One of the things that makes solving complex problems difficult is, well, their complexity. The more information that you need to have at hand to work through the problem, the more likely you will be to lose track of some information that you really do need to solve a problem. Organizing the information that you are given in the problem statement and organizing the intermediate answers you get will help you remember what you already know. This same organizational strategy is used by many other people in their jobs...Would you go to an accountant that didn't organize information neatly for you?

Keeping track of all the information presented is essential to the solution of most engineering problems.  An overlooked, or misplaced part of a problem statement can be the difference between spending minutes or hours on your homework.  An organized approach to answering the questions, "what do I know?" and "what can I do with what I know?" also provides an accurate picture of the problem solving process.  This can be important not only when looking for the right answer to a problem, but this also goes a long way when fishing for partial credit (just in case).

A simple method for "book-keeping" or accounting on most material balances involves the use of  a table to present flowrate and flow composition values.  This method provides an organized record of given information and allows you to recognize how you can go about solving the problem. After sketching and labeling the process in a question, a table can be constructed of  all of the stream data given.  Each of the rows of the table will represent one of the streams, and each column will represent either one of the component balances or a total balance for the system.

There is a standard way of writing an equation to describe which stream you are interested in and which part of that stream you are interested in. You can see this standard way (which we will use on all example problems) here.

Please follow this example problem:

Question:
One thousand kilograms per hour of a mixture of benzene (B) and toluene(T) that contains 50% benzene by mass are separated by distillation into two fractions. The mass flow rate of benzene in the top stream is 450 kg B/h, and that  of toluene in the bottom stream is 475 kg T/h.  The operation is at steady state.  Write balances on benzene and toluene to calculate the unknown component flow rates in the output streams.

Solution:
After finding out what a distillation column is, drawing and labeling the process should be a snap.

Now, because this is a simple problem, "what are you looking for?" may seem like an obvious question. However, not all problems will seem this way.  Now is a good time to draw a table to represent the given information.  From the sketch you could see that the process has three streams.  Upon rereading of the problem you make sure that there are only two components flowing in the system.  Thus, we know to make our table 3 x 3, to accomodate total, benzene, and toluene mass flowrates for all three streams.

Here's what the table looks like:
 

Streams\mass flow rateTotalBenzeneToluene
Feed---------
Overhead---------
Bottoms---------

Let's look back at the problem statement again to see what we can fill in.


One thousand kilograms per hour of a mixture of benzene (B) and toluene(T) that contains 50% benzene by mass are seperated by distillation into two fractions. The mass flow rate of benzene in the top stream is 450 kg B/h, and that  of toluene in the bottom stream is 475 kg T/h.  The operation is at steady state.  Write balances on benzene and toluene to calculate the unknown component flow rates in the output streams.
 

Now that you have worked through one directed example problem, let's reflect on how we can use the table to solve other problems.

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2007 Arizona Board of Regents for The University of Arizona