Laminar Case

Calculation of pumping work required to control concentration polarization is more complex in the laminar (entrance region) case than in the turbulent case, because we now must specify channel length y and channel dimensions (2d) in addition to the variables that are of importance in the turbulent case.

A s shown in Section VIII, A, concentration polarization φί is deter­

mined (in the entrance region with a well-rejecting membrane) by the parameter ζ [Eq. (8.46)], which in turn is a function of v0 , d, y , and

ύ (in addition to ^2) . If two of these are specified (e.g., y and d)> then the work Wl per unit volume of product required to maintain a given concentration polarization may be obtained from the relation

Wl = 3ηΰ²Μ (8.68)

which is obtained from the relations

Wx = AP'udlv0y (8.69)

and

ΔΡ' = 3uvy/d². (8.70)

To illustrate, one may obtain for a selected allowable concentration polarization a corresponding value of ζ from Fig. 8.19. From ζ, the transmission rate of the membrane in question, the salt-diffusion coefficient, and the channel dimensions, the necessary circulation velocity ΰ is determined, and the pumping work is calculated from Eq. (8.68). If cgs units (poise, cm, sec) are used in Eq. (8.68), Wx will be in dynes/cm²; multiplication by 9.87 X 10~⁷ converts to atmospheres.

IX. Equipment

A. EXPERIMENTAL ASSEMBLIES

As the discussion in Section III indicates, the hyperfiltration experi­

ment in principle is simple. The systems constructed by different groups at the present time usually resemble one another. The necessary com­

ponents are a source of pressure and a support for the membrane. In general, a method of circulating or stirring the feed solution is needed to decrease the effect of salt build-up at the membrane interface as product water is withdrawn through the membrane.

In early studies gas pressurization was frequently used (Re-59a, Mc-59, Mo-62a); dissolved gases were believed not to interfere (Re-59a).

Agitation was achieved by rocking (Mo-62b, Tr-52) and by thermal convection (Re-59a, Mc-59). In the latter, feed flows from the reservoir to a point on the circumference of the membrane and is withdrawn from the opposite edge to the reservoir through a heated tube.

The trend has been toward pressurization (Re-60b) and circulation by pumps. In some devices large volumes have been pressurized, and pumps operating at pressure have circulated the brine over the membrane (Lo-63a, Lo-63f, Sk-63). In others (Ba-65, So-64b, Mi-64c, Lo-64d), the reservoir is at atmospheric pressure, and the feed is pumped to

experimental pressure, passed by the membrane, and bled back through a valve to reservoir pressure. Usually some sort of damper (e.g., com-pressed gas or springs separated from the solution by a piston or a back-pressure regulator) is incorporated to minimize pressure fluctua-tions during back strokes of the pump. W h e n constancy of pressure is of importance, however (i.e., in the study of the effect of pressure on rejection), pressurization of the reservoir is advantageous.

The required circulation velocities will, of course, depend on the details of the geometry of the equipment and on the transmission rates of the membrane (for details and methods of estimating necessary flows, see Section VIII). With some small cells at moderate transmission rates, flows past the membrane of ca. 2 cm/sec have appeared to be sufficient to minimize concentration polarization (Lo-63a, Ba-65).

Porous plates are usually used to support the membrane and to pass on the permeating solution. Stainless steel, Monel, titanium, and ceramic frits have been used, sometimes with a cushion of filter paper (e.g., Whatman 4 1 H ) or a millipore HA membrane (Lo-63g); a porous plastic sheet appears also satisfactory for this purpose (Sk-63). Cells exposing to the feed membranes of from less than 1 inch (Ba-65) to 15 inches (Lo-61) (Lo-62a) diameter have been employed. Small apparatus has obvious advantages in experimental high-pressure work, although of course industrial applications will require large assemblies;

with larger membrane areas from which to collect samples, experiments can sometimes be carried out more quickly. Photographs of a number of assemblies may be found in the 1963 O S W Annual Report (OSW-63a).

Usually, the membrane is placed at the bottom of the high-pressure cell. It would seem more logical (Section VIII) for it to be at the top, or vertical or properly tilted, to take advantage of gravity mixing from density gradients when desalination occurs. In one of our assemblies, the membrane orientation can be changed at pressure during an experiment. W e have found significant differences in rejection at slow flow rates of feed with the membrane in the up or down position (Ba-65).

