I
DONALD S. MORTON The M. W. Kellogg
Co., New York, N. Y.
Thermal Design of Heat Exchangers This generalized presentation of methods and data should provide an understanding of and the approaches to the problems which face the heat exchanger designer
THE of heat exchange equipment is a wide and detailed subject. THERMAL DESIGN
T h e thermal designer has a wealth of published data on which to base his design, and the techniques employed in industry vary widely. This difference in opinion and application is a healthy atmosphere for competition, and more important, it serves to encourage experimental work in areas where considerable disagreement still exists. In this presentation, an effort is made to generalize whenever possible ; however, the methods and data described should provide an understanding of and the approaches to these problems facing the exchanger designer.
Over-all Heat Transfer Coefficient
The over-all heat transfer coefficient must be calculated in order to set the surface area requirement of the exchanger. This coefficient can be represented as the sum of the resistances to the flow of heat from a fluid inside the tubes to a fluid outside the tubes. The figure below illustrates a cross-section of a typical exchanger tube showing these resistances. Considering the over-all coefficient analogous to a sum of electrical resistances 1/U = l / h
0
Conduction. The transfer of heat from one body to another by physical contact. Radiation. The transfer of heat by the absorption of radiant energy, transformed into heat in surrounding bodies. Convection. T h e transfer of heat by the mixing or movements of fluids or fluids with a solid.
474
(2)
As the over-all coefficient, U , and the total surface, A , are normally based on the outside surface of the tubes, the term h, must be modified to relate its value to the outside surface of the tube. The ratio of these surfaces is T X I.D. tube thus h, is multiplied by the x x O.D. tube ratio of the inside to outside diameter of the tube. Neglecting the tube wall reS H E L L SIDE SCALE T U B E WALL
S H E L L SIDE LAMINAR FILM
The most common applications of heat transfer are a combination of one or more of these basic modes. O u r primary- concern is with heat transfer between two fluids flowing through a shell-and-tube heat exchanger. I n a shell-and-tube heat exchanger, the total duty, or rate of heat transfer per unit time, can be represented as: Q = UAAT (1 1 where: Q = total duty (B.t.u. per hour) 4 = total area of heat transfer surface (square feet) AT = log mean temperature difference (" F.) U = over-all heat transfer coefficient (B.t.u. per hour per square foot per O F.)
rw
h, = shell side convection film coefficient d, = shell side fouling resistance r, = tube wall resistance d, = tubeside fouling resistance h, = tubeside convection film resistance
Basic Theory
Heat is transferred from points of higher temperature to points of lower temperature by direct contact of particles of matter or by the emission and absorption of radiant energy. The three basic classifications or modes of heat transmission may be defined as follows :
+ dt + + d, -I- I / h s
sistance, which generally is of small magnitude, Equation 2 may be rewritten
The scale or fouling resistances represent a safety factor intended to increase the surface of the heat exchanger, so that the full process duty requirements may be attained for a reasonable time between cleaning periods. When an exchanger is first placed in operation there is no dirt or scale on the tubes, and consequently the over-all resistance consists of the film and tube wall resistances. During operation, scale or dirt accumulates on the surfaces of the tubes, and the over-all heat transfer rate drops off as the dirt build-up increases. The rate of this scale or dirt build-up is dependent on the cleanliness or fouling tendency of the flowing medium. Based on a reasonable time between cleaning periods, TEMA and other publications have listed fouling resistances for a number of fluids. For some common fluids, such as crude oil and water, they have provided for variations in temperature and velocity. Typical fouling resistances are given in the table. The remaining film coefficients may be determined by direct experimental measurements on similar equipment. Or, if such values are not available or easily attained, the individual coefficients must be calculated, as will be illustrated. Log Mean Temperature Difference
Tb
TUBE SIDE LAMINAR FILM
T U B E SIDE SCALE
A cross section of a typical exchanger showing the resistances to the flow of heat
INDUSTRIAL AND ENGINEERING CHEMISTRY
Process conditions determine the quantities of fluids to be heated or cooled, and the total heat must be transferred. When two fluids are passed through a heat exchanger, the heat transferred in either sensible or latent heat fixes their inlet and outlet temperatures. Figure 1 shows a temperature profile of two fluids in countercurrent flow through a heat exchanger, plotted against the length of travel. As the temperature difference between the fluid is not linear, the log mean temperature must be determined. The formula for determining the log
HEAT EXCHANGERS
I
Some Typical Fouling Resistances Expressed as B.t.u./hr./sq.
