Proposed Model for Shale Compaction Kinetics

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.

Shale Compaction Kinetics

The grain-to-grain stress vertically 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 φ 4m/3 , (1 − φ) 4n/3 , and one or more Arrhenius functions A exp(−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 porosities less than 0.5. Single activation energies for each well are obtained in the range 15-33 kJ/mole, close to pressure solution of quartz, 24 kJ/mol. Values of m and n are in the range 1 to 0.8, indicating nearly fractal pore-matrix spaces and water-wet interfaces. Results are independent of over- or under-pressure of pore water. This model explains shale compaction quantitatively. Given porosity-depth data and accurate activation energy, E, one can infer paleo-geothermal-gradient and from that organic maturity, thus avoiding unnecessary drilling.

Shale Compaction Kinetics

1 Abstract The grain-to-grain stress vertically 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), φ being the porosity. It is proposed that the fractional reduction of this ratio, Λ, with time is given by the product of φ 4m/3) , (1 − φ) 4n/3 , and one or more Arrhenius functions A exp(−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. A single activation energy of 23+-5 kJ/mole, indicating pressure solution of quartz, 24 kJ/mol, was obtained. The average value of m is 1, indicating fractal pore-matrix spaces and water-wet interfaces. Grain-to -grain interfaces may be fractal with m close to 1, but can have lower values suggesting smooth surfaces and even grain-to-grain welding. Results are independent of over- or under-pressure of pore water. This model explains shale compaction quantitatively.

Optimal spectral templates for triggered feedback experiments

In the field of songbird neuroscience, researchers have used playback of aversive noise bursts to drive changes in song behavior for specific syllables within a bird’s song. Typically, a short (~5-10 msec) slice of the syllable is selected for targeting and the average spectrum of the slice is used as a template. Sounds that are sufficiently close to the template are considered a match. If other syllables have portions that are spectrally similar to the target, false positive errors will weaken the operant contingency. We present a gradient descent method for template optimization that increases the separation in distance between target and distractors slices, greatly improving targeting accuracy. Applied to songs from five adult Bengalese finches, the fractional reduction in errors for sub-syllabic slices was 51.54±22.92%. At the level of song syllables, we use an error metric that controls for the vastly greater number of distractors vs. target syllables. Setting 5% average error (misses + false positives) as a minimal performance criterion, the number of targetable syllables increased from 3 to 16 out of 61 syllables. At 10% error, targetable syllables increased from 11 to 26. By using simple and robust linear discriminant methods, the algorithm reaches near asymptotic performance when using 10 songs as training data, and the error increases by <2.3% on average when using only a single song for training. Targeting is temporally precise, with average jitter of 3.33 msec for the 16 accurately targeted syllables. Because the algorithm is concerned only with the problem of template selection, it can be used as a simple and robust front end for existing hardware and software implementations for triggered feedback.

Disruption of Alfvénic turbulence by magnetic reconnection in a collisionless plasma

We calculate the disruption scale$\unicode[STIX]{x1D706}_{\text{D}}$at which sheet-like structures in dynamically aligned Alfvénic turbulence are destroyed by the onset of magnetic reconnection in a low-$\unicode[STIX]{x1D6FD}$collisionless plasma. The scaling of$\unicode[STIX]{x1D706}_{\text{D}}$depends on the order of the statistics being considered, with more intense structures being disrupted at larger scales. The disruption scale for the structures that dominate the energy spectrum is$\unicode[STIX]{x1D706}_{\text{D}}\sim L_{\bot }^{1/9}(d_{e}\unicode[STIX]{x1D70C}_{s})^{4/9}$, where$d_{e}$is the electron inertial scale,$\unicode[STIX]{x1D70C}_{s}$is the ion sound scale and$L_{\bot }$is the outer scale of the turbulence. When$\unicode[STIX]{x1D6FD}_{e}$and$\unicode[STIX]{x1D70C}_{s}/L_{\bot }$are sufficiently small, the scale$\unicode[STIX]{x1D706}_{\text{D}}$is larger than$\unicode[STIX]{x1D70C}_{s}$and there is a break in the energy spectrum at$\unicode[STIX]{x1D706}_{\text{D}}$, rather than at$\unicode[STIX]{x1D70C}_{s}$. We propose that the fluctuations produced by the disruption are circularised flux ropes, which may have already been observed in the solar wind. We predict the relationship between the amplitude and radius of these structures and quantify the importance of the disruption process to the cascade in terms of the filling fraction of undisrupted structures and the fractional reduction of the energy contained in them at the ion sound scale$\unicode[STIX]{x1D70C}_{s}$. Both of these fractions depend strongly on$\unicode[STIX]{x1D6FD}_{e}$, with the disrupted structures becoming more important at lower$\unicode[STIX]{x1D6FD}_{e}$. Finally, we predict that the energy spectrum between$\unicode[STIX]{x1D706}_{\text{D}}$and$\unicode[STIX]{x1D70C}_{s}$is steeper than$k_{\bot }^{-3}$, when this range exists. Such a steep ‘transition range’ is sometimes observed in short intervals of solar-wind turbulence. The onset of collisionless magnetic reconnection may therefore significantly affect the nature of plasma turbulence around the ion gyroscale.

Mechanical Solutions for Hot Forward Extrusion under Plane Strain Conditions by upper Bound Method

This paper present a study focused on hot forward extrusion by upper bound method. In particular, hot forward extrusion of plates through square face dies under plane strain conditions. Slater defines the models used for large fractional reduction. Different models have been taken in account; they are dissimilar in relation to the dead metal zone (if covers or not the entire die face, partially or totally). Triangular rigid patterns of velocity discontinuities have been validated by analytical methods and a range of use for the selected configurations has been established. This methodology has been applied to other process with good results. Thus, the mechanical parameters analysed are fractional reduction, dead metal zone, length die and friction. Finally the calculation of the energy has been achieved by upper bound method. The results allow researching an optimisation of use of upper bound method in hot forward extrusion.

Density-dependent reduction of nitric oxide diffusing capacity after pneumonectomy

Airway lengthening after pneumonectomy (PNX) may increase diffusive resistance to gas mixing (1/DG); the effect is accentuated by increasing acinar gas density but is difficult to detect from lung CO-diffusing capacity (Dl CO). Because lung NO-diffusing capacity (Dl NO) is three- to fivefold that of Dl CO, whereas 1/DG for NO and CO are similar, we hypothesized that a density-dependent fractional reduction would be greater for Dl NO than for Dl CO. We measured Dl NOand Dl CO at two tidal volumes (Vt) and with three background gases [helium (He), nitrogen (N2), and sulfur hexafluoride (SF6)] in immature dogs 3 and 9 mo after right PNX (5 and 11 mo of age). At maturity (11 mo), background gas density had no effect on Dl NO, Dl CO, or Dl NO-to-Dl CO ratio in sham controls. In PNX animals, Dl NO declined 25–50% in SF6 relative to He and N2, and Dl NO/Dl CO declined ∼50% in SF6 relative to He at a Vt of 15 ml/kg, consistent with a significant 1/DG. At 5 mo of age, Dl NO/Dl CO declined 25–45% in SF6 relative to He and N2 in both groups, but Dl CO increased paradoxically in SF6 relative to N2 or He by 20–60%. Findings suggest that SF6, besides increasing 1/DG, may redistribute ventilation and/or enhance acinar penetration of the convective front.