A Novel Approach To Predict Gas Flow in Entire Knudsen Number Regime through Nanochannels with Various Geometries

SPE Journal ◽  
2021 ◽  
pp. 1-20
Author(s):  
Yu Pang ◽  
Dian Fan ◽  
Shengnan Chen
Keyword(s):  
Velocity Profile ◽  
Gas Flow ◽  
Gas Transport ◽  
Knudsen Diffusion ◽  
Bulk Diffusion ◽  
Second Order ◽  
Gas Velocity ◽  
Cross Sectional ◽  
Novel Approach ◽  
The Cross

Summary Various unified gas flow (UGF) and apparent permeability models have been proposed to characterize the complex gas transport mechanisms in shale formations. However, such models are typically expressed as combinations of multiple gas flow mechanisms so that they cannot predict gas velocity profile. In this study, we develop a novel approach to predict the gas velocity profile in the entire Knudsen number (Kn) regime for circular and noncircular (i.e., square, rectangular, triangular and elliptical) nanochannels and investigate the effects of cross-sectional geometry on gas transport in nanochannels. To this end, a new UGF model is proposed to describe the gas flow behaviors in the entire Kn regime, considering the effects of gas slippage, bulk diffusion, Knudsen diffusion, surface diffusion, and cross-sectional geometry of flow channel. In addition, the boundary condition of the semianalytical second-order slip model applicable to various cross-sectional geometries is modified by adjusting the slip coefficients through the comparison between the proposed UGF model and the Navier-Stokes (N-S) equation with second-order slip boundary condition. As a result, the velocity profile of free gas in the entire Kn regime for the nanochannel with a specific cross section can be determined by solving the second-order slip model with adjusted slip coefficients via the finite element method. The results indicate that the geometry of the cross section has a significant influence on the mass flow rate and gas velocity profile in nanochannels. The predicted mass flow rates for the nanochannels with identical hydraulic diameter decrease with the cross-sectional geometry in the sequence as ellipse > equilateral triangle > rectangle > square > circle. However, the ranking of velocity profiles for such nanochannels, which is governed by the cross-sectional geometry, also varies with Kn. These findings indicate that the developed approach can predict the synergetic gas transport (i.e., gas slippage, bulk diffusion, Knudsen diffusion, and surface diffusion) and gas velocity profile in nanochannels with different cross-sectional geometries for a wide range of Kn, which gives insight into the characterization of gas flow behaviors in nanoporous shale.

Effect of Tapering on Pulsatile Flow Through a U-Tube Model of the Human Aortic Arch

2010 ◽  
Author(s):  
Masaru Sumida
Keyword(s):  
Velocity Profile ◽  
Pulsatile Flow ◽  
Velocity Profiles ◽  
Cross Sectional Area ◽  
Flow Rate Ratio ◽  
Sectional Area ◽  
Cross Sectional ◽  
Turn Angle ◽  
Flow Through ◽  
The Cross

An experimental investigation of pulsatile flow through a tapered U-tube was performed to study the blood flow in the aorta. The experiments were carried out in a U-tube with a curvature radius ratio of 3.5 and a 50% reduction in the cross-sectional area from the entrance to the exit of the curved section. Velocity measurements were conducted by a laser Doppler velocimetry for a Womersley number of 10, a mean Dean number of 400 and a flow rate ratio of 1. The velocity profiles for pulsatile flow in the tapered U-tube were compared with the corresponding results in a U-tube having a uniform cross-sectional area. The striking effects of the tapering on the flow are exhibited in the axial velocity profiles in the section from the latter half of the bend to the downstream tangent immediately behind the bend exit. A depression in the velocity profile appears at a smaller turn angle Ω in the case of tapering, although the magnitude of the depression relative to the cross-sectional average velocity decreases. The value of β, which indicates the uniformity in the velocity profile over the cross section, decreases with increasing Ω, whereas it rapidly increases immediately behind the bend exit.

Identification of the piston machine combustion chamber tightness

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Piotr Jan Bielawski
Keyword(s):  
Combustion Chamber ◽  
Measurement System ◽  
Gas Flow ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Content Type ◽  
Flow Through ◽  
The Cross ◽  
Pneumatic Sensor

