A graphical-analytical method, analogous to stagewise calculations of unit operations, has been developed for the design of straight-through and tapered reverse osmosis plants, irrespective of the geometrical configuration of their modules. Given the fractional water recovery, using data specifications of commercial modules and knowing the other operating conditions, the method predicts the number of parallel lines of modules M the number of series modules M,, and the average product concentration E, by simple explicit equations. &!hen the value of the dimensionless parameter A , is chosen in the range 0.02-0.1, the method proposed here, applied to the design of commercial desalination systems, gives the same figures for M,, practically identical values for E,, and errors never exceeding 2.5 % for M, if compared to rigorous calculations. The same procedure can also be applied to other pressuredriven membrane processes such as ultrafiltration.

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A numerical method has been developed for the performance prediction of spiral wound modules with constant and tapered permeate spacers. It takes into account the pressure drop in the brine and permeate channels and makes use of a three parameter model for the mass transfer through the membrane. For a given application and operating conditions, optimum geometrical characteristics of modules can be found. Tapering the permeate spacer the specific permeation rate can be increased by 10-30%, the wider the membrane the higher the value.

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high surface area of the silica gel, the Ni and V removals were only 9% and 13%, respectively (Table IX). In the second approach, the residue in toluene solution was allowed to contact pulverized bituminous coal for 72 h at room temperature. The bituminous coal at room temperature is obviously not reactive. Ni and V demetalation were merely 2% and 1%, respectively. These observations suggest that physical adsorption makes a very small contribution to the total demetalation observed with bitu-