Dear Mudhar,

Please read the following text and for more information use the link depicted at the end of the text:

Modeling of a spiral-wound module and estimation of model parameters using numerical techniques

by Aruj Ahluwalia, S. Senthilmurugan and Sharad K. Gupta

Desalination 173 (2005) 269-286

Abstract

A model for a spiral-wound reverse osmosis system using the three-parameter membrane transport model by Spiegler–Kedem is presented. The pressure drops in the permeate channel, feed channel and also the variation of the mass transfer coefficient along the feed channel were taken into account. An analytical solution was not possible due to the large number of nonlinear model equations; therefore, a computer solution utilizing finite differences was employed. The data generated by the simulation of the proposed model clearly indicate that neglecting the variation in the mass transfer coefficient and pressure drop along the flow channels can lead to errors in permeate concentration, though the effect on permeate flow rate may not be significant. The significance of the reflection coefficient in the membrane transport model was also investigated. A method for estimation of the model parameters is also presented; previously reported experimental data were analyzed. Using this parameter-estimation program, a correlation for the mass transfer coefficient in the feed channel is proposed and compared with the correlation available in the literature.Authors

S. Senthilmurugan (1), Sharad K. Gupta (1), Aruj Ahluwalia (1)Tags

CFSK model (1)

... in the feed channel is proposed and compared with the correlation available in the literature. Keywords: Reverse osmosis; Spiral-wound module; CFSK model; Parameter estimation 1. Introduction Reverse osmosis (RO) is a pressure-driven process used to separate solute and solvent of the same orde ...

Reverse osmosis (180)

A model for a spiral-wound reverse osmosis system using the three-parameter membrane transport model by Spiegler–Kedem is presented. The pressure drops in the permeate channel ...

Spiral-wound module (5)

A model for a spiral-wound reverse osmosis system using the three-parameter membrane transport model by Spiegler–Kedem is presented. The pressure drops in the permeate... to the solution–diffusion model. Since the SK model is known to be the most accurate membrane transport model, the present model for spiral-wound modules may provide more accurate results for design and analysis for reverse osmosis systems. The data generated also show that the pressure drop in th ...

Parameter estimation ()

A model for a spiral-wound reverse osmosis system using the three-parameter membrane transport model by Spiegler–Kedem is presented. The pressure drops in the permeate channel, feed channel and also the variation of the... rate may not be significant. The significance of the reflection coefficient in the membrane transport model was also investigated. A method forestimation of the model parameters is also presented; previously reported experimental data were analyzed. Using this parameter-estimation program, ...

Conclusion

It was found that for lower values of the reflection coefficient, the overall permeate produced is much higher and the permeate concentration differs substantially from that obtained for F = 1 where the SK model mathematically is reduced to the solution–diffusion model. Since the SK model is known to be the most accurate membrane transport model, the present model for spiral-wound modules may provide more accurate results for design and analysis for reverse osmosis systems. The data generated also show that the pressure drop in the flow channels as well as the mass transfer coefficient variation cannot be neglected. Disregarding the above can lead to considerable errors in the predicted results. The membrane performance parameters have been estimated for the experimental data of Taniguchi [2] and Boudinar et al. [4], and the results clearly show that the present model predicts data very well, and the estimated membrane parameters remain constant for a variety of operating conditions. The mass transfer correlations were found for the both Roga and FilmTech spiral-wound modules, and these correlations compare very well with correlations available in the literature.

