Transport in Porous Media - Science topic

Dear Arun Mathew, the case can be solved by having a 2D axisymmetric boundary so that fluent can solve that in polar coordinates.

After creating the geometry of the inner pipe, the outer porous layer is to be generated as a plane as a FROZEN material so that it will be created as a separate body. Hence it can be defined as a porous media in FLUENT.

In FLUENT,

I have provided my response to your question. If it has been helpful, please let me know. If you have any further doubts or if my explanation was not clear enough, please do not hesitate to let me know. I am happy to assist you further.

Hi Arvind Kumar ,

There are two class of liquid-vapour mass transfer models available (limited to pore-scale simulation):

#1 First type calculates the mass flux based on KINETIC THEORY, and its derivative models such as Hertz-Knudsen, Schrage-Mills, Lee etc. can be used for large problem domains.

#2 Second type is called ENERGY-JUMP CONDITION, uses thermal resistance at the liquid-vapour interface to calculate the heat flux, which finally calculates the mass flux.

I recommend you to follow this review work:

Bonjour, I think you should activate the extra dimension that is available when you use a porous medium in COMSOL. Coupling of "Heat Transfer in Porous Media" and "Heat Transfer in Solids and Fluids" at boundary conditions.

Dear Manoj, I would suggest rereading Section 2.2.1 in the following review paper where it compared the continuum model versus the discrete model:

Hi, anyone has solved this problem? Amin Komeili

thanks!

The Mathieu equation has periodic solutions and therefore it is possible to use finite difference approximations to obtain an equivalent matrix eigenvalue problem. The matrix will of tridiagonal kind with an extra two coefficients, one top right and the other bottom left when second order accurate differences are used.

Also see:

Dear all;

I searched among some examples and I figured out that an output image for omega could be easily generated by adding these few lines to the writeGifs function in the CPP file.

imageWriter.writeScaledGif(createFileName("omega", iter, 6),*computeOmega(lattice , Box2D(0,nx-1, 0,ny-1)),

imSize, imSize );

Thank you for your contributions and precious answers.

Regards;

Elahe

I think that you should revisit the derivation of the Navier-Stokes equations and take a look at the work by KR. Rajagopal et al.

Rajagopal, KR. On implicit constitutive theories for fluids. J Fluid Mech 2006; 550: 243–249.

Take a look at this paper:

DOI: 10.1615/JPorMedia.2021025407

For a cement slurry for oil and gas wells its rheological characterisation has been carried out by many authors (i.e. Bourgoyne A. et al 1991, Technip 1982 and many of the service company manuals/books & publications). This characterisation has been based on a number of assumptions such as that temperature has no influence on the rheology until the slurry is in place. In other words that its rheological behaviour is either assumed at surface or downhole temperature and prior to the onset of dehydration and setting of the slurry. Passage of the slurry through the porous media (invasion) has been modelled by Chin W. (Formation Invasion 1995) which is worth reading. Invasion (Also know as filtrate invasion) can also be modelled using the algorithms used to calculate fluid loss in fracturing treatments, they are based on viscosity, pressure and rock properties. These can be found in most manuals of hydraulic fracturing. I hope it helps

A small matter in the scheme of things..... in the question you have mixed singular and plural. It should end with either, "in a porous medium" or "in porous media". This grammatical error is very widespread indeed and about 1/3rd of papers that I review have the error. Perhaps this is because one hears "the news media" being treated as a single group.

have you an example of 1D Advection Diffusion

I don't really understand how rank correlation could be helpful here. If both curves (experimental and simulated) are strinktly monotonousley increasing, the rank correlation will be perfect, no matter how similar the two curves are.

I think the Kolmogorov-Sminov statistic should be a natural choice (https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test).

If you can take the saturation (as a variable strincly in (0,1)) as a probability value, you might even use the Kulback-Leibler divergence to measure the (dis-)similarity between two curves (https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence).

see

Radial symmetry of solutions to diffusion equations with discontinuous nonlinearities

Joaquim SerraJournal:Journal of Differential EquationsYear:2013

best luck

Dear Albero,

This is not my area of expertise at all, but we have previously looked at the viosco-elastic properties of biofilms, and have recently looked at the impact of increasing liquid viscosity on biofilm-formation.

