scholarly journals Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects

2021 ◽  
Vol 3 ◽  
Author(s):  
Francisco J. Valdés-Parada ◽  
Didier Lasseux
Keyword(s):  
Boundary Condition ◽  
Porous Media ◽  
Mass Transport ◽  
Gas Flow ◽  
Macroscopic Model ◽  
Type Model ◽  
Pore Scale ◽  
Advective Transport ◽  
Apparent Permeability ◽  
Slip Effects

In this work, a macroscopic model for incompressible and Newtonian gas flow coupled to Fickian and advective transport of a passive solute in rigid and homogeneous porous media is derived. At the pore-scale, both momentum and mass transport phenomena are coupled, not only by the convective mechanism in the mass transport equation, but also in the solid-fluid interfacial boundary condition. This boundary condition is a generalization of the Kramers-Kistemaker slip condition that includes the Knudsen effects. The resulting upscaled model, applicable in the bulk of the porous medium, corresponds to: 1) A Darcy-type model that involves an apparent permeability tensor, complemented by a dispersive term and 2) A macroscopic convection-dispersion equation for the solute, in which both the macroscopic velocity and the total dispersion tensor are influenced by the slip effects taking place at the pore-scale. The use of the model is restricted by the starting assumptions imposed in the governing equations at the pore scale and by the (spatial and temporal) constraints involved in the upscaling process. The different regimes of application of the model, in terms of the Péclet number values, are discussed as well as its extents and limitations. This new model generalizes previous attempts that only include either Knudsen or diffusive slip effects in porous media.

Macroscopic Modeling of Turbulent Mass Transport in Heterogeneous Porous Media

2004 ◽  
Author(s):  
Maximilian S. Mesquita ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Porous Media ◽  
Mass Transport ◽  
Transport Model ◽  
Control Volume ◽  
Fluid Phase ◽  
Heterogeneous Porous Media ◽  
Macroscopic Model ◽  
Simple Method ◽  
Macroscopic Modeling ◽  
Flow Equations

In this work, results for a macroscopic mass transport model are presented for a parallel plate channel filled with a fluid saturated heterogeneous porous medium. The numerical methodology herein employed is based on the control volume approach. Turbulence is assumed to exist within the fluid phase. High and low Reynolds k-e models were used to model such non-linear effects. The flow equations at the pore-scale were numerically solved using the SIMPLE method applied to a non-orthogonal boundary-fitted coordinate system. Integrated mass fraction results were compiled leading to correlations for the mass dispersion coefficients in the x and y directions. Application of the macroscopic model using the proposed correlations showed the role of dispersion mechanism in the overall transport in porous media.

Comparison of Competing Invasion-Percolation Models for Simulation of Multiphase Flow in Porous Media 

2021 ◽  
Author(s):  
Ishani Banerjee ◽  
Anneli Guthke ◽  
Kevin Mumford ◽  
Wolfgang Nowak
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Gas Flow ◽  
Flow Regimes ◽  
Flow In Porous Media ◽  
Invasion Percolation ◽  
Pore Scale ◽  
Discontinuous Flow ◽  
Model Version ◽  
Water Saturated

<p>Invasion-Percolation (IP) models are used to simulate multiphase flow in porous media across various scales (from pore-scale IP to Macro-IP). Numerous variations of IP models have emerged; here we are interested in simulating gas flow in a water-saturated porous medium. Gas flow in porous media occurs either as a continuous or as a discontinuous flow, depending on the rate of flow and the nature of the porous medium. A particular IP model version may be well suited for predictions in a specific gas flow regime, but not applicable to other regimes. Our research aims to compare various macro-scale versions of IP models existing in the literature and rank their performance in relevant gas flow regimes.</p><p>We test the performance of Macro-IP models on a range of gas-injection rates in water-saturated sand experiments, including both continuous and discontinuous flow regimes. The experimental data is obtained as a time series of images using the light transmission technique. To represent pore-scale heterogeneities of sand, we let each model version run on several random realizations of the initial entry pressure field. As a metric for ranking the models, we introduce a diffused version of the so-called Jaccard index (adapted from image analysis and object recognition). We average this metric over time and over all realizations per model version to evaluate each model’s overall performance. This metric may also be used to calibrate model parameters such as gas saturation. </p><p>Our proposed approach evaluates the performance of competing IP model versions in different gas-flow regimes objectively and quantitatively, and thus provides guidance on their applicability under specific conditions. Moreover, our comparison method is not limited to gas-water phase systems in porous media but generalizes to any modelling situation accompanied by spatially and temporally highly resolved data.</p>

scholarly journals An improved macroscale model for gas slip flow in porous media