ft./O
Fouling factor is reciprocal of fouling resistance Alkylation Wate; Cooling tower 0.001 Isobutane tower feed River 0.002 Isobutane product 0.002 Gas oil Brackish Sea water 0.001 Butane product Steam condensing 0.0005 Cat Former Hydrocarbons Condensing Reactor feed 0.00125 Reactor product Depropanizer bottoms Hydrocarbons Vaporizing Deurouanizer feed Gaso1i-m 0.002 Fluid Cat Cracker Light gas oil Naphtha Gas oil Stripper trapout Heavy gas oil Depropanizer bottoms Depropanizer feed Butane product Gasoline prodact Debutanizer bottoms Debutanizer feed Sponge oil Recycle oil Intermediate reflux Gas oil slurry Rerun bottoms
Crude Unit Naphtha Kerosine Diesel Gas oil Crude
0.002 0.002 0.002 0.002
0.003
Vacuum Unit Vacuum gas oil Vacuum tar
0.002 0.005
Delayed Coking Gas oil Intermediate reflux Reduced crude Tar
0.002 0.002 0.004 0.005
mean temperature difference (L.M.T.D.) is as follows: L.M.T.D. = Where
At1 ~
- At2
At Log -l At2
(3)
is the larger terminal difference 4t2 is the smaller terminal difference (7'2 tl).
(TI - $2) and
-
F.
0.002 0.00125 0.002 0.00125
0.00167 0.00167 0.00167 0.00167 0,001
LENGTH OF TRAVEL
0.00167 0.00167 0.002 0.002 0.005 0.00125 0.00125 0.00125 0.00167 0.00167 0.00167 0.00167 0.00167 0.002 0.002 0.002
Because of exchanger construction restrictions, true counterflow is not common. The usual arrangement, shown below, is one shell pass and two or more tube passes. Counterflow exists in the top half of the exchanger and concurrent flow in the bottom half. Correction factors must be applied to correct the log M.T.D.
Figure 1. A temperature profile of two fluids in countercurrent flow through a heat exchanger
to an effective M.T.D. Published curves illustrate the correction factor plotted in terms of two dimensionless parameters. I n using these correction factors, remember that the factor 0.8 results when the outlet temperatures of hot side and cold side fluids are the same. If it is necessary to cool the hot fluid below the outlet temperature of the cold fluid, two or more shell passes in series should be used. Film Coefficients
As mentioned earlier, the individual film coefficients must usually be calculated. Fluids traveling inside or outside tubes a t a constant mass rate are influenced by mass velocity, viscosity, thermal conductivity, specific heat, and tube or shell side effective hydraulic diameters. Much experimental and empirical work has been done in correlating expressions for tube side coefficients. The most widely used relationship is illustrated in Figure 2. A dimensionless j factor is plotted against Reynolds' number.
I n this equation, all the properties of the fluid are determined a t the average bulk temperature with the exception of 2, which represents the viscosity at the tube wall. T h e
TUBE INLET In heat exchangers, pure counterflow is uncommon, there is usually one shell pass and two or more tube passes
(3
--0.14
viscosity term is added to the equation to compensate for the wall effect of viscosity on the heat transfer when heating or cooling takes place. This compensation factor can be significant when very viscous fluids are being considered. Note that below Reynolds' number of 17 the slope of the curves change appreciably. This illustrates the viscous flow region. Any heat transfer done in the viscous flow region is exVOL. 52, NO. 6
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tremely uneconomical owing to the low heat transfer rates involved and should be avoided whenever possible. The shell side film coefficient may be found in a similar manner, and the curve shown in Figure 3 may be used. The major difference between the determination of tube side and shell side coefficients is the method by which the mass velocity is determined. The tube side mass velocity:
where
G, = mass velocity (pounds per second per square foot) W = flow (pounds per hour) N , = No. of tube passes A , = Cross-sectional area of one tube (square feet) Nc = No. of tubes
The number of tube passes may be altered to achieve the optimum mass velocity based on available pressure drop. This optimum mass velocity usually varies between 200 to 350 pounds per second per square foot for liquids. The shell side mass velocity is not as straightforward to find. I n the cross sectional view of a shell and tube exchanger (page 474), the fluid flowing on the shell side must travel across the bundle between the baffles and along the tubes through the baffle window area. A separate mass velocity must be calculated for the flow across the tubes between the baffles, and for the flow along the tubes through the baffle window. Then a geometric mean mass velocity is determined. The long flow mass velocity: GL =
W X 144 3600 X NFA X C
(6)
where GL = long flow mass velocity (pounds per second per square foot) W = flow (pounds per hour) NFA = net shell free area (square inches) I / ~ [ Tx (I.D. shell)2 - Nt X T X (O.D. tube)2]
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INDUSTRIAL
C = baffle cut, per cent of net shell free area
The cross flow mass velocity:
‘
W X 144 = 3600 X B X D f
(7)
where Go = cross flow mass velocity (pounds per second per square foot) LV = flow (pounds per hour) B = baffle spacing, inches D, = free diameter, inches The free diameter represents the sum of spaces between tubes, and between the outside tubes and the shell, perpendicular to the fluid flow between baffles. Once the long flow and cross flow mass velocities are determined, the geometric mean shell mass velocity may be found as follows: G, = (G,X GL)”’
(8)
