Biot poroelasticity of a chemically active shale

1993 ◽  
Vol 440 (1909) ◽  
pp. 365-377 ◽  
Keyword(s):  
Porous Material ◽  
Pore Pressure ◽  
Applied Stress ◽  
Chemical Potential ◽  
Chemical Species ◽  
Important Variable ◽  
Pore Fluid ◽  
Biot Theory ◽  
Chemical Potentials ◽  
Osmotic Effects

The Biot theory of poroelasticity relates the strain ε of a porous material to changes of the applied stress σ and of the pore pressure p . Additional osmotic effects are present in some rocks, such as shales. This paper modifies the thermodynamic arguments used by Biot in order to include the chemical potentials μ r of all the chemical species within the pore fluid. In the limit in which salt is unable to move into or out of the shale, the deformation depends only on the chemical potential μ w of the water and the applied stress. In the limit of a chemically inert rock, the standard Biot analysis is obtained, and the pore pressure p is again the important variable. Real shales lie somewhere between these two limits.

scholarly journals More on complex Sachdev-Ye-Kitaev eternal wormholes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Pengfei Zhang
Keyword(s):  
Black Hole ◽  
Ground State ◽  
Effective Action ◽  
Chemical Potential ◽  
Specific Charge ◽  
Zero Temperature ◽  
Small Coupling ◽  
Chemical Potentials ◽  
Quench Dynamics ◽  
Two Sides

Abstract In this work, we study a generalization of the coupled Sachdev-Ye-Kitaev (SYK) model with U(1) charge conservations. The model contains two copies of the complex SYK model at different chemical potentials, coupled by a direct hopping term. In the zero-temperature and small coupling limit with small averaged chemical potential, the ground state is an eternal wormhole connecting two sides, with a specific charge Q = 0, which is equivalent to a thermofield double state. We derive the conformal Green’s functions and determine corresponding IR parameters. At higher chemical potential, the system transit into the black hole phase. We further derive the Schwarzian effective action and study its quench dynamics. Finally, we compare numerical results with the analytical predictions.

scholarly journals Smart optical cross dipole nanoantenna with multibeam pattern

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Seyyed Mohammad Mehdi Moshiri ◽  
Najmeh Nozhat
Keyword(s):  
Radiation Pattern ◽  
Chemical Potential ◽  
Monolayer Graphene ◽  
Absorption Characteristic ◽  
Radiation Beam ◽  
Directional Radiation ◽  
Chemical Potentials ◽  
Different Types ◽  
Absorption Power ◽  
Maximum Directivity

AbstractIn this paper, an optical smart multibeam cross dipole nano-antenna has been proposed by combining the absorption characteristic of graphene and applying different arrangements of directors. By introducing a cross dipole nano-antenna with two V-shaped coupled elements, the maximum directivity of 8.79 dBi has been obtained for unidirectional radiation pattern. Also, by applying various arrangements of circular sectors as director, different types of radiation pattern such as bi- and quad-directional have been attained with directivities of 8.63 and 8.42 dBi, respectively, at the wavelength of 1550 nm. The maximum absorption power of graphene can be tuned by choosing an appropriate chemical potential. Therefore, the radiation beam of the proposed multibeam cross dipole nano-antenna has been controlled dynamically by applying a monolayer graphene. By choosing a suitable chemical potential of graphene for each arm of the suggested cross dipole nano-antenna without the director, the unidirectional radiation pattern shifts ± 13° at the wavelength of 1550 nm. Also, for the multibeam nano-antenna with different arrangements of directors, the bi- and quad-directional radiation patterns have been smartly modified to uni- and bi-directional ones with the directivities of 10.1 and 9.54 dBi, respectively. It is because of the graphene performance as an absorptive or transparent element for different chemical potentials. This feature helps us to create a multipath wireless link with the capability to control the accessibility of each receiver.

scholarly journals Use of thermodynamic chemical potential diagrams (µCaO, µCO2) to understand the weathering of cement by a slightly carbonated water

Cerâmica ◽  
2008 ◽  
Vol 54 (331) ◽  
pp. 356-360 ◽  
Author(s):  
A. Blandine ◽  
G. Bernard ◽  
B. Essaïd
Keyword(s):  
Chemical Weathering ◽  
Chemical Potential ◽  
Chemical Elements ◽  
Continuous Solid Solution ◽  
The Core ◽  
Chemical Potentials ◽  
Knowing That ◽  
Cement System ◽  
Calcium Silicates ◽  
Hydrated Calcium

