frequency geoelectrical method based on the observation of effects related to the temporary storage of electrical charges in the probed subsurface region in response to the injection of an alternating current.
This reversible storage of electrical charges produces a phase lag between the current injected using two current electrodes and the voltage difference measured between two potential electrodes e. A number of researchers have tried to connect the key parameters describing the observed SIP phase spectra to various textural characteristics of porous media, which in turn tend to be more or less strongly related to the permeability.
Indeed, several studies have documented reasonably strong relationships between permeability and parameters derived from induced polarization IP measurements in porous media e. Slater provides a comprehensive review of the corresponding methodological foundations and of the pertinent literature.
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Arguably, the most important textural characteristics in the given context are i the pore size or the raw moments of pore size distribution e. Kormiltsev ; Titov; Revil and ii the grain size or the raw moments of the grain size distributions e. At low frequencies, IP- and SIP-type phenomena are related to the existence of polarization length scales associated with the accumulation or depletion of charge carriers, notably ions in the case of saturated porous media, under the effect of an imposed electrical field.
If, and only if, these polarization length scales can be associated with the geometrical parameters controlling permeability, then IP- or SIP-type measurements over a broad range of frequencies, typically 1— Hz, can be used to assess permeability.
Schwarz developed the theoretical foundations for linking the diameter of suspended spheres with the relaxation time. This theoretical framework was adapted by Leroy to account for polarization processes in the Stern layer formed by counterions, which maintain their hydration shells and are weakly sorbed to the mineral surface.
- Grain-size dynamics beneath mid-ocean ridges: Implications for permeability and melt extraction
This model is based on the assumption that the diffuse layers around grains are interconnected in granular porous media such as sand. Hence, only the polarization of the Stern layer at the surface of the grains and the related polarization length scales can be directly associated with the size of individual grains. Charge movements related to polarization processes in the Stern layer are predominantly parallel to the grain surfaces, as slow diffusion processes hinder perpendicular movements, which implies that the dominant sizes of the corresponding polarization cells, and hence the associated SIP relaxation times, can be directly related to the prevailing grain size.
Estimating permeability based on grain size
The data presented in this study correspond to samples of quartz sands, which vary significantly in terms of their grain size and textural characteristics and thus allow for exploring the effects of different levels of sorting and compaction on the phase amplitude in SIP Koch The transition between high and low permeability regions occurs across a boundary that is steeply inclined toward the ridge axis.
We hypothesize that such a permeability structure generated from the variability of the mean grain size may focus melt toward the ridge axis, analogous to Sparks and Parmentier -type focusing. This focusing may, in turn, constrain the region where significant melt fractions are observed by seismic or magnetotelluric surveys.
This interpretation of melt focusing via the grain-size permeability structure is consistent with MT observation of the asthenosphere beneath the East Pacific Rise. The grain-size field beneath MORs can vary over orders of magnitude The grain-size field affects the rheology and permeability of the asthenosphere The grain-size field may focus melt toward the ridge axis Keywords: The asthenospheric dynamics beneath and near MORs are driven mostly by spreading of lithospheric plates, which is a consequence of far-field tectonic stresses e.
The passive asthenospheric flow caused by imposed plate spreading is dominantly controlled by the material properties of the asthenosphere and, in particular, its viscosity.
Furthermore, asthenospheric flow beneath a ridge causes melting; this melt segregates to fuel MOR volcanism and production of oceanic crust. Melt segregation is controlled by the permeability of the partially molten asthenosphere.
Both mantle permeability and viscosity are sensitive to mantle grain size, a key property that has received little consideration in most previous models. Grain size is a fundamental structural property of a polycrystalline material that can vary in response to conditions including stress, strain rate, temperature, and the presence of melt. Grain size growth and reduction are assumed to be consequences of independent and simultaneous processes [e.
In situations where these rates are balanced, a steady state grain size can be established. However, predictions of grain dynamics are complicated by the nonlinear relationships between the grain size, viscosity, and stress, which can lead to reinforcing feedbacks. Ductile strain localization is a well-studied example of a grain-size feedback [Poirier, ; Jessell and Lister, ; Drury et al. It occurs when the viscosity is positively correlated with grain size.Porosity and Permeability
Deformational work reduces the local grain size, which in turn reduces the viscosity. A decrease in viscosity allows the local strain rate to increase, which further reduces the local grain size. In the simple form discussed here, it does not rely on the presence of fluid or melt. However, strain localization in the presence of melt may lead to the generation of melt bands, which can lead to additional feedbacks on the localization process [Katz et al.
A second feedback in which grain size plays a role is associated with reactive flow of magma through a permeabile mantle matrix [Kelemen et al. Magma rising under buoyancy is undersaturated in SiO2 and hence dissolves pyroxene and precipitates olivine; this process leaves a dunite residue as evidence of extensive reaction [Morgan and Liang,].
If pyroxene is a pinning phase that limits the growth of olivine grains [Evans et al. Since permeability depends on the square of grain size [e. These two examples of feedback mechanisms emphasize the importance of grain-size variations in time and space for controlling the dynamics of mantle processes.
Unfortunately, there are no direct measurements of in situ grain size in the Earth's mantle. Mantle xenoliths [Twiss, ; Ave Lallemant et al. Moreover, it is difficult to assess how much these samples have evolved during emplacment, and thus how representative the recorded grain sizes are of normal mantle conditions. Similarly seismic attenuation, which is a strong function of grain size [Karato, ], typically cannot resolve grain-size variations on the length-scales that are important for controlling ridge dynamics.
An alternative approach for assessing grain-size variations in the mantle is to couple numerical models with experimentally derived flow laws and grain-size evolution models.
As part of their study they compared the models of Hall and Parmentier [ ] and Austin and Evans [ ] with experimental data for deformed wet and dry olivine.
RELATION BETWEEN PERMEABILITY AND GRAIN SIZE OF MOULDING SANDS
They found that the Austin and Evans [ ] model provided closer agreement with the laboratory experiments. The steady state grain size was calculated under the assumption that a constant fraction of mechanical work acts to reduce grain size.
They found that the mean grain-size reaches a minimum of 15—20 mm at a depth of approximately km. They also found that the structure of mean grain size is a good fit to the low seismic shear-wave velocity zone in the upper oceanic mantle.
They predicted that dislocation creep is the dominant deformation mechanism for all depths of the upper mantle. However, Behn et al. Moreover, the assumption of a constant fraction of mechanical work reducing the mean grain size, as opposed to a fraction of dislocation work [Austin and Evans, ], removed a potentially important coupling between the deformation mechanism and mean grain size. The goal of this study is to characterize the variations in grain-size beneath a mid-ocean ridge, with particular focus upon the implications for the permeability structure beneath the ridge.
The permeability structure is an important control on melt migration and has been implicated as a key component in focusing of partial melt toward the ridge axis. In such focusing models [e.
The buoyancy-driven vertical transport of melt is inhibited beneath this barrier by a compaction pressure gradient that balances melt buoyancy.
If the thermal boundary were perpendicular to the gravity vector, then melt would be trapped at this boundary. However, the thermal boundary layer is inclined toward the ridge axis, such that a component of the compaction pressure gradient, which acts normal to the permeability barrier, drives melt toward the ridge axis.
However, permeability-based models of melt focusing have yet to consider the contribution of spatial variations in grain size beneath the ridge axis.