Placing the membrane in the up position (or vertical) should also help alleviate problems arising from settling of solid matter in the feed onto the membrane.

Recently a method was developed (Ra-65a) which permits testing of transmission and rejection properties of membranes in an unstirred system. The equipment consists of a glass "Tuberculin" syringe to which a membrane is attached; the plunger of the syringe is used to create the necessary pressure. The effluent salt concentration is monitored with a microconductance cell and the concentration-time curves com-pared with those calculated theoretically taking concentration

polariza-tion into account (see Secpolariza-tion III). Although long-term testing with this technique is not easily done, it has the advantage of permitting the rapid establishment of necessary parameters with very small samples of membranes.

Corrosion can be a serious problem in hyperfiltration experiments, not only because of its effect on the durability of equipment, but also because of possible effects of corrosion products on the performance of membranes. W e have found, for example (Ba-65), that properties of ion-exchange membranes are sometimes severely modified by the presence of polyvalent counterions, even at low concentrations; con-sequently titanium, which is highly corrosion-resistant in most media, has been our material of choice for equipment in contact with salt water.

Cellulose acetate membranes do not seem as sensitive as ion-exchange membranes to such impurities, but one should be on guard in any given study for such interferences. Some other materials which have been used or which are reported to be useful in salt water (Ge-59) are Monel, nickel, Hastelloy C, some of the stainless steels, and zirconium; aluminum (with or without anodization) (OSW-63a) is also being considered.

This discussion of experimental equipment has been limited to those experiments which strictly deal with "hyperfiltration." However, many other measurements are, of course, feasible, which help to characterize membranes and permit deductions regarding their performance. Among these are: measurement of diffusion and distribution coefficients, of water content, of emf of concentration cells, and conductance. All these require specialized approaches whose discussion is beyond the scope of this review article (for discussion of some of these with particular reference to ion-exchange materials, see Chapter 6).

B. PILOT PLANTS AND PLANT DESIGNS

Up to the present no industrial-scale hyperfiltration plants have been constructed, and even the pilot plants are relatively small. The U C L A group has constructed and operated bench-scale testing units (up to 500 gpd) (Lo-62a, Lo-62e, Lo-63e), and, based on their experience, have with the Fluor Corp., carried out a preliminary economic study (Mc-63) of a 25,000-gpd and a 10⁶-gpd plant for brackish water. Under O S W sponsorship, a 1000-gpd "pilot" plant has been assembled by Aerojet (AJC-64). Economic aspects will be discussed in Section X ; here we shall only touch on a few trends in the development of equipment for large-scale operation.

Many of the designs for plant and pilot-plant equipment are based on what might be called a "filter-press" scheme. In it, solution flows in

channels across membranes located on both sides of a flat support.

Solution is withdrawn through the edge of the support, which may be porous. In this design there is only a compressive force on the support, which need not carry the applied pressure; the latter is retained by the pressure chamber. The plates are close to each other and flow is almost certainly laminar. The fragile cellulose acetate membranes are separated from the support by various materials which tend to maintain the integrity of the membranes. The actual designs differ primarily in the types of support selected and the material chosen for the cushion.

The U C L A group in earlier developments, and the Aerojet present design, use porous metal backing with membranes on either side, with appropriate " 0 " - r i n g seals to separate feed and product streams. The U C L A group has more recently used a ^-inch metal plate, separated from the membranes on each side by layers of hardened filter paper and nylon parchment fabric; the product water flows laterally through the fabric to small collection slits in the plate. Aerojet is considering a similar arrangement with fibrous glass cloth for the collecting layer.

Plastic supports are also under investigation (Lo-63e).

In the U C L A design for both the 25,000-gpd and 10⁶-gpd plants (Mc-63), cells containing many membranes of 36-inch diameter, over which the feed flows in series, are utilized. In the smaller installation, 50 membranes are contained in each of 4 cells, while for the larger plant, there are 150 membranes in each of 54 cells. Whatman 4 1 Η filter paper is used as membrane backing between the nylon parchment fabric and the membranes. Millipore would perform better, but not enough to compensate for differences in cost. The output of each membrane is to be monitored separately and output through any defective membrane can be shut off. The flow rate of feed by the membrane is 12 ft/min (0.2 ft/sec). The channel between plates is 1/4 inch wide, which after insertion of the membranes and backing materials is probably not more than 5 mm wide; we estimate the Reynolds' number to be NKe = ca. 600.