I would presume the oscillations you see are the effects of random vibrations of small sections of the agarose network stretching and recovering in the water flow. This should be random, but as parts of the agarose bock start to vibrate in synchrony, the amplitude of the vibrations should increase until sections of the agar break and you get less restricted liquid flow through that part. Perhaps you could test this, as I would assume that below some critical flow rate (perhaps related to the agarose/gel concentration) the vibrations would not start to buildup, and above this the rate of failure should increase as fluid flow increases. You could also look to see what happens if you stiffen up the agarose gel (using different suppliers, using metal ions, etc.) or increase the viscosity of the fluid you use!

Hope this helps, Andrew.

Adib Amini be welcome, I hope you fix the problems!

Il est préférable d'utiliser un mélange poreux de différents matériaux bien choisi.

Mahmudul Alam Shakib

An electrical double layer is being studied to modify cement for various applications. Cement is a complex mixture of oxides that hydrate differently depending on the composition of the cement and their concentration in the solution. It is impossible to mathematically simulate a double layer. You can take one oxide and work with it to simulate a double layer experiment.

Dear Dr. Abdelilah El Abbassi ,

I apologize for my incorrectly interpreting your question; I send you the link to a paper, hoping it will help you:

-Adsorption Basics: Part 1

By Alan Gabelman, P.E.

American Institute of Chemical Engineers (AIChE) (2017)

Available at: https://www.aiche.org/sites/default/files/docs/pages/adsorption_basics_part_1.pdf

Good work and my best regards, Pierluigi Traverso.

The Influence of fluid property on permeability and form drag coefficient is characterized by the friction factors fv, fD, fi and ft. The total friction factor ft depends mainly on both Reynolds number Re, and Darcy number (Dp and φ). Three regions for the behavior appear

 Re≤100, fi is negligible, fD and fv shares with the main part.

 100≤ Re≤10000 , transition region in which the two types of friction factors fD and fv decrease sharply while the inertia friction factor fi increases sharply.

 Re>10000 , ft curve overlaps with the line of fi, the two types of friction fD and fv are neglected and fi/ft asymptotes to the value 1. i.e. the flow depends mainly on the inertia friction fi which is constant with Re.

You can find additional details in the attached file

Gamal Bedair , at this stage I think yes, thank you. I will discuss with my colleague who has an experimental machine about further details and maybe new questions will appear.

Lyu Kefeng

Yeah, of course.

No one answered this question here, so i asked this question on CFD-Online's forum. A user named LuckyTran gave me this answer:

"I don't think there is any special interface treatment.

When you select the laminar zone option, Fluent sets the turbulent production in that zone to zero. The variables (k, epsilon, etc.) are still transported through the laminar zone.

There is another option (accessed using TUI commands) that allows you to also set the turbulent viscosity to zero in the laminar zone. But again, they are simply transported.

The pressure drop due to the porous media is handled by adding an extra volumetric momentum sink. If you need a reference, refer to the user manual section on Porous Media Conditions (see 7.2.1-3).

There is only one momentum equation. Refer to my previous post for why there is only one momentum equation when you use a laminar zone option. Interface treatment is needed in general when you actually have two separate sets of governing equations. But that is not the case."

(the link for this discussion on CFD-Online's forum:

https://www.cfd-online.com/Forums/fluent/221063-porous-fluid-interface-treatment.html#post746058 )

I wrote my understanding from this statements for the reviewer, fortunately, he/she accepted it and here is our published paper:

Best regards.

Thank you. After some internet survey, I find that during drilling there is a pump to control the pressure of drilling mud , which is used for carry cuttings out of the hole. However, I do not know the setting pressure of the pump.

