Reformulation of the solution-diffusion theory of reverse osmosis

Paul, Donald R

doi:10.1016/j.memsci.2004.05.026

Cited by 410 publications

(319 citation statements)

References 41 publications

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“…This model describes the mass transport through RO membranes and enables the prediction of the retention behavior of organic multi-component solutions. Because many of the simplifications in the classical theory for the solution-diffusion mechanism become inappropriate for separation of aqueous solutions of organic molecules, the classical solution-diffusion theory for modeling RO systems was recently reformulated (Paul, 2004).…”

Section: Introductionmentioning

confidence: 99%

Reverse osmosis processing of organic model compounds and fermentation broths

Diltz¹,

Marolla

Henley³

et al. 2007

Bioresource Technology

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Section: Introductionmentioning

confidence: 99%

Reverse osmosis processing of organic model compounds and fermentation broths

Diltz¹,

Marolla

Henley³

et al. 2007

Bioresource Technology

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“…(16) into Eq. (17), the following relation for the maximum recovery ratio is obtained (18) Equation (18) gives the maximum recovery ratio as a function of the osmotic pressure ratio. Now, the effectiveness is defined as (19) Substituting Eq.…”

Section: Ro Effectivenessmentioning

confidence: 99%

“…These models can be divided into three main groups: the irreversible thermodynamic models, where the local fluxes of solute and solvent are related to the chemical potential differences across the membrane [12][13][14]; the porous flow model, which assumes that water both diffuses and advects through the membrane pores [1,15,16]; and the solution-diffusion model, which assumes that both water and solutes diffuse between the interstitial spaces of the membrane polymer chains [11,17,18].…”

Section: Introductionmentioning

confidence: 99%

“…The solution-diffusion model, developed by Lonsdale, Merten, and Riley in 1965 [17], is one of the most useful models despite its simplicity and some drawbacks that have been discussed elsewhere [6,18,19]. Much research has been conducted on the physics of the solution-diffusion model [7,18,[20][21][22] and many numerical studies have been applied to account for the more complex effects of concentration polarization, salt diffusion, and fouling [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

“…Much research has been conducted on the physics of the solution-diffusion model [7,18,[20][21][22] and many numerical studies have been applied to account for the more complex effects of concentration polarization, salt diffusion, and fouling [23][24][25][26][27]. Other studies have applied the solution-diffusion model for the design of RO modules such as spiral wound, hollow fiber, and crossflow long channels [25,[28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effectiveness-mass transfer units (ε-MTU) model of a reverse osmosis membrane mass exchanger

Banchik

Sharqawy

Lienhard

2014

Journal of Membrane Science

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A strong analogy exists between heat exchangers and osmotic mass exchangers. The effectiveness -number of transfer units (-NTU) method is well-known for the sizing and rating of heat exchangers. A similar method, called the effectiveness -mass transfer units (ε-MTU) method, is developed for reverse osmosis (RO) mass exchangers. Governing equations for an RO mass exchanger are nondimensionalized assuming ideal membrane characteristics and a linearized form of the osmotic pressure function for seawater. A closed form solution is found which relates three dimensionless groups: the number of mass transfer units, which is an effective size of the exchanger; a pressure ratio, which relates osmotic and hydraulic pressures; and the recovery ratio, which is the ratio of permeate to inlet feed flow rates. A novel performance parameter, the effectiveness of an RO exchanger, is defined as a ratio of the recovery ratio to the maximum recovery ratio. A one-dimensional numerical model is developed to correct for the effects of feed-side external concentration polarization and nonlinearities in osmotic pressure as a function of salinity. A comparison of model results to experimental data found in the literature resulted in an average error of less than 7.8%. The analytical ε-MTU model can be used for design or performance evaluation of RO membrane mass exchangers. Keywords

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The Solution–Diffusion Model: A Unified Approach to Membrane Permeation

Wijmans

Baker

2006

Materials Science of Membranes for Gas and Vapor Separation

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Over the last 40 years membrane technology has grown from a few analytical applications to a widely used industrial and medical process. Membrane sales are in the multibillion-dollar per year range. Our understanding of the underlying theory and science of membrane processes has also grown during these years. This paper covers the solutiondiffusion model, the most widely used description of permeation through reverse osmosis, pervaporation and gas separation membranes. In the past, these different processes were often treated as completely separate entities. The solution-diffusion model allows these processes to be described in a single, unified way, as we will show.Our approach is first to derive the base equations of the solution-diffusion model for a one-component fluid, and to illustrate the overall unity of the model. We then apply the model to multicomponent mixtures and explain the behavior of membranes when used to perform practical separations. At a number of points, rather than deriving the analytical solution to a specific problem, we simply present the basic equations and show the results of a computer calculation in graphical form. This approach avoids long, tedious derivations and reflects the reality of modern research. Even with the use of computers, this paper has more than 100 equations.A subject like this requires a balance between rigor and clarity. Too much rigor produces a paper only a handful of theoreticians will read. Too much clarity at the expense of rigor and the paper is clear but superficial. This paper is the collaboration of coworkers with different backgrounds. We have tried to present our combined thinking in a way that will be accessible to all, yet solid. 'May the Force be with you'! The Solution-Diffusion ModelThe most easily understood description of a membrane is a porous structure containing a network of tiny pores that separate large from small molecules in a manner similar to a filter. This is a reasonably accurate description of a microfiltration membrane, with pores in the 1000 Å diameter range. Even ultrafiltration membranes, in which the pores are small enough to separate dissolved polymer molecules from water, are best described as 'ultrafine' filters. However, the pore model of membrane transport breaks down when the pore diameter falls to 5 Å or less. The pore diameter is then within the range of the thermal motion of the polymer chains from which the membrane is made. Permeation is no longer a pressure-driven flow through tiny pores but a diffusive process controlled by the motion of the polymer chains.In the past, the transition point between pore flow and molecular diffusion, based on pore diameter, was an assumption. During the last

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Reformulation of the solution-diffusion theory of reverse osmosis

Cited by 410 publications

References 41 publications

Reverse osmosis processing of organic model compounds and fermentation broths

Reverse osmosis processing of organic model compounds and fermentation broths

Effectiveness-mass transfer units (ε-MTU) model of a reverse osmosis membrane mass exchanger

The Solution–Diffusion Model: A Unified Approach to Membrane Permeation

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