Modelling reverse osmosis by irreversible thermodynamics (original) (raw)
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Reverse osmosis of multicomponent electrolyte solutions Part II. Experimental verification
Journal of Membrane Science, 1997
A model is developed to treat reverse osmotic separations of electrolyte solutions. Transport in the model is based on the Extended Nernst-Planck equation, which includes diffusion, convection, and electromigration. Boundary conditions include a distribution coefficient that is due to a specific interaction potential representing repulsion of ions from the membrane material. Boundary conditions also include potential jumps known as Donnan
Desalination, 2019
A framework of reformulation of the classic solution-diffusion model is presented by combining the film theory and electrolyte theory to include the concentration polarization and thermodynamic non-idealities in mass transport of NaCl/NH 4 Cl solutions during reverse osmosis in a large range of feed concentrations. In this activityderived model, concentration polarization was evaluated using the film theory to estimate the salt concentrations at the membrane surface. Non-ideal thermodynamic effects from the electrolyte theory were considered to correct the activity coefficients due to the strong concentration dependence. The concentration polarization modulus and salt activities were found to substantially affect the effective local salt transport coefficients (B a). At low salt concentrations, the combined result of the two effects was negligible (i.e., B a ≈ B). However, at high feed concentrations (> 0.09 mol L −1 for both NaCl and NH 4 Cl), the influence of the two effects was significant: the ratio B a /B ranged from 1.12 to 1.50. The concentration polarization effects on the osmotic coefficient and the effective local water transport coefficient (A fm) were very small. This activity-derived model indicates that the concentration dependence of the salt and water transport in RO is a complex function of the combined effects from concentration polarization and thermodynamic non-idealities.
International Journal of Molecular Sciences
Reverse electrodialysis (RED) is an electro-membrane process for the conversion of mixing energy into electricity. One important problem researchers’ face when modeling the RED process is the choice of the proper membrane transport equations. In this study, using experimental data that describe the membrane Nafion 120 in contact with NaCl aqueous solutions, the linear transport equation of irreversible thermodynamics was applied to calculate the power density of the RED system. Various simplifying assumptions about transport equation (i.e., four-, three-, and two-coefficients approaches) are proposed and discussed. We found that the two-coefficients approach, using the membrane conductivity and the apparent transport number of ions, describes the power density with good accuracy. In addition, the influence of the membrane thickness and the concentration polarization on the power density is also demonstrated.
Desalination, 2007
A novel protocol is developed to characterize nanofiltration (NF) and reverse osmosis (RO) membranes that employ the Spiegler-Kedem membrane-transport model based on irreversible thermodynamics coupled with a Film Theory description of the concentration polarization. The novel aspect of this characterization protocol is extracting the concentration polarization boundary-layer thickness as well the three membrane transport parameters from permeation data. This methodology is applied to four dilute aqueous salt systems for a Dow Filmtech NF-255 membrane and one dilute aqueous salt system for a Dow Filmtech BS-30 membrane that were studied using a wellmixed flat sheet membrane permeation cell. Interestingly, the total volumetric flux and intrinsic rejection can be described quite well over the entire range of studied feed concentration, flow rates, and transmembrane pressures using constant membrane transport coefficients in the Spiegler-Kedem model. However, it should be emphasized that the conclusions drawn from this study are restricted to the dilute aqueous salt solutions that were employed. Some prior studies of aqueous salt systems have found it necessary to employ concentration-dependent transport coefficients to describe the permeation behavior. It is possible that the more exacting method for determining the thickness of the concentration boundary-layer thickness that is used in this study properly accounts for volumetric flow rate effects that have been attributed to nonconstant membrane transport coefficients. A design correlation for the intrinsic rejection of an NF or RO membrane as a function of the total volumetric flux is developed that encompasses the full range of concentrations used in the experiments, flow rates, and transmembrane pressures for a specified binary aqueous salt system. This design correlation formalism in principle can be used to characterize any NF or RO membrane irrespective of the type of membrane contactor employed.
Reverse osmosis of ammonium and sodium salt solutions and its model description
DESALINATION AND WATER TREATMENT, 2018
The tested models of membrane transport were based on the steric, dielectric (Born and image force effects), and Donnan exclusions. Generally, the models with the concentration-dependent electrolyte permeability described the retention data satisfactorily, irrespectively of the origin of that dependence (dielectric or Donnan effect). Regarding the steric-dielectric exclusion, the same goodness of fit was obtained for many pairs of pore radius and dielectric constant. However, it was not possible to explain the differences in the electrolyte permeabilities, because of the inconsistency of the dielectric constant of a pore solution and/or an effective membrane thickness. Much too high values of that thickness obtained for the pure Donnan exclusion indicated that this type of exclusion was of marginal importance.