For unknown materials, a BET surface area analysis (by gas adsorption) is a good place to start... this at least will reveal how much gas accessible surface there is and one can make certain inferences about the extent of meso and microporosity by combing the BET calculation with the t-plot method. A complete description of (gas accessible) micropore space requires low relative pressure gas adsorption isotherms and appropriate mathematical models (DFT, not BJH for micropores). Remember that gas molecular/atomic size plays a role in accessing the smallest of micropores; CO2 at 273K can access smaller pores than can N2 at 77K for example. Mesopore and small macropore size distribution can be done by gas adsorption up to a few hundred nm pore diameter. Gas adsorption isotherm hysteresis can reveal something about the connectivity of pores. Larger macropores are quickly evaluated using mercury intrusion porosimetry... up to ~1mm in diameter. The value of these fluid-based methods (gas adsorption and mercury intrusion) is that pore volume can be known directly, unlike diffraction and microscopy techniques. They still have a role to play of course to understand the underlying solid structure that is giving rise to the porosity. CAT scans can be useful in the meso/macro scale but cannot easily give quantitative values and of course rely on good X-ray contrast. Small angle scattering techniques really come into their own for amorphous and soft materials.

The following "Classic" books can help you for sure:

1- As said above by Pascale: Conduction of heat in solids by Carslaw and Jaeger.

2- The mathematics of diffusion by John Crank.

3- Cannon JR (2008) The one-dimensional heat equation, encyclopedia of mathematics and its applications. Cambridge University Press, Cambridge.

4- van Genuchten MT, Alves WJ (1982), Analytical solutions of the one-dimensional convective–dispersive solute transport equation. U.S. Department of Agriculture, Technical, Bulletin No. 1661, p 151.

5- A. D. Polyanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary/Partial/Nonlinear Differential Equations, 2nd Edition, Chapman & Hall/CRC Press, Boca Raton, 2003 

(Last one is a series on books)

Dear Dr. Majid Heydari ,

It would be appreciated if you explain more about the method you used to simulate the POROUS MEDIA for your Ph.D. thesis.

Best regards,

Mehdi

Separate the domain(s) that you want it to be as a porous media in your problem by selecting "add frozen" option in "Geometry" section. Then choose a certain name for your porous media domain in order to be distinguished from other domains. Next, go to "setup" section and select "cell zone conditions". Then, double click on porous media zone determined in previous step. Now, you can check "porous zone" and insert your porous media details such as porosity and permeability.

Dear Hitesh Aggarwal

I understand your situation. I faced that situation in my PhD 2nd publication.

You want to use porous media model because the computational cost using the real geometry of hole shape is too high.

In porous media, you can mimic the hole shape behavior by modifying the permeability (inverse resistance) and dynamic loss through an User Defined Function (UDF) macro in Fluent named as DEFINE_PROFILE. Here is an example of that macro:

#include "udf.h" DEFINE_PROFILE(porosity_function, t, nv) { cell_t c; real time=CURRENT_TIME; begin_c_loop(c,t) { C_PROFILE(c,t,nv) = 5000000000000+2000000000000*time+4000000000*pow(time,2); } end_c_loop(c,t) }

source: https://www.cfd-online.com/Forums/fluent-udf/94746-udf-viscous-resistance-porous-media-time-variable.html

Now the problem is determination of important parameters that can represent the hole shape behavior. You can follow our multi-scale CFD approach in those papers:

The general idea of this method is: We do the CFD for dual scales where the bigger scale is porous media, the smaller scale is real hole shape but just for a representative element volume (you can use 1 hole or several holes). In the smaller scale, you need to run the simulation for a wide range of BC to capture the full range possible in the bigger scale.

I hope you enjoy it.

Good luck.

Dear Bharath Ram Ravi,

The ratio of inertial to viscous resistance in a porous media depends for a STEADY flow (constant pressure difference imposed across the medium) on the Reynolds number Re defined as: Re=U d/nu. U is a characteristic flow velocity (filter velocity), d is a typical pore diameter and nu is the kinematic viscosity (dynamic viscosity divided by density) of the fluid. For an imposed harmonic unsteady pressure difference with frequency f one should consider the ratio of unsteady inertial force and viscous forces ( 2 pi f U)/(nu U/d^2)=(2 pi f d^2)/nu, where pi=3.14... Hence the answer depends on the characteristic flow conditions you are considering. These are best described in terms of dimensionless numbers. Regards, Mico

Veli Uygur Yes Sir, I prepared ferrihydrite with different concentrations of P, and confirmed. but I didn't find a suitable reference for my work i.e. the digestion of P sorbed iron colloids, the way I did.

