A Practical Gas Apparent Permeability Model: Multi-Scale Simulations of Rarefied Gas Flow in Matrix

A common practice in gas-shale reservoir simulation, which arbitrarily increases intrinsic matrix permeability to match the production data, has been proven inefficient and unreliable. Alternatively, accurate estimations of gas apparent permeability (AP) in matrix is desired. This work presents an analytical AP model considering rarefaction in nanopores and coupling experimentally confirmed mechanisms in shale matrix for theoretical completeness. Meanwhile, physical terms in AP model are simplified with semi-empirical correlations for the practicability in large-scale field simulation. Compared with other gas transport models in nanopores, the newly-developed analytical model has been successfully validated against molecular dynamic (MD) simulation, direct simulation Monte Carlo (DSMC), Lattice Boltzmann (LB) simulation, and experimental flux results for five types of gases (i.e., methane, nitrogen, helium, argon, and oxygen) with the minimum deviation. It is observed that analytical models excluding Knudsen diffusion mechanism cannot fully characterize rarefaction effect. Next, Knudsen diffusion cannot be explained as the only underlying mechanism of rarefaction because the mass flux is largely underestimated in transition flow regime. However, the weighted superposition of second-order slip boundary and Knudsen diffusion can provide the satisfactory fitting with data. This work provides an analytical model which not only considers non-negligible multi-physics in shale reservoirs (i.e., rarefaction effect, multilayer adsorption, surface diffusion and confinement effect) but also simplifies non-linear physical terms using semi-empirical linear correlations to facilitate AP calculations in core-scale simulations.

Effect of misalignment and rarefaction effect on the comprehensive characteristic of MEMS gas bearing

Purpose Owing to the development of the smaller-sized rotational machinery, the demand for the high-speed and low-resistance gas bearing increases rapidly. The research of micro gas bearing in the condition of rarefied gas state is still not satisfied. Therefore, the purpose of this paper is to present a numerical investigation of the effect of misalignment and rarefaction effect on the comprehensive performance of micro-electrical-mechanical system (MEMS) gas bearing. Design/methodology/approach The Fukui and Kaneko model is expanded to 2D solution domain to describe the flow field parameters. The finite element method is used to discretize the equation. Newton–Raphson method is used to solve the nonlinear equations for the static performance of gas bearing, and partial deviation method is adopted for the solution of dynamic equations. Findings The static and dynamic characteristics of MEMS gas bearing are calculated, and the comparison is made to study the influence of rarefaction effect and misalignment. The results show that the rarefaction effect will decrease bearing load capacity compared with traditional solution of Reynolds equation, and the misalignment will reduce the stability of bearing. The influence of misalignment on gas film thickness is also analyzed in this paper. Originality/value The investigation of this paper emerges the change regularity of comprehensive performance of MEMS gas bearing considering rarefaction effect and misalignment, which provides a reference for the actual manufacturing of MEMS gas bearing and for the safety operation of micro dynamic machinery. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-01-2020-0023/

The Importance of a Filament-like Structure in Aerial Dispersal and the Rarefaction Effect of Air Molecules on a Nanoscale Fiber: Detailed Physics in Spiders’ Ballooning

Synopsis Many flying insects utilize a membranous structure for flight, which is known as a “wing.” However, some spiders use silk fibers for their aerial dispersal. It is well known that spiders can disperse over hundreds of kilometers and rise several kilometers above the ground in this way. However, little is known about the ballooning mechanisms of spiders, owing to the lack of quantitative data. Recently, Cho et al. discovered previously unknown information on the types and physical properties of spiders’ ballooning silks. According to the data, a crab spider weighing 20 mg spins 50–60 ballooning silks simultaneously, which are about 200 nm thick and 3.22 m long for their flight. Based on these physical dimensions of ballooning silks, the significance of these filament-like structures is explained by a theoretical analysis reviewing the fluid-dynamics of an anisotropic particle (like a filament or a high-slender body). (1) The filament-like structure is materially efficient geometry to produce (or harvest, in the case of passive flight) fluid-dynamic force in a low Reynolds number flow regime. (2) Multiple nanoscale fibers are the result of the physical characteristics of a thin fiber, the drag of which is proportional to its length but not to its diameter. Because of this nonlinear characteristic of a fiber, spinning multiple thin ballooning fibers is, for spiders, a better way to produce drag forces than spinning a single thick spider silk, because spiders can maximize their drag on the ballooning fibers using the same amount of silk dope. (3) The mean thickness of fibers, 200 nm, is constrained by the mechanical strength of the ballooning fibers and the rarefaction effect of air molecules on a nanoscale fiber, because the slip condition on a fiber could predominate if the thickness of the fiber becomes thinner than 100 nm.

Performance of novel air foil thrust bearings with taper-groove on surface of top foil

To improve the load capacity of air foil thrust bearing, the micro taper-grooves on the surface of top foil was introduced and studied. A modified Reynolds equation considering the gas rarefaction effect was established, in which the Knudsen number was affected by the film thickness and pressure. A new bump stiffness model was built with the consideration of bump rounding, friction, and bending stiffness of foil. By considering the variation of gas film thickness, the load capacity, friction torque, and power loss of novel bearing with grooves were calculated by the finite difference method. Moreover, the effect law of groove parameters, groove shape and grooves number on the novel bearing performance was studied systematically. The results show that the predicted axial load capacity considering gas rarefaction effect is decreased slightly in smaller clearance and more consistent with the actual test data. The novel air foil thrust bearing with taper-groove can weaken the air end leakage and enhance the local dynamic pressure efficiently in the parallel portion of top foil, thus improving the static characteristics of bearing. For the novel air foil thrust bearing with taper-groove depth of 10 µm, the load capacity can be increased by about 13.33%, compared with traditional bearing. With the increments of taper-groove depth and length on top foil, the load capacity can be increased. However, the friction torque is decreased when there is a longer taper-groove in the circumferential direction. Meanwhile, the optimal groove width ratio is about 0.5, and the structure of multi-grooves is beneficial to the decreased friction torque. The validity of presented theoretical model has been verified by the literature data, and the results are expected to be helpful to bearing designers, researchers, and academicians concerned.