B-5: SHELL AND TUBE HEAT EXCHANGER

Benedum Engineering Hall SB-92

Introduction The most common type of heat exchanger used in industry contains a number of parallel tubes enclosed in a shell and is thus called a shell and tube heat exchanger. These heat exchangers are employed when a process requires large quantities of fluid to be heated or cooled. Due to their compact design, these heat exchangers contain a large amount of heat transfer area and also provide a high degree of heat transfer efficiency. Over the years, many different types of shell and tube heat exchangers have been designed to meet various process requirements. In order to accomplish as much transfer of energy in as little space as possible, it is desirable to utilize multiple passes of one or both fluids. These heat exchangers are denoted by a pair of numbers which indicates the number of shell and tube side passes. For example, in a 1-2 heat exchanger, the shell side fluid will traverse the heat exchanger once while the tube side fluid will traverse the exchanger twice. Although variations on the number of tube-and-shell passes are encountered in numerous applications, it is not common practice to use more than two shell-side passes. Good mixing of the shell-side fluid is accomplished using baffles. Without the use of baffles, the fluid becomes stagnant in certain parts of the shell5. In this experiment, each of the four 1-2 heat exchangers have different baffle configurations. Heat exchangers in industry are most often designed with the aid of software programs. Given the required specifications for a heat exchanger, these simulators perform the appropriate calculations. In this experiment, students will run B-JAC in the rating mode (enter hx details, both inlet streams, and duty via specifying at least one outlet stream ; BJAC determines the actual area of your hx and the area required the duty you specified) or the simulation mode (enter hx details and both inlet streams, BJAC will determine both outlet streams, hx area and the duty) to determine the characteristics of the four 1-2 heat exchangers in the lab. Objectives Your instructor will specify which of these 3 tasks you should perform. 1. Using B-JAC in the simulation mode, determine the fouling factors for each heat exchanger. Vary these coefficients until the model matches your outlet stream data. (It is advisable to set the shell-side fouling factor = tube-side fouling factor.) 2. Perform a ‘simulation’ calculation for one of the 1-2 heat exchanger experiments by hand/spreadsheet. You must develop an algorithm that you can use to determine the pressure drop on the shell and tube sides and the outlet hot and cold stream temperatures. The input for your algorithm includes all heat exchanger details, all hot and cold inlet stream data, and correlations required for the determination of U, hi, ho and pressure drops. Compare your results with those obtained from a B-JAC simulation of the same problem. 3. Verify the constant in the empirical correlations used for the estimation of heat transfer coefficients. For example, keep the shell-side conditions constant and perform numerous runs changing the tube side conditions. Plot your results in such a manner that you can determine the constant in the dimensionless correlation. Compare your results with literature values.

Experimental Apparatus A diagram of the apparatus to be used in this experiment is shown in Figure 1. The unit consists of a four-pass steam condenser and four 1-2 heat exchangers in series. There are eighteen thermocouples strategically placed throughout the apparatus to measure the inlet and outlet temperatures to each heat exchanger. Steam is admitted to the condenser via a steam regulator. A pneumatic control valve is used to control the flow rate of steam to the condenser. A pressure gauge located on the steam inlet to the condenser is used to monitor the steam pressure. Steam flows through the condenser and then through a steam trap. The inlet water stream is split into two different streams. One stream flows into the steam condenser and the other stream flows into the shell side of the 1-2 heat exchangers. The flow rate of each stream is controlled using a valve in series with a rotameter. (Hot and cold water inlet pressures are about 90 psi). Valves are located on the inlet and outlet to the shell side and the tube side of the 1-2 heat exchangers. The valves are provided in order to isolate one of the heat exchangers. This experiment is performed using one of the exchangers at a time. Additional data about the apparatus is given below: Steam Condenser: Shell internal diameter = 0.1016 meters Wall thickness = 0.00211 meters 40 copper tubes, each 0.9047 meters in length There are 4 tube passes Internal diameter of tubes = 0.00616 meters External diameter of tubes = 0.00794 meters Internal area of tubes = 0.700 sq. meters External area of tubes = 0.901 sq. meters 1-2 Heat Exchangers: Shell internal diameter = 0.1016 meters Wall thickness = 0.001055 meters 48 copper tubes, each 1.22 meters in length There are 2 tube passes Internal diameter of tubes = 0.007391 meters External diameter of tubes = 0.009565 meters Baffle Detail:

Baffles: 0.0762 meters cut-out, 8.128 x 10-4 meters thick, 25%cut (the length of the baffle, 0.0762m, from the shell to the flat edge of the baffle is 75% of the diameter of 0.1016m)

Area of segment = 9.475 x 10-4 sq. meters Free area contains 9 tubes 0.0119 meter centers, triangular pitch, Spacing = Length in Table 1

Table 1. Baffle Information for each Heat Exchanger Exchanger number Number of Baffles Spacing (meter centers)

1 43 0.0254 2 29 0.0381 3 22 0.0508 4 16 0.0699

The diagrams below illustrate the tube layout, pitch, and overall orientation of Exchanger #2. Similar illustrations can be obtained from B-JAC for each of the four heat exchangers. One of the heat exchangers has been cut in half for your inspection.

