If the transmembrane partial pressure driving forces for H2 and CO are 240 psi and 80 psi, respectively, calculate the transmembrane fluxes in kmol/(m2-s). Compare the hydrogen flux with the hydrogen flux in the commercial application discussed at the beginning of this chapter. In the application discussed at the beginning of this chapter, the flux of H2 is for the polymer membrane. The asymmetric and thin-film, composite, polymer membrane materials described in the previous section are available in one or more of the three forms shown in Figure 14.4a, b, and c.
However, macroporous membranes are widely used to support thin microporous and dense membranes when significant pressure differences across the membrane are required to achieve a reasonable throughput. If the pore diameter is large compared to the molecular diameter, and a pressure difference exists across the membrane, bulk or convective flow occurs through the pores, as shown in Figure 14.6a. Such a flow is generally undesirable because it is not perm-selective and therefore no separation between components of the feed takes place.
It is desirable to pass water at 70°F through a supported polypropylene membrane, with a coating thickness of 0.003 cm and 35% porosity, at a rate of 200 m3/m2-day. Pores can be considered as flat cylinders of uniform diameter equal to 0.2 microns. If the pressure on the downstream side of the membrane is 150 kPa, estimate the pressure required on the upstream side of the membrane.
Liquid Diffusion in Pores
Gas Diffusion
Dialysis and Electrodialysis
In 1861, chemist Thomas Graham (how Graham's law developed) used the process of dialysis, a process used to separate colloidal particles from dissolved ions or molecules. A semi-permeable membrane is a membrane that allows some molecules to pass through it while others do not (Figure 1). Dialysis is the separation of colloids from dissolved ions or molecules of small dimensions, or crystalloid, in a solution.
A colloid is any substance made of particles that are extremely small: larger than atoms, but generally have a size of 10-7 cm, ranging up to 10-3 cm. A crystalloid is a substance that has some or all of the properties of a crystal or a substance that forms a true solution and diffuses through a membrane by dialysis. In a dialysis membrane separation process, shown in Figure 14.12, the feed is a liquid, at pressure PI, containing solvent, type A solutes and type B solutes, and/or insoluble, but dispersed, colloidal material.
A rinsing liquid or washing liquid of the same solvent is fed to the other side of the membrane at pressure P2. The membrane is thin with micropores of such a size that solutes of type A can pass through it by a concentration driving force. Solutes of type B are larger in molecular size than those of type A and cross the membrane with difficulty or not at all.
A countercurrent, plate-and-frame dialyzer is to be sized to process 0.78 m3/h of an aqueous solution of 300 kg/m3 HSO4 and minor amounts of copper and nickel sulfates. From batch laboratory experiments with an acid-fast vinyl membrane, in the absence of external mass transfer resistances, a permeance of 0.025 cm/min for the acid and a water transport number of +1.5 are measured. For these flow rates, experience with plate-and-frame dialyzers indicates that the flow will be laminar and the combined external fluid-film mass transfer coefficients will be 0.020 cm/min.
In the final sections, there is an anode and a cathode, between which a potential difference is used to propel ions through electrolyte solutions and membranes. Two types of membranes are used: one that is preferentially permeable to the transport of anions (anion-selective) and one that is preferentially permeable to cations (cation-selective). The solution to be desalinated is stored in one compartment and during current flow, anions move through the anion exchange membrane in the direction of the anode to the adjacent compartment, while cations move in the opposite direction to the adjacent compartment on the other side.
Reverse Osmosis
If mass transfer resistances are negligible on each side of the membrane, calculate the flux of water in ga/ft2-day and the flux of salt in g/ft2-day.
Gas Permeation
The first (b), Knudsen diffusion, applies at very low pressures, where lighter molecules can move across the membrane faster than heavier ones, in a material with relatively large pores.[4] The second (c), molecular sieving, is a case where the pores of the membrane are too small to admit a single component, a process that is not usually practical in gas applications since the molecules are too small to form adequate pores. In these cases, the motion of the molecules is best described by pressure-driven convective flow through the capillaries, which is quantified by Darcy's law. However, a more general model in gas applications is solution diffusion (d), where particles first dissolve on the membrane and then diffuse through it at different rates.
This model is used when the pores in the polymer membrane appear and disappear faster than the movement of the particles. With 25% of the membrane area inoperative (part b3), the hydrogen recovery decreases by approx. 15%, but the permeability is approx. 1% higher. Overall, percentage changes in hydrogen recovery and purity are smaller than the percentage changes in feed flow rate, feed composition, and membrane area, which tends to confirm the insensitivity of gas permeation separators to changes in operating conditions.
Pervaporation
A pervaporation module can operate with heat transfer or adiabatically with the enthalpy of vaporization provided by sensible enthalpy of the feed. For an enthalpy-datum temperature of To, give an enthalpy balance, in terms of mass flow rates, m, liquid sensible heat, Cp, and heat of vaporization, A HVaP. Hydrophobic membranes are often polydimethylsiloxane based where the actual separation mechanism is based on the solution-diffusion model described above.
To overcome the intrinsic shortcomings of polymer membrane systems, ceramic membranes have been developed in the last decade. Therefore, as the concentration of ethanol in the feed liquid increases, the sorption of the feed liquid by the membrane decreases, resulting in a decrease in polymer swelling. Previous results show that as swelling decreases, ethanol permeability decreases faster than water permeability, thereby increasing water selectivity.
Ultrafiltration
Batch ultrafiltration
It can then be shown that the average flux, Javg, for the batch process is approximately. The yield, Yi, of solute, i, defined as the amount of solute remaining in the retentate, is obtained from (14-88). Continuous ultrafiltration rarely does this; instead, it operates in a multipass mode, as shown in Figure 14.28, called single-stage feed and-bleed.
In fact, the feed to the membrane is the sum of fresh feed and recycle retentate. The bleed is that part of the rent that is not recycled, but is withdrawn as product rent.
Diafiltration
Ultrafiltration
