Permeate concentration

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. 

Permeate concentration The solute concentration in the permeate may be approximated by the ratio of the solute to water fluxes, i.e.. 

N, and solute passage Si needed to produce desired retentate product with impurity concentrations Cj and retentate product yield Mj/Mjo. Permeate product characteristics for batch operation can be determined by mass balances using a permeate volume of Vp = Vo(l 1/X + N/X), a mass of solute i in the permeate as Mj perme e = Mjo(l — and the permeate concentration as the ratio of the... 

Figure 10.16 Trade-offs for permeate concentration, membrane area and hydrogen recovery for Example 10.6.

Figure 10.18 Trade-offs for stage cut, retentate concentration, permeate concentration and membrane area for the reverse osmosis separation in example.

Here S is the solubility of the lignin in neutral water, X is the fraction of phenolic groups that have been ionized, and Ka is the dissociation constant of the phenolic groups. The pKa was determined to be approximately 11.4 from light scattering results and the solubility limit was measured to be about 0.16 mass fraction. A reasonable fit of the permeate concentration from ultrafilter experiments with a 10,000 molecular weight cutoff (MWCO) was obtained. 

Alkalinity. The FAM solution was divided into several aliquots and the pH was adjusted with H2SO4 to a pH ranging from 8.5 to 13.8, each at a concentration of about 11 g/L. Each solution was individually ultrafil-tered and a permeate sample obtained. The pH 8.5 solution was titrated with 0.1M NaOH to several alkalinities and ultrafiltered. The permeate concentrations and rejection coefficients are presented in Table I, and the permeate molecular weight distributions are shown in Figure 1. 

The numbers are the permeate concentrations divided by the bulk concentration. All the corrections to determine the degree of association are not yet known, but a decrease in this number is evidence of an increase in the degree of association. The solute is Indulin AT. The permeate data are obtained from the intercept of figures similar to Figure 4. 

Qj from Permeation Rates calculated by Dalton s Law Q2from ratio of Permeate Concentrations... 

Figure 4.1 shows the concentration gradients that form on either side of a dialysis membrane. However, dialysis differs from most membrane processes in that the volume flow across the membrane is usually small. In processes such as reverse osmosis, ultrafiltration, and gas separation, the volume flow through the membrane from the feed to the permeate side is significant. As a result the permeate concentration is typically determined by the ratio of the fluxes of the components that permeate the membrane. In these processes concentration polarization gradients form only on the feed side of the membrane, as shown in Figure 4.3. This simplifies the description of the phenomenon. The few membrane processes in which a fluid is used to sweep the permeate side of the membrane,...

The increase or decrease of the permeate concentration at the membrane surface cio, compared to the bulk solution concentration c,h, determines the extent of concentration polarization. The ratio of the two concentrations, ciolcib is called the... 

This is called the membrane-selectivity-limited region, in which the membrane performance is determined only by the membrane selectivity and is independent of the pressure ratio. There is, of course, an intermediate region between these two limiting cases, in which both the pressure ratio and the membrane selectivity affect the membrane system performance. These three regions are illustrated in Figure 8.13, in which the calculated permeate concentration ( , ) is plotted versus pressure ratio pressure ratio of 1, feed pressure equal to the permeate pressure, no separation is achieved by the membrane. As the difference between the feed and permeate pressure increases,... 

Figure 3.1 Concentrate and instantaneous permeate concentration as functions of recovery.

Cf = influent concentration of a specific component Cp = permeate concentration of a specific component... 

ATI = osmotic pressure of the solution (a function of the feed, concentrate, and permeate concentrations)... 

The ROSA output continues in Figure 10.3. This figure shows the actual and projected water quality throughout the RO system. The "Feed" column represents the raw feed water to the system. "Adjusted Feed" is the projected water quality after pH-adjust or after softening. In this case, "Stage 2 Concentrate" is the project quality of the overall concentrate from the RO. If 3 stages were used, then the "Stage 3 Concentrate" would be the project quality of the overall concentrate from the RO. "Permeate Total" is the projected overall permeate concentration from the system. 

Figure 11.4 depicts a cross-section of a membrane with a layer of calcium carbonate scale on the surface. The concentration of calcium at the membrane surface, Z, is higher than that in the bulk feed, X, since the concentration at the surface has reached saturation. The membrane passes salts based on what concentration is actually next to the membrane. In this case, the membrane is exposed to a saturated concentration, not the lower bulk solution concentration. Even though the percent passage of calcium through the membranes stays constant, the scaled membrane will yield higher permeate concentration of calcium. This is because the concentration of calcium that the membrane is exposed to at the membrane surface is higher than the bulk solution concentration of calcium, [Z],[X]. 

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