Experimental Procedure • In the condenser, cold water is heated by admitting live steam to the shell of the condenser. A pneumatic control valve (shown in Figure 1) is used to regulate the steam pressure to the condenser. Initially, this pneumatic control valve should be opened and the house air line turned on. • Open the condensate drain valve located in the steam supply line. The valve on the steam supply line should then be opened slowly in order to remove the condensate from the line. When all of the condensate has been removed (ie: live steam flows out of the line) close the condensate drain valve. Use the pneumatic control valve to slightly open the regulator in order to remove all non-condensable gases from the system. This purge should be maintained throughout the experiment. • Once this is completed, the condenser is operational and the steam pressure can be regulated by adjusting the pneumatic control valve. This valve is very sensitive to small adjustments. The reading on the pressure gauge does not respond immediately after the valve position has been changed. Therefore, adjustments should be made slowly, and care must be exercised so as not to exceed a pressure of 10 psig. • Open one of the tube side valves (A, B, C, or D) and the corresponding shell side valve

(E, F, G, or H) for one of the 1-2 heat exchangers. • Water can then be admitted to the condenser tubes by opening valve “V1”. The flow rate of the water can be determined using the rotameter along with the calibration curve given in Figure 2. • The heated water from the condenser is then passed through the tubes of one of the 1-2 heat exchangers. Open valve “V2” to allow the cooling water to flow through the shell side of the exchanger. With the calibration curve (given in Figure 2) the cooling water flow rate can be determined using the rotameter. • At this time, the data acquisition system should be turned on. For complete operating

instructions, please see the “Automated Data Acquisition” section of this procedure. • Copper-constantan thermocouples are used to acquire temperature data at various points throughout the apparatus. The thermocouples are designated T1 through T18, and their locations are shown in Figure 1. A personal computer equipped with a printer has been installed to log temperatures automatically at fixed time intervals. Temperature readings are taken once every minute, and sent to the computer screen and the printer. • Steady state is achieved when the thermocouple readings remain fairly constant over a 5

minute time interval. Once steady state has been reached, both the hot water and cold water flows can be directed to the next 1-2 heat exchanger. To do this, open the shell and tube side valves to the next exchanger. Then, close the shell and tube side valves to the heat exchanger used in the previous experiment. Make sure the shell and tube side valves are opened to both heat exchangers before closing the valves to the first heat exchanger.

• Repeat successive trials for each of the four 1-2 heat exchangers. Obtain steady state temperature data for each exchanger. Note the hot and cold water flow rates used. • Once the experimental data has been obtained, use it to run the BJAC simulations, which

are located in Benedum Room 1122, the ChE Computer Lab. • To obtain data for calculating the shell and tube side individual film coefficients, select

one of the 1-2 heat exchangers. Perfom several runs with this exchanger, varying the hot water flow rate (tube side) for each trial.

Automated Data Acquisition Procedure Please see the lab technician concerning the curret configuration of the data acquisition and experimental control software. B-JAC Procedure Run BJAC in the simulation mode. Enter the appropriate data for the heat exchanger equipment, the inlet streams, and one outlet stream. Enter values for as many of the fields as possible. (The outlet stream serves only as an initial estimate for the calculation). BJAC will then determine both outlet streams. **Note: The objective of this section is to equate the shell and tube side fouling factors and to then vary their value until the outlet streams are matched as closely as possible. (It is impossible to match both exactly.) The heat exchangers have 48 tubes, so specify that value. Check the tube sheet drawing to verify that there are 48 tubes in the B-JAC output file. B-JAC will automatically adjust the number of tubes to fit into the shell area if it “thinks” that your 48 tubes cannot fit in the shell ID you specified. If the number of tubes is less than 48, increase the shell side area slightly until all 48 tubes appear.

