Abstract
Shales are the most abundant class of sedimentary rocks, distinguished by being very fine-grained, clayey, and compressible. Their physical and chemical properties are important in widely different enterprises such as civil engineering, ceramics, and petroleum exploration. One characteristic, which is studied here, is a systematic reduction of porosity with depth of burial. This is due increases in grain-to-grain stress and temperature. Vertical stress in sediments is given by the overburden less the pore fluid pressure, σ, divided by the fraction of the horizontal area which is the supporting matrix, (1−φ), where φ is the porosity. It is proposed that the fractional reduction of this ratio, Λ, with time is given by the product of φ4m/3, (1−φ)4n/3, and one or more Arrhenius functions Aexp(−E/RT) with m and n close to 1. This proposal is tested for shale sections in six wells from around the world for which porosity-depth data are available. Good agreement is obtained above 30–40 °C and fractional porosities less than 0.5. Single activation energies for each well are obtained in the range 15–33 kJ/mole, close to the approximate pressure solution of quartz, 24 kJ/mol. Values of m and n are in the range 1 to 0.8, indicating nearly fractal water-wet pore-to-matrix interfaces at pressure solution locations. Results are independent of over- or under-pressure of pore water. This model attempts to explain shale compaction quantitatively. For the petoleum industry, given porosity-depth data for uneroded sections and accurate activation energy, E, paleo-geothermal-gradient can be inferred and from that organic maturity, indicating better drilling prospects.
Highlights
Σ divided by the fractional area of solid matrix (1 − φ) supporting this stress can be relieved by pressure solution, breakage, relative movement of grains or fluid flow
Laboratory measurements of the pressure solution of quartz aggregates [16] give 24 ± 15 kJ/mol, suggesting that this is the rate-limiting reaction occurring in shales
The higher activation energies obtained for Akita and Oklahoma wells are well within the 44 ± 4 kJ/mol activation energy upper bound for solubility of quartz with no load [6], and the Oklahoma well is known to have lost at least 360 m of overburden [8]
Summary
For overburden S and pore pressure p, the vertical stress difference σ ≡ ( S − p ),. Can be changed by sedimentation, erosion or fluid flow through rock in this one-dimensional model. Σ divided by the fractional area of solid matrix (1 − φ) supporting this stress can be relieved by pressure solution, breakage, relative movement of grains or fluid flow. The first term deals with local porosity changes, while the second term deals with deposition, erosion, and fluid flow. The second term was treated previously [1,2,3]. Focus here is on the first term, proposing and supporting with previously published porosity data for shale sections a chemical-type expression describing the time evolution of the vertical grain-to-grain pressure, or frame pressure
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