Permeate composition

Combining these equations and rearranging, the permeate composition may be solved exphcitly ... 

Equation (22-106) gives a permeate concentration as a function of the feed concentration at a stage cut, 0 = 0, To calculate permeate composition as a function of 0, the equation may be used iteratively if the permeate is unmixed, such as would apply in a test cell. The calculation for real devices must take into account the fact that the driving force is variable due to changes on both sides of the membrane, as partial pressure is a point function, nowhere constant. Using the same caveat, permeation rates may be calciilated component by component using Eq. (22-98) and permeance values. For any real device, both concentration and permeation require iterative calculations dependent on module geometiy. 

Conversely, when Ot, pressure ratio loses its importance, and permeate composition is ... 

Design a minimum-TAC RON that can produce at least 10.7 m /hr of permeate at a maximum allowable permeate composition of 0.0012 kmol/m (70 ppm). 

As can be seen from the plots, the minimum TAC is about 55,OOQ/yr. The opdmal permeate composition is about 0.0005 kmol/m which conesponds to a feed pressure of 48 atm. It is interesting to note that the optimum value of Cp is significantly less than the required target composition (0.0012 kmol/m ). In other words, more separation can be obtained for less cost It is also worth mentioning that in some cases, environmental regulations tnay allow the bypass of a fraction of the feed and later mix it with the over-separated permeate to attain the requited target composition. In such cases, lower costs than the ones shown in Figs. 11.5 and 11.6 can be accomplished. 

Equation (9.1) is the preferred method of describing membrane performance because it separates the two contributions to the membrane flux the membrane contribution, P /C and the driving force contribution, (pio — p,r). Normalizing membrane performance to a membrane permeability allows results obtained under different operating conditions to be compared with the effect of the operating condition removed. To calculate the membrane permeabilities using Equation (9.1), it is necessary to know the partial vapor pressure of the components on both sides of the membrane. The partial pressures on the permeate side of the membrane, p,e and pje, are easily obtained from the total permeate pressure and the permeate composition. However, the partial vapor pressures of components i and j in the feed liquid are less accessible. In the past, such data for common, simple mixtures would have to be found in published tables or calculated from an appropriate equation of state. Now, commercial computer process simulation programs calculate partial pressures automatically for even complex mixtures with reasonable reliability. This makes determination of the feed liquid partial pressures a trivial exercise. 

It should also be noted that the symbol Ki is utilized for the mol fraction ratio y, /x, in comparing the permeate composition to the reject or raffinate composition, as will be developed in Example 19.4. This is the usual symbolism as used in phase equilibria, say that of the X-value or equilibrium vaporization ratio for correlating the behavior of vapor/liquid systems—and, ideally, reflects Raoult s law. The foregoing illustrates the general problem... 

Figure 3. (a) Selectivity versus permeate pressure (PDMS) Xj = 5.010 (b) EB recovery and permeate composition based on EB content in feed stream. 

Wu et al. used Eq. (9.34) to simulate the permeate composition and separation factor for H2/N2, H2/C0 and He/O2 gas mixtures and compared them with experimental results obtained on a Membralox asymmetric membrane system. 

Performance of a specific membrane with a particular feed is typically determined in a laboratory experiment. A heated quantity of feed is run over the membrane in a batch pervaporation test, and samples of feed and permeate are taken periodically and analyzed. Permeate rate is also measured. The temperature of the circulating liquid is thermostatically controlled and the permeate pressure is kept low, perhaps 5-lOmbar. Overall flux rates for permeating and nonpermeating components are determined by mass balance and plotted together with permeate composition against the feed composition. 

If Vp is eliminated between this equation and Equation 18.40, the following expression is obtained for the permeate composition in a stage ... 

All procedures for executing the numerical simulation of a multicomponent separation are similar to those described for a binary system, except for evaluating the Initial permeate composition at the residue end of the stripper. Again, the Initial permeate composition will be that of the mixture which permeates through the endmost Increment of the membrane. The appropriate relations are ... 