Cement is a ubiquitous material that may suffer hazardous weathering. The chemical weathering of cement in natural environment is mostly characterized by the leaching of CaO and the addition of CO2. The different weathering zones that develop at the expense of the cement may be predicted by the help of chemical potential phase diagrams; these diagrams simulate the behaviour of systems open to some chemical elements. Some components have a so-called inert status, that is to say the system is closed for these components, their amount in the system remains constant; some other components have a mobile status, that is to say these components can be exchanged with the outside of the system, their amount can vary from one sample zone to another. The mobile components are represented in the model by their chemical potentials (linked to their concentrations) that are variable in the external environment. The main features of the weathering of a cement system open to CaO and CO2 are predicted in a phase diagram with µCaO et µCO2 as diagram axes. From core to rim, one observes the disappearance of portlandite, ettringite and calcium monosulfoaluminate, the precipitation of calcite and amorphous silica, the modification of the composition of the CSH minerals (hydrated calcium silicates) that see a decrease of their c/s ratio (CaO/SiO2) from the core to the rim of the sample. For the CSH minerals, we have separated their continuous solid solution into three compositions defined by different CaO/SiO2 ratios and called phases 1, 2 and 3: CaO = 0.8, 1.1, 1.8 respectively for one mole of SiO2 knowing that H2O varies in the three compositions.

scholarly journals Tunable Coupled-Resonator-Induced Transparency in a Photonic Crystal System Based on a Multilayer-Insulator Graphene Stack

Materials ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2042 ◽  
Author(s):  
Hanqing Liu ◽  
Jianfeng Tan ◽  
Peiguo Liu ◽  
Li-an Bian ◽  
Song Zha
Keyword(s):  
Photonic Crystal ◽  
Optical Sensors ◽  
Chemical Potential ◽  
Structural Parameters ◽  
Multilayer Graphene ◽  
Crystal System ◽  
Chemical Potentials ◽  
Nonlinear Devices ◽  
Induced Transparency ◽  
Coupled Resonator

We achieve the effective modulation of coupled-resonator-induced transparency (CRIT) in a photonic crystal system which consists of photonic crystal waveguide (PCW), defect cavities, and a multilayer graphene-insulator stack (MGIS). Simulation results show that the wavelength of transparency window can be effectively tuned through varying the chemical potential of graphene in MGIS. The peak value of the CRIT effect is closely related to the structural parameters of our proposed system. Tunable Multipeak CRIT is also realized in the four-resonator-coupled photonic crystal system by modulating the chemical potentials of MGISs in different cavity units. This system paves a novel way toward multichannel-selective filters, optical sensors, and nonlinear devices.

Temperature and equilibrium

2021 ◽  
pp. 49-78
Author(s):  
James P. Sethna
Keyword(s):  
Statistical Mechanics ◽  
Chemical Potential ◽  
Density Fluctuations ◽  
High Dimensional ◽  
High Dimensions ◽  
Chemical Potentials ◽  
The World ◽  
Particle Velocities ◽  
The Cost ◽  
Taste And Smell

Statistical mechanics explains the comprehensible behavior of microscopically complex systems by using the weird geometry of high-dimensional spaces, and by relying only on the known conserved quantity: the energy. Particle velocities and density fluctuations are determined by the geometry of spheres and cubes in dimensions with twenty three digits. Temperature, pressure, and chemical potential are defined and derived in terms of the volume of the high-dimensional energy shell, as quantified by the entropy. In particular, temperature is the inverse of the cost of buying energy from the rest of the world, and entropy is the currency being paid. Exercises discuss the weird geometry of high dimensions, how taste and smell measure chemical potentials, equilibrium fluctuations, and classic thermodynamic relations.

scholarly journals Comparison of Fluid Pressure Wave between Biot Theory and Storativity Equation

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Guangquan Li ◽  
Kui Liu ◽  
Xiang Li
Keyword(s):  
Wave Velocity ◽  
Pressure Wave ◽  
Pure Water ◽  
Fluid Pressure ◽  
Pressure Profile ◽  
Pore Fluid ◽  
Biot Theory ◽  
Physical Processes ◽  
Apparent Permeability ◽  
Very High

Compressibilities of pore fluid and rock skeleton affect pressure profile and flow velocity of fluid in aquifers. Storativity equation is often used to characterize such effects. The equation suffers from a disadvantage that at infinite large frequency, the predicted velocity of fluid pressure wave is infinitely large, which is unrealistic because any physical processes need certain amounts of time. In this paper, Biot theory is employed to investigate the problem. It is shown that the key equations of Biot theory can be simplified to storativity equation, based on low-frequency assumption. Using Berea sandstone as an example, we compare phase velocity and the quality factor between Biot theory and storativity equation. The results reveal that Biot theory is more accurate in yielding a bounded wave velocity. At frequency lower than 100 kHz, Biot theory yields a wave velocity 8 percent higher than storativity equation does. Apparent permeability measured by fluid pressure wave (such as Oscillatory Hydraulic Tomography) may be 14 percent higher than real permeability measured by steady flow experiments. If skeleton is rigid, Biot theory at very high frequencies or with very high permeabilities will yield the same velocity as sound wave in pure water. The findings help us for better understanding of the physical processes of pore fluid and the limitations of storativity equation.

