Membrane area calculations

The total membrane area calculates to a value pronouncedly less than for the accumulations as obtained in Appendix 4 for an assigned number of stages and, at that, for a much sharper separation. 

The energy needed to transport ions across the membrane is obtained by the cell in chemical reactions occurring in it that is, the oxidation of organic substances with oxygen (for more details, see Section 30.2). Every second about 10 to 10 ions are transported across 1 m of membrane area. This process requires 20 to 30% of all energy generated by the cell. It has been calculated that the total power of the ionic pumps in the cells of the brain is about 1 watt. 

Assume that 1 kmol of gas occupies 22.4 m3 at standard temperature and pressure (STP). For stage-cut fractions from 0.1 to 0.9, calculate the purity of hydrogen in the permeate, the membrane area and the fractional hydrogen recovery for a single-stage membrane. 

Current is transferred to these meshes using distributors called spiders . The spiders have legs which distribute current to the mesh. The location of the spiders and the distribution of the anode and cathode spider legs has been developed via extensive calculation and trial to minimise the resistance of the spider/membrane/ mesh combination and to ensure that the resistance to current flow is equal across the whole membrane area, thus ensuring that there are no localised non-uniform current paths. The spiders are shown in Fig. 18.5 and the distribution pattern is shown in Fig. 18.6. 

We have used voltammetric measurements in the absence of the electroactive species to quantitatively evaluate this heat-sealing procedure. The magnitude of the double layer charging current can be obtained from these voltammograms [25,68-70], which allows for a determination of the fractional electrode area (Table 1). This experimental fractional electrode area can then be compared to the fractional pore area calculated from the known pore diameter and density of the membrane (Table 1). In order to use this method, the double layer capacitance of the metal must be known. The double layer capacitance of Au was determined from measurements of charging currents at Au macro-disk electrodes of known area (Fig. 6, curve A). A value of 21 pF cm was obtained. 

MD simulations of model membrane systems have provided a unique view of lipid interactions at a molecular level of resolution [21], Due to the inherent fluidity and heterogeneity in lipid membranes, computer simulation is an attractive tool. MD simulations allow us to obtain structural, dynamic, and energetic information about model lipid membranes. Comparing calculated structural properties from our simulations to experimental values, such as areas and volumes per lipid, and electron density profiles, allows validation of our models. With molecular resolution, we are able to probe lipid-lipid interactions at a level difficult to achieve experimentally. 

The analysis of transfer mechanisms of drugs across the intestinal epithelial layer has passed a long way since the theory of lipid pore membrane [118] in which the total pore area of the intestinal membranes was calculated (and found to be low compared with the total surface of the mucosal aspect of the gut), through the Fickian diffusion calculations of the transport of unionized moieties of drug molecules (the Henderson-Hasselbach equation), which led to the conclusion that acidic drugs are absorbed in the stomach [119,120]. 

In the case of the counter-flow/sweep membrane module illustrated in Figure 4.18(c) a portion of the dried residue gas stream is expanded across a valve and used as the permeate-side sweep gas. The separation obtained depends on how much gas is used as a sweep. In the calculation illustrated, 5 % of the residue gas is used as a sweep even so the result is dramatic. The concentration of water vapor in the permeate gas is 13 000 ppm, almost the same as the perfect counter-flow module shown in Figure 4.18(b), but the membrane area required to perform the separation is one-third of the counter-flow case. Mixing separated residue gas with the permeate gas improves the separation The cause of this paradoxical result is illustrated in Figure 4.19 and discussed in a number of papers by Cussler et al. [16]. 

Figure 4.19 The effect of a small permeate-side, counter-flow sweep on the water vapor concentration on the permeate side of a membrane. In this example calculation, the sweep flow reduces the membrane area by two-thirds...

The required membrane area for a given capacity plant can be calculated from the current density in a stack that again depends on feed and product solution concentration. It can be calculated for a solution containing a single monovalent salt such as NaCl from the total current passing through the stack which is given by ... 

Ultrafiltration experiments were carried using the same setup, except the flat-sheet membrane module had a filtration area 38 mm long, 29 mm wide, and 1.6 mm high, with a surface area of 11 cm2. The permeate side had 11 grooved channels that supported the membrane, leaving an effective filtration area of 6.4 cm2. However, the total membrane area including the supports was used in calculating the fluxes. The feed consisted of cellulase enzyme solution (5.0 g/L of supplied cellulase, unless noted otherwise). 