Figures 7 and 8 incorporate calculated tube- and shell-side concentration profiles for the unique CO2-N2 and O2-N2 (air) data, and also Illustrate local permeate composition variation. Each figure shows that the concentration of more permeable gas steadily decreases in the direction of flow along the high-pressure (tube)...

Equations (26.16) or (26.17) can be used to show how the local permeate composition depends on the pressure ratio, the selectivity, and the feed composition. In the limit as R approaches zero, Eq. (26.16) is used because Eq. (26.17) becomes indeterminate. Then... 

At a pressure ratio of 1.0, no separation occurs in a binary system, since there is no driving force for diifusion. If a third component is added to the permeate side as a sweep gas, the partial pressures of A and B in the permeate are lowered, and separation of A and B can take place, but trial-and-error calculations are needed to determine the permeate composition. 

Effects of selectivity and pressure ratio on local permeate composition. 

Multicomponent mixtnres. To predict the performance of a membrane separator for a multicomponent mixture, the flux equations for each component are written in the same form as Eq. (26.10X and a trial-and-error procedure is used to get the amount of permeate and the local permeate compositions for each increment of area. To start the calculation, the permeate composition can be assumed the same as the feed composition, which makes the estimated driving force for each species (Pi — P2)Xi. The fluxes are summed to get the total flux and the local permeate composition, and the calculation is repeated using the corrected composition. If p2 11 only a few trials are needed for convergence, and the residue composition is then calculated by material balance. The procedure is continued for a succession of area increments until the design goal is met. As with other multicomponent... 

Example 26A An air-separation membrane has an O2/N2 selectivity of 5.0, and the O2 permeability is 0.2 scf/ft -h-atm. (a) For a counterflow separator operating with a residue containing 95 percent N2, what is the permeate composition and the fraction of the feed obtained as permeate if the feed pressure is 150 Ib /in. absolute and the permeate pressure 15 Ib /in. absolute (i) What membrane area is needed for a feed rate of 300 scfm ... 

The permeate composition differs by 3.3 percent from the approximate solution. The changes in local and cumulative permeate compositions are plotted against the stage cut, which is defined as the fraction of feed recovered as permeate, in Fig. 

The first commercial application of pervaporation was for ethanol-water separation. The dilute solution produced by fermentation is distilled to produce an overhead product with 90 to 95 percent alcohol (close to the azeotrope), and this solution is fed to the membrane unit to give nearly pure ethanol (99.9 percent). The permeate stream with about 20 to 40 percent alcohol is recyled to the distillation column. The vapor-liquid equilibrium curve and the vapor and liquid compositions for a poly(vinyl alcohol) membrane are shown in Fig. 26.16. The membrane gives a permeate that is always richer in water than the liquid, in contrast to distillation, where alcohol is the more volatile component over most of the range. The shape of the curve for permeate composition indicates strongly... 

Permeate compositions for pervaporation with a PVA membrane and an ethanol-water feed at 60 C. 

Example 26.3. Laboratory tests of a pervaporation membrane exposed to liquid with 90 weight percent ethanol and 10 percent water at 60°C showed a flux of 0,20 kg/ra -h and a permeate compostion of 7.1 percent ethanol when the downstream pressure was 15 mmHg. (a) Calculate the permeability of the membrane to ethanol and to water at the test conditions and the selectivity for water. (6) Predict the local permeate composition for 90 percent ethanol and 60°C if the downstream pressure is kept at 30 mm Hg by a water-cooled condenser. What is the condensing temperature (c) Calculate the local permeate composition for 95 percent, 99 percent, and 99.9 percent ethanol at 60°C and 30 ram Hg assuming the permeabilities are the same as for part... 

Permeate compositions for pervaporation of ethanol-water mixtures. Example 26.3... 

Laboratory tests of a membrane for H2/CH4. separation gave a permeate composition of 80 percent and a residue of 42 percent Hj when the feed had 50 percent Hj and the feed and permeate absolute pressures were 100 and 151by /in.. The permeate flow was 20 percent of the feed flow, (a) What is the membrane selectivity (h) About what permeate composition would have been obtained if a vacuum had been used on the downstream side ... 

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