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.

Diffusion-Based Modeling of Gas Transport in Organic-Rich Ultratight Reservoirs

SPE Journal ◽  
2021 ◽  
pp. 1-26
Author(s):  
Zizhong Liu ◽  
Hamid Emami-Meybodi
Keyword(s):  
Diffusion Coefficient ◽  
Adsorption Capacity ◽  
Surface Diffusion ◽  
Diffusion Coefficients ◽  
Gas Transport ◽  
Knudsen Diffusion ◽  
Gas Production ◽  
Hydrocarbon Transport ◽  
The Impact ◽  
And Storage

Summary The complex pore structure and storage mechanism of organic-rich ultratight reservoirs make the hydrocarbon transport within these reservoirs complicated and significantly different from conventional oil and gas reservoirs. A substantial fraction of pore volume in the ultratight matrix consists of nanopores in which the notion of viscous flow may become irrelevant. Instead, multiple transport and storage mechanisms should be considered to model fluid transport within the shale matrix, including molecular diffusion, Knudsen diffusion, surface diffusion, and sorption. This paper presents a diffusion-based semianalytical model for a single-component gas transport within an infinite-actingorganic-rich ultratight matrix. The model treats free and sorbed gas as two phases coexisting in nanopores. The overall mass conservation equation for both phases is transformed into one governing equation solely on the basis of the concentration (density) of the free phase. As a result, the partial differential equation (PDE) governing the overall mass transport carries two newly defined nonlinear terms; namely, effective diffusion coefficient, De, and capacity factor, Φ. The De term accounts for the molecular, Knudsen, and surface diffusion coefficients, and the Φ term considers the mass exchange between free and sorbed phases under sorption equilibrium condition. Furthermore, the ratio of De/Φ is recognized as an apparent diffusion coefficient Da, which is a function of free phase concentration. The nonlinear PDE is solved by applying a piecewise-constant-coefficient technique that divides the domain under consideration into an arbitrary number of subdomains. Each subdomain is assigned with a constant Da. The diffusion-based model is validated against numerical simulation. The model is then used to investigate the impact of surface and Knudsen diffusion coefficients, porosity, and adsorption capacity on gas transport within the ultratight formation. Further, the model is used to study gas transport and production from the Barnett, Marcellus, and New Albany shales. The results show that surface diffusion significantly contributes to gas production in shales with large values of surface diffusion coefficient and adsorption capacity and small values of Knudsen diffusion coefficient and total porosity. Thus, neglecting surface diffusion in organic-rich shales may result in the underestimation of gas production.

scholarly journals Analysis of gas transport behavior in organic and inorganic nanopores based on a unified apparent gas permeability model

2019 ◽  
Vol 17 (1) ◽  
pp. 168-181 ◽  
Author(s):  
Qi Zhang ◽  
Wen-Dong Wang ◽  
Yilihamu Kade ◽  
Bo-Tao Wang ◽  
Lei Xiong
Keyword(s):  
Pore Pressure ◽  
Surface Diffusion ◽  
Pore Radius ◽  
Gas Transport ◽  
Gas Permeability ◽  
Knudsen Diffusion ◽  
Permeability Model ◽  
Real Gas ◽  
Apparent Gas Permeability ◽  
Transport Behavior

Abstract Different from the conventional gas reservoirs, gas transport in nanoporous shales is complicated due to multiple transport mechanisms and reservoir characteristics. In this work, we presented a unified apparent gas permeability model for real gas transport in organic and inorganic nanopores, considering real gas effect, organic matter (OM) porosity, Knudsen diffusion, surface diffusion, and stress dependence. Meanwhile, the effects of monolayer and multilayer adsorption on gas transport are included. Then, we validated the model by experimental results. The influences of pore radius, pore pressure, OM porosity, temperature, and stress dependence on gas transport behavior and their contributions to the total apparent gas permeability (AGP) were analyzed. The results show that the adsorption effect causes Kn(OM) > Kn(IM) when the pore pressure is larger than 1 MPa and the pore radius is less than 100 nm. The ratio of the AGP over the intrinsic permeability decreases with an increase in pore radius or pore pressure. For nanopores with a radius of less than 10 nm, the effects of the OM porosity, surface diffusion coefficient, and temperature on gas transport cannot be negligible. Moreover, the surface diffusion almost dominates in nanopores with a radius less than 2 nm under high OM porosity conditions. For the small-radius and low-pressure conditions, gas transport is governed by the Knudsen diffusion in nanopores. This study focuses on revealing gas transport behavior in nanoporous shales.

