Separative power and value function

One demands V7i(x,y), the value function, to be such that SU is independent of feed and product compositions. The quantity SU then indicates the net increase in the value of products over that of the feed stream, and is therefore a measure of the separator capability or separation achieved. 

There exists no general solution for Va Xij) to make SU independent of feed and product compositions. For a few special cases, solutions for Va xtj) satisfying such a requirement are available. One such case is close separation, for which both x,i and x,2 are sufficiently close to Xjyto permit a Taylor series expansion of Va xtj) around Va xif)  

For dose separations, use relation (2.2.2h) with x,i Xj2 = Xif on the right-hand side and substitute in (2.2.37d)  

To make SU independent of compositions of various streams, assume 

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