So, today is my last day in my home town for a while. Tomorrow, I leave to travel to my summer internship at Dow!!! I’m rather excited for the switch from real world problems in an academic setting to those posed by private industry. A copy of the job description is after the jump. From what I can gather, I will be assisting with designing and implementing data analysis systems for experimental data using JMP, a powerful and flexible statistical analysis program. This will be really interesting, as a long time interest and hobby of mine has been artificial neural networks and intelligent control design. Stretching, flexing, and building those mental muscles will be a welcome change from my past research focus on process design for fluid phase multi-component energy and mass transfer (heat exchangers, distillation columns, liquid-liquid extraction columns, etc) in the context of use for the Unit Ops Lab. Getting a taste of work in the industry between undergrad and grad school will help me decide on which primary career path I want to take after I get my next degree: work in the general private sector or continue with academia. I’ll have about ten weeks to fully immerse myself in a new set of challenges. This will be a lot of fun!

Continue reading »

**Note: This article is part of a series on a specific research project*: Part 1, Part 2, Part 3, Part 4

**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.*

# 5.0 Conclusions

Since there were several motivations for this derivation, the conclusions that may be drawn from it overall will be broken down into two relevant categories for discussion and summary.

Continue reading »

**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 plates, each of which is associated with a feed stream (, , and ), a side draw stream (, , and ), a liquid overflow entering from above ( and ) and underflow leaving below ( and ), a vapor overflow leaving above ( and ) and underflow entering from below ( and ), and the distillate and waste streams with their associated values as described in part 1.

## 4.3.0 Method of Model Generalization

This is just a summary of many of the definitions and identities I find useful when working with the basic thermodynamics of a system or process. It is not meant to be a comprehensive list.

# Mathematical Identities

Using the reasoning behind the notation used for derivatives of thermodynamic potentials, there are some useful identities given the following prototypical system

Eq. 1)

This equation represents a generic thermodynamic potential of an arbitrary system or process as a function of two implicitly extensive thermodynamic potentials. Adopting the notation

Eq. 2)

To denote the relationship between intensive variables, extensive variables, and the size of the system allows for the trivial conversion between system size dependent and system size agnostic thermodynamic relationships. The total differential for the extensive form of the thermodynamic potential for the prototypical system is given by

Continue reading »

When I took my process thermodynamics course as an undergraduate student, I was told to use what I had initially considered to be a completely redundant notation for partial derivatives for thermodynamic potentials. The notation involved wrapping the partial derivative in a set of parentheses and noting which variables were “held constant” as a subscript.

Ex.

The derivation leading to this was woefully devoid of the mathematical basis for this apparently redundant notation. Furthermore, so was the general literature on the subject, most of which consisted of fleeting introductions to their respective application. As I played with the idea, it became clear why this notation was indeed very necessary. It was only as I was solving a separate problem on my own that such notation yielded valuable information about the nature of the potentials being described.

**Note: 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 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.*

# 3.0 Proof of the Equivalence of Methods 1 and 2

## 3.1.0 Geometric Basis for Equivalence

### 3.1.1 The Rationale of the Method for Comparison

Given that method 1 and method 2 involve plotting the exact same enriching and stripping operation lines, the enriching and stripping operation lines are by definition not parallel for any real physical system that does not involve an azeotrope**, and the combined streams q-line from method 2 also passes through the intersection of said enriching and stripping operation lines, there exists at the point of intersection of these three lines a set of three different means of determining the coordinates of the point based on the intersection of a pair of lines. Two of these lines, the enriching and stripping operation lines, are present in both methods and are defined by Eq. 1-10 and Eq. 1-45 in method 1. The third line, the combined streams q-line, is defined by Eq. 2-5 in method 2. As a matter of geometric consistency, evaluation of the ratio of x-ordinates or y-ordinates for a pair of such intersections should result in unity. In other words, when taking the ratio of a single ordinate between a pair of definitions for the intersection of the three lines, all variables should cancel exactly.

