Reverse osmosis modeling

Reverse osmosis models can be divided into three types irreversible thermodynamics models, such as Kedem-Katchalsky and Spiegler-Kedem models nonporous or homogeneous membrane models, such as the solution—diffusion (SD), solution—diffusion—imperfection, and extended solution—diffusion models and pore models, such as the finely porous, preferential sorption—capillary flow, and surface force—pore flow models. Charged RO membrane theories can be used to describe nanofiltration membranes, which are often negatively charged. Models such as Dorman exclusion and the... 

Reverse osmosis membrane process, 27 637 Reverse osmosis membrane cleaning citric acid application, 6 647 Reverse-osmosis membranes, 75 811, 825 development of, 75 797 Reverse osmosis models, 27 638-639 Reverse osmosis permeators, 76 19 Reverse osmosis seawater desalination process, 26 85 Reverse osmosis systems blending in, 26 80-81 brackish and nanofiltration, 26 80-83 Reverse osmosis technology... 

Kedem- Katchalsky -reverse osmosis models [REVERSE OSMOSIS] (Vol 21)... 

Transport Models. Many mechanistic and mathematical models have been proposed to describe reverse osmosis membranes. Some of these descriptions rely on relatively simple concepts others are far more complex and require sophisticated solution techniques. Models that adequately describe the performance of RO membranes are important to the design of RO processes. Models that predict separation characteristics also minimize the number of experiments that must be performed to describe a particular system. Excellent reviews of membrane transport models and mechanisms are available (9,14,25-29). 

Given the first type of simulation, it is advantageous to be able to design a system of RO modules that can achieve the process objective at a minimal cost. A model has been iategrated iato a process simulation program to predict the stream matrix for a reverse osmosis process (132). In the area of waste minimization, the proper placement of RO modules is essential for achieving minimum waste at a minimum cost. Excellent details on how to create an optimal network of RO modules is available (96). 

H. Mehdizadeh, "Modeling of Transport Phenomena in Reverse Osmosis Membranes," dissertation, McMaster University, Hamilton, Ont., Canada, 1990. 

J. Siler, "Reverse Osmosis Membranes-Concentration Polarization and Surface Fouling Predictive Models and Experimental Verifications," dissertation. University of Kentucky, Lexington, Ky., 1987. 

Ultrafiltration separations range from ca 1 to 100 nm. Above ca 50 nm, the process is often known as microfiltration. Transport through ultrafiltration and microfiltration membranes is described by pore-flow models. Below ca 2 nm, interactions between the membrane material and the solute and solvent become significant. That process, called reverse osmosis or hyperfiltration, is best described by solution—diffusion mechanisms. 

Over the past three decades, there has been a growing industrial interest in using reverse osmosis for several objectives such as water purification and demineralization as well as environmental plications (e.g.. Comb, 1994 Rorech and Bond, 1993, El-Halwagi, 1992). The first step in designing the system is to understand the operating principles and modeling of RO modules. 

Soltanieh, M., and Gill, W. N. (1984). An experimental study of the complete mixing model for radial flow hollow fiber reverse osmosis systems. Desalination, 49, 57-88. 

Most theoretical studies of osmosis and reverse osmosis have been carried out using macroscopic continuum hydrodynamics [5,8-13]. The models used include those that treat the wall as either nonporous or porous. In the nonporous models the membrane surface is assumed homogeneous and nonporous. Transport occurs by the molecules dissolving in the membrane phase and then diffusing through the membrane. Mass transfer across the membrane in these models is usually described using the solution-diffusion... 

Irreversible thermodynamics has also been used sometimes to explain reverse osmosis [14,15]. If it can be assumed that the thermodynamic forces responsible for reverse osmosis are sufficiently small, then a linear relationship will exist between the forces and the fluxes in the system, with the coefficients of proportionality then referred to as the phenomenological coefficients. These coefficients are generally notoriously difficult to obtain, although some progress has been made recently using approaches such as cell models [15]. 

C. S. Slatter, C. A. Brooks. Development of a simulation model predicting performance of reverse osmosis batch systems. Sep Sci Tech 27 1361, 1992. 

H. Mehdizadeh, J. M. Dickson. Theoretical modifications of the finely porous model for reverse osmosis. J Appl Polym Sci 42 1143, 1991. 

A. E. Yaroshchuk, S. S. Durkhin. Phenomenological theory of reverse osmosis in macroscopically homogeneous membranes and its specification for the capillary charged model. J Memb Sci 79 133, 1993. 

This can be further integrated from the wall to the boundary layer thickness y = 8, where the component is at the bulk concentration Cj,. Substituting / = - o and k = D/o, the mass-transfer coefficient yields the stagnant film model [Brian, Desalination by Reverse Osmosis, Merten (ed.), M.I.T. Press, Cambridge, Mass., 1966, pp. 161-292] ... 

Landau-Fermi liquid, 23 840 Landau quasiparticle model, 23 840 Land cost, 9 527 Landering, 8 438-439 Land-farming, 3 768 defined, 3 759t Landfill gas, 25 880 Landfill leachate treatment, reverse osmosis in, 21 646-647 Landfill liners, 25 877-878... 

Transport equations, for the surface force-pore flow model, 21 640—641 Transport gasifier, 6 798 Transport models, reverse osmosis, 21 638-639... 

Dense membranes are used for pervaporation, as for reverse osmosis, and the process can be described by a solution-diffusion model. That is, in an ideal case there is equilibrium at the membrane interfaces and diffusional transport of components through the bulk of the membrane. The activity of a component on the feed side of the membrane is proportional to the composition of that component in the feed solution. 

The composition at the permeate-phase interface depends on the partial pressure and saturation vapour pressure of the component. Solvent composition within the membrane may vary considerably between the feed and permeate sides interface in pervaporation. By lowering the pressure at the permeate side, very low concentrations can be achieved while the solvent concentration on the feed-side can be up to 90 per cent by mass. Thus, in contrast to reverse osmosis, where such differences are not observed in practice, the modelling of material transport in pervaporation must take into account the concentration dependence of the diffusion coefficients. 

Model and Preliminary Experiments on Membrane Fouling in Reverse Osmosis... 

In the literature, there are many transport theories describing both salt and water movement across a reverse osmosis membrane. Many theories require specific models but only a few deal with phenomenological equations. Here a brief summary of various theories will be presented showing the relationships between the salt rejection and the volume flux. 

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