PurposeThe lack of integrity of the piston machine combustion chamber manifests itself in leakages of the working fluid between the piston and the cylinder liner, at valves mounted in the cylinder head and between the head and the liner. An untight combustion chamber leads to decreased power output or efficiency of the engine, while leaks of a fluid may cause damage to many components of the chamber. The actual value of working chamber leak is a desired and essential piece of information for planning operations of a given machine.Design/methodology/approachThis research paper describes causes and mechanisms of leakage from the working chamber of internal combustion engines. Besides, the paper outlines presently used methods and means of leak identification and states that their further development and improvements are needed. New methods and their applicability are presented.FindingsThe methods of leak identification have been divided into diagnostic and non-working machine leak identification methods. The need has been justified for the identification of leakage from the combustion chamber of a non-working machine and for using the leakage measure as the value of the cross-sectional area of the equivalent leak, defined as the sum of cross-section areas of all leaking paths. The analysis of possible developments of tightness assessment methods referring to the combustion chamber of a non-working machine consisted in modelling subsequent combustion chamber leaks as gas-filled tank leak, leak from another element of gas-filled tank and as a regulator of gas flow through a nozzle.Originality/valueA measurement system was built allowing the measurement of pressure drop in a tank with the connected engine combustion chamber, which indicated the usefulness of the system for leakage measurement in units as defined in applicable standards. A pneumatic sensor was built for measuring the cross-sectional area of the equivalent leak of the combustion chamber connected to the sensor where the chamber functioned as a regulator of gas flow through the sensor nozzle. It has been shown that the sensor can be calibrated by means of reference leaks implemented as nozzles of specific diameters and lengths. The schematic diagram of a system for measuring the combustion chamber leakage and a diagram of a sensor for measuring the cross-sectional area of the equivalent leak of the combustion chamber leakage are presented. The results are given of tightness tests of a small one-cylinder combustion engine conducted by means of the set up measurement system and a pre-prototype pneumatic sensor. The two solutions proved to be practically useful.

scholarly journals Second-order flexibility-based model for nonlinear inelastic analysis of composite steel-concrete frameworks with partial composite action and semi-rigid connections

2018 ◽  
Author(s):  
Cosmin G Chiorean ◽  
Marius S Buru
Keyword(s):  
Concrete Slab ◽  
Finite Size ◽  
Composite Beams ◽  
Second Order ◽  
Integral Approach ◽  
Cross Sectional ◽  
Composite Action ◽  
Inelastic Analysis ◽  
The Cross ◽  
Composite Steel

This paper presents an efficient computer method for large deflection distributed plasticity analysis of 3D semi-rigid composite steel-concrete frameworks. A novel second-order inelastic flexibility-based element has been developed by combining the Maxwell-Mohr rule and the second-order force based functions for computation of the generalized displacements. The proposed model allows explicit and efficient modeling of the combined effects of nonlinear geometrical effects, gradual spread-of-plasticity, partial shear connection of composite beams, finite-size joints and joint flexibility by using only one 2-noded beam-column element per physical member. For composite beams, based on elasto-plastic cross-sectional analyses the model is able to take into account the effects of partial composite action between the concrete slab and the steel beam. At the cross-sectional level the proposed method addresses computational efficiency through the use of path integral approach to numerical integration of the cross-sectional nonlinear characteristics and residual stresses, enabling in this way the accurate geometrical specifications and precise modeling of cross-sections. The proposed nonlinear analysis formulation has been implemented in a general nonlinear static purpose computer program, NEFCAD. Several computational examples are given to validate the accuracy and efficiency of the proposed method.

The Study of Exhausting Accumulated Liquid in Upward Inclined Pipe Using a Swirl Tool

2019 ◽  
Author(s):  
Zhenqiang Xie ◽  
Xuewen Cao ◽  
Fachun Liang ◽  
Jun Zhang
Keyword(s):  
Flow Pattern ◽  
Cross Section ◽  
Centrifugal Force ◽  
Annular Flow ◽  
Gas Flow ◽  
Swirling Flow ◽  
Flow Patterns ◽  
Gas Production ◽  
Gas Velocity ◽  
The Cross

