Membranes performance prediction

Table II. Mixed Matrix Membrane Performance, predicted vs observed.

The many details of this theory are omitted here. Nothing dealing with chemical groups and the forces that drive the morphology of ionomers is factored into this model, which limits its use in predicting fuel cell membrane performance. Moreover, it seems impossible to relate the quasi-percolation threshold to the real structure. Nonetheless, the view of conductance from the perspective of percolation is very appropriate. 

For a membrane specified in terms of A and D /K6, eq 14 and 15, together with eq 11, enable one to predict membrane performance (Xy 3 and N3, and hence f and (PR)) for any feed concentration X i and any chosen feed flow condition as specified in terms of k. Several theoretical and experimental methods of specifying k for different solutes under different conditions are available in the literature (6c,6d,18b,90,100). The quantities f and (PR) are related to Xy 3 and Ng through the following equations ... 

The effects of the most important operating parameters on membrane water flux and salt rejection are shown schematically in Figure 5.2 [14]. The effect of feed pressure on membrane performance is shown in Figure 5.2(a). As predicted by Equation (5.1), at a pressure equal to the osmotic pressure of the feed (350 psi), the water flux is zero thereafter, it increases linearly as the pressure is increased. The salt rejection also extrapolates to zero at a feed pressure of 350 psi as predicted by Equation (5.6), but increases very rapidly with increased pressure to reach salt rejections of more than 99% at an applied pressure of 700 psi (twice the feed solution osmotic pressure). 

El-Sayed, E., et al. (1997). Prediction of RO membrane performance for Arabian Gnlf seawater. Desalination. 113, 1, 39-50. 

Membranes need to be characterized to ascertain which may be used for a certain separation or class of separations (13). Membrane characterization is to measure structural membrane properties, such as pore size, pore size distribution, free volume, and crystallinity to membrane-separation properties. It helps gather information for predicting membrane performance for a given application. 

Very simple. Quantitative predictions of membrane performance cannot be obtained. 

With these thoughts in mind, it is time to restrict RO performance predictions using the solution-diffusion model to some specially prepared, defect-free, dense films. Such films are unrelated to any functional membrane of either the integrally-skinned or the thin film composite type. 

The advantage of the preferential sorption-capillary flow approach to reverse osmosis lies in its emphasis on the mechanism of separation at a molecular level. This knowledge is useful when it becomes necessary to predict membrane performance for unknown systems. Also, the approach is not restricted to the so-called "perfect", defect-free membranes, but encompasses the whole range of membrane pore size. Until recently, the application of a quantitative model to the case of solute preferential sorption has been missing. Attempts to change this situation have been made by Matsuura and Sourirajan (21) by using a modified finely porous model. In addition to the usual features of this model (9-12), a Lennard-Jones type of potential function is Incorporated to describe the membrane-solute interaction. This model is discussed elsewhere in this book. 

Previous work with aqueous solution systems has been successful In treating both completely Ionized salts as well as Incompletely Ionized salts (, 6). This work Incorporates both of these cases In methanol solutions and uses the Klmura-Sourlrajan analysis for the treatment of reverse osmosis data (.7). The surface excess free energy parameters (.-tAG/KT) for the Ions and Ion pairs Involved were determined by the methods established earlier (8). The predictability of membrane performance by the use of data on free energy parameters obtained In this work has been tested. 

Predictability of Membrane Performance. New membranes were placed in the cells as before and an experiment was done with a reference solute (NaCl). With the use of the transport equations (eq. (2), (3), (6), and (7)) and the correlation of k with A, eq. (14), ( AM/X6)jjg(.2 was determined. The appropriate (AAff/RT) j s were used from Table VI to determine C aC] each membrane. Calculations of (PR) and f for several salts at various concentrations and pressures were made and compared to the experimental results with the new membranes and these are summarized in Figure 4 and Tables VIII, and IX. The satisfactory agreement between predicted and experimental results obtained indicates the practical utility of the correlations and parameters generated in this work. 

In summary, the established WQP is a useful measure of membrane performance. It appears that membrane pore diameter is the best criterion to predict achievable water quality. While pore diameter is easily accessible for MF, a calculation using a molecular weight and size relationship (such as that used in this study see Chapter 4) is required for UF. For NF, where the presence of pores is moot, the application of theoretical models (as described in Chapter 3) is required. The use of marker tests is useful for a pore diameter estimation, but solute molecule structure is an issue for such small membrane polymer voids. 

A correct performance prediction of a PRO plant requires several assumptions regarding membrane permeability and pressure drop of the stream along the modules, efficiencies of the turbine, the pumps and the energy recovery device, length and geometry of the ducts and pressure drops introduced by the filtration system. Ambient conditions and salinity concentration for both freshwater and seawater have to be known as well. 

The theoretical description of the transport through a hybrid membrane with different phases composing the matrix is a very important tool because it could lead to the prediction of the membrane performance, but from a mathmatical point of view it is a complex Systran to solve. In the following, several approaches are proposed that can give a theoretical description of different effects on the transport mechanism in hybrid membranes. 

Prediction of Membrane Performance Involving Single Solute... 

It is possible to predict reverse osmosis performance data under different operating conditions. The method can be extended to the prediction for the separation of different solutes, either organic or inorganic, if the separation data of sodium chloride solute arc known for a membrane. Furthermore, the separation of individual ions involved in the mixture of electrolyte solutes can also be predicted on the basis of the separation data of sodium chloride. The method was established by Sourirajan and co-workers for asymmetric cellulose acetate and aromatic polyamide membranes, but should be applicable for other types of membranes. The prediction is made on the basis of a set of equations derived by Kimura and Sourirajan [51],[103]-[109. ... 

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