Membranes bubble-point calculation

Note When V/F = 0, essentially only a drop of the feed has permeated through the membrane. The determination corresponds to a bubble-point calculation as practiced in vapor-liquid phase separations (where V —> 0). When V/F = 1, essentially all the feed material has permeated through the membrane, leaving a drop of reject as calculated. The calculation corresponds to that of a... 

Fig. 6 depicts the type of relationship that might be found between downstream gas flow rate and upstream gas pressure in a typical in-process automated bubble point test. The transition pressure is not clearly defined. Actual bubble points (transition pressures) obtained with this type of equipment differ from theoretical bubble points calculated for the same membrane from direct measurement of pore size, and from laboratory-type bubble point testing. 

The single-stage membrane unit becomes equivalent to a so-called flash vaporization. The flash vaporization calculation itself is straightforward, with the vapor and liquid phases assumed at equilibrium, and is presented in a number of references." " The limits correspond to the dew-point and bubble-point calculations for vapor-liquid equilibrium, which are special or limiting cases for the flash vaporization calculation. It is the object, therefore, to adapt the membrane calculation to the techniques for the flash vaporization calculation and thereby take advantage of the relative simplicity of the latter. 

The membrane pore size can be calculated from the measured bubble point Pj, by using the dimensionally consistent Equation 10.9. This is based on a simphstic model (Figure 10.6) that equates the air pressure in the cyhndrical pore to the cosine vector of the surface tension force along the pore surface [6] ... 

The bubble point test is a popular single-point physical integrity test for disc filter membranes based on Eq. (21). A fdter medium is wetted with a liquid, and test gas pressure is slowly raised until a steady stream of bubbles appears from a tube or hose attached to the downstream side of the filter and immersed in water (Fig. 9). The pressure at which the bubbles first appear is recorded as the bubble point and is related to the largest pores in the fdter medium. A pore size can be calculated from Eq. (21) however, it must be realized that the bubble point test does not measure the actual pore size, but only allows correla-... 

The mean pore size and pore size distribution can be evaluated by performing this measurement by a stepwise increase of the pressure. In this case the gas flow across the wet defect-free membrane is recorded (Fig. 4.18) as a function of the applied pressure difference across the sample ("wet curve"). The point of first flow is identified as the "bubble point". This continues until the smallest detectable pore is reached. Then the flow rate response corresponds to the situation in a completely dry sample. The measurement of gas flow through the same membrane in a dry state gives a linear function of the applied pressure difference ("dry curve"). The pressure at which the "half-dry" curve intersects with the "wet" curve can be used to calculate an average pore diameter. Pore number distributions can also be derived from flow distribution curves. 

First, the membrane is completely wetted with liquid and then a gas pressure is applied to one side. As the gas pressure is gradually raised (see Figure 2.12), there will be no gas flow through the pores until capillary forces are overcome releasing liquid from the pore. Obviously, from equation (1), the first gas bubble will emerge from the largest pore-where the capillary forces are lowest. The pressure at which this occurs is called the "bubble-point" pressure. The maximum pore size may then be calculated.7... 

Wet the membrane and raise the air pressure until the first air-bubble appears this is the "bubble point" and may be used to calculate the maximum pore size. 

To verify the theoretical equation for bubble point, a series of 0.2 H capillary pore membranes were made with extremely low pore densities. The lowest densities virtually eliminated all doublets and triplets and yielded bubble points equal to the theoretical value. Though the low density rendered the membrane useless for applications requiring a reasonable flow rate, it nevertheless demonstrated that a membrane can be made where a direct measurement of the pores (with S.E.M.) agreed with that calculated from the bubble-point. 

Since the effective pore size is estimated from the molecular diameter of globular proteins which are retained 90% by the membrane, it is obvious that larger pores do exist. The measurement of a membrane s bubble point (see the section on the bubble point test in Chapter 2) permits calculation of the maximum pore size in the skin of the membrane. 

Figure 3.22 shows the bubble point measured with isopropanol (IPA) on polyvinylidene difluoride UF membranes with MWCO s between 10,000 and 1,000,000. A 300,000 MWCO membrane (F300) should have an estimated effective pore size of 0.02 ju yet the bubble point indicates a maximum pore size in the skin over 0.4 ju. This is one reason why UF membranes can be less retentive for bacteria than MF membranes. However, Figure 3.22 also indicates that a 10,000 MWCO membrane can have a (I.P.A.) bubble point of 100 psi. Equation 3 of Chapter 2 may be used to calculate a maximum pore diameter of 0.12 jtt which should be retentive for all bacteria. Indeed, small laboratory discs of these membranes can be subjected to high challenge levels of bacteria with absolute retention (zero passage). However, industrial scale UF modules often employ 10 to 100 square feet of membrane area it is difficult to manufacture a pinhole-free module with this much area. Broken fibers, bubbles in glue-line seals, and other defects provide leak paths for bacteria. 

The surface tension forces that must be overcome to allow displacement of a liquid from a membrane are mainly a function of the size of the perimeter (the ctrctimferencc)) of the pore. The hydrostatic forces that promote displacement of the liquid are mainly a function of the area of the pore. At the bubble point, when these two sets of forces are in equilibrium, the smallest diameter d of an elliptical pore can be calculated from the equation... 

The feed composition, membrane permeability, and operating pressure levels are assigned as before, and a trial-and-error bubble-point type calculation performed for V/F = 0. This results in a value for V", which is not directly required for determining the degree of separation, other than being incorporated into the K -values but would be necessary in further determining membrane areal requirements. Thus, the bubble-point type calculation simultaneously establishes the values for K and K-, which are used in the separation calculations. 

Figure 4.4 shows calculated capillary pressures for the typical pore size of each layer in typical ceramic membranes used for three-phase reactions. Vospernik et al. (2003b) have measured the displaced water by the application of an increasing transmembrane pressure. The importance was pointed out of a proper transmembrane pressure application when gas is fed from the support side. It must be underlined that the presence of defects in the top and intermediate layers will set a critical pressure that, if overcome, will result in the formation of gas bubbles. Therefore, the quality of the top-layer membrane is an important issue in the development of suitable catalytic membranes. 

---