Overall Heat Exchanger Coeficient

The basic design equation for a heat exchanger is

dA = dQ/U DT (11-1)

where dA is the element of surface area required to transfer an amount of heat dQ at a point in the exchanger where the overall heat transfer coefficient is U and where the overall bulk temperature difference between the two streams is DT. The overall heat-transfer coefficient is related to the individual film heat-transfer coefficients and fouling and wall resistances by Eq. (11-2). Basing Uo on the outside surface area Ao results in

Uo = 1/ (1/ho + Rdo + xAo/KwAwm + (1/hi + Rdi)Ao/A ) (11-2)

Equation (11-1) can be formally integrated to give the outside area required to transfer the total heat load QT:

To integrate Eq. (11-3), Uo and DT must be known as functions of Q. For some problems, Uo varies strongly and nonlinearly throughout the exchanger. In these cases, it is necessary to evaluate Uo and DT at several intermediate values and numerically or graphically integrate. For many practical cases, it is possible to calculate a constant mean overall coefficient Uom from Eq. (11-2) and define a corresponding mean value of DTm, such that

Ao = QT /Uμm dTm (11-4)

Care must be taken that Uo does not vary too strongly, that the proper equations and conditions are chosen for calculating the individual coefficients, and that the mean temperature difference is the correct one for the specified exchanger configuration.

Mean Temperature Difference The temperature difference between the two fluids in the heat exchanger will, in general, vary from point to point. The mean temperature difference (DTm or MTD) can be calculated from the terminal temperatures of the two streams if the following assumptions are valid:

1. All elements of a given fluid stream have the same thermal history in passing through the exchanger.*
2. The exchanger operates at steady state.
3. The specific heat is constant for each stream (or if either stream undergoes an isothermal phase transition).
4. The overall heat-transfer coefficient is constant.
5. Heat losses are negligible.

Heat Exchanger Type

TEMA-style shell-and-tube-type exchangers constitute the bulk of the unfired heat-transfer equipment in chemical-process plants, although increasing emphasis has been developing in other designs. These exchangers are illustrated in Fig. below, and their features are summarized in list.




TEMA Numbering and Type Designation Recommended practice for the designation of TEMA-style shell-and-tube heat exchanger by numbers and letters has been established by the Tubular Exchanger Manufacturers Association (TEMA). This information from the sixth edition of the TEMA Standards is reproduced in the following paragraphs.

It is recommended that heat-exchanger size and type be designated by numbers and letters.

1. Size: Sizes of shells (and tube bundles) shall be designated by numbers describing shell (and tube-bundle) diameters and tube lengths as follows:
2. Diameter: The nominal diameter shall be the inside diameter of the shell in inches, rounded off to the nearest integer. For kettle reboilers the nominal diameter shall be the port diameter followed by the shell diameter, each rounded off to the nearest integer.
3. Length: The nominal length shall be the tube length in inches. Tube length for straight tubes shall be taken as the actual overall length. For U tubes the length shall be taken as the straight length from end of tube to bend tangent.
4. Type: Type designation shall be by letters describing stationary head, shell (omitted for bundles only), and rear head, in that order, as indicated in Figure.

Typical Examples

(A) Split-ring floating-heat exchanger with removable channel and cover, single-pass shell, 591-mm (23d-in) inside diameter with tubes 4.9 m (16 ft) long. SIZE 23–192 TYPE AES.

(B) U-tube exchanger with bonnet-type stationary head, split-flow shell, 483-mm (19-in) inside diameter with tubes 21-m (7-ft) straight length. SIZE 19–84 TYPE GBU.

(C) Pull-through floating-heat-kettle-type reboiler having stationary head integral with tube sheet, 584-mm (23-in) port diameter and 940-mm (37-in) inside shell diameter with tubes 4.9-m (16-ft) long. SIZE 23/37–192 TYPE CKT.

(D) Fixed-tube sheet exchanger with removable channel and cover, bonnettype rear head, two-pass shell, 841-mm (33s-in) diameter with tubes 2.4 m (8-ft) long. SIZE 33–96 TYPE AFM.

(E) Fixed-tube sheet exchanger having stationary and rear heads integral with tube sheets, single-pass shell, 432-mm (17-in) inside diameter with tubes 4.9-m (16-ft) long. SIZE 17–192 TYPE CEN. Functional Definitions Heat-transfer equipment can be designated by type (e.g., fixed tube sheet, outside packed head, etc.) or by function (chiller, condenser, cooler, etc.). Almost any type of unit can be used to perform any or all of the listed functions. Many of these terms have been defined by Donahue [Pet. Process., 103 (March, 1956)].

Equipment Function:
Chiller: Cools a fluid to a temperature below that obtainable if water only were used as a coolant. It uses a refrigerant such as ammonia or Freon.
Condenser: Condenses a vapor or mixture of vapors, either alone or in the presence of a noncondensable gas. Partial condenser Condenses vapors at a point high enough to provide a temperature difference sufficient to preheat a cold stream of process fluid. This saves heat and eliminates the need for providing a separate preheated (using flame or steam). Final condenser condenses the vapors to a final storage temperature of approximately 37.8°C (100°F). It uses water cooling, which means that the transferred heat is lost to the process.

Cooler: Cools liquids or gases by means of water. Exchanger Performs a double function: (1) heats a cold fluid by (2) using a hot fluid which it cools. None of the transferred heat is lost.

Heater: Imparts sensible heat to a liquid or a gas by means of condensing steam or Dowtherm.
Reboiler: Connected to the bottom of a fractionating tower, it provides the reboil heat necessary for distillation. The heating medium may be either steam or a hot-process fluid.

Thermosiphon: Natural circulation of the boiling medium is reboiler obtained by maintaining sufficient liquid head to provide for circulation. Forced-circulation A pump is used to force liquid through the reboiler.

Steam generator: Generates steam for use elsewhere in the plant by using the available high-level heat in tar or a heavy oil.

Superheater: Heats a vapor above the saturation temperature.
Vaporizer: A heater which vaporizes part of the liquid. Waste-heat boiler Produces steam; similar to steam generator, except that the heating medium is a hot gas or liquid produced in a chemical reaction.

Lift Check Valve and Titling Disk Check Valve

Lift Check Valves

These valves are made in three styles. Vertical lift check valves are for installation in vertical lines, where the flow is normally upward; globe check valves are for use in horizontal lines; angle check valves are for installation where a vertical line with upward flow turns horizontal. Globe and angle

Tilting-Disk Check Valves

These valves may be installed in a horizontal line or in lines in which the flow is vertically upward. The pivot point is located so that the distribution of pressure in the fluid handled speeds the closing but arrests slamming. Compared with swing check valves of the same size, pressure drop is less at low velocities but greater at high velocities.

Closure at the instant of reversal of flow is most nearly attained in these valves. This timing of closure is not the whole solution to noise and shock at check valves. For example, if cessation of pressure at the inlet of a valve produces flashing of the decelerating stream downstream from the valve or if stoppage of flow is caused by a sudden closure of a valve some distance downstream from the check valve and the stoppage is followed by returning water hammer, slower closure may be necessary. For these applications, tilting-disk check valves are equipped with external dashpots. They are also available with low-cost insert bodies.

Valve Trim various alloys are available for valve parts such as seats, disks, and stems which must retain smooth finish for successful operation. The problem in seat materials is fivefold:

1. Resistance to corrosion by the fluid handled and to oxidation at high temperatures,
2. Resistance to erosion by suspended solids in the fluid,
3. Prevention of galling (seizure at point of contact) by differences in material or hardness or both,
4. Maintenance of high strength at high temperature, and
5. Avoidance of distortion.

All valve trim materials have coefficients of thermal expansion which exceed those of cast or forged carbon steel by 24 to 45 percent and tend to cause distortion of seats and disks. To some extent leakage from this cause is prevented by closing the valve more tightly. Inserting a ring of high-temperature elastomeric or plastic, either in or alongside the trim metal in the seat or disk, prevents leakage from this cause.

Butterfly and Check Valve

Butterfly Valves

These valves occupy less space in the line than any other valves. Relatively tight sealing without excessive operating torque and seat wear is accomplished by a variety of methods, such as resilient seats, piston rings on the disk, and inclining the stem to limit contact between the portions of disk closest to the stem and the body seat to a few degrees of curvature.

Fluid-pressure distribution tends to close the valve. For this reason, the smaller manually operated valves have a latching device on the handle, and the larger manually operated valves use worm gearing on the stem. This hydraulic unbalance is proportional to the pressure drop and, with line velocities exceeding 7.6 m/s (25 ft/s), is the principal component in the torque required to operate the valves. Compared with other valves for low-pressure drops, these valves can be operated by smaller hydraulic cylinders. In this service butterfly valves with insert bodies for bolting between existing flanges with bolts that pass by the body are the lowest-first-cost valve in pipe sizes 10 in and larger. Pressure drop is quite high compared with that of gate valves.

Swing Check Valves

These valves are used to prevent reversal of flow. Normal design is for use only in horizontal lines, where the force of gravity on the disk is at a maximum at the start of closing and at a minimum at the end of closing. Unlike most other valves, check valves are more likely to leak at low pressure than at high pressure, since fluid pressure alone forces the disk to conform to the seat. For this reason elastomers are often mounted on the disk. Swing check valves are available with low cost insert bodies. Other kind of check valve are lift check valve.