scholarly journals INVASION PERCOLATION WITH A HARDENING INTERFACE UNDER GRAVITY

2010 ◽  
Vol 21 (07) ◽  
pp. 903-914 ◽  
Author(s):  
C. L. N. OLIVEIRA ◽  
F. K. WITTEL ◽  
J. S. ANDRADE ◽  
H. J. HERRMANN
Keyword(s):  
Porous Medium ◽  
Capillary Forces ◽  
Bond Number ◽  
Invasion Percolation ◽  
Hardening Behavior ◽  
Hardening Effect ◽  
Buoyancy Forces ◽  
Capillary Pressures ◽  
A Site ◽  
Invasion Patterns

We propose a modified Invasion Percolation (IP) model to simulate the infiltration of glue into a porous medium under gravity in 2D. Initially, the medium is saturated with air and then invaded by a fluid that has a hardening effect taking place from the interface towards the interior by contact with the air. To take into account that interfacial hardening, we use an IP model where capillary pressures of the growth sites are increased with time. In our model, if a site stays for a certain time at interface, it becomes a hard site and cannot be invaded anymore. That represents the glue interface becoming hard due to exposition with the air. Buoyancy forces are included in this system through the Bond number which represents the competition between the hydrostatic and capillary forces. We then compare our results with results from literature of non-hardening fluids in each regime of Bond number. We see that the invasion patterns change strongly with hardening while the non-hardening behavior remains basically not affected.

Invasion Percolation Quantities on Correlated Networks

1998 ◽  
Vol 09 (06) ◽  
pp. 827-836 ◽  
Author(s):  
A. M. Vidales ◽  
E. Miranda ◽  
G. Zgrablich
Keyword(s):  
Heterogeneous Media ◽  
Front Velocity ◽  
Invasion Percolation ◽  
Final State ◽  
Bond Model ◽  
Correlation Degree ◽  
The Mean ◽  
A Site ◽  
Correlated Networks

Invasion percolation is studied on correlated square networks described through a site-bond model which has proven to be useful for the characterization of real heterogeneous media. It is shown how the correlation degree affects the mean front velocity, the number of islands of trapped defender fluid (which are completely surrounded by invaded elements), their size distribution and total number of steps to reach the final state. The correlation degree seems to affect the fractal dimension of the percolating cluster. A characteristic correlation length is found to exist which maximizes the mean invasion velocity.

Mixed Convective Heat Transfer From a Heated Horizontal Plate in a Porous Medium Near an Impermeable Surface

1988 ◽  
Vol 110 (2) ◽  
pp. 390-394 ◽  
Author(s):  
P. H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Saturated Porous Medium ◽  
Forced Flow ◽  
Horizontal Plate ◽  
Flowing Fluid ◽  
Buoyancy Forces ◽  
Two Dimensional Flow

Two-dimensional flow over a horizontal plate in a saturated porous medium mounted near an impervious adiabatic horizontal surface and subjected to a horizontal forced flow has been numerically investigated. The plate is heated to a uniform temperature that is higher than the temperature of the flowing fluid. The conditions considered are such that the buoyancy forces have an effect on the flow and, therefore, on the heat transfer rate from the plate. The full governing equations, written in dimensionless form, have been solved for a range of values of the governing parameters using the finite element method. The heat transfer rate from the plate is influenced both by the dimensionless depth of the plate below the surface and the importance of the buoyancy forces, the latter having been characterized by a parameter which is equal to the ratio of the Darcy–Rayleigh number to Peclet number. The conditions under which these parameters have a negligible effect on the heat transfer rate are discussed.

Effects of capillary number, Bond number, and gas solubility on water saturation of sand specimens

2013 ◽  
Vol 50 (2) ◽  
pp. 133-144 ◽  
Author(s):  
Bruce L. Kutter
Keyword(s):  
Capillary Number ◽  
Water Saturation ◽  
Fluid Pressure ◽  
Infiltration Rate ◽  
Capillary Forces ◽  
Bond Number ◽  
Pore Fluid ◽  
Degree Of Saturation ◽  
Fluid Viscosity ◽  
Viscous Forces

To better understand how to prepare completely water-saturated specimens or centrifuge models from dry sand, the mechanisms of the infiltration and filling of pores in sand are studied. Complete saturation has been shown by others to be especially important in studies involving the triggering of liquefaction. This paper discusses how the degree of saturation obtained during infiltration increases with the “Bond number”, Bo (ratio of body forces and capillary forces), and the “capillary number”, Ca (ratio of viscous forces and capillary forces), as well as the solubility of gas bubbles in the pore fluid. Bo is varied by changing the particle size, fluid density, and centrifugal acceleration. Ca is varied by changing the fluid viscosity and infiltration rate. The dissolution of gas is encouraged by replacing pore air by CO2 (56 times more soluble in water than N2), by de-airing the liquid prior to infiltration or by increasing the pore fluid pressure after infiltration. Infiltration experiments performed at 1g and in a centrifuge are presented. A new technique for measuring the degree of saturation is also presented. Quantitative pressure–saturation relations are presented for different gasses, illustrating the importance of replacement of air by CO2. Spinning a specimen in a centrifuge during infiltration is also useful for speeding up the saturation process and for achieving higher degrees of saturation.

scholarly journals Analytical Investigation into Effects of Capillary Force on Condensate Film Flowing over Horizontal Semicircular Tube in Porous Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Tong-Bou Chang ◽  
Bai-Heng Shiue ◽  
Yi-Bin Ciou ◽  
Wai-Io Lo
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Capillary Force ◽  
Heat Transfer Performance ◽  
Capillary Forces ◽  
Gravity Force ◽  
Transfer Performance ◽  
Capillary Suction ◽  
Condensate Film ◽  
Energy Balance Approach

A theoretical investigation is performed into the problem of laminar filmwise condensation flow over a horizontal semicircular tube embedded in a porous medium and subject to capillary forces. The effects of the capillary force and gravity force on the condensation heat transfer performance are analyzed using an energy balance approach method. For analytical convenience, several dimensionless parameters are introduced, including the Jakob number Ja, Rayleigh number Ra, and capillary force parameter Boc. The resulting dimensionless governing equation is solved using the numerical shooting method to determine the effect of capillary forces on the condensate thickness. A capillary suction velocity can be obtained mathematically in the calculation process and indicates whether the gravity force is greater than the capillary force. It is shown that if the capillary force is greater than the condensate gravity force, the liquid condensate will be sucked into the two-phase zone. Under this condition, the condensate film thickness reduces and the heat transfer performance is correspondingly improved. Without considering the capillary force effects, the mean Nusselt number is also obtained in the present study as N u   ¯ | V 2 ∗ = 0 = 2 R a   D a / J a 1 / 2 ∫ 0 π 1 + cos   θ 1 / 2 d θ .

scholarly journals Permeability alteration by salt precipitation: numerical and experimental investigation using X-Ray Radiography

2020 ◽  
Vol 146 ◽  
pp. 03001
Author(s):  
Olivier Lopez ◽  
Souhail Youssef ◽  
Audrey Estublier ◽  
Jostein Alvestad ◽  
Christin Weierholt Strandli
Keyword(s):  
Porous Medium ◽  
Partial Pressure ◽  
Gas Injection ◽  
Capillary Forces ◽  
Salt Transport ◽  
Salt Crystallization ◽  
Salt Precipitation ◽  
X Ray ◽  
Vapor Partial Pressure ◽  
Permeability Alteration

The injection of a gas phase through a water saturated porous medium can reduce the water saturation not only by displacement mechanisms but also by evaporation mechanisms. In the presence of brine, this process can induce salt crystallization and precipitation within the porous medium with a risk of permeability alteration. In the field of gas production and storage, the occurrence of such a phenomenon can have detrimental consequence on the well productivity or injectivity. In this work, we investigated experimentally and numerically the effect of dry gas injection on salt precipitation and permeability impairment. State of the art equipment designed for high throughput coreflood experimentation was used to capture the dynamic of salt migration using X-Ray radiography. A set of experiments have been conducted on a sample of Bentheimer sandstone (10mm in diameter and 20 mm in length) as well as a two layers composite sample with a significant permeability contrast. Experiments were conducted using Nitrogen and KBr brine with different boundary conditions (i.e. with and without capillary contact). Results showed that salt precipitation results from the interplay of different parameters, namely pressure gradient, brine salinity, capillary forces and vapor partial pressure. Experimental observations indicate that in the case of dry gas injection, salt systematically precipitates but permeability alteration is observed only if a capillary contact is maintained with the brine. We built a 2D flow model integrating two-phase Darcy flow, capillary forces, salt effect on vapor partial pressure, dissolved salt transport, as well as the different PVT equilibria needed to describe properly the systems. Once calibrated, the model showed good predictability of lab scale experiment and thus can be used for parametrical study and upscaled to the well bore scale.

Features of wave propagation in the sand of different saturation

2011 ◽  
Vol 8 (1) ◽  
pp. 25-38
Author(s):  
A.T. Akhmetov ◽  
S.V. Lukin ◽  
D.M. Balapanov ◽  
S.F. Urmancheev ◽  
N.M. Gumerov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Porous Media ◽  
Wave Propagation ◽  
Water Saturation ◽  
Weak Shock ◽  
Capillary Forces ◽  
Theoretical Studies ◽  
Longitudinal Waves ◽  
Experimental And Theoretical Studies

There are the results of experimental and theoretical studies on the propagation of weak shock waves in the wet sand at different water saturation. There are mathematical model and numerical analysis of propagation of pressure pulses in porous media, taking into account capillary forces. Non-monotonic dependence of the amplitude of the wave resulting in a wet porous medium vs. the degree of water saturation is installed. The evolution of the fast, slow and filtration waves depends on the saturation of the system with water is analyzed. The influence of capillary forces on the propagation of longitudinal waves is evaluated.

Quasi-Static Capillary Impregnation of a Porous Fiber Bed

1999 ◽  
Author(s):  
J. He ◽  
M. C. Altan
Keyword(s):  
Fiber Volume Fraction ◽  
Volume Fraction ◽  
Capillary Forces ◽  
Bond Number ◽  
Contact Angles ◽  
Flow Equation ◽  
Creeping Flow ◽  
Experimental Result ◽  
Fiber Volume ◽  
Front Motion

Abstract The impregnation of a fiber bed by capillary forces in a gravity field is analyzed. Fiber bed is modeled as infinitely long, parallel cylinders arranged in a hexagonal pattern. Quasi-static creeping flow equation is used to obtain the fluid front location and shape during impregnation of the fiber bed. The fluid front motion during impregnation are presented for different Bond numbers, contact angles and fiber volume fractions. It is found that impregnation velocity is significantly affected by contact angle and fiber volume fraction at the initial stages of impregnation. The influence of the Bond number becomes more significant when the fluid front approaches its final position where gravity balances capillary forces. The permeability of the fiber bed is also obtained from the time-dependent motion of the fluid front. The permeability predictions agree with the published experimental result and with those obtained by using lubrication theory.

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>

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