Page 154 - Plant design and economics for chemical engineers

128 PLANT DESIGN AND ECONOMICS FOR CHEMICAL ENGINEERS

the foregoing commercially available programs, there are many proprietary
flow-sheeting programs such as Exxon’s COPE, DuPont’s CPES, and Union
Carbide’s IPES.
An overall structure similar to that of many of the flow-sheeting programs
is shown in Fig. 4-6.t
The unit operations, reactors, and other process features are represented
by unit-module routines. These routines include operations associated with the
equipment of the process (e.g., distillation columns and compressors) as well as
changes occurring due to flow arrangements (e.g., composition and temperature
changes that can occur when two or more streams are combined into one stream
by connecting pipelines or are added simultaneously to a vessel). The descrip-
tion of a process consists of selecting the appropriate modules that represent
the process and identifying the streams that flow into and out of each module.
From a list of modules and stream connections, the process arrangement can be
interpreted by a flow-sheeting program. Each unit-module routine consists of a
program containing a mathematical model for the performance of one process
unit. The model consists of equations relating the input and output stream
conditions and the equipment parameters (specifications that determine the
behavior of the equipment, such as reflux ratio and number of plates for a
distillation column).

Degrees of Freedom

The number of unknowns and the number of equations relating these unknowns
can become very large in a process-design problem. The number of unknowns
and independent equations must be equal in order that a unique solution to a
problem exists. Therefore, it is necessary to have a systematic method for
enumerating them. The total number of independent extensive and intensive
variables associated with each stream in a process is C’ + 2, where C’ is the
number of independent chemical components in the stream. The quantity and
the condition of the stream are completely determined by fixing the flow rate of
each component in the stream (or, equivalently, the total flow rate and the mole
or mass fractions of C’ - 1 components) and two additional variables, usually
the temperature and pressure, although other choices are possible. This number
includes situations where physical and chemical equilibrium exist.*
If all the inlet stream conditions to an operation are known, (C’ + 2)
equations are required in order to calculate all the conditions of each outlet
stream. For S outlet streams, a total of S *CC’ + 2) equations is necessary to
relate the outputs to the inputs of the operation. The model of an operation

?A. W. Westerberg, H. P. Hutchison, R. L. Motard, and P. Winter, “Process Flowsheeting,” p. 12,
Cambridge University Press, Cambridge, England, 1979.
$A. W. Westerberg, H. P. Hutch&m, R. L. Motard, and P. Winter, “Process Flowsheeting,” pp.
115-120, Cambridge University Press, Cambridge, England, 1979.