Abstract The problem of accumulated liquid is very common in wet gas gathering pipelines which varies with the topography, this phenomenon is much more serious especially in upward inclined pipelines. The existence of accumulated liquid at the bottom of the pipeline would decrease the area of the cross section that gas flows through. This makes the gas velocity fluctuate unpredictably and even results in shocks and blocks in pipelines which may cause danger in the safety management of oil and gas production. Swirl tool is a kind of rigid tool which can transfer different flow patterns to a flow pattern similar to annular flow and it has been successfully used to exhaust accumulated liquid in oil fields. However, the mechanism of swirling flow generation in a swirl tool is not fully understood and few researchers have explained how the annular-similar flow decays. In this paper, the formation mechanism of swirling flow in a swirl tool is analyzed using a physical method. The flow pattern transfer procedure and distribution of gas and liquid in the cross section of the pipeline in the swirl tool is simulated with FLUENT (a commercial CFD code). Following the swirling flow formation analysis, the decay of the annular-similar flow from the outlet of the swirl tool is also simulated with FLUENT (a commercial CFD code). Also, the effects of different superficial gas velocities and different liquid rates on the decay of the annular-similar flow are studied with the swirl tool fixed at the bottom of the upward inclined pipeline. The results show that the formation of swirling flow in a swirl tool is mostly affected by the geometric structure of the swirl tool. The centrifugal force is the main force which transfers different flow patterns to a flow pattern similar to annular flow. The centrifugal force that acts on liquid is larger than that of gas since the density of the liquid is much bigger than gas. The annular-similar flow starts to take shape in the swirl tool after the first thread pitch, but the annular-similar flow is nonuniform. After about three thread pitches, the annular-similar flow becomes uniform with liquid surrounding the inner wall of the pipe and gas flowing in the core region of the pipe. The distance of the annular-similar flow sustains longer when the superficial gas velocity increases which means the decay of the swirling flow is slower. Since sufficient liquid rate is critical to maintain annular-similar flow after the tool when the gas flow rate is fixed, the distance of the annular-similar flow goes longer if there is a little increase in liquid rate.

Effect of Capillary Condensation on Gas Transport in Shale: A Pore-Scale Model Study

SPE Journal ◽  
2016 ◽  
Vol 21 (02) ◽  
pp. 601-612 ◽  
Author(s):  
Binh T. Bui ◽  
Hui-Hai Liu ◽  
Jinhong Chen ◽  
Azra N. Tutuncu
Keyword(s):  
Mass Transport ◽  
Transport Process ◽  
Gas Flow ◽  
Gas Transport ◽  
Capillary Condensation ◽  
Knudsen Diffusion ◽  
Scale Model ◽  
Pore Geometry ◽  
Pore Scale ◽  
Pore Throat

Summary The condensation of the gas inside nanopores at pressures lower than the dewpoint pressure, or capillary condensation, is an important physical phenomenon affecting the gas flow/transport process in shale. This work investigates the underlying transport mechanism and governing factors for the gas transport at a pore scale associated with capillary condensation. We numerically simulate and compare the gas-transport process within pores for two cases, with and without capillary condensation, while Knudsen diffusion, wall slippage, and phase transition are included in the numerical model. In each case, the simulations are performed for two pore geometries corresponding to a single pore and two parallel-connected pores. The main objective is to determine whether capillary condensation blocks or enhances gas transport during production. The results show that the presence of the liquid phase in the pore throat initially enhances the gas flow rate to the outlet of the pore, but significantly reduces it later. This blockage depends on pore geometry and the properties of the oil and gas phases. The relatively low mobility of the condensed liquid in the pore throat is the main factor that reduces the mass transport along the pore. The reduction of overall mass transport in a single pore is more significant than that for the parallel pore geometry. Implications of this work for predicting large-scale gas transport in shale are also discussed.

scholarly journals Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3381 ◽  
Author(s):  
Qiang Wang ◽  
Yongquan Hu ◽  
Jinzhou Zhao ◽  
Lan Ren ◽  
Chaoneng Zhao ◽  
...  
Keyword(s):  
Shale Gas ◽  
Gas Flow ◽  
Gas Transport ◽  
Fractal Theory ◽  
Knudsen Diffusion ◽  
Slip Flow ◽  
Clear Understanding ◽  
Apparent Permeability ◽  
Permeability Model ◽  
Shale Gas Transport

Based on fractal geometry theory, the Hagen–Poiseuille law, and the Langmuir adsorption law, this paper established a mathematical model of gas flow in nano-pores of shale, and deduced a new shale apparent permeability model. This model considers such flow mechanisms as pore size distribution, tortuosity, slippage effect, Knudsen diffusion, and surface extension of shale matrix. This model is closely related to the pore structure and size parameters of shale, and can better reflect the distribution characteristics of nano-pores in shale. The correctness of the model is verified by comparison with the classical experimental data. Finally, the influences of pressure, temperature, integral shape dimension of pore surface and tortuous fractal dimension on apparent permeability, slip flow, Knudsen diffusion and surface diffusion of shale gas transport mechanism on shale gas transport capacity are analyzed, and gas transport behaviors and rules in multi-scale shale pores are revealed. The proposed model is conducive to a more profound and clear understanding of the flow mechanism of shale gas nanopores.

