February 29, 2012  Tagged with: , , , , , , , ,  Comments Off on Distillation of a Binary Mixture in a Distillation Column of Arbitrary Design, Part 4

*Note: This article is part of a series on a specific research project: Part 1, Part 2, Part 3
*Note: This article assumes you have rudimentary knowledge of how a simple distillation column operates. Though much of the basics of the simple model for a distillation column will be covered below, it should not be considered as a stand alone reference.

# 4.0 Generalization to Columns of Arbitrary Design

## 4.1.0 Motivation for Generalizing to an Arbitrary Design

The motivation to generalize to a system with an arbitrary topology is simply to take the next logical step and expand on what has already been accomplished. The case for two feed/side streams was itself an extension of the simple case of a single feed stream.

## 4.2.0 Physical Description for a Generalized Column Model

To generalize to an arbitrary topology, some choices as far as the idealized general topology have to be made. This leads to the least complex yet most regularly structured limit of including a single feed stream and a single side stream placed optimally at each theoretical plate. So, the column is now comprised of $\displaystyle n$ plates, each of which is associated with a feed stream ($\displaystyle F_i$, $\displaystyle x_{F_i}$, and $\displaystyle q_{F_i}$), a side draw stream ($\displaystyle S_i$, $\displaystyle x_{S_i}$, and $\displaystyle q_{S_i}$), a liquid overflow entering from above ($\displaystyle L_{i-1}$ and $\displaystyle x_{i-1}$) and underflow leaving below ($\displaystyle L_i$ and $\displaystyle x_i$), a vapor overflow leaving above ($\displaystyle V_i$ and $\displaystyle y_i$) and underflow entering from below ($\displaystyle V_{i+1}$ and $\displaystyle y_{i+1}$), and the distillate and waste streams with their associated values as described in part 1.