2016 ◽  
Vol 805 ◽  
pp. 118-146 ◽  
Author(s):  
Didier Lasseux ◽  
Francisco J. Valdés Parada ◽  
Mark L. Porter
Keyword(s):  
Porous Media ◽  
Knudsen Number ◽  
Slip Flow ◽  
Permeability Tensor ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Nonlinear Dependence ◽  
Pore Scale ◽  
First Order ◽  
Apparent Slip

We report on a refined macroscopic model for slightly compressible gas slip flow in porous media developed by upscaling the pore-scale boundary value problem. The macroscopic model is validated by comparisons with an analytic solution on a two-dimensional (2-D) ordered model structure and with direct numerical simulations on random microscale structures. The symmetry properties of the apparent slip-corrected permeability tensor in the macroscale momentum equation are analysed. Slip correction at the macroscopic scale is more accurately described if an expansion in the Knudsen number, beyond the first order considered so far, is employed at the closure level. Corrective terms beyond the first order are a signature of the curvature of solid–fluid interfaces at the pore scale that is incompletely captured by the classical first-order correction at the macroscale. With this expansion, the apparent slip-corrected permeability is shown to be the sum of the classical intrinsic permeability tensor and tensorial slip corrections at the successive orders of the Knudsen number. All the tensorial effective coefficients can be determined from intrinsic and coupled but easy-to-solve closure problems. It is further shown that the complete form of the slip boundary condition at the microscale must be considered and an important general feature of this slip condition at the different orders in the Knudsen number is highlighted. It justifies the importance of slip-flow correction terms beyond the first order in the Knudsen number in the macroscopic model and sheds more light on the physics of slip flow in the general case, especially for large porosity values. Nevertheless, this new nonlinear dependence of the apparent permeability with the Knudsen number should be further verified experimentally.

Leakage Predictions for Static Gasket Based on the Porous Media Theory

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Pascal Jolly ◽  
Luc Marchand
Keyword(s):  
Porous Media ◽  
Gas Flow ◽  
Molecular Flow ◽  
Intrinsic Permeability ◽  
Slip Boundary Conditions ◽  
Apparent Permeability ◽  
Slip Boundary ◽  
Porous Media Theory ◽  
Porous Media Model ◽  
Different Gases

In the present work, the annular static gaskets are considered as porous media and Darcy’s law is written for a steady radial flow of a compressible gas with a first order slip boundary conditions. From this, a simple equation is obtained that includes Klinkenberg’s intrinsic permeability factor kv of the gasket and the Knudsen number Kn′o defined with a characteristic length ℓ. The parameters kv and ℓ of the porous gasket are calculated from experimental results obtained with a reference gas at several gasket stress levels. Then, with kv and ℓ, the inverse procedure is performed to predict the leakage rate for three different gases. It is shown that the porous media model predicts leak rates with the same accuracy as the laminar-molecular flow (LMF) model of Marchand et al. However, the new model has the advantage of furnishing phenomenological information on the evolution of the intrinsic permeability and the gas flow regimes with the gasket compressive stress. It also enables quick identification of the part of leakage that occurs at the flange-gasket interface at low gasket stresses. At low gas pressure, the behavior of the apparent permeability diverges from that of Klinkenberg’s, indicating that the rarefaction effect becomes preponderant on the leak.

scholarly journals A Numerical Study on Gas Flow through Anisotropic Sierpinski Carpet with Slippage Effect

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Shuxia Qiu ◽  
Lipei Zhang ◽  
Zhenhua Tian ◽  
Zhouting Jiang ◽  
Mo Yang ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Gas Flow ◽  
Gas Permeability ◽  
Fractal Model ◽  
Numerical Results ◽  
Pore Scale ◽  
Gas Slippage ◽  
Slippage Effect ◽  
Flow Through

