Page 79 - Applied Process Design For Chemical And Petrochemical Plants Volume III

66131_Ludwig_CH10B 5/30/2001 4:17 PM Page 57

Heat Transfer 57

t t 2 t 1
31410 16724
Substituting: T 2 min 167 1410 1672
11257 1672
1
121410 16722
T 2 min 167 55°F
1actual2 T 2 min 222°F

Maximum temperature cross:

3t 2 T 2 4 12 2 1>2 2 12 1>2 12
0.1715
1
3T 1 t 1 4 2 > 2
The theoretical maximum possible temperature cross in
this style exchanger (t 2 T 2 min ) 0.1715.
Theoretical (t 2 T 2 ) max 0.1715 (T 1 t 1 )
Then, theoretical T 2 min t 2 (t 2 T 2 ) max
Then, for the example: the theoretical maximum possible
temperature cross:

1t 2 T 2 2 max 0.1715 1410 1672 41.6°F
Theoretical T 2min 257 41.6 215.4°F

or, when, T 1 t 1 T, then the following approximation
Figure 10-32. Typical temperature situations that contain cross-over applies:
points, preventing exchanger operation. (Adapted and used by per-
mission: Brown and Root, Inc.) t
T 2 min t 1 1T 1 t 1 2c 1 d 1T 1 t 1 2 t>2
21T 1 t 1 2
Use the preceding equation when (T 1 t 1 )
50.

Counter-current or co-current flow of the two (usual) fluids
T Shell-side fluid, °F
in a heat transfer operation is the most efficient of the several t Tube-side fluid, °F
alternate design combinations. The most efficient transfer T 2Min Minimum hot fluid exit temperature achievable, °F
occurs in a straight-through, single-pass operation, such as 1 Inlet (hot)
shown in Figures 10-2 and 10-29, and design-wise Figure 10-1H 2 Outlet (cool)
(but not as a reboiler). Usually for these cases the logarithmic
mean temperature difference may be applied as Murty 132 dis- In vaporization, one fluid, B, vaporizes at constant temper-
cusses a calculation method for establishing the maximum ature while the second fluid, A, is cooled from T 1 to T 2 .
possible cross in a parallel counterflow exchanger, Figure 10- When a refrigerant such as propylene is being vaporized to
13. In the following example, this technique is outlined. condense ethylene vapors, the unit actually operates at a
fixed temperature difference for the entire length of the
Example 10-3. One Shell Pass, 2 Tube Passes Parallel- exchanger. In this latter situation, t 1 equals t 2 and T 1 equals
Counterflow Exchanger Cross, After Murty 132 T 2 . In an evaporator, one fluid is vaporized as the heating
fluid is cooled to T 2 .
Find the minimum temperature that a hot fluid at 410°F
can be cooled if the cold fluid is heated from an inlet tem-
Mean Temperature Difference or Log Mean Temperature
perature of 167°F to 257°F. Also find the theoretical tem-
Difference
perature cross and theoretical minimum hot fluid shell-side
outlet temperature, T 2 .
For these cases, the logarithmic mean temperature dif-
Using equations from reference 132:
ference may be applied as:
1T 1 t 1 2
T 2 min t 1 1T 1 t 1 2 (10-12) t LMTD MTD t 2 t 1 t 2 t 1 (10-13)
1 t2
1 ln t 2 t 2
121T 1 t 1 22 t 1 2.3 log 10 t 1