Investigation of Shale Permeability Evolution considering Bivalued Effective Stress Coefficients for CO2 Injection

Because of the existence of multiscale pores from nano- to macroscale, a multimechanistic shale gas flow process involving the Darcy and Knudsen flows occurs during gas shale well depletion. The respective contribution of the Darcy and Knudsen flows to the permeability is constantly changing with pressure evolution. In this study, laboratory measurements of shale permeability with CO2 injections were carried out under hydrostatic conditions, using the transient pulse-decay method. The “U”-shape permeability curve resulted in both positive and negative effective stress coefficients (Biot’s coefficient) χ . A permeability turning point was thus created to partition permeability curves into the Darcy and Knudsen sections. The Knudsen effect was proven to be significant at low pressure/late time in the laboratory. Effective stress and sorption-induced deformation have been found to govern the Darcy permeability evolution under the tested experimental conditions. Thus, negative effective stress coefficients, together with the positive ones, should be applied to a nonmonotonic pressure-permeability evolution to explain the concurrent effect of the Darcy flow and Knudsen flow at different pore pressures.

Viscous and Knudsen gas flow through dry porous cometary analogue material

According to current theories of the formation of stellar systems, comets belong to the oldest and most pristine class of bodies to be found around a star. When approaching the Sun, the nucleus shows increasing activity and a pressure increase inside the material causes sublimated and trapped gas molecules to stream away from their regions of origin towards the surface. The present work studies two essential mechanisms of gas transport through a porous layer, namely the Darcy and the Knudsen flow. Gas flow measurements are performed in the laboratory with several analogue materials, which are mimicking dry cometary surface properties. In this first series of measurements, the aim was to separate gas transport properties from internal sources like local sublimation or release of trapped gases. Therefore, only dry granular materials were used and maintaining a low temperature environment was unnecessary. The gas permeability and the Knudsen diffusion coefficient of the sample materials are obtained, thereby representing the relative importance of the respective flow mechanism. The experiments performed with air at a stable room temperature show that the grain size distribution and the packing density of the sample play a major role for the permeability of the sample. The larger the grains, the bigger the permeability and the Knudsen diffusion coefficient. From the latter we estimated effective pore diameters. Finally, we explain how these parameters can be adapted to obtain the gas flow properties of the investigated analogue materials under the conditions to be expected on the comet.

Effect of coating steps on uniformity and gas permeability of mesoporous layers in ceramic membranes

Porous silica, silica-cobalt, silica-zirconia and zirconia membranes were synthesized by the sol-gel method. Multi-step coating (two, six, and ten steps) was used to reduce the defectiveness of the mesoporous layer. Scanning electron microscopy (SEM) images indicated that an increase in the number of coating steps improved the mesoporous layer quality. The results obtained from gas permeability tests with nitrogen and argon, however, indicated a reduction in the gas permeability with increasing coating steps. The reduction in gas permeability from two to six coating steps was more pronounced than from sixto ten- coating steps. It was found that six-step coating was economically justified in obtaining a uniform mesoporous layer. The results of pore radius calculations by Knudsen flow mechanism revealed that the pores in the silica, silica-cobalt, and zirconia membranes were in the mesoporous range. The sols with a mean particle size more than 100 nm are not recommended for synthesis of mesoporous layer free of defects. Furthermore, the type of acid used as a catalyst is also important in obtaining a layer without defectiveness.

Molecular Dynamics Simulation of Methane and Carbon Dioxide Permeation Through A Layered Inorganic Membrane

Molecular dynamics simulations are performed to investigate the permeation and separation of methane and carbon dioxide mixture through a layered inorganic membrane at high temperature to circumvent carbon dioxide adsorption on membrane surface. The simulations show that a single layer membrane with narrow cylindrical-pore favors methane permeation over carbon dioxide. When a slit-space is present along with the cylindrical-pore in a layered inorganic membrane, the membrane can be tailored to favor carbon dioxide over methane. The comparison of the permeation rates obtained directly from simulation and those from Knudsen flow calculation highlights the prominence of molecular sieving mechanism in determining the permeation behaviors of methane and carbon dioxide through a narrow opening.

Gas Velosity and Mass Flowrate Scaling Modeling in Microelectronics’ Thermal Control Systems

In the present research we investigate pressure driven flow in the transition and free-molecular flow regimes with the objective of developing unified flow models for microchannels. These models are based on a velocity scaling law, which is valid for a wide range of Knudsen number. Simple slip-based descriptions of flowrate in microchannels are corrected for effects in the transition and free-molecular flow regimes with the introduction of a rarefaction factor. The resulting models can predict the velocity distribution, mass flowrate, pressure and shear stress distribution in rectangular microchannels in the entire Knudsen flow regime.

Влияние фокусировки на распространение фононов и теплопроводность в монокристаллических пленках с различным типом анизотропии упругой энергии

The influence of the anisotropy of elastic energy on the phonon propagation and phonon transport in single crystal nanofilms with different types of anisotropy of elastic energy in a Knudsen flow of a phonon gas is studied. The angular distribution of phonon mean free paths in the planes of the films and in their cross section is analyzed. The physical reasons leading to the dependence of the thermal conductivity on the orientation of the film planes and the directions of the heat flux relative to the crystal axes are studied. An analysis of the effect of focusing on the phonon propagation made it possible to explain the qualitative difference between the anisotropy of phonon mean free paths in films of cubic nanocrystals of various types having different orientations of the planes.