I agree der Boer but, I’m using a porous region in CCM+z I forgot to mention that. As result my porous region does not explicitly solve the porous medium. instead it uses Viscous and inertial coefficient resistance to determine the pressure drop. That’s why I wanted to include a force mimicking the capillary force counteracting the gravity.

Dear Spencer,

In this benchmark exercise you have 5 codes that can do so:

https://www.researchgate.net/publication/329043106_Benchmarking_of_reactive_transport_codes_for_2D_simulations_with_mineral_dissolution-precipitation_reactions_and_feedback_on_transport_parameters

In this other benchmark you have a couple of codes more:

I hope this helps you

Best regards

Vanessa

Try to run without porous zone first to sure the mesh interface was corrected.

Usually the BC between two porous layers is interior. The things that make them be different are permeability and porosity.

In Fluent, there is no permeability (K), but the viscous resistance (1/K) in the form of momentum source term.

In case that your permeability is extreme high, you can increase it gradually. But the value of K in your case is not so high, so you can apply it directly.

Hi Deewakar Sharma

You can use star ccm+, in this software you can define most fluids such an

Newtonian and non-Newtonian and chemical process and multiphase of them.

Best Regards

Dear Mr.Parag C,

Y+ is only needed for turbulent flows. However as yours is a laminar flow problem you need not worry about it.

Thanks.

Saurav

Sounds great! All the best.

If you have no experience of numerical methods, then I would suggest that you should start with something straightforward in order to build up your expertise and experience. Just having someone else's code will give you no long-term skills. Perhaps a good starting point might be to solve Fourier's equation, theta_t = theta_xx, subject to the initial condition, theta=sin(pi*x) at t=0 and the boundary conditions, theta=0 at x=0,1. Forward differences should be used in time, and central differences in space. The analytical solution is theta=exp(-t)*sin(pi*x) for comparison purposes. Details on how to discretise this may be found in any textbook which covers the numerical solution of PDEs. In addition, when you have a working code, then you will notice that the method becomes numerically unstable when dt > 0.5 dx^2, and therefore timesteps need to be smaller than (dx^2)/2 so that the numerical solution decays just as the analytical solution decays.

The problem which you are trying to solve is a modification of this, although it really is quite an extensive and complicated modification because it involves separate domains, three dependent variables and interface conditions.

To maintain the pH at 7.5 you must use a buffer (a phosphate buffer can be used for this purpose). You have to check the buffer capacity to ensure that it can maintain the pH at the desired value.

I don't know the other details of your research, but I'm supposing the use of the buffer doesn't interfere with your experiments

Yes ofcourse , there are essentiallye two methods to obtain fluid saturations in porous medi. one is by X-raya and the other one is with using the volumetric method/material balance (the one you mentioned to). However, remember to account for the dead volumes and do pump flood at the end of your experiment to examine the impact of the capillary end effect so that you ensure that your data are accurate and reliable.

Regards

I fully agree with previous answers. But your question is not clear enough.

the distribution of fluids (previous history) and wettability (if the viscosities are similiar) are the controlling factors for the pressure needed to flow. involving capillary pressure muddles the issue.

For example, if your water saturation is 40 % and all the other variables are the same. Not all the pores have 40%! some will have 100% and others 20%. Therefore, the pressure drop will be different for different pore size distributions, mainly if they are not unimodal.

Also, during imbibition and drainage at the same saturation you will have different fluid distributions and as a consequence different pressures.

Hi Feichen and all.

OK: no loose particles migration and pore blocking. Then, the porous medium itself could be undergoing compression during experiment, thus reducing its permeability (Cf. Darcy’s Law). In this case, a constant flow rate would give what you getting: an increasing pressure drop. Try a constant very small flow rate. It will give a very small pressure drop, hopefully not enough to compress the medium and the pressure drop will be constant. If that is the case, you’re dealing with very compressible porous medium. If it is unavoidable to deal with this medium, for a given flow rate, you will need a large cross section so as to have low velocity and low pressure drop.

We have to remember about convective heat transfer in fluid phase as well - if LTE consists of a sum of NLTE equations, convective part concerning fluid remains in LTE equation - so as fluid flows through the foam, heat transfer between phases occurs, so yes, ratio of thermal conductivity have impact

Performing calculations with the assumption of plug flow and additionally assuming that the process takes place in one phase - the gas phase, will allow you easily to test the kinetic equation. The mass balance equation will take the form:

dα_ArS/dz = (m_c/(F_ovc_ArSo)) r_ArS(α_ArS), α_ArS(0) = 0,

where α_ArS - conversion of ArS, z = m/m_c, m_c - total mass of catalyst, F_oV - volumetric flow rate, c_ArSo - initial concentration of ArS.

It is necessary to know the values of c_ArSo, c_H2o, F_oV, m_c and temperature for calculations. It is also necessary to specify the stoichiometric equation (in particular, the number of hydrogen moles), because without this the stoichiometric analysis will be impossible. Regards,

Industrial grade reservoir simulators like IMEX/ECLIPSE/INTERSECT/... are probably unsuited for the type of work you want to perform. You likely need to access and tweak the physical engine of the simulator. R&D codes are what you are looking for. Some source code, which allows you to tweak physics at core, are open source. Google MRST, ADGPRS, OPENFOAM, etc. I would expect some tweaks to be already available in those codes. This will require some investment on your side into the selected code. It is probably advisable that you select one that is used by people around you.

A very crude alternative is to tweak an industrial grade simulator with restarts or use some of the options that exist in some of those "a little bit far". But this is very crude and messy, I would not recommend that.

The steps required to solve numerically the phenomena of turbulent natural convection in porous media are:

1- Define your physical case shape

2- Define your Turbulent Model

3- Derive your Governing Equations

4- Identify Boundary Conditions

5- Select a software to solve your governing equations with identified boundary conditions

6- Or Solve your system of equations by Fortran or similar

7- Expect your results and sole for Outputs like Velocity distribution, temperature distribution, Dimensionless Numbers relations, ........

Dear Tufail, please find enclosed some of the literature on your desire subject. Beside this, you may also read some of my publication on biosynthesis of phosphorus nano-particles and its effect on crop plants may be available under research gate.

You can link them using "FREEWAT" open source platform based on QGIS. There are many detailed tutorials ! It's free and only you must to register for downloading!

Hi Stainstaw Anweiler,

I want to make a trickle regime that gas and liquid simultaneously flow through a soild porous medium and the problem is with making the physical flow. I read some papers about trickle flow and the minimum depth that i found was about 3cm for rectangular cross section and in one paper the *hydraulic* diameter for an annulus bed was 2cm. for the most 2D beds, depth was smaller than 1cm. but i don't want a 2D bed.

I will be happy if it's possible to make a rectangular cross section trickle bed with 1.4cm depth.

thanks for your answer

A new present of ANSYS is the model of Magnetic Field Data and you can add that data in Fluent.

Dear Omar Rafae Alomar,

I learnt VOF from the following papers/chapters:

(1) Volume of Fluid (VOF) Method for the Dynamics of Free Boundary by Hirt and Nichols (1981)

(2) Volume-Tracking Methods for Interfacial Flow Calculations by M. Rudman (1997)

(3) Time-Dependent Multi-material Flow with Large Fluid Distortion by D. L. Youngs (1982)

(4) A new volume of fluid advection algorithm: The defined donating region scheme by Harvie and Fletcher (2001)

(5) A geometrical area-preserving Volume-of-Fluid advection method by Aulisa et al. (2002)

(6) Second-order accurate volume-of-fluid algorithms for tracking interfaces by Pilliod and Puckett (1997)

(7) A New Volume of Fluid Advection Algorithm: The Stream Scheme by Harvie and Fletcher (2000)

(8) Conservative Volume-of-Fluid method for free-surface simulations on Cartesian-grids by Weymouth and Yue (2010)

(9) Reconstructing Volume Tracking by Rider and Kothe (1999)

and I (dare) list my own article as the tenth entry :) 

(10) A redistribution-based volume-preserving PLIC-VOF technique by Saincher and Banerjee (2015)

The following book will also prove to be helpful...