The use of the charts is straight forward. For each recovery, there are two corresponding charts. One determines the optimum time cycle and the other determines the optimum diafiltration volume. For the case where the initial volume, membrane flux, desired recovery, and the time cycle are specified or known, the required membrane area can be determined from the corresponding Time Cycle Chart. The procedure is to first calculate P and Q based on an assumed area. Then, the time cycle is found from the chart. Finally, the area is adjusted until the time cycle read from the chart matches the specified time cycle. Once the area is determined, the optimum relative diafiltration volume can be found from the corresponding relative diafiltration Volume Chart. 

Permeate flux is defined as the permeation rate per unit of membrane area. Thus, maximizing the flux will reduce system size and cost. Permeate flux can be calculated as follows (15) ... 

A difficulty with whatever the juxtaposition or arrangement is the mathematical means for representation and calculation. We will therefore be predominantly concerned with the necessary derivations and their simplifications. Of prime importance is the separation that can be achieved. Also of interest is the necessary sizing of the membrane area. 

Various and random membrane information has been tabulated as a matter of course in previous sections and tables. For the calcula-tional purposes here, a representative set of comparative values follows for a membrane of low selectivity between the key components components i and j, with operating pressure levels in the ratio of 3 to 2. The units are unstated inasmuch as the entities calculated will absorb the conversion factors— which are not necessary for calculating the degree of separation and are therefore immaterial except in determining membrane area. The procedure follows that provided in Example 3.1 of Floffman (2003). 

The costs of the filtration processes include module and energy cost. The module cost depends on the membrane area (inversely related to flux), so the module cost per unit filtrate can be calculated by... 

Pilot plant smdied have also been performed by Larsen et al. [37], who obtained stable operation and more than 95% SO2 removal from flue gas streams with a gas-side pressure drop of less than 1000 Pa. The importance of the membrane structure on the SO2 removal has been studied by Iversen et al. [6], who calculated the influence of the membrane resistance on the estimated membrane area required for 95% SO2 removal from a coal-fired power plant. Authors performed experiments on different hydrophobic membranes with sodium sulfite as absorbent to measure the SO2 flux and the overall mass-transfer coefficient. The gas mixture contained 1000 ppm of SO2 in N2. For the same thickness, porosity, and pore size, membranes with a structure similar to random spheres (typical of stretched membranes) showed a better performance than those with a closely packed spheres stmcture. 

C over 24 h. Initial pH was adjusted with HCl (5 N) and NaOH (5 N) solution. Batch ultrafiltration was performed in a stirred cell (Amicon model 52, feed volume 50 ml, effective membrane area 12.5 cm ), usually at 3 bars, with membrane YM5 (Amicon, mw cut off 5,000 Dalton). The first 10 ml of permeate were discarded. The next two consecutive 10 ml were analysed to determine the mercury concentration with an atomic absorption spectrophotometer. The rejection coefficient (R) defined as below, was calculated from the feed and permeate concentration of mercury. 

For a binary mixture of components A and B, the flux can be expressed for the entire permeate (J, total flux) or each component and u, the flux of component A and B, respectively), having dimensions of mass/(area x time). The flux can be calculated provided the mass of the permeating component, the membrane area and the time of measurement are known. To this end, the following expression can be used ... 

The membrane areas required for the exit feed CO concentration of <10ppm in the H2 product were calculated with five different C02 permeabilities ranging from 1000 to 8000 Barrer, while the other parameters for the reference case were kept constant. As demonstrated in Figure 9.15, the required membrane area or hollow-fiber number dropped rapidly as permeability increased from 1000 to 4000 Barrer. Beyond that,... 

In order to obtain a sufficiently large membrane area on an industrial scale, hollow fibre ultrafiltration modules are applied (similar types to those used for protein purification). Since the concentration of NAD(H) does not change in the steady state and there is no NAD(H) in the entrance or exit flow, it becomes clear that the actual concentration of pyruvate in the reactor is equal to the concentration in the feed. Since there is a non-zero concentration of pyruvate in the reactor (and in the exit flow), some pyruvate has to be added to the reactor continuously in order to keep the reaction going. The rate equations of both reactions are required to calculate the precise rate of pyruvate addition. 

Membrane area not calculated because no estimation of the permeation for idecil membranes has been made. 

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