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.

scholarly journals A methodology to predict the gas permeability parameters of tight reservoirs from nitrogen sorption isotherms and mercury porosimetry curves

2021 ◽  
Vol 76 ◽  
pp. 32
Author(s):  
Christos D. Tsakiroglou ◽  
Adnan Al Hinai ◽  
Reza Rezaee
Keyword(s):  
Diffusion Coefficient ◽  
Pore Structure ◽  
Percolation Theory ◽  
Gas Permeability ◽  
Critical Path ◽  
Knudsen Diffusion ◽  
Absolute Permeability ◽  
Desorption Isotherms ◽  
The Absolute ◽  
Adsorption Desorption

A methodology is suggested for the explicit computation of the absolute permeability and Knudsen diffusion coefficient of tight rocks (shales) from pore structure properties. The pore space is regarded as a pore-and-throat network quantified by the statistical moments of bimodal pore and throat size distributions, pore shape factors, and pore accessibility function. With the aid of percolation theory, analytic equations are developed to express the nitrogen (N2) adsorption/desorption isotherms and mercury (Hg) intrusion curve as functions of all pertinent pore structure parameters. A multistep procedure is adopted for the successive estimation of each set of parameters by the inverse modeling of N2 adsorption–desorption isotherms, and Hg intrusion curve. With the aid of critical path analysis of percolation theory, the absolute permeability and Knudsen diffusion coefficient are computed as functions of estimated pore network properties. Application of the methodology to the datasets of several shale samples enables us to evaluate the predictability of the approach.

Gas flow through porous cometary media

2020 ◽  
Author(s):  
Maria Schweighart ◽  
Günter Kargl ◽  
Patrick Tiefenbacher ◽  
CoPhyLab Team
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Gas Flow ◽  
Gas Transport ◽  
Glass Beads ◽  
Sample Material ◽  
Flow Measurements ◽  
Lower Volume ◽  
Flow Experiments

<p>Over the last few decades, our picture of comets has been continuously changing and growing due to several successful space missions, as well as cometary simulation projects in the laboratory (e.g. KOSI 1987-1992, CoPhyLab 2018 - 2021). This work aims for a better understanding of the gas transport through a porous cometary surface layer. Therefore, gas flow measurements have been performed in our laboratory to investigate the permeability of several analogue materials, which have been chosen to mimic cometary surface properties.</p><p>For the first measurements, which we are reporting here, only dry materials, free of volatiles have been selected, to isolate the gas transport from gas production inside the materials. They include glass beads made of soda lime glass, which are sieved into separate fractions to obtain distinct grain size ranges from 45 µm up to 4.3 mm. The Mars simulant JSC-Mars 1 is used in the experiments, as well as JSC-1 as a lunar soil simulant. Furthermore, an Asteroid analogue material named UCF/DSI-CI-2 from the Exolith Lab in Florida is also used. A quartz sand called UK4 mined at a local quarry in Graz is investigated as well. In a further step, a sample is created by mixing different grain size fractions of the glass beads replicating the grain size distribution of the Asteroid simulant.</p><p>The materials are also treated on a shaking table in order to obtain the packing properties of the samples. For the gas flow experiments a cylindrical sample container, with 4 cm diameter, is filled with the sample (30 mm in height) and placed inside of the vacuum chamber at the interface of two separate volumes. Four pressure sensors covering different pressure ranges monitor the gas pressure in the two volumes. A vacuum pump in the lower volume removes the gas from the chamber and through a gas inlet a defined flow of the test gas (compressed air) is inserted into the upper volume. Due to this set-up, the gas flow can only pass through the sample material. To avoid particle fluidisation and thus a texture change in the sample the gas flow is intentionally directed downwards through the sample. The gas flow is controlled by regulators from 0.15 mg/s up to 19.2 mg/s. Via the measured pressure difference between the upper and lower volume, in equilibrium flow, the gas permeability and the Knudsen diffusion coefficient of the sample material are obtained. The gas flow experiments show that the grain size distribution and the packing density of the sample play a major role for the permeability of the sample. From the analysis of the permeability measurements it is clearly visible that the larger the grains the bigger the permeability. The measured permeability values range from 10<sup>-13</sup> to 10<sup>-8</sup> m². This work is part of the CoPhyLab project funded by the D-A-CH programme (DFG GU1620/3-1 and BL 298/26-1 / SNF 200021E 177964 / FWF I 3730-N36).</p>

