Page 124 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

5.2 Energy-capital trade-off e two-stream problem 121

5.2 Energy-capital trade-off e two-stream problem
Based on the aforementioned laws, the scope of heat recovery can be determined by plotting the
streams on a temperatureeenthalpy (T H) graph. A two-stream problem or a process with one hot
and one cold stream is the simplest case. The cold stream is heated from a start temperature, TS c ð CÞ to

a target temperature, TT c ð CÞ by the hot stream that in turn cools from TS h ð CÞ to TT h ð CÞ in a

counter-current heat exchanger. Assuming a constant heat capacity flow rate [product of mass flow rate
_
and specific heat capacity, CP ¼ Mc p ] for both the hot (CP h ) and the cold stream (CP c ), one gets two
1
lines as shown in Fig. 5.2. The temperature or enthalpy changes for the streams i.e. the slope of the
T H lines cannot be changed for a particular fluid but the relative position of the streams can be
changed by sliding either or both the curves parallel to the enthalpy axis in order to meet the specified
DT min criteria. This is possible because the reference enthalpy of the two streams is independent of
each other. The region of overlap between the two streams determines the amount of heat recovery
(q rec ) possible for the specified DT min and utilities are necessary for the remaining portions, i.e. in
Fig. 5.2 cold utility is required to recover (q ) amount of heat from the hot stream and hot utility is

required to supply (q ) amount of heat to the cold stream.
þ
T q +
TS c q c,rec TT c
TT h q – T h,rec rec TS h
Temperature (°C) TS c Hot Cold
h
TT
stream
T
c,rec
T h,rec
ΔT min stream
TS c q c
TT h q h
q – q rec q +
Enthalpy (kW)
FIGURE 5.2
Heat exchanger example for a two-stream problem.

The amount of energy saving by the heat recovery process can be estimated as follows e The heat
required by the cold stream is
(5.1)
q c ¼ CP c ðTT c TS c Þ
and the heat available in the hot stream is
(5.2)
q h ¼ CP h ðTS h TT h Þ

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This feature is justified for every practical process, with and without phase change. If the heat capacities vary significantly,
the nonlinear P CP c line for a stream can be represented by a series of linear segments.