Source: http://www.desline.com/articoli/6111.pdf

Read more: http://www.lenntech.com/abstracts/1416/modeling-of-a-spiral-wound-module-and-estimation-of-model-parameters-using-numerical.html#ixzz43YheaNRn

http://www.lenntech.com/abstracts/1416/modeling-of-a-spiral-wound-module-and-estimation-of-model-parameters-using-numerical.html

Hoping this will be helpful,

Rafik

Dear Dr. Rafik,

it is my fault to exactly describe what I am looking for (i have corrected it now) .. i was asking if you know any published models written in three dimensions (x and) in each channel (feed and permeate channels) and z direction for water and solute fluxes through the membrane

this what i am looking for

accept my best regards

mudhar

Dear Mudhar,

Herein the requested publication:

Biofouling in spiral wound membrane systems: Three-dimensional CFD model based evaluation of experimental data

J.S. Vrouwenvelder a,b,∗, C. Picioreanub, J.C. Kruithof a, M.C.M. van Loosdrecht b

ARTICLE in JOURNAL OF MEMBRANE SCIENCE 346(1-2):71-85 · JANUARY 2010

ABSTRACT

A three-dimensional (3D) computational model describing fluid dynamics and biofouling of feed channels of spiral wound reverse osmosis and nanofiltration membrane systems was developed based on results from practice and experimental studies. In the model simulations the same feed spacer geometry as applied in practice and the experimental studies was used. The 3D mathematical model showed the same trends for (i) feed channel pressure drop, (ii) biomass accumulation, (iii) velocity distribution profile, resulting in regions of low and high liquid flow velocity also named channeling. The numerical model predicted a dominant biomass growth on the feed spacer, consistent with direct in situ observations on biofouling of spiral wound membrane modules and monitors using Magnetic Resonance Imaging (MRI). The model confirms experimental results that feed spacer fouling is more important than membrane fouling. The paper shows that mathematical modeling techniques have evolved to a stage that they can be used hand-in-hand with experiments to understand the processes involved in membrane fouling.

To view the full publication, please use the following link:

https://www.researchgate.net/publication/254023802_Biofouling_in_spiral_wound_membrane_systems_Three-dimensional_CFD_model_based_evaluation_of_experimental_data

Hoping this will be helpful,

Rafik

Article Biofouling in spiral wound membrane systems: Three-dimension...

Thank you Dr. Rafik

You are so helpful and kind but hopefully you might have other works since the above one contains no mathematical written model which exactly I am looking for 

But please accept my appreciate

Mudhar

I would suggest that given the complexities of 3D fluid dynamics, and associated mass transfer of solute to and away from the feed concentrate side of the membrane, let alone the modeling of the mass transfer at the membrane itself, that you will not find a published model in the literature. It is also unlikely that someone would give you a copy of a model that they have spent hundreds of hours creating, as it would represent significant intellectual property to the research group that created it. Best wishes in your search.

thank you Mr. Robert Huehmer for your kind response to my question

Actually i am not asking to get a copy of 3D model related the transport phenomena in spiral wound reverse osmosis but i am checking if there is an earlier work where i can to be aware not to repeat the same idea in building my prospective 3D model. You know each research student has to know all the previous work so he can introduce something new or to do some improvements that might consider as an extra contribution. i tried to check the internet and collected some of these works but hopefully i can find other works from introducing my question in this media.

regards

mudhar

Dear Mudhar,

3D modeling of membrane modules is not very difficult, but simulations require a lot of computational power. One more problem is related to defining the geometry of spacers in the flow channels. Thus, we average out all variables in a dimension, which is the direction of the thickness of the flow channels, and simplified the model in 2D. 2D models give sufficiently accurate predictions.

3D modeling is only used for analyzing the effects of spaces on pressure drop, concentration polarization or fouling, but in these studies, only small sections of modules are analyzed. 3D modeling for predicting the performance of entire module is yet not published.

For 3D modeling, you have to use CFD software and incorporate membrane mass transport models as the boundary conditions at the surface of the membrane. You can also use COMSOL Multiphysics software.  

Thank you Mr. Manish Jain for your clarifications and hope to ask you if i can consider the variation of solute concentration along the thickness of the membrane in addition to measure the impact of spacer'c geometry as well. Hope you have a link for such studies you can guide me to add it to what i have found.

please accept my regards

Mudhar

You can consider the concentration variations along the thickness of the membrane. COMSOL software is quite use full for this type of modeling.

With Regards 

Manish Jain

Thank you sir for this advice i will try to find  this software and who to use it