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Separation Process Engineering: Includes Mass Transfer Analysis, Third Edition by Phillip C. Wankat

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17.4.4 RO with Concentrated Solutions

A more complicated situation occurs when xr, and hence xw, are concentrated and osmotic pressure depends upon xp in a nonlinear fashion. An Advanced RT equation can be developed if the osmotic pressure of permeate is linear in xp, πp = a′xp. Since permeate is quite dilute, this equation is often valid even if π is not a linear function of x at xin and xout. Start with Eq. (17-16a) and substitute in xw = Mxr and πp(xp) = axp. Solve resulting equation and Eq. (17-18) for Image. Then set equal and rearrange.

Image

(17-38) ...

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