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### Process Analysis vs Process Design

Process analysis and process design are two versions of the same problem situation; they differ only in the identities of knowns and unknowns. In the general analysis problem, the inputs to the process are known and we are to compute the outputs. But in the general design problem, we know the outputs and are to compute the inputs.

To illustrate, consider a simple, double-tube heat exchanger that uses water to cool a hot air stream. The exchanger is well-insulated; the mass and energy flows are all at steady states. The mass flow rates are Mair for air and Mwater for water. The air enters the exchanger at Tair(in) and leaves at Tair(out) < Tair(in). Similarly, the water enters at Twater(in) and leaves at Twater(out) > Twater(in). To satisfy environmental constraints, we require that the increase in water temperature be ΔTwater = Twater(out) – Twater(in) < 15 F°.

We can pose this heat-exchange situation as either a design or an analysis problem. Note that both versions, analysis and design, are described by the same equations: the steady-state material and energy balances.

## Process Analysis

In the analysis version, we know values for the inputs: Mair, Tair(in), Mwater, Twater(in), and ΔTwater; then we are to solve the material and energy balances for the outputs Tair(out) and Twater(out). Analysis problems usually arise when we are assessing the performance of a process that is in place and operating. For example, we often apply an analysis when trouble-shooting a malfunctioning process. We measure inputs and outputs, then do an analysis to test whether the measured outputs are consistent with the computed outputs.

## Process Design

In the design version, we know values for the outputs: Mair, Tair(out), Mwater, Twater(out), and ΔTwater; then our job is to solve the material and energy balances for the inputs Tair(in) and Twater(in). Design problems arise when we are contriving a new process to meet customer demands. The customer imposes specifications on the outputs, and we, as part of the design, must find inputs that provide the required outputs.

Note that if a design problem is ill-posed, then it may have no unique solution. Two ill-posed situations can arise:

1. Design overspecified, in which case there may be no physically meaningful solution. In our heat exchanger example, this happens if Tair(out) < Twater(out). (Why?)
2. Design underspecified, in which case there may be multiple solutions. In the above example, this happens when only ΔTwater is specified, leaving Twater(in) and Twater(out) to be determined. Underspecified situations are desirable, for they allows us to impose additional constraints, such as those required by economic and safety considerations.