Environmental Engineering Reference
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the amounts of water and/or activated carbon used over some time period (one month, for
example) as well as the separation performance of a given batch are of primary interest,
then the C.V. would be treated as an open system.
For the material presented in this topic, the control volume is fixed in space (distillation
columns usually don't move very much!). Mass can flow across the control surface. The
conditions at the surface will be used in the balances as described below.
A component mass balance in words is:
The net rate at which the mass of a component enters the control volume (mass into
minus mass out of the C.V.) plus the rate of mass of this component generated within the C.V.
(i.e., chemical reactions) equals the rate of change of the mass of this component (i.e., accu-
mulation) within the C.V. with respect to time.
Accumulation
=
Input
Output
+
Generation.
(3.1)
Accumulation is a positive quantity if there is an increase in the mass of the specific
component with respect to time. A negative value implies a decrease. Likewise, the gen-
eration of a specific component by a chemical reaction would be a positive term while
consumption in a chemical reaction would be a negative term.
A simple example at this point will illustrate the balance concept.
Example 3.1
Problem:
In a given year, 2,000 people moved to Boulder, CO, 500 people moved out, 1,500
were born and 1,000 died. Write a balance on the population of the city for this period.
Is this a component or total balance?
Solution:
Accumulation
=
Input
Output
+
Generation
Input
=
2,000
=
Output
500
Generation
=
1,500 - 1,000.
Substituting:
Accumulation
2,000.
For that year, there was a net increase of 2,000 people. This is a total balance on the
population of the city. If the number of women were selected for the balance, then this
would be a component balance of the total population.
=
2,000 - 500
+
1,500 - 1,000
=
Mass balances for separation processes can refer to:
(a) Total mass (mass is normally used for liquid and solid flowrate measurements);
(b) total moles (gas flow);
(c) mass of a chemical compound (component balance);
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