### 3.1.2 The Points to be Examined

The pair of definitions for the intersection of the three lines will be taken as the intersection of the enriching and stripping operation lines and the intersection of the enriching operation line and the combined streams q-line. The latter selection was made due to the relative simplicity of the definition of the enriching operation line over that of the stripping operation line.

## 3.2.0 Proof of Equivalence

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

# 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

I decided to swing by the Florida license website to check my application status and discovered that I’m now certified as an engineer in training (EIT). This is really exciting! Now I just need to fulfill the experience requirement and take the principles and practices of engineering exam to be certified as a professional engineer (PE). The hope is to end up working in a state that allows for submission of an awarded higher degree (such as the Ph.D. I will be pursuing later this year) in lieu of years of work experience so that I may begin the process for the PE license sooner rather than later.

# Introduction

While taking my separations and mass transfer operations course at UF, I took a particularly interesting exam where I was tasked with predicting the performance of a distillation column with two inputs. This may be getting ahead of myself, as the problem’s information was written into the proof, but the problem was as follows:

## The Test Problem

Given a distillation column separating n-pentane and n-heptane, with a feed rate of 200 kgmol/hr of a 40 mol% n-pentane liquid at bubble point, a 95 mol% distillate stream, a 5 mol% bottoms stream, a 30 mol% side stream with a flow rate out equal to that of the bottoms leaving, a reflux ratio equal to twice that of the minimum, and a 50% average tray efficiency, use the McCabe-Thiele graphical method and the provided vapor-liquid equilibrium data to determine a) the flow rate and composition of all streams, b) the minimum reflux ratio, c) the number of theoretical plates required, and d) the optimum placement of the feed stream and side stream.

So, the information given so far is

- (negative sign due to opposite orientation)

Over the next few months I will be posting about many of the independent projects and research projects I did as an undergraduate. They range from metabolic models to full process designs and cover a diverse selection of chemical engineering principles, several with significant real world applications. Starting things off will be a walk through of a proof I wrote in response to a test grade I did not agree with and how the results of the proof may be used both to simplify and enhance a graphical method for predicting distillation column behavior. This proof will be the basis for a paper I will be writing on the subject as well.

So, I submitted and defended my undergraduate honors thesis a week ago and it passed with flying colors. The database of undergraduate honors theses can be found here. In light of that great news, here is the abstract and links to the document and the presentation I used during my oral defense.

**Design of a Packed Distillation Column for a Unit Operations Laboratory**

The design for a new packed distillation column for consideration as a new experiment for the University Of Florida Department Of Chemical Engineering Unit Operations Laboratory was created to demonstrate the separation of water and isopropanol (i-Pr) and to evaluate a parallel applied multi-correlation approach to creating a high accuracy process model based on correlations with known margins of error. The final design produced features a core distillation unit, capable of batch, semi-batch, and continuous operation, and a surrounding recycle and waste management system, which is not covered in this paper. The nominal core system configuration was continuous operation with 20 mol% i-Pr, 10 mol% i-Pr, and 60 mol% i-Pr compositions and 10.4 USGPH, 6.6 USGPH, and 3.9 USGPH flow rates for the feed, bottoms, and distillate material streams, respectively. This configuration had a 6.65 inch tall HTU, requires 3.42 NTU, and a minimum required height of 1.89 ft. The final column design used a 6 ft high packing of ¼ in. Raschig Rings and had a 23.1% nominal “average tray efficiency,” which was an expectedly low value due to the presence of an azeotrope at 67 mol% i-Pr.

So I was intrigued by how clearly I could see thermal counter diffusion gradients in my whiskey, and I took a bunch of pictures of it. The shape of my rocks glass did a great job diffracting the light from my computer monitor, which incidentally emphasized the density and refractive index differences at the surfaces of the protruding fingers of cold water.