This geometric mean velocity is then used in conjunction with Figure 3 to determine the shell side heat transfer coefficient. As might be expected, there are leakages involved with shell side flow. These leakages include bypassing between the bundle and the shell, leakage between tube holes and tubes at baffles, and leakage between baHe periphery and shell. Due to manufacturing requirements, certain tolerances must be maintained to facilitate ease of fabrication. The rating curves in use in industry have been adjusted to reflect losses in heat transfer effectiveness due to bypass or leakage. Considerable experimental work must still be done before shell side coefficients may be determined with the same accuracy as tube side coefficients. Pressure Drop
The heat transfer coefficient of a shell and tube exchanger is only acceptable
AND ENGINEERING CHEMISTRY
if the design conforms to the limits of pressure drop allowed for the streams being heated or cooled. Heat transfer coefficients may always be improved at the expense of pressure drop. The selection of the optimum allowable pressure drop for exchanger design is a function of the over-all process design. On vacuum or low pressure overhead condensers, only a few millimeters pressure drop is available for the exchanger, while in pump discharge circuits, drops from 10 to 100 p.s.i. are feasible. Operating pumping costs must always be balanced against exchanger investment, and in turn, exchanger designers should always utilize all the available pressure drop for the most efficient heat transfer. The tube side pressure drop calculation for flow along the tubes is derived from the Fanning correlation for flow in straight tubes or pipes. I n addition, there are entrance and exit losses encountered between tube passes at the channel or floating tube sheet cover due to the sudden enlargements and contractions as the fluid enters and leaves the tubes. An accepted method is to add 1.5 velocity heads for each tube pass to account for these losses. The shell side pressure drop is similar to the shell side heat transfer coefficient in that it involves a pressure drop along tubes through the baffle window opening as well as a pressure drop across the tube bank between the baffles. In addition, compensations must be made for leakage flows and bundle bypassing which have a far greater effect on pressure drop than on heat transfer coefficient. Boiling Very often the thermal design of exchangers involves heating a fluid to a point where boiling takes place. I n this case the heat is transferred through a boiling film rather than a convection film. If Equation 3 is considered with a boiling liquid on the shell side, the over-all heat transfer
HEAT EXCHANGERS coefficient may be represented as follows:
where hab = boiling coefficient (B.t.u. per hour per square foot per O F.) When boiling takes place on a tube, the heat supplied to the fluid, through the tube wall, forms bubbles which are displaced from the tube surface due to their lighter density. As the amount of heat input is increased, the rate of bubbling or boiling will increase and the heat transfer will improve until the heat input is supplied at a rate which is too high to allow the liquid to continually displace the rising bubbles in a natural fashion. When this takes place, the heating surface becomes vapor bound and the over-all heat transfer rate is slowed down, as any heat flow must pass through this vapor film which acts as an insulator. T h e heat input per unit area Q / A is referred to as flux. If this flux US. the temperature difference between the tube wall and the main liquid body is plotted, point B represents the critical temperature or the point of maximum heat input (Figure 4). This curve is representative of the boiling rate for all substances. However, other factors influence boiling rate besides the temperature difference. A few of these factors are surface tension, operating pressure, nature of boiling surface, and physical properties of the fluid such as specific heat, latent heat of vaporization, viscosity, and thermal conductivity. I n general, higher boiling coefficients result when surface tension is low and when the boiling surface area is rough, permitting easier formation and release
B
t N C'
G
3:
i(-
rP
I I
A
Atztw-ts tw tg
i
(OF)
-
TEMP. OF TUBE WALL
TEMP OF BULK LIQUID
Figure 4. Point 8 is the critical temperature, or point where film boiling .occurs
of vapor bubbles. Also, increased pressure has the effect of increasing boiling coefficients. Although much experimental work has been done in determining maximum flux limitations and maximum heat transfer coefficients, the practice in industry is the use of a maximum flux of 12,000 to 15,000 B.t.u. per hour per square foot, and a maximum boiling coefficient of 300 to 500 B.t.u. per hour per square foot per O F. for most liquid hydrocarbons. With steam, the maximum boiling coefficient has been limited to 2000 B.t.u. per hour per square foot per F., though published data indicate that much higher rates may be attained. Condensers
I n practically every process, it is desirable to condense vapors generated during a fractioning operation. When the condensing takes place in a shell and tube exchanger, the procedure for calculating the over-all heat transfer coefficient is similar to that described for reboilers-that is, a condensing film coefficient is utilized in Equation (2a) in lieu of a liquid film coefficient. T h e methods for calculation of condensing coefficients vary widely. These differences stem from the manner in which the mechanisms of film condensation are considered. Some of these mechanisms are as follows : 0
Convection heat transfer between the vapor and condensate film a t the film-vapor interface. Condensation of vapors at the filmvapor interface. Conduction and convection through the condensate.