Experimental Calculations for Task 3 To perform an enthalpy balance around one of the heat exchangers, the hot water and cold water flow rates should be set to desired values, and the system should be allowed to come to equilibrium (This should take about 15-20 minutes). Once steady state is reached, the temperatures should be recorded for each of the hot and cold streams entering and exiting the exchanger. After an adequate number of readings have been obtained, the flow rate(s) can be changed and the experiment can be repeated. The heat exchanged between the shell-side and tube-side fluids can be found by performing a simple energy balance around the appropriate section of the apparatus. For each heat exchanger, the following relationship applies: (Energy lost by hot stream) = (Energy gained by cold stream) + (Energy lost to the environment) The heat transferred from the hot stream to the cold stream can be calculated by applying the First Law of Thermodynamics4 to the cold fluid:

Q mC Tp= & ∆

where Q = The rate of heat transfer (Joules/sec), m = The mass flow rate of water (kg/sec), Cp = The heat capacity of water (Joules/kg⋅K), ∆T = The temperature difference between the inlet and outlet streams (K). The heat lost by the hot stream can be determined by applying the same equation to the hot fluid. The overall heat-transfer coefficient, U, is a common way of expressing the heat-transfer rate for a given system. A detailed derivation of the overall heat-transfer coefficient can be found in Welty, Wicks, and Wilson5. The result can be written as:

Q = U As FT ∆TLM where U = Overall heat transfer coefficient (J/m2⋅sec⋅K), As = The surface area available for heat transfer (m2), FT = Correction factor to allow for shell and tube configuration of exchanger (See Figure 15-2 of Peters and Timmerhaus4, or Figure 4.9-4a in Geankoplis6.) ∆TLM = The logarithmic-mean temperature difference (must be in Kelvins) The logarithmic-mean temperature difference5 between the inlet and outlet streams can be determined as follows:

( )∆

∆ ∆∆ ∆

TT T

T TLM =−2 1

2 1ln

The individual film coefficients for both the shell and tube sides can be calculated using two different methods. The first method5 is applicable when the Reynolds number is greater than 10,000. The second method3 can be used when you have flow in the transition region. This region includes Reynolds numbers between 2100 to 10,000. Use both methods to calculate the film coefficients. Method 1 – Fully Turbulent Regime; Re, flow in tube>10,000

Use Excel to generate a plot of 1/U versus 1/(Re)0.8 only for your data in the fully turbulent regime on the tube-side. The slope of the line is 1/α’, where α’ is a constant. Using the following equation, the constant α can be determined:

( )α α' Pr .= ⋅

kD

f

i

0 4

This constant is used to determine the tube side film coefficient (hi) from the equation shown below. The literature value for α is 0.023 5 Note that the temperature-effect-on-viscosity correction term (µi/µw)0.14 is not used because it is not significant for this lab.

( ) ( )hkDi

f

i

= ⋅

α Re Pr. .0 8 0 4

The shell side film coefficient (ho) can be calculated using the overall heat transfer coefficient (Ui), which is expressed as the sum of the resistances to heat transfer. These resistances include individual film transfer coefficients and, the thermal resistance of the tube itself. (You must run your expt. in such a manner that the last two terms remain constant!)

1 1U h

X Dk D

DD hi i

w i

m LM

i

o o

= + +

Xw = Wall thickness (m), kM = Thermal Conductivity of the metal (J/m⋅sec⋅K), DLM = Log mean Diameter (m) Method 2 – Transition Flow Regime; 2100>Re>10000 Use Excel to generate a plot of 1/U versus 1/[(Re)2/3-125] only if you have data in the transitional flow regime for tube side flow. The slope of the line is 1/β’, where β’ is a constant. Using the following equation, the constant β can be determined:

( )β β' Pr= ⋅

kD

f

i

23

kf = The thermal conductivity of the fluid (J/m⋅sec⋅K), This constant is used to determine the tube side film coefficient (hi) from the equation shown below:

( )[ ]( )hkDi

f

i

= ⋅

−β Re Pr

23

13125

The shell side film coefficient (ho) can be calculated using the same equation from Method 1, where:

1 1U h

X Dk D

DD hi i

w i

m LM

i

o o

= + +

(You must run your expt. in such a manner that the first two terms remain constant!) Literature value for β is 0.116 3. Method 3 – Laminar Flow; Re, tube side < 2100 (Avoid this regime!) It is unlikely that your Reynolds number in the tubes will be less than 2100. If so you will be in the laminar flow regime. You are responsible for determining the appropriate correlation to use in this case, and how to verify the constant in the correlation. It is recommended, however, that you design your experiment such that NONE of your data is in the laminar flow regime. Pressure Drop Calculation -Task 2 In calculating the pressure drop across a heat exchanger: • Friction of flow, contractions, expansions, and direction changes must be considered • Kinetic terms, potential terms, ∆Z, and V2 terms can be ignored • Pressure drops are usually on the order of several psi • Both tube and shell side pressure drops can be computed Tube Side Pressure Drop The tube side pressure drop calculation is similar to that for flow in pipes, with the addition of heat transfer and the resultant temperature change of the fluid. The pressure drop may be expressed as follows, with the subscript “i” referring to the inside of the tube at the bulk temperature.4

− =

∆P B

f G Lng Di

i p

c i i i

2 2

ρ φ

fi = The Fanning Friction Factor, calculated using the arithmetic-average temperature of the fluid. (See Moody Diagram, Figure 3 in manual.) G = Mass velocity inside tube, (mass/time⋅cross sectional area) L = Length of heat transfer surface np = The number of tube passes. gc = Gravitational conversion factor (necessary when English units are used) ρi = Density of tube-side fluid at the bulk temperature Di = Inside diameter of tube φi = The non-isothermal flow correction Assume this factor is 1 for this lab φi = 1.1(µi/µw)0.25 if (DiG)/µi < 2100 Laminar Flow φi = 1.02(µi/µw)0.14 if (DiG)/µi > 2100 Turbulent Flow µi = Fluid viscosity at bulk arithmetic average temperature µw = Fluid viscosity at average temperature of inside wall surface Bi = Correction factor which accounts for friction due to sudden contraction, sudden expansion, and flow reversal. (Dimensionless.)

( ) ( )BF F F

f G L g Dic e r

i z i i i

= ++ +

12 2 2ρ φ

For smooth pipes, turbulent flow, and no phase change,

( )

( )( )B

K n T

T T C ki

p fi i w

p i

≅ +−

1051 1

0 28

2 1

0 67

. .

.

∆ µ µ

µ

Again, the subscript “i” refers to the inside of the tube at the bulk temperature. K1 = Dimensionless constant used for evaluation of correction factor Bi (Can be calculated using equation below.) ∆Tfi = The temperature change across the film on the inside. (T2 - T1) = The total change in fluid temperature as the fluid flows through the exchanger tubes. k = The thermal conductivity of the pipe.

µi/µw = viscosity correction Assume this factor is unity for this lab

KSS

Kn

ni

Hc

p

p1

2

1 0 51

= −

+ +

−

.

(Si/SH) = The ratio of total inside-tube cross sectional area per pass to header cross- sectional area per pass. It should be less than unity, and ≈ 0.5 For staggered tubes,

SS

AreaArea

D

base heighti

H

Circle

Triangle

=

=

⋅

⋅ ⋅1 2

205 4

05

.

.

π

Figure 4 Where D = the inside diameter of the tube, and the dimensions of the triangle can be determined from the geometry of the heat exchanger. (See Figure 4.) Kc = The loss coefficient due to friction for sudden contraction in a pipe. (See Peters and Timmerhaus, Table 14.1) Kc is dimensionless, and can be calculated using the following equation:

KAAc = −

0 4 125 1

2. . Note:

AA

1

2 can be approximated as

SS

i

H.

∆Tfi. How is ∆Tfi determined? Determine the average hot bulk fluid temperature and the average cold bulk fluid temperature. Estimate the overall heat transfer coefficient using the inside convective coefficient (hi), the thermal conductivity of the tube wall, and the outside convective heat transfer coefficient (ho), the wall thickness, and a knowledge of the tube inside and outside diameters. This is enough information for you to determine the temperature profile from the average bulk hot fluid T to the average bulk cold fluid T; ∆Tfi is simply the difference between the average bulk temperature of the inside fluid and the inner tube wall temperature. To calculate

h

Tube

the overall heat transfer coefficient, U, use the equations for U and hi given in the previous section of this manual. The equation for ho, below, will also be needed: Or for a rough estimate of ∆Tfi. Because the shell and tube side are both water undergoing sensible temperature changes, we can assume that the temperature drop across the film on both sides are comparable, and the temperature drop across the tube wall is small. Therefore simply estimate ∆Tfi as 45% of the difference between the average shell side temperature and the average tube side temperature. To calculate the overall heat transfer coefficient, U, use the equations for U and hi given in the previous section of this manual. The equation for ho, below, will also be needed:

( ) ( )hk

D fof

o s= ⋅

⋅

α Re Pr. /0 6 1 3

fs = Safety factor of 1.6 (dimensionless). