Page 107 - Applied Process Design For Chemical And Petrochemical Plants Volume III

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Heat Transfer 75

Latent duty: q 1 740.3 12652 196,180 Btu>hr 50 5
LMTD 19.5°F
Sensible duty: q 2 740.3 10.32 146.4 352 2532 Btu>hr 50
ln
Total heat duty: Q q 1 q 2 198,712 Btu>hr 5
2. Corrections to LMTD (See Figure 10-34.)
Transfer Area
t 2 t 1 T 1 T 2
P R
2
The heat transfer area, A ft , in an exchanger is usually T 1 t 1 t 2 t 1
established as the outside surface of all the plain or bare
tubes or the total finned surface on the outside of all the (a) Counterflow
finned tubes in the tube bundle. As will be illustrated later, No correction factor, F 1.0, corrected LMTD 25.5°F.
factors that inherently are a part of the inside of the tube (b) Shell and tube, 1–2 (This is part parallel, part counterflow.)
(such as the inside scale, transfer film coefficient, etc.) are
often corrected for convenience to equivalent outside con- 98 88 10
P 0.2
ditions to be consistent. When not stated, transfer area in 138 88 50
conventional shell and tube heat exchangers is considered 138 103 35
R 3.5
as outside tube area. 98 88 10

Example 10-7. Calculation of LMTD and Correction F read from Figure 10-34A 0.905
Corrected LMTD (0.905) (25.5) 23.1°F
An oil cooler is to operate with an inlet of 138°F and an (c) Parallel flow
outlet of 103°F, and the cooling water enters at 88°F and is Correction factor does not apply,
to be allowed to rise to 98°F. What is the corrected MTD for LMTD 19.5 F
this unit, if it is considered as (a) a concentric pipe counter-
flow unit, (b) a single-pass shell—two-pass tube unit, and (c) 3. For an exchanger design, the unit requiring the
a parallel flow unit? smallest area will be the counterflow having the largest
corrected LMTD 25.5°F for this example.
1. Diagram the temperature pattern
Correction factors should seldom be used when they fall
(a) Counterflow
below a value that lies on a curved portion of the P—R curves,
Figure 10-34. That is, values on the straight portions of the
T 1 138°F S 103°F T 2
curves have little or no accuracy in most cases. For the “sin-
t 2 98°F d 88°F t 1
t 2 40°F t 1 15°F gle-shell pass—two or more than two passes” unit chart, an F
of less than about 0.8 would indicate consideration of a two-
40 15
LMTD 25.5°F shell pass unit. As a general guide, F factors less than 0.75
40
ln are not used. To raise the F factor, the unit flow system, tem-
15
perature levels, or both must be changed.
(Calculate or read from Figure 10-33.)
(b) Shell and tube 1—2 (1 pass shell—2 pass tubes) Temperature for Fluid Properties Evaluation—
Caloric Temperature
T 1 138°F S 103°F T 2
For most exchanger conditions, the arithmetic mean tem-
t 2 98°F d 88°F t 1
peratures of the shell side and tube side, respectively, are sat-
t 2 40°F t 1 15°F
isfactory to evaluate the properties of the fluids, which in
40 15 turn can be used to determine the overall coefficient, U.
LMTD 25.5°F
40 This means that the LMTD as determined is correct.
ln
15 When you can determine that the overall coefficient U or
fluid properties vary markedly from the inlet to the exit con-
(c) Parallel flow ditions of the unit, the arithmetic mean is no longer satisfac-
tory for fluid property evaluation. For this case, the proper
T 1 138°F S 103°F T 2 temperature of each stream is termed the caloric temperature for each
fluid. The F fraction is the smallest of the values calculated and
t 1 88°F S 98°F t 2
t 2 50°F t 1 5°F applies to both streams. Although the caloric temperature