An investigation has been made of the relations among porosity, permeability, and texture of artificially mixed and packed sand, to determine the approximate porosity and permeability values to be expected for unconsolidated sand of eight grain-size subclasses and six sorting groups. The sand samples were prepared so that the weight fractions were distributed normally about the median grain size. Porosity values were determined for two packings, designated as "dry-loose" and "wet-packed." Porosity data for "wet-packed" sand samples remain about the same for changes in grain size of a given sorting, but decrease from an average of 42.4 percent for extremely well-sorted sand to 27.9 percent for very poorly sorted sand. These experimental data agree within 5 porosity percent with framework porosity values obtained for natural packing of 25 Holocene barrier-island sand samples of a limited size-sorting range, and appear to be representative of minimum porosities expected for natural packing of most unconsolidated, clay-free sand. The 48 artificially mixed and wet-packed experimental sands selected for porosity measurement also were used to determine permeability. Inasmuch as there are some irregularities in the experimental data caused by the inability to pack each sample uniformly, an average adjusted permeability value has been calculated. The average adjusted permeability values become progressively lower with decreasing grain size and poorer sorting, and agree well with permeability values computed by the Krumbein and Monk formula for most grain-size and sorting classes. Reference photographs or visual textural comparators enable a rapid estimation of grain shape, roundness, size, and sorting. Grain-size-sorting comparators, representing photomicrographs of thin sections of the porosity and permeability test samples, are especially useful in estimating original textural parameters form thin sections of severely compacted and silica-cemented sandstones.

Influence of Texture on Porosity and Permeability of Unconsolidated Sand

Previous theoretical and empirical investigations of the relation between particle size and intergranular permeability have resulted in the well-known formula for intrinsic permeability (k) 






where d is particle diameter, and c is a dimensionless constant. Statistical power regression analyses were per- formed on 19 sets of published data on size and laboratory permeability of unconsolidated sediments. The exponent of grain diameter ranged from 1.11 to 2.05, but most values were significantly less than 2.0. Results indicate that the permeability/grain size relation alternatively may be expressed, from an empirical basis, as 








Values of c and the exponent both generally decrease with decreased textural maturity and increased induration.

Correlations of Permeability and Grain Size

Petrophysical relations are derived to predict porosity and hydraulic conductivity from grain size distributions considering particle packing in sediment mixtures First, we develop a fractional packing model for porosity that considers the fraction of intrapore fines that occur as the fines content increases Then, a fractional packing Kozeny-Carman relation for hydraulic conductivity is developed by examining which particle sizes dominate the pore structure, and which averaging procedure best represents the mean grain diameter in any given sediment mixture The relations developed here perform well for a wide range of sediment mixtures regardless of confining pressure Graphs are presented that show hydraulic conductivity versus weight fraction of fines for mixtures of coarse- and fine-grained sediment commonly observed in the field, such as clayey gravel and silty sand These graphs show that the wide range of hydraulic conductivity values reported for sediment mixtures can display a 5 order of magnitude variation over a few percent fines Finally, a field scale application using grain size distributions from a quantitative depositional model shows that these petrophysical relations successfully predict more than 90% of hydraulic conductivity values to within 1 order of magnitude over 7 orders of magnitude of spatial variability

Fractional packing model for hydraulic conductivity derived from sediment mixtures

[1] We argue that the observed conduit-barrier behavior of fault zones in siliciclastic sedimentary aquifer systems can be understood by considering a strongly anisotropic hydraulic structure in the fault. Hydraulic anisotropy in the fault is expected from a variety of mechanisms including clay-smearing, drag of sand, grain re-orientation and vertical segmentation of the fault plane. In this paper, we present an algorithm to predict fault zone width, lithological heterogeneity and hydraulic anisotropy. Estimation of these parameters is based upon the amount of fault throw and the clay-content of the lithologies flanking the fault zone. A suite of steady-state flow models are presented using an idealized stratigraphy consisting of alternating clay and sand-rich layers that are offset by a fault zone. These conceptual simulations show the impact of a fault zone on shallow (<500 m) fluid flow patterns and solute transport for different scenarios of fault throw. Fault width varies along the fault zone and increases from an average width of ~2 m for a throw of 50 m to ~8 m for a throw of 200 m. Hydraulic anisotropy in the fault zone in these scenarios is predicted to range between two to three orders of magnitude. Our results show that faults can form a preferential path way between aquifers at different depths over vertical distances of several hundreds of meters (that are otherwise separated by confining units) when fault permeability is strongly anisotropic. However, in the same scenario anomalously high hydraulic head gradients across the fault would still suggest that they act as an effective barrier to lateral groundwater flow. This has important implications for the assessment of the risk of a spread of contaminated groundwater or the reconstruction of hydrocarbon migration within sedimentary basins.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2005WR004480

Faults as conduit-barrier systems to fluid flow in siliciclastic sedimentary aquifers

This paper presents new developments of regression-based models to predict the saturated hydraulic conductivity of compacted soils from grain-size distribution. The models incorporate parameter values that adequately represent the distribution of grain sizes. Alternative representations of the grain-size distribution, the fractal dimension and entropy of the distributions, as well as porosity, soil density, and fines content are used in the models to estimate the hydraulic conductivity. These parameters that characterize the textural and hydraulic properties of the soil are combined and used in a multidimensional analysis to estimate the hydraulic conductivity. The predictions of the developed models are compared with those of existing models and laboratory measurements of hydraulic conductivity. The results suggest that the newly developed models outperform the existing models in predicting hydraulic conductivity using information from grain-size distribution. The presented models are suggested as alternatives to, for example, laboratory measurements of the hydraulic conductivity of certain soils that may be difficult to prepare or that may take several days or perhaps weeks to perform. In certain circumstances it may also be used to give first-hand information about the hydraulic properties in a field environment.

Hydraulic conductivity of soils from grain-size distribution: new models

Core analysis data for 78 cores taken from Upper Miocene sands were used to develop correlations between porosity and permeability of unconsolidated cores and their grain-size analyses. The grain-size distributions of these cores are best described mathematically by the Rosin-Rammler equation. The two parameters of this equation together with two other easily measured parameters of grain size were grouped to give correlations with porosity and permeability. Porosities were correlated to within 2 percent for 80 percent of the samples and permeabilities were correlated to within a factor of 2 for 70 percent of the samples.

John D. Huppler

Papers

Porosity and permeability of unconsolidated, upper Miocene sands from grain-size analysis