Reverse Draw Solute Permeation in Forward Osmosis: Modeling and Experiments
Environmental Science & Technology, 2010
Osmotically driven membrane processes are an emerging set of technologies that show promise in water and wastewater treatment, desalination, and power generation. The effective operation of these systems requires that the reverse flux of draw solute from the draw solution into the feed solution be minimized. A model was developed that describes the reverse permeation of draw solution across an asymmetric membrane in forward osmosis operation. Experiments were carried out to validate the model predictions with a highly soluble salt (NaCl) as a draw solution and a cellulose acetate membrane designed for forward osmosis. Using independently determined membrane transport coefficients, strong agreement between the model predictions and experimental results was observed. Further analysis shows that the reverse flux selectivity, the ratio of the forward water flux to the reverse solute flux, is a key parameter in the design of osmotically driven membrane processes. The model predictions and experiments demonstrate that this parameter is independent of the draw solution concentration and the structure of the membrane support layer. The value of the reverse flux selectivity is determined solely by the selectivity of the membrane active layer. . dJ s S dz ) -D S d 2 c dz 2 + J w dc dz ) 0
Engineering, 2022
When designing and building an optimal reverse osmosis (RO) desalination plant, it is important that engineers select effective membrane parameters for optimal application performance. The membrane selection can determine the success or failure of the entire desalination operation. The objective of this work is to review available membrane types and design parameters that can be selected for optimal application to yield the highest potential for plant operations. Factors such as osmotic pressure, water flux values, and membrane resistance will all be evaluated as functions of membrane parameters. The optimization of these parameters will be determined through the deployment of the solution-diffusion model devolved from the Maxwell Stephan Equation. When applying the solution-diffusion model to evaluate RO membranes, the Maxwell Stephan Equation provides mathematical analysis through which the steps for mass transfer through a RO membrane may be observed and calculated. A practical study of the use of the solution-diffusion model will be discussed. This study uses the diffusion-solution model to evaluate the effectiveness of a variety of Toray RO membranes. This practical application confirms two principal hypotheses when using the diffusion-solution model for membrane evaluation. First, there is an inverse relationship between membrane and water flux rate. Second, there is a proportional linear relationship between overall water flux rate and the applied pressure across a membrane.
Emergence of thermodynamic restriction and its implications for full-scale reverse osmosis processes
The production rate of permeate in a reverse osmosis (RO) process controlled by mass transfer is proportional to the net driving pressure and the total membrane surface area. This linear relationship may not be the only mechanism controlling the performance of a full-scale membrane process (typically a pressure vessel holding six 1 -m-long modules in series) which utilizes highly permeable membranes. The mechanisms that control the performance of an RO process under various conditions were carefully examined in this study. It was demonstrated that thermodynamic equilibrium can impose a strong restriction on the performance of a full-scale RO process under certain circumstances. This thermodynamic restriction arises from the significant increase in osmotic pressure downstream of an RO membrane channel due to the accumulation of rejected salt within the RO channel as a result of permeate water production. Concentration polarization is shown to have a weaker influence on the full-scale RO process performance than the thermodynamic restriction. The behavior of the process under thermodynamic restriction is quite different from the corresponding behavior that is controlled by mass transfer. The transition pressure for an RO process to shift from a mass transfer controlled regime to a thermodynamically restricted regime was determined by the basic parameters of the full-scale RO process.
Journal of Membrane Science, 1993
The problem of transport of binary electrolyte solutions through macroscopically homogeneous membranes under reverse osmosis conditions with arbitrary thermodynamic forces has been solved in quadratures in terms of irreversible thermodynamics. Phenomenological coefficients have been specified for the model of straight cylindrical capillaries with an arbitrary cross-section and surface forces of an arbitrary nature. These general expressions have been further specified for the space-charge model and identical capillaries with a circular cross-section. A new technique to describe the structure of strongly and moderately overlapped double electrical layers has been developed. As a result, analytical expressions for the main characteristics of charged reverse osmosis membranes have been derived at arbitrary fixed charge densities. Limiting rejection, hydrodynamic permeability, filtration potential and the rate of approaching limiting rejection have been calculated as functions of fixed charge density, pore size, binary electrolyte concentration, valency type and the ratio of cation and anion mobilities. A comparison with experiment has been carried out for model membranes having identical straight circular cylindrical pores with radius 40 or 50 A.
Journal of Membrane Science, 2018
The classic Merten and Lonsdale transport model for reverse osmosis membranes was reformulated to explicitly demonstrate the effects of concentration polarization and solution phase thermodynamic non-idealities on salt transport. A framework presented here accounts for the concentration dependence of ion activity coefficients in salt solutions, which was not explicitly included in the classic model. This approach was applied to four salt solutions, NaCl, MgCl 2 , CaCl 2 , and Na 2 SO 4 , tested in cross-flow conditions for a commercial RO membrane, Dow Filmtec TM BW30XFR. Salt transport coefficients corrected for concentration polarization and non-ideal thermodynamic effects, , were calculated as a function of permeate flux and compared with apparent salt transport coefficients, B. These corrections were significant, resulting in values greater than B values by a factor of 1.3~2.1 for 2:1 and 1:2 salts (i.e., MgCl 2 , CaCl 2 , and Na 2 SO 4). values for NaCl (a 1:1 salt), however, were similar to or somewhat smaller than B values. Keywords: Reverse osmosis (RO); membranes; desalination; the Merten and Lonsdale model; salt transport Highlights A theoretical framework accounting for concentration polarization and non-ideal thermodynamic effects on salt transport in RO membranes is proposed. The influence of concentration polarization and thermodynamic non-idealities on salt transport coefficients (i.e., B values) in RO membranes was quantified. This framework was applied to four common salt solutions, NaCl, MgCl 2 , CaCl 2 , and Na 2 SO 4. Corrections for concentration polarization and non-ideal thermodynamic effects (i.e., values) were significant, resulting in values that were greater than B values by a factor of 1.3~2.1 for MgCl 2 , CaCl 2 , and Na 2 SO 4 solutions.