Required membrane area

Let Q0 be the volumetric flow rate of feed, Q2 the volumetric flow rate of concentrate, C0 the solute concentration in the feed, C2 the solute concentration in the concentrate, F the volumetric flow rate of membrane permeate, and A the required membrane area. 

In addition to the symbols previously defined, Q will be taken as the volumetric flowrate of retenate at the intermediate point, C the concentration of solute in the retentate at this point, F and F2 the volumetric flowrates of membrane permeate in the first and second stages respectively, and Ai and A2 the required membrane areas in these respective stages. 

Capital-related costs The capital costs are determined mainly by the required membrane area for a certain plant capacity and feed and required product concentration. Other items such as pumps and process control equipment are considered as a fraction ofthe required membrane area. This fraction depends on the plant capacity. The same is true for the required land that also depends on the location of the plant. 

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 ... 

Here, A is the required membrane area, i is the current density, >p is the product volume flow, F is the Faraday constant, q is the current utilization and Cp is the concentration of the product. 

The required membrane area A refers actually to a unit cell area that contains a bipolar membrane, and a cation- and an anion-exchange membrane. Since in strong acids and bases the useful life of the bipolar membrane as well as the anion-exchange membrane is rather limited, the stack-related investment costs are dominating the total investment costs. 

For practical applications in the food industry, where large-volume production is conducted, it is especially important to obtain high disperse-phase flux. Abrahamse et al. [8] reported on the industrial-scale production of culinary cream. In this study they evaluated the required membrane area for different types of membranes an SPG membrane, an a-Al203 membrane and a microsieve filter. The requirements for culinary cream production were a droplet size between 1 and 3 pm and a production volume of 20 m3/h containing 30% disperse phase. They concluded that to produce large quantities of monodisperse emulsions the most suitable was a microsieve with an area requirement of around 1 m2. 

Thus, in order to achieve interaction between the reaction process and the transport process the required membrane area per mass of catalyst must be in the following range ... 

Then, water is added continuously while the filtration continues at nearly constant flux. This latter filtration stage, when water is added to maintain a constant flux, is referred to as diafiltration. Proper choice of the diafiltration starting time can minimize the required membrane area, which is often the major part of the capital cost in an ultrafiltration process. 

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. 

Set out the basis for solving the problem. The problem involves determination of the membrane area required to produce 0.010 m3/s of water and the TDS concentration of the permeate. If the permeate TDS concentration is well below 200 g/m3, blending of feed and permeate will reduce the required membrane area. 

The filtration rate must be as high as possible so that the required membrane area is minimum. Flux rate (/) through the ultrafiltration membrane is related to the applied pressure AP by Darcy s law ... 

More recently HF modules have been used in a different configuration that based on similar fundamentals tries to minimize the required membrane area, that is, emulsion pertraction technology. In this case, the organic and back-extraction phases are emulsified before the entrance to the HF module and they can be separated at the module outlet. Although there are only a few references to this alternative, its viability to the recovery of Cr(Vl) and Cu from polluted waters [44 6] as well as to the removal of hydrocarbons [47] has been shown, but much effort is needed on the modeling of this technology before additional successful applications can be developed. 

Membranes scale to a hydrogen purification application based on a simple linear relationship if hydrogen throughput is increased by two times then, the required membrane area will increase by two times (all other factors held constant). This... 

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,... 

Figure 9.15. Effect of C02 permeability on required membrane area for autothermal reforming syngas. (Reprinted with permission from Huang et al.,6 Copyright 2005 Elsevier.)...

Figure 9.17. Effect of inlet feed temperature on required membrane area for autothermal reforming syngas.

The results show that increasing the operating pressure reduces the required membrane area significantly, yet increases the power requirement only slightly. The power requirement of 355 kW at 800 psi corresponds to an energy requirement of 0.37 kWh/gal of 50-volZ ethanol product. Clearly, it would be desirable to operate the CCRO system at the maximum possible pressure. 

It is required to lower the concentration of CUSO4 in the diffusate to 0.075 kmol/m. Calculate the required membrane area and the compositions of the diffusate and dialysate. It may be assumed that no water permeation occurs. 

It is required to design a reverse osmosis unit to process 2500 mVh of seawater at 25°C containing 3.5 wt% dissolved salts, and produce purified water with 0.05 wt% dissolved salts. The pressure will be maintained at 135 atm on the residue side and 3.5 atm on the permeate side, and the temperature on both sides at 25°C. The dissolved salts may be assumed to be NaCl. With the proposed membrane, the salt permeance is 8.0 x 10 m/h and the water permeance is 0.085 kg/rn-.h.atrn. The density of the feed seawater is 1020 kg/m ( of the permeate, 997.5 kg/nv and of the residue (with an estimated salt content of 5 wt%), 1035 kg/rnc Assuming a perfect mixing model and neglecting the mass transfer resistances, determine the required membrane area and calculate the product flow rates and compositions. 

Nitrogen is to be separated from methane in a perfect-mixing membrane separator as specified below. Calculate the required membrane area, the methane permeance, and the product rates. 

The pressure is 3500 kPa on the residue side and 140 kPa on the permeate side. The composition on the permeate side is specified at 95 mol%. Assuming a perfect-mixing model, calculate the required membrane area. Use a fraction of feed permeated, 0 = 0.15. Calculate the product rates and compositions, and check if 0 needs to be modified. 

Capital costs for an electrodialysis stack include the stack housing, pumps, membranes, and electric rectifiers. The cost of an electrodialysis plant is strongly dependent on the total membrane area (denoted as A) needed to produce a given concentration change. The required membrane area, in turn, is directly proportional to the solution flow rate and specified concentration change and is inversely proportional to the applied current density and current utilization [132, 156] ... 

To calculate the required membrane area, a series of values of yJA (greater than T,A.0 and less than Yia./) are substituted into Eq. (20.6-13), giving a series of 9 values. These values then are used to integrate Eq. (20.6-14) numerically from X (T,A = iAlo) 10 r()iA TJAl/). 

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