For the balance of the enriching section applies: \begin{equation} \qquad \dot{G}^{Enr} = \dot{D} + \dot{L}^{Enr} \qquad \end{equation} [eq. 1] and \begin{equation} \qquad \dot {G}^{Enr} \cdot y^{Enr} = \dot{D} \cdot x^D + \dot{L}^{Enr} \cdot x^{Enr} \qquad\end{equation} [eq. 2]. Substitute eq. 1 into eq. 2: \begin{equation} \qquad \dot{L}^{Enr} \ \cdot \end{equation}
\begin{equation}+ \dot{D} \end{equation} \begin{equation} \cdot \ y^{Enr} \end{equation} \begin{equation} = \dot{D} \cdot x^D \ + \end{equation}
\begin{equation} \cdot \ x^{Enr} \end{equation} Divided by the flow \begin{equation} \dot{D} \end{equation} results in the following equation: \begin{equation} \qquad \frac{\dot{L}^{Enr}}{\dot{D}}\ \cdot \end{equation} \begin{equation} y^{Enr} \ + \end{equation}
$$ = $$
\begin{equation} + \frac{\dot{L}^{Enr}}{\dot{D}} \ \cdot x^{Enr} \end{equation} Considering that the reflux ratio \begin{equation} R^L \end{equation} is defined as: \begin{equation} \qquad R^L = \end{equation}
Inserted and transformed, the following equation results according to the linear function \begin{equation} y = m \cdot x + n \end{equation} for the enriching line: \begin{equation} \qquad y^{Enr} = \dfrac{R^L}{R^L + 1} \cdot x^{Enr} + \dfrac{x_D}{R^L + 1} \end{equation} |