scholarly journals ON THE CHIRAL PERTURBATION THEORY FOR TWO-FLAVOR TWO-COLOR QCD AT FINITE CHEMICAL POTENTIAL

2006 ◽  
Vol 21 (07) ◽  
pp. 559-569 ◽  
Author(s):  
TOMÁŠ BRAUNER
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Effective Theory ◽  
Einstein Condensation ◽  
Chiral Perturbation ◽  
Physical Content ◽  
Chemical Potentials ◽  
Bose Einstein ◽  
Quark Flavors

We construct the chiral perturbation theory for two-color QCD with two quark flavors as an effective theory on the SO(6)/SO(5) coset space. This formulation turns out to be particularly useful for extracting the physical content of the theory when finite baryon and isospin chemical potentials are introduced, and Bose–Einstein condensation sets on.

The effect of adsorption and Knudsen diffusion on the steady-state permeability of microporous rocks

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. D75-D83 ◽  
Author(s):  
Adam M. Allan ◽  
Gary Mavko
Keyword(s):  
Steady State ◽  
Pore Pressure ◽  
Effective Permeability ◽  
Knudsen Diffusion ◽  
Adsorbed Layer ◽  
Pore Fluid ◽  
Fluid Simulation ◽  
Apparent Permeability ◽  
Pore Pressures ◽  
The Continuum

Microporous rocks are being increasingly researched as novel exploration and development technologies facilitate production of the reserves confined in the low-permeability reservoir. The ability to numerically estimate effective permeability is pivotal to characterizing the production capability of microporous reservoirs. In this study, a novel methodology is presented for estimating the steady-state effective permeability from FIB-SEM volumes. We quantify the effect of a static adsorbed monolayer and Knudsen diffusion on effective permeability as a function of pore pressure to better model production of microporous rock volumes. The adsorbed layer is incorporated by generating an effective pore geometry with a pore pressure-dependent layer of immobile voxels at the fluid-solid interface. Due to the steady-state nature of this study, surface diffusion within the adsorbed layer and topological variations of the layer within pores are neglected, potentially resulting in underestimation of effective permeability over extended production time periods. Knudsen diffusion and gas slippage is incorporated through computation of an apparent permeability that accounts for the rarefaction of the pore fluid. We determine that at syn-production pore pressures, permeability varies significantly as a function of the phase of the pore fluid. Simulation of methane transport in micropores indicates that, in the supercritical regime, the effect of Knudsen diffusion relative to adsorption is significantly reduced resulting in effective permeability values up to 10 nanodarcies ([Formula: see text]) less or 40% lower than the continuum prediction. Contrastingly, at subcritical pore pressures, the effective permeability is significantly greater than the continuum prediction due to rarefaction of the gas and the onset of Knudsen diffusion. For example, at 1 MPa, the effective permeability of the kerogen body is five times the continuum prediction. This study demonstrates the importance of, and provides a novel methodology for, incorporating noncontinuum effects in the estimation of the transport properties of microporous rocks.

Scaling law of static liquefaction mechanism in geocentrifuge and corresponding hydromechanical characterization of an unsaturated silty sand having a viscous pore fluid

2015 ◽  
Vol 52 (6) ◽  
pp. 708-720 ◽  
Author(s):  
Amin Askarinejad ◽  
Alexander Beck ◽  
Sarah M. Springman
Keyword(s):  
Pore Pressure ◽  
Scaling Laws ◽  
Scaling Law ◽  
Pore Fluid ◽  
Silty Sand ◽  
Excess Pore Pressure ◽  
Geotechnical Centrifuge ◽  
Time Scaling ◽  
Static Liquefaction ◽  
Viscous Solution

Fast landslides induced by rainfall impose considerable damage on infrastructure and cause major casualties worldwide. Static liquefaction is one of the triggering mechanisms mentioned frequently in the literature as a cause of this type of landslide. The scaling laws required to model this mechanism in the geotechnical centrifuge are developed, and it is shown that either a reduction in the soil pore size or use of a viscous pore fluid is needed to unify the time scaling factors of contractive volume change of the saturated voids and dissipation of the excess pore pressure generated. The latter option was used in this research; therefore, the influences of the viscous pore fluid on the hydromechanical characteristics of a silty sand were investigated. Subsequently, geocentrifuge tests were conducted to compare the behaviour of a slope having a viscous solution as the pore fluid with that of a model with water as the pore fluid. Both slopes were subjected to rainfall, and the evolution of the pore pressure and surface movements were monitored.

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