Viscous and Knudsen gas flow through dry porous cometary analogue material

2021 ◽  
Author(s):  
M Schweighart ◽  
W Macher ◽  
G Kargl ◽  
B Gundlach ◽  
H L Capelo
Keyword(s):  
Diffusion Coefficient ◽  
Gas Flow ◽  
Gas Transport ◽  
Gas Permeability ◽  
Knudsen Diffusion ◽  
Flow Measurements ◽  
Knudsen Flow ◽  
Internal Sources ◽  
Trapped Gas ◽  
Knudsen Gas

Abstract 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.

scholarly journals A non-empirical model for gas transfer through circular nanopores in unconventional gas reservoirs

2021 ◽  
Vol 11 (5) ◽  
pp. 2217-2232
Author(s):  
Jiangtao Li ◽  
Jianguang Wei ◽  
Liang Ji ◽  
Anlun Wang ◽  
Gen Rong ◽  
...  
Keyword(s):  
Gas Flow ◽  
Gas Transport ◽  
Transport Model ◽  
Knudsen Diffusion ◽  
Slip Flow ◽  
Gas Reservoirs ◽  
Permeability Model ◽  
Proposed Model ◽  
Unconventional Gas Reservoirs ◽  
Empirical Coefficients

AbstractIt is difficult to predict the flow performance in the nanopore networks since traditional assumptions of Navier–Stokes equation break down. At present, lots of attempts have been employed to address the proposition. In this work, the advantages and disadvantages of previous analytical models are seriously analyzed. The first type is modifying a mature equation which is proposed for a specified flow regime and adapted to wider application scope. Thus, the first-type models inevitably require empirical coefficients. The second type is weight superposition based on two different flow mechanisms, which is considered as the reasonable establishment method for universal non-empirical gas-transport model. Subsequently, in terms of slip flow and Knudsen diffusion, the novel gas-transport model is established in this work. Notably, the weight factors of slip flow and Knudsen diffusion are determined through Wu’s model and Knudsen’s model respectively, with the capacity to capture key transport mechanism through nanopores. Capturing gas flow physics at nanoscale allows the proposed model free of any empirical coefficients, which is also the main distinction between our work and previous research. Reliability of proposed model is verified by published molecular simulation results as well. Furthermore, a novel permeability model for coal/shale matrix is developed based on the non-empirical gas-transport model. Results show that (a) nanoconfined gas-transport capacity will be strengthened with the decline of pressure and the decrease in the pressure is supportive for the increasing amplitude; (b) the greater pore size the nanopores is, the stronger the transport capacity the nanotube is; (c) after field application with an actual well in Fuling shale gas field, China, it is demonstrated that numerical simulation coupled with the proposed permeability model can achieve better historical match with the actual production performance. The investigation will contribute to the understanding of nanoconfined gas flow behavior and lay the theoretical foundation for next-generation numerical simulation of unconventional gas reservoirs.

Review of Flow Patterns in a Column Reactor for Photobioreactor Application

2014 ◽  
Author(s):  
Gary A. Anderson ◽  
Anil Kommareddy ◽  
Taylor Suess ◽  
Stephen P. Gent
Keyword(s):  
Gas Flow ◽  
Plug Flow ◽  
Flow Patterns ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Gas Velocity ◽  
Gas Flow Rate ◽  
Cross Sectional ◽  
Reactor Volume ◽  
Superficial Gas Velocity

Photobioreactors (PBRs) and chemical reactors are often vertical columns with either circular or rectangular cross sections. The reactors are frequently referred to as column reactors and are treated as if they perform in the same manner. The reactors can have two different types of flow established in them regardless of cross sectional shape depending on the saprger/diffuser type and location within the reactor. The flow patterns in the reactors are induced by gas that is bubbled into the reactor volume usually near the bottom of the reactor. When the gas bubbles rise up through the reactor in a plug flow fashion, most of the mixing is in the radial direction which tends to make the reactor liquid and gas more homogeneous across the width of the reactor. The gas bubbles in the reactor may not move up through the reactor in a plug flow fashion, but may instead move vertically up through a portion of the reactor cross-section. This will establish a column of bubbles and liquid rising from the bottom of the reactor up to the surface and, in turn, induce a column(s) of liquid moving downward from the top of the reactor to the bottom. This behavior is similar to an air lift reactor which generally has walls physically dividing the upward (riser) and downward (down comer) flows. Without physical separation of the flows, the percent of cross sectional area of the reactor acting as the riser and down comer is established by the gas flow rate through the reactor, reactor cross sectional area, and the reactor volume. Velocity of flow(s) in the reactors is often based on the superficial gas velocity, which is the incoming gas flow rate divided by the gross cross sectional area of the reactor volume. This parameter may not relate to the two flows in the same manner. The two different flow patterns will be discussed in relation to superficial gas velocity, light in a PBR, chemical reactions in the reactor, and riser and down comer size.

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