Page 107 - Chemical process engineering design and economics

92 Chapter 3

constraints, including financial feasibility, then we design the process for the
minimum total cost,

(3.21)
C T =C D + Q + C G
which is the sum of direct, indirect, and general costs.
For a quicker solution to a design problem than that obtained by solving
Equation 3.21, we could use a "rule-of-thumb." For example, for a heat exchanger
using water to cool a process stream, we can assign an approach temperature dif-
ference between the exiting water stream and entering process stream. Thus, for
this particular heat exchanger we may write the approach temperature difference,
based on economic experience, as

t P -t w = 5K (3.22)

Equation 3.22 means that as the exit temperature of the water, t w, ap-
proaches its maximum value, t P, the heat-exchanger surface area will become lar-
ger and larger. When t P = t w, the area will be infinite.
If we use Equation 3.22 in place of Equation 3.21 to find the optimum, cool-
ing-water temperature, we assume that the calculated heat-exchanger area will
approximate an optimum value. The approach-temperature difference is not a con-
stant, but it will vary with time and location, reflecting equipment, and local en-
ergy, labor, and other costs. Because of the oil embargo in the 1970s and the sub-
sequent rise in oil prices, and its effect on all energy costs, many of the old rules-
of-thumb appearing in early publications required revision. Now, oil prices are
again high, so rules-of-thumb must reflect the change.
There are other rules-of-thumb based on economic experience, which the
reader will recognize, such as the optimum reflux ratio in distillation and the opti-
mum liquid to gas ratio in gas absorption. You may also specify recoveries of
key components or their concentrations hi an exit stream for separators. When we
use any of these rules, the assumption is that the calculated separator size will be
of reasonable cost, approximating the optimum-size separator. Similarly, for
chemical reactors we may specify conversion of a desirable compound, its exit
composition or an approach temperature difference. For chemical reactors, the
approach temperature difference is the difference between the actual temperature
and the chemical-equilibrium temperature. Again, we assume that a reactor that
approximates the optimum-size reactor will result when using this rule.

PROCESS ANALYSIS EXAMPLES

To illustrate the foregoing discussion, we will begin first by analyzing single proc-
ess units. Later, we will assemble the individual process units into a process. Af-
ter writing the appropriate relations for a process unit, we calculate the degrees of

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