Other factors which have bearing on the condensing rate are the amount of noncondensable vapors passing through the exchanger as an inert medium. the amount of desuperheating of vapor that must take place before condensation, and the physical arrangement of tube rows in the path of the condensing vapor. The basic work in deriving a theory for condensation was done by Nusselt. Most of the recent correlations have followed the pattern of Nusselt's findings. However, experimental results yield condensing rates somewhat higher than the theoretical values. This difference is as much as GO to 70% in some cases. The reasons for these deviations have been attributed to differences between the assumptions made by Nusselt and actual experience. For example, Nusselt's assumptions included isothermal condensation of a pure vapor, laminar condensate drainage, and no frictional drag at the liquid interface. Experimental work has indicated that vapor
I TEMPERATURE-'E
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Figure 5. When mixed vapors are condensed, the heat release is usually nonlinear
velocities have a decided effect on the heat transfer as frictional drag becomes appreciable at higher velocities. Also the condensate flow downward through a nest of tubes evidently produces appreciable turbulence due to splattering and splashing. This is especially true when high condensate rates exist. When condensing mixed vapors, the heat release very often does not follow a straight line. Figure 5 illustrates a typical heat release curve for a mixture of steam and hydrocarbon. The dew point of the steam has a different dew point from the hydrocarbon. In this case, the actual M.T.D. could differ from the straight line M.T.D. by as much as 10 to 15%. T o obtain the corrected M.T.D., the duty is broken down into zones, each of which can be represented by a straight line. The coolant temperatures for each zone are found by determining the temperature rise of coolant in proportion to the amount of duty per zone. Then a mean temperature difference is calculated for each zone. The final weighted M.T.D. is then determined as follows: M.T.D.(wTD)=
total duty duty per zone M.T.D. per zone
Design Considerations
When first examining a process requirement for heat exchange, the initial consideration is the shell flow arrangement. A quick estimation yields the approximate surface requirements. As the size of exchangers is frequently limited by handling facilities for purposes of cleaning and maintenance, the number of shells to contain the surface is determined. I n most installations a 42- to 45-inch size is considered maximum. VOL. 52, NO. 6
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JUNE 1960
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Factors Which Would Influence the Selection
. . . of Shell Side
. .. of Tube Side 0
CORROSION.When special alloy materials are necessary to minimize corrosion, it is more economical to place the corrosive fluid in the tubes. Only the tubes, tube sheets, and channel need to be alloy. In comparison, if the shell side was selected, the shell and baffles would have to be alloy in addition to the tubes and tube sheets. EXCESSIVE FOULING. If mechanical cleaning is desired, the fouling medium should be placed in the tube side. This enables the tubes to be cleaned without removing the bundle from the shell.
0
HIGH TEMPERATURE. If high temperature service requires special alloy construction, the cost of an alloy shell and bonnet will be saved by using the tube side.
0
CONDENSING SERVICE. T h e larger free area on the shell side permits minimum pressure drop arrangements as well as higher condensate loadings.
0
BOILINGSERVICE. Vapor disengaging space may be provided on the shell side which eliminates the need for a separate dry drum. CRITICALPRESSURE DROP. By varying the baffle spacing, very low pressure drops may be attained.
