CENG 301 Material and Energy Balances

Chapter 1: Material Balances

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1.1: Discussion

The object of analyzing a system that models the behavior of a chemical plant is to determine the flow rates of all chemical species in the streams that enter and leave the plant. This tells us how much of each raw material is used and how much of each product (along with some wastes) are obtained from the plant. Normally this requires that we determine the flow rates of all the species in all streams that connect major units as well. Thus we will find it convenient to:

a) Draw a detailed block diagram of the units in the plant. (See section 1.2)
b) List and number the chemical species that will be followed.
c) List and number all streams that enter, leave or connect the units in the plant.

The block diagram could be as simple as that shown below as a generalized version of Figure 2.2 in Reklaitis

				
                         _______
                        |       |   ----->	Product: A+B
 Feed: A+B     ----->   | Plant |
                        |       |
                        |_______|   ----->	Waste: A+B

It (later in the course) could be as complicated as the diagram shown in Figure P5.26 in Reklaitis.

Then we should fill in on the block diagram all the specified information about the streams and the units in the plant. In our simple case, the problem may say that we have a mixture of 20 mol % B as a feed and wish to separate it into a stream containing 99 mol % A and one containing 90 mol % B. Then the diagram would look like:

                         _______
                        |       |   ----->	Product: A+B
 Feed: A+B     ----->   | Plant |                 99% A
                        |       |
       20% B            |_______|   ----->	Waste: A+B
                                                  90% B

 

Framemaker (see CENG 303 Framemaker Notes), Word, Excel, similar PC based programs will help you draw diagrams you can print out on a laser printer. The exact program used to draw is not important, just a neat and clear presentation of the information about the process. View a (much) more complicated flow diagram here.

Once we have completed the diagram, it may be convenient to then start filling in the information shown in the tables in section 1.1.3 below. The first of these tables gives the desired flow rates. They are shown as molar flow rates, but in many systems mass flows may be more appropriate. Do not confuse molar flow rates (mol fractions) with mass flow rates (mass fractions). The second table lists reaction rates that will be important in any plant used to convert some compounds into others. Reaction rates are always given in molar units.

Eventually we would like to complete all the entries in both tables. Many of the entries are given in the problem statement. This includes zeros for flow rates of species that are not present in certain streams and zeros for reaction rates that do not occur in certain of the reactors.

As an aid in determining the order of calculation for treating the units in the plant, a degree of freedom table should be prepared for all except the simplest systems. This calculation is discussed in 1.6.

The two tables on the next two pages illustrate a simple plant in which there may be no more than six compounds and twelve streams. In modern chemical plants both of these numbers could be in the hundreds. Note that each compound flow rate that is not specified must be treated as an unknown to be determined. Similarly each unspecified reaction rate is an unknown. The larger this total number of unspecified flow and reaction rates the more information we need to solve for the plant performance.

Information that is useful in determining the plant performance includes:

a) Material balances
b) Given compositions of streams
c) Given stream (or compound) flow rates
d) Given flow ratios
e) Given reaction conversions
f) Splitter restrictions

Information about the plant may be given in other forms, but these are the most common ones for steady state chemical plants in which energy effects are not important.

1.1.1 Template for Typical Problem

Table of Molar Flow Rates

Comp No.
Name

1

2

3

4

5

6

Total

Stream
Number

From Unit*

To Unit*

1

2

3

4

5

6

*If the stream does not connect units, the stream should be designated as a plant feed or product stream.

Note:To print out a more useful template of the above table, click here, then print.

Table of Reaction Rates

Reactor

Reaction
Number

Reaction

1

2

3

1

2

3

4

Note:To print out a more useful template of the above table, click here, then print.


The next few sections of these notes will examine increasingly complicated systems. They will make use of the MATLAB programs developed for this course to take a large part of the tedium out of the required calculations. We will start with simple modules with exactly the right data given for them so that we can determine all flow rates and reaction rates directly. Then we will move to simple units with the right amount of data given but in a form that requires more work to get all our flows and reaction rates. We will also see examples where we need to combine some of the modules to model our units. These combinations will be simple enough so that the final units still involve only a few streams. Finally we will look at plants that start to approach reality. In these the use of some organization of the known plant data will be very useful in helping to see where to start our solution. Thus the degree of freedom approach is given to show how to organize the solution procedure.


1.1.2 Example and Exercise on Flow Rates

Let's take the very simple system posed at the beginning of this chapter on page 7 to show how we would proceed in calculating the flows for a plant that just separates two compounds. First we note that no flow rates were given in the statement of the problem. Thus, we are free to choose a basis in solving the problem. A convenient basis is 100 mols of the feed. Then without much difficulty, we can state that the feed stream must have 80 mols of A and 20 mols of B. We can fill this into our flow rate table as:

1.1.3 Problem: General Plant Separation

Table of Molar Flow Rates

Comp
No.Name

1
A

2
B

Total

Stream
Number

From Unit*

To Unit*

1

Feed

Plant

80

20

100

2

Plant

Product

.99N2

.01N2

N2

3

Plant

Product

.10N3

.90N3

N3


Assume that all we do in the plant is prepare a product that is 99 mol % A by some type of separation. We know the total mols in the two product streams must be 100. Thus:

N2 + N3 = 100

We also know that the amount of A in the two streams must be 80. Thus:

.99N2 + .10N3 = 80

Solving these two equations in MATLAB, we find:

>> [1 1; .99 .1]\[100 80]' 
ans =
   78.6517
   21.3483


Thus we can fill in the rest of our table and check the MATLAB solution.

Revised Table of Molar Flow Rates

Comp No.
Name

1
A

2
B

Total

Stream
Number

From Unit*

To Unit*

1

Feed

Plant

80

20

100

2

Plant

Product

77.8652

.0.7865

78.6517

3

Plant

Product

2.1348

19.2135

21.3483

If you cannot immediately see that the flows make sense in that both A and B are conserved, you should be able to do so later in this course.

Suppose the molecular weight of A is 40 and that of B is 20. A program that converts from mol fractions to mass fractions is called moltomas. Help used on this function gives:

>> help moltomas 
  function w=moltomas(x,mw)
  x gives the mol fractions of the compounds in a stream
  mw gives the molecular weights of the compounds
  w returns the mass fractions of the compounds

The mass fraction of the feed and product streams would then be found by:

>> mw=[40 20];         
>> moltomas([.8 .2],mw)     
ans =
    0.8889    0.1111
>> moltomas([.99 .01],mw)
ans =
    0.9950    0.0050
>> moltomas([.1 .9],mw) 
ans =
    0.1818    0.8182


As an exercise, pick 100kg of the feed as a basis and find all the flows in the feed and product streams in mass units. Show that the answers obtained in mass units are consistent with those found in the mol flow rate example.

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Last modified July 31, 1998.