Page 99 - Chemical process engineering design and economics

84 Chapter 3

1. list the appropriate relations and unknown variables for the problem
2. calculate the degrees of freedom
3. specify or unspecify variables until the degrees of freedom are zero
4. determine a solution procedure
5. solve the equations
6. organize the results in tabular or graphical form
7. check the solution.

When implementing this procedure, proceed step-by-step. Do not carry out a
step before completing the preceding step, particularly when executing step one.
Also, do not combine steps, e.g., attempting to carry out steps four and five before
completing steps two and three. Formulate the problem first, i.e., complete steps
one to three. Then, it will be certain that a solution exists. Frequently, steps one
to four are executed simultaneously. The numerical solution to the problem is
begun, and equations are introduced along the way as needed. Eventually a solu-
tion is obtained. With experience the process engineer can recognize that certain
problems have solutions, however, in most cases, it is not initially evident that
there is enough information or what the most efficient solution procedure should
be.
Polya [1], who has examined the nature of problem solving, has devised a
similar procedure. He states, "First, we have to understand the problem; we have
to see clearly what is required. Second, we have to see how the various items are
connected, how the unknown is linked to the data, in order to obtain the idea of the
solution, to make a plan. Third, we carry out our plan. Fourth, we look back at
the completed solution, we review and discuss it."
Executing the steps systematically uncovers what information is missing and
results in better insight into the structure of the problem. We learn continuously.
Polya [1] again states that, "Our conception of the problem is likely to be rather
incomplete when we start the work; our outlook is different, when we have made
some progress; it is again different when we have almost obtained the solution."

PROCESS-CIRCUIT RELATIONSHIPS

Executing steps one to three in the procedure is the process of defining a problem.
Before solving a set of equations, you must clearly show that the number of equa-
tions equals the number of unknowns. Circumventing this step will result in con-
siderable wasted effort. The relationship between the number of equations and
unknowns is expressed by

F = V-R (3.1)

where F is the degrees of freedom, V the number of variables, and R the number
of independent relations. If F is positive, the number of variables is in excess and

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