February 9, 2012  Tagged with: , , , , , , , ,

*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.

# 2.0 Solution Method 2: The Combined Streams Modification of the McCabe-Thiele Method

## 2.1.0 Defining the Combined Feed/Side Stream

The new stream will be defined as a combined side stream with flow rate $\displaystyle M$, composition $\displaystyle x_M$, and fractional quality $\displaystyle q_M$.

### 2.1.1 The New Flow Rate

The flow rate for the combined side stream is defined as the following sum

Eq. 2-1) $\displaystyle\boxed{M=F+G}$

### 2.1.2 The New Composition

The composition for the combined side stream is defined as the following weighted average

Eq. 2-2) $\displaystyle\boxed{x_M=\frac{Fx_F}{M}+\frac{Gx_G}{M}}$

This is a classic application of the lever rule.

### 2.1.3 The New Fractional Quality

The fractional quality of the combined side stream is defined as the following weighted average

Eq. 2-3) $\displaystyle\boxed{q_M=\frac{Fq_F}{M}+\frac{Gq_G}{M}}$