**Note: This article is part of a series on a specific research project*: Part 1

**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 , composition , and fractional quality .

### 2.1.1 The New Flow Rate

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

Eq. 2-1)

### 2.1.2 The New Composition

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

Eq. 2-2)

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)

## 2.2.0 Defining Relevant Operation Lines and q-Lines

### 2.2.1 The Enriching Operation Line

The enriching line is the same as was previously defined by Eq. 1-10 in part 1

Eq. 2-4)

### 2.2.2 The New q-Line

The q-line for stream is given by definition as

Eq. 2-5)

### 2.2.3 The Stripping Operation Line

The stripping operation line is the same as was previously defined by Eq. 1-45 in part 1

Eq. 2-6)

## 2.3.0 Solving the Initial Problem

At this point, the solution method is the trivial case of a column with a single feed and a defined enriching operation line. Rather than waste time here, though I may come back to it later, I will instead refer to the Wikipedia article, which does a decent enough job given the more complicated construction already demonstrated in part 1.

Part 3 is on the way! It is the real meat of the proof where I show that both methods are equivalent using some simple geometry and a ratio test.

**Short URL:**http://dlvr.it/1BBGd7

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[…] This article is part of a series on a specific research project: Part 1, Part 2 *Note: This article assumes you have rudimentary knowledge of how a simple distillation column […]

[…] 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 […]