Page 100 - Chemical process engineering design and economics

Process Circuit Analysis 85

the problem is under-specified. If F is negative, the number of equations is in ex-
cess, and the problem is over-specified. Only if F is zero can you calculate values
for all variables. Usually, when formulating the problem, the number of variables
is in excess and we must specify additional variables. First, however, you must be
certain that you have not omitted any relations. The excess variables are called
degrees of freedom, supposedly because we are "free" to designate numerical val-
ues for any of the variables in the equation set to obtain zero degrees of freedom.
To execute step one requires knowing what relations are available for ana-
lyzing process circuits. Mass and energy balances h'ave already been mentioned.
Below is a list of relations.

1. mass balance
2. energy balance
3. momentum balance
4. rate equations
a) heat transfer
b) mass transfer
c) chemical reaction
5. equilibrium relations
a) phase
b) chemical
6. economic relations
7. system property relationships
a) thermodynamic
b) transport
c) transfer
d) reaction
e) economic data

Generally, when analyzing process circuits our only interest is in the macro-
scopic behavior of each process unit, i.e., the relationship between the inlet and
outlet streams. We will not consider the microscopic behavior of the components
within the unit. At this point, our interest is in what the process unit does, not how
it accomplishes its task. To do otherwise will greatly increase the complexity of
the analysis. The problem usually is: given the flow rates, compositions, tempera-
tures, and pressures of all inlet streams, determine these properties for all the outlet
streams. One way to avoid considering the detailed behavior of a process unit is to
obtain a relationship between the exit streams. For example, for a partial con-
denser, the exit streams are the vapor and liquid streams. To predict accurately the
composition of the exit streams will require considering simultaneous heat and
mass transfer rates in the condenser and integrating a set of differential equations.
Integration requires knowing the length of the condenser, which is the objective of
the analysis. A quicker approach is to specify recoveries, compositions or an ap-
proach to equilibrium of the components, whatever we know from experience or

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