Material Balance

Upon studying this section, you should be familiar with the following:

A Material Balance Intro


Chemical processes are often very elaborate, with many types of equipment used to obtain a desired product. Chemical engineers are interested in many of the physical parameters associated with each process, such as the flow rate of material that enters and leaves a piece of equipment, as well as several other parameters including the temperature of the material, and the pressure exerted by material. Learning to keep track of the materials and their physical properties in chemical processes is the objective of this course.

For material balances, you will be expected to be able to perform balances on single and multiple pieces of equipment, as well as on processes that have recycle and bypass streams. Later on in the course, you'll need to be able to do balances for processes that include reactors where the number of atoms of each species is changing. We keep track of the material in the process with flow charts.

Each flow chart has boxes that physically represent pieces of equipment (distillation columns that can be several stories tall, or huge tank heaters, etc.) and streams (arrows) that physically represent pipes. Keeping track of the amount of material in each stream is the objective of this chapter.

The following are examples of flow charts:

Simple single and multiple unit processes (the purpose of each process could be to purify A (say, an alcohol) from B (say, water) (thus giving a more concentrated alcohol)):

Recycle and Bypass processes: (the purpose of the recycle stream could be to reuse A, say water, and the purpose of the bypass would be to have some B, such as a natural juice, skip the process to give the final produce better flavoring.)

A reaction process:

The Mass Balance Equation

The Complete Equation:

In - Out + Generation - Consumption = Build-up

This reads: what goes in minus what comes out plus what was generated minus what g was consumed equals what is left over in the box.
An example could use population, so let's say we want to apply this equation to a ship wreck where many people were stranded on an island for a number of years. The "In" refers to the population entering the island; the "Out" refers to the leaving population; the generation term represents any children born; and the consumption term accounts for those who died.
To get back to chemical engineering, in and out in our case would refer to the inlet and outlet streams of the piece of equipment, while the generation and consumption terms refer to the products and reactants of a chemical reaction. The Build-up term (often called accumulation) is the material that has accumulated in the piece of equipment.

When there is no build-up (Accumulation = 0):

In - Out + Generation - Consumption = 0

and we say that we are at steady state. There won't be any problems that include a build-up term in this class until the very end (but there will be in other follow-up courses).

No chemical reaction:

In - Out + 0 - 0 = 0, or In = Out

If there are no chemical reactions present and no build up, what enters the piece of equipment leaves it.

Batch and Continuous Processes

definitions and examples:

BatchSystem empties or fills from some time onwardmaking cookies
ContinuousSystem does not empty or filla power plant
Semi-Batchcontinuous process that stopsand startspumping gas, digesting food

For the most part, we will be doing balances on only continuous processes.

Flow Charts


In this course, you will be asked to take a complex problem statement with some information and be expected to find unknown quantities. The first step in this process, after reading the problem statement, is to turn the problem into a picture, or a flow chart. Examples of flow charts were given above in the Intro section.

Degrees of Freedom


There are two main points here: The first has to do with drawing "balance boundaries", that is, the number of systems where you can write the Material Balance Equation. There are three rules for drawing system boundries:

  1. Draw a boundary around each process unit.
  2. Draw a boundary around junction points.
  3. Draw a bounadry around the entire process (unless there is only one boundry).
The second point has to do with how many equations you can write for each drawn boundary. You can write as many equations as you there are unique components passing through the boundary (Often, it is not necessary to write the equations if you are using a table to solve for the unknowns like we will do throughout this course. However, understanding when you can write equations is important when you have to solve a system of equations or when you are dealing with reactions). Examples at the end of the section will help explain what we are talking about here.

Setting up a Table


Material balance problems can be solved by listing and solving a series of equations, or by use of a table where we keep track of information. Using a table keeps your information organized and allows you to work through a problem without have to write and solve so many equations. So, you will learn to use the table, but you can't solve two equations and two unknowns with a table. It will be therefore important to learn to recognize when it is required to solve a system of equations using the table method.

To set up a table, you first need an accurate flow chart before you do a boundary analysis (See Degree of Freedom section above). The columns of the table will represent the unique species in the process while the rows will repressent the streams.

Below, the examples only show how to set up a table.

An Example


Again, chemical engineers are intimately concerned with the movement of fluids and materials. In this chapter, we begin to learn systematic methods of keeping track of exactly how much we have in each stream. To do this, we set up flow charts of real processes and then perform the mathematics. Here, take the second flow chart given in the intro section above where we want to do the following:

  • draw balance boundries
  • write the number of unique equations and/or set up table
This example exercises the first steps of the solution process for the rest of the problems you will encounter in this course.

Here, we will use the flow chart given above.

We can see that we have a total of 5 boundaries (3 process units, 1 junction, and 1 big boundary for the whole process. For each, we can write our balance equations). We also needed to label each stream.

For the first boundary, we can write to following equations (four equations in total, but just three are unique because the fourth one is the sum of the other three. So, in doing the math, we have our choice on which of the three equations we want to use).

A: F1,A = F2,A + F3,A

B: F1,B = F2,B

C: F1,C = F2,C + F3,C

Total: F1,total = F2,total + F3,total

Boundary 2: (3 components, so we could use 3 of the following equations)

A: F2,A = F5,A + F4,A

B: F2,B = F5,B

C: F2,C = F5,c + F4,C

Total: F2,total = F5,total + F4,total

Boundary 3: (there are 2 components, so we could use 2 of the following equations):

A: F3,A + F4,A = F6,A + F7,A

C: F3,C + F4,C = F6,C + F7,C

Total: F3,total + F4,total = F6,total + F7,total

The Complete Process Boundary: (there are 3 components, so we could use 3 of the following equations)

A: F1,A = F5,A + F6,A + F7,A

B: F1,B = F5,B

C: F1,C = F5,C + F6,C + F7,C

Total: F1,total = F5,total + F6,total + F7,total

And we could set up our table to keep track of information in the following way:


Here, I would like to make one point about the significance of the equations written in this example. Problems in this course will often be solved just using the table because it is so useful, allowing us to possibly not have to write as many equations. However, not all problems can be solved this way. Many problems will require that we solve simultaneous equations. Processes involving reactions require that we are able to write equations around boundaries in addition to being able to set up extents of reaction equations. Lastly, while tables will be used in this course to solve problems, all the problems can be solved by writing out and solving the equations.

So, in choosing whether to use the Table Method or to Solve Equations in completing material flow problems, I offer these three comments:

  • All problems can be worked out and solved by writing and solving the equations.
  • If problems don't require the solving of simultaneous equations, a table method of solving is an excellent and efficient way of finishing quickly.
  • In any case, a table should always be used to keep track of stream information and intermediate answers.


Repeat the above problem for the first flow chart given above, and for the reaction flow chart.

Go to | Check Answer For Flow Chart 1
Goto | Check Answer For Flow Chart 3

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