0
VISCOUSFLUIDS.If mechanical cleaning is not required, higher heat transfer rates may be obtained by placing the viscous fluid on the shell side. Due to the flow pattern across the tube bank, turbulent flow may be maintained on the shell side at mass velocities which would yield laminar flow on the tube side.
HIGH PRESSURE. Tubes, tube sheets, and channel need be designed only for high pressure if the tube side is utilized. Also integral tube sheet and channel design may be used, thus eliminating one gasketed joint.
If multiple sections are required, the choice between series and parallel arrangement arises. Series arrangement results in the most economical investment cost. Also, series arrangement may be necessary if a temperature cross exists as mentioned previously when the M.T.D. was developed. HOWever, limitations in pressure drop may necessitate the use of parallel sections or a combination of series and parallel sections. This is especially true in compressor circuits where pumping costs are appreciable. The next major item to decide is the selection of the fluids €or flow through the tube or shell side of the exchanger. This decision is influenced by the corrosion and fouling characteristics of the flowing media, as well as the pressure and temperature levels involved. Analytical Procedure
When rating shell and tube exchanger, a standard procedure may be followed. The solution is obtained by a trial and error calculation; however with experience, accurate initial approximations will shorten the calculating time. This procedure would be as follows: Calculate the mean temperature difference. Evaluate the fluid bulk and film temperature. Determine fluid properties at these bulk and film temperatures. These properties include viscosity, specific gravity or density, specific heat, and thermal conductivity. Estimate an over-all heat transfer coefficient and determine surface area required. With this surface area requirement, evaluate how many shells will be re-
478
quired and their size, series, or parallel arrangement, and selection of tube or shell side for flowing media. Calculate tube side pressure drop and determine the number of tube passes that are required. Calculate tube side film coefficient. Calculate shell side pressure drop to determine maximum allowable shell side mass velocity. Calculate shell side film coefficient. Add film resistances and fouling resistances using Equation 3. If overall heat transfer coefficient is equal to that assumed in the fourth step above, the calculation is complete. If the calculated coefficient is different from that assumed, size or pressure drop changes must be made toaccommodate the design. Special Designs
I n addition to the shell-and-tube type exchangers, there are several other types of heat exchange equipment which are commonly used depending on their specific need or requirement. Some of these are double pipe exchangers and air cooled exchangers. The design calculation for a double pipe exchanger is very similar to that described for a shell and tube type. In order to increase the total heat transfer surface, fins are usually attached to the inside pipe. When fins are utilized, the heat transfer surface is increased 4 to 12 times. However, the over-all coefficient must be corrected for the fin effectiveness. This may reduce the over-all coefficient by as much as ”3 to ‘/4 the bare tube value. I n air cooler design, the process stream is in the tubes and the film coefficient may be easily obtained. The air side coefficient is dependent on the volume of air forced across the bundle by fans. I n air cooler design, because
INDUSTRIAL AND ENGINEERING CHEMISTRY
of the poor hcat transfer properties of air, aluminum fins are attached to the outside of the tubes to increase the effectiveness of the air side. The ratio of finned surface to bare tube surface is usually in the magnitude of 16 to 1. The air side coefficient correlations, M hich have been determined experimentally by most air cooler manufacturers, include the resistance of the fin metal, the effect of fin efficiency, and the bond resistance between the fin and the tube. These air side coefficients are generally referred to the tube outside diameter for calculation purposes. The air quantity used is based on overall economics of investmen t us. operating costs. When the tube side coefficient i s ~ O T Y as , in the case when viscous oils are being cooled, the low air side coefficient is not as critical in magnitude and lower air velocities may be used. Conversely when the tube side coefficient is high, the low air side coefficient is critical and highest practical air velocities must be used to achieve higher air side coefficients. References (1) Donahue, D. A,, “Heat Exchanger
Design,” Petroleum Processing Reprint, March 1956. (2) Kern, D. O., “Process Heat Transfer,” McGraw-Hill, New York, 1950. (3). M$dams, W. H., “Heat Transmission, 3rd ed., McGraw-Hill, New York, 1954. (4) Tubular Exchanger Manufacturers Association, “Standards of Tabular Exchanger Manufacturers Association,” 3rd ed., 1952. RECEIVED for review February 25, 1960 ACCEPTED February 29, 1960 Division of Industrial and Engineering Chemistry, 137th Meeting, ACS, Cleveland, Ohio, April 1960.
