Permeability of shaly sands

Abstract

Abstract. The permeability of a sand shale mixture is analyzed as a function of shale fraction and the permeability of the two end-members, i.e., the permeability of a clay-free sand and the permeability of a pure shale. First, we develop a model for the permeability of a clay-free sand as a function of the grain diameter, the porosity, and the electrical cementation exponent. We show that the Kozeny-Carman-type relation can be improved by using electrical parameters which separate pore throat from total porosity and effective from total hydraulic radius. The permeability of a pure shale is derived in a similar way but is strongly dependent on clay mineralogy. For the same porosity, there are 5 orders of magnitude of difference between the permeability of pure kaolinite and the permeability of pure smectite. The separate end-members' permeability models are combined by filling the sand pores progressively with shale and then dispersing the sand grains in shale. The permeability of sand shale mixtures is shown to have a minimum at the critical shale content at which shale just fills the sand pores. Pure shale has a slightly higher permeability. Permeability decreases sharply with shale content as the pores of a sand are filled. The permeability of sand shale mixtures thus has a very strong dependence on shale fraction, and available data confirm this distinctive shale-fraction dependence. In addition, there is agreement (within 1 order of magnitude) between the permeabilities predicted from our model and those measured over 11 orders of magnitude from literature sources. Finally, we apply our model to predict the permeabilities of shaly sand formations in the Gulf Coast. The predictions are compared to a data set of permeability determination made on side-wall cores. The agreement between the theoretical predictions and the experimental data is very good.

Modeling the evolution of complex conductivity during calcite precipitation on glass beads

“…Indeed, permeability can be estimated according to the particle size and shape (Revil & Cathles 1999;Revil & Florsch 2010). We also showed that the Stern layer of calcite controls the measured imaginary conductivity response of glass beads pack reported in Wu et al (2010) and that the diffuse layer polarization cannot be ignored because it significantly decreases the relaxation time of the Stern layer of calcite.…”

“…It works well to describe the electrical properties of uncompacted and uncemented granular media with small contiguity between the grains (Revil 2000). The complex conductivity of the porous medium σ * is calculated using the following equations (Revil & Cathles 1999):…”

Air entry–based characteristic length for estimation of permeability of variably compacted earth materials

“…Computed G G o for given n 0 Àn 1Àn 0 values using equation (21) for the agricultural soils (symbols) and the corresponding relationships based on equation (13) for three values of d (solid lines) and equations (14) and (15) (23) and drops drastically toward low values after certain degree of compaction, ( n à n o ), is reached and at which apparently the whole structure collapses. For the sandstones investigated by Revil and Cathles [1999], G G o even reverses trend and decreases sharply after its linear increase up to ( n à n o ). Assuming that pore shape factor remains unaffected by compaction, this type of behavior means that during the early stages of densification, tortuosity decreases with porosity and, as densification increases, tortuosity reverses trend and increases significantly with further decrease in porosity [Bernabé et al, 2003].…”

“…[24] The data set for the rocks contains measured relationships between permeability and porosity for (1) Fontainbleau sandstone (Bourbié et al [1987] as presented by Mavko and Nur [1997]), (2) hot-pressed calcite (Bernabé et al [1982] as presented by Mavko and Nur [1997]), (3) finegrained and silty sandstones (Chilindar [1964] as presented by Revil and Cathles [1999]), (4) sandshale mixtures, GA, and HB sands (clayey sand and sandy shale subgroups reported by Revil and Cathles [1999]), and (5) sandstones at hydrostatic loading presenting a wide range of porosity, grain size and clay content (reported by David et al [1994] and Zhu and Wong [1997]). In some cases, the k-n data were digitized from the reported relevant figures.…”

“…The value of a characteristic length squared defining k for a porous medium of interest was deduced from different pore related attributes [Bernabé and Bruderer, 1998] including the hydraulic radius [Kozeny, 1927;Scheidegger, 1960], a weighted hydraulic radius [Johnson and Schwartz, 1989]; a threshold (pore entry) capillary pressure [Thomeer, 1960]; a pore radius derived from the critical path analysis [Katz and Thompson, 1986]; or a critical channel diameter associated with mercury porosimetry measurements [Arns et al, 2005]. For granular materials, mean grain diameter provides a useful characteristic length [Revil and Cathles, 1999]. Doyen [1988] suggested that the permeability can be expressed as the ratio of two characteristic lengths, the dimensions of a characteristic pore throat and pore chamber, that are related to porosity.…”