A pore-scale model has been developed to study the gas flow through multiscale porous media based on a two-dimensional self-similar Sierpinski carpet. The permeability tensor with slippage effect is proposed, and the effects of complex configurations on gas permeability have been discussed. The present fractal model has been validated by comparison with theoretical models and available experimental data. The numerical results show that the flow field and permeability of the anisotropic Sierpinski model are different from that of the isotropic model, and the anisotropy of porous media can enhance gas permeability. The gas permeability of porous media increases with the increment of porosity, while it decreases with increased pore fractal dimension under fixed porosity. Furthermore, the gas slippage effect strengthens as the pore fractal dimension decreases. However, the relationship between the gas slippage effect and porosity is a nonmonotonic decreasing function because reduced pore size and enhanced flow resistance may be simultaneously involved with decreasing porosity. The proposed pore-scale fractal model can present insights on characterizing complex and multiscale structures of porous media and understanding gas flow mechanisms. The numerical results may provide useful guidelines for the applications of porous materials in oil and gas engineering, hydraulic engineering, chemical engineering, thermal power engineering, food engineering, etc.

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.

Experimental Study of Boiling in Porous Media

2013 ◽  
Author(s):  
Paul Sapin ◽  
Paul Duru ◽  
Florian Fichot ◽  
Marc Prat ◽  
Michel Quintard
Keyword(s):  
Porous Media ◽  
Test Section ◽  
Cooling System ◽  
Macroscopic Model ◽  
Experimental Setup ◽  
Pore Scale ◽  
Pressurized Water Reactor ◽  
Pressurized Water ◽  
Temperature Detector ◽  
Thermal Measurements

Following a long-lasting failure in the cooling system of a pressurized water reactor (PWR), the superheated core can be efficiently cooled down by reflooding. The macroscopic model used at the French Institute of Radioprotection and Nuclear Safety (IRSN) to simulate this process is based on strong assumptions on the microscopic flow patterns. This paper describes the experimental setup designed for the study of boiling in porous media with the emphasis on various pore-scale boiling regimes. The final experimental setup is a two-dimensional porous medium made of 392 cylinders randomly placed between two ceramic plates. Each heating cylinder is a RTD probe (Resistance Temperature Detector), that can give thermal measurements in every point of the test section as well as heat generation. This paper presents preliminary results: pool boiling is characterized for a single cylinder mounted in the test section and reflooding of a line of 9 cylinders is observed.

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 Micromodel Study on Pore Scale Mechanisms associated with Permeability Impairment in Porous Media

2020 ◽  
Author(s):  
Safna Nishad ◽  
Riyadh Al-Raoush
Keyword(s):  
Porous Media ◽  
Gas Flow ◽  
Fine Particles ◽  
Gas Production ◽  
Polystyrene Latex ◽  
Continental Margins ◽  
Pore Scale ◽  
Two Phase ◽  
Hydrate Bearing Sediments ◽  
Permeability Impairment

Recently, researchers have been attracted towards the gas production from hydrate bearing sediments considering its abundance in marine continental margins and persisting demand for alternate energy. Dissociation of hydrate into gas and water is the preliminary technique for gas production in hydrate bearing sediments. Expanded fluid volume and gas pressure upon dissociation detach the fines from the grain surface and result in pore throat entrapment. Migration of fines associated with gas flow greatly influence the alteration of permeability of the sediment by clogging pore throats in the flow path. A pore-scale visualization study was implemented to provide a clear insight into the actual mechanisms associated with mobilization and clogging of fines during two-phase flow through a microfluidic chip. Carboxylate modified polystyrene latex particles deposited in the porous media were migrated during drainage with CO2 gas. The detachment of fine particles from the grain surfaces was observed and were retained on the new interface; gas-water interface. The images and videos captured during the experiment were helpful in observing additional pore scale mechanisms responsible for permeability impairment in the porous media. Interface pinning, deformation and resistance to coalescence were found to be other mechanisms in addition to pore clogging.

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