Computational Methods for Multiphase Flow. By A. Prosperetti & G. Tryggvason (I have attached a link to the book's webpage at Cambridge)

Regarding you question about the best reference...I do not think there exists an article/chapter that is self-contained in terms of all the information that is required to implement a VOF-algorithm...the above articles/chapters complement each other in terms of necessary information and thus should be read in conjunction.

Best regards,

Shaswat Saincher

Instead of searching for MATLAB codes, I think it is advisable to study Wellflo design and analysis software. This will help you with the basics on how to develop your own unique MATLAB code.

Thank you all, your recommendations were so helpful.

Especially you Michael.

Greetings,

Jaime

Hi David

I am guessing that you can use micro models to design at least some of the properties. That said, you would need physical measurement to verify the end result or, at least, measurement would be a prudent step to secure the end result.

Have fun

Claes

you need to go for the stable suspension with a lesser concentration. 

Which type of suspension you are preparing??

Given that the question was in 2014, this answer may now be superfluous....

I agree with Prof Dong Chen - you need to have two different heat transport equations, one for the solid phase and one for the fluid phase. This is known as Local Thermal NonEquilibrium (LTNE), and is now well-studied.

Good luck!

In my opinion you must go with VOF HRIC model to carry out your simulation

Normally, you can get quick results with the no slip boundary. You can also set it as wetted wall but you have to know the contact angle of the fluid on the solid.

thanks so much man ... 

I did not use the method you said since I would like to carry out two phases flow, and brinkman equation is not available for two phases, this has been proved, thanks@Mohammad Ghalambaz

if you have a body inside the box, the equilibrium prescribes that the surface integral of  the pressure balances the integral of the stresses...

Assuming Int [V] v dV = 0 at any time, you have from integration of the momentum (fixed and non-permeable walls), remembering that Grad p = Div (pI)

Int [t0,t] dt ( Int[S]  n p - n. 2mu Grad v dS) =0

 Dear Sir,

please read the attached paper which may help.

Regards

Dominique

Hello,

Please read this article : Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations by Ariel Narvaez (doi:10.1088/1742-5468/2010/11/P11026)

There's a link between the viscosity and the boundary conditions, which may be reduced when the MRT algorithm is used.

Dear Miomir,

For humidity in asphalt only have experience with neutron backscatter measurement. Troxler portable gauges for field measurement.

If you are using abaqus, I suggest using for 3D analysis C3D8 and for 2D analysys CPS4. You also can use C3D8R and CPS4R with reasonable accuracy and less computational demand.

After X-ray tomography you have the freedom to select (by masking) your different density domain from histogram by selecting/specifying the grey values. In the present case I believe that you have 2 phases. Solid and air(open void)can be separated individually and simultaneously from the histogram. It is available in image processing softwares like scanip(pretty much sure) and in volumegraphics. After masking you have option to mesh your solid and air domain separately.

I am a Ph.D candidate in Shanghai Jiao Tong University. I am working on visualization of two-phase flow in a tiny 2D nozzle when the fluid is superheated. We already see the fuel evaporated inside the nozzle. For the superheated condition, we use two methods to reach various superheated conditions. One is keep the pressure constant, and heat the liquid. Another one is decrease the ambient pressure and keep the fuel temperature constant. Two reaserch papers are under review process now. You can find some related results in my two latest journal papers.

Under Comsol, normally via the Two Phase Darcy law module we can simulate immiscible fluids flow in porous media, in that way we need to define the capillary pressure i.e. its variation with saturation. Well, the initial capillary pressure can be guessed through the contact angle and the surface tension coefficient but to describe pc=f(s), a model is required (ven Genuchten, Brooks Corey...), the problem is that I'm not finding a rigorous definition of these models parameters (IvG, mvG, lambda) in a way to adjust them according to the treated problem.

I don't know if my approach is correct or I'm missing something.