This clearly makes the flow pattern laminar and the corresponding considerations of Section VIII, A should be applicable. Although the flow pattern in this system is complicated, we shall assume a channel length χ = 70 cm; for this design ζ then becomes ca. 3.6 and φ1 should be ca. 7 at the exit end of the membrane at 20 gal f t^{- 2} d a y^{- 1}.

One volume of product is projected for two volumes of feed (2500 ppm salt). The cellulose acetate membranes specified are of a variety especially suitable for brackish water, in which some rejection is sacrified in the interest of higher permeation rates; they anticipate a production rate of 20 gal f t^{- 2} d a y^{- 1} at 600-psi pressure. Centrifugal pumps are used to raise the feed to pressure, and in the larger plant recovery of energy from the

reject brine is planned. It is estimated that one man per shift, plus another for extra maintenance on the day shift, could operate and main-tain the larger plant.

The Aerojet 1000-gpd pilot plant (AJC-64) aims at study of desalina-tion of both brackish and sea waters. The cell has three modules of 15 plates each, of porous sintered bronze (20 % free volume). Each plate supports two 16-inch-diameter membranes, of which 1 4 f inches are exposed to feed; the total membrane area per cell is thus about 100 ft². Feed enters at the top of the cell and can flow back and forth between the plates at a flow rate of 1 ft/sec. Channel width is not given, but appears to be no more than 2.5 mm, and the Reynolds number thus seems less than 1600. This design thus probably also operates with laminar flow and may have polarization troubles at reasonable transmission rates.⁵ (We estimate cjcf = 1.6 at the proposed 10 gal f t^{- 2} d a y^{- 1}. ) A triplex piston type of pump raises the feed to pressure (1500 psi). Some work has been carried out toward development of membranes in tubular configuration.

A different design has been proposed by Havens (An-64). In this method water is "pumped under pressure through porous glass-fiber tubes lined with a membrane" of the L.-S. cellulose acetate type. A pilot plant delivering ca. 300 gal/day was constructed. For sea-water desalination, two stages are required. The tubes are 1/2-inch internal diameter, pressure is 800 psi (1st stage) and 500 psi (2nd stage). Yields are 4 gpd per 8-ft tube in the 1st stage and 7 gpd per 8-ft tube in the 2nd stage.

Since these tubes have an internal area of 1.05 ft²/8 ft length, produc-tion rates are 4 to 7 gal d a y^{- 1} f t^{- 2}, depending on the stage. The combined output is 2.6 gpd/ft² installed surface. Since no costs of installation are given in this article, it is difficult to reconcile these low output figures per unit area with the final statement made there (An-64): "The ( U C L A ) process could not be an economic proposition until the lined glass fibre tube was developed."

Very recently (An-65) a pilot plant, designed to eventually reach 7000 gal/day, has been put into operation on brackish feed at Coalinga, California, by the U C L A group. Metal tubular membrane supports and membranes cast from cellulose acetate-acetone-formamide (Ma-65) solutions are used. The experience with this system should be of great interest.

5 Footnote added in proof. A report (A J C - 6 4 a ) concerning operation of the pilot plant has recently come to our attention. It appears that considerable concentration polarization was encountered.

A wrapped membrane configuration has recently been developed at General Dynamics (Br-65). It consists of a rolled sandwich of 2 mem­

branes glued to the two sides of a flexible porous sheet. The product is drawn away through the porous support while feed passes between the sheets, which are held apart by a plastic screen. This configuration is now being evaluated at the 1000 gpd level.

Tubes (or hollow fibers) of membrane material of exceedingly small cross section (50 μ and 5 to 10 μ wall thickness) have been proposed by Mahon (Ma-63a). These tubes are small enough to withstand the necessary pressures without any backing materials. W e do not know how far this interesting process has been developed since its first description.

A specialized application of hyperfiltration, recovery of water from urine in space ships, has been described by Meier and Everett (Me-63c).

Immersion of a hyperfiltration cell to a depth at which the pressure exceeds the osmotic pressure of sea water has been suggested as a means of obtaining potable water for marine craft (Ca-62, Ch-64).