Optimum Cut of Separating Element as Function of Total Separation Factor and Mole Fraction of Component to be Separated

Abstract

For a simplified model of separating elements where a total separation factor αβ is independent of values of cut ϑ (0≤ϑ≤1), an optimum cut ϑopt in the sense that the cut makes a separative power δU maximum, was derived in terms of αβ, and a mole fraction xF (0≤x F≤1) of the component to be separated. When values of xF is nearly equal to zero, the optimum cut ϑxF opt≃0 decreases and approaches to near 0, as the total separation factor becomes larger. On the contrary, when xF is nearly equal to 1, the optimum cut ϑxF opt≃1 was found from calculation to be 1-ϑxF opt≃0, and increases and approaches to near 1, as the total separation factor becomes larger. Moreover, in the case of xF =0.5, the optimum cut is 0.5 regardless of αβ. Generally, the optimum cut ϑopt(xF ) was solved to be in the form of a linear interpolation of the boundary values, ϑxF opt≃0 and ϑxF opt≃1.