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.

Gas flow in ultra-tight shale strata

2012 ◽  
Vol 710 ◽  
pp. 641-658 ◽  
Author(s):  
Hamed Darabi ◽  
A. Ettehad ◽  
F. Javadpour ◽  
K. Sepehrnoori
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Gas Flow ◽  
Gas Permeability ◽  
Knudsen Diffusion ◽  
Initial Pressure ◽  
Flow In Porous Media ◽  
Upper And Lower Bounds ◽  
Apparent Permeability ◽  
Permeability Function

AbstractWe study the gas flow processes in ultra-tight porous media in which the matrix pore network is composed of nanometre- to micrometre-size pores. We formulate a pressure-dependent permeability function, referred to as the apparent permeability function (APF), assuming that Knudsen diffusion and slip flow (the Klinkenberg effect) are the main contributors to the overall flow in porous media. The APF predicts that in nanometre-size pores, gas permeability values are as much as 10 times greater than results obtained by continuum hydrodynamics predictions, and with increasing pore size (i.e. of the order of the micrometre), gas permeability converges to continuum hydrodynamics values. In addition, the APF predicts that an increase in the fractal dimension of the pore surface leads to a decrease in Knudsen diffusion. Using the homogenization method, a rigorous analysis is performed to examine whether the APF is preserved throughout the process of upscaling from local scale to large scale. We use the well-known pulse-decay experiment to estimate the main parameter of the APF, which is Darcy permeability. Our newly derived late-transient analytical solution and the late-transient numerical solution consistently match the pressure decay data and yield approximately the same estimated value for Darcy permeability at the typical core-sample initial pressure range and pressure difference. Other parameters of the APF may be determined from independent laboratory experiments; however, a pulse-decay experiment can be used to estimate the unknown parameters of the APF if multiple tests are performed and/or the parameters are strictly constrained by upper and lower bounds.

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.

scholarly journals Direct Simulation Monte Carlo investigation of fluid characteristics and gas transport in porous microchannels

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Vahid Shariati ◽  
Mohammad Hassan Ahmadian ◽  
Ehsan Roohi
Keyword(s):  
Monte Carlo ◽  
Gas Transport ◽  
Gas Permeability ◽  
Knudsen Diffusion ◽  
Direct Simulation Monte Carlo ◽  
Current Data ◽  
Direct Simulation ◽  
Apparent Permeability ◽  
Knudsen Numbers ◽  
Simulation Monte Carlo

AbstractThe impetus of the current research is to use the direct simulation Monte Carlo (DSMC) algorithm to investigate fluid behaviour and gas transport in porous microchannels. Here, we demonstrate DSMC’s capability to simulate porous media up to 40% porosity. In this study, the porous geometry is generated by a random distribution of circular obstacles through the microchannel with no interpenetration between the obstacles. The influence of the morphology along with rarefaction and gas type on the apparent permeability is investigated. Moreover, the effects of porosity, solid particle’s diameter and specific surface area are considered. Our results demonstrate that although decreasing porosity intensifies tortuosity in the flow field, the tortuosity reduces at higher Knudsen numbers due to slip flow at solid boundaries. In addition, our study on two different gas species showed that the gas type affects slippage and apparent gas permeability. Finally, comparing different apparent permeability models showed that Beskok and Karniadakis model is valid only up to the early transition regime and at higher Knudsen numbers, the current data matches those models that take Knudsen diffusion into account as well.

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