*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
2.1.2 The New Composition
The composition for the combined side stream is defined as the following weighted average
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
2.2.0 Defining Relevant Operation Lines and q-Lines
2.2.1 The Enriching Operation Line
2.2.2 The New q-Line
The q-line for stream is given by definition as
2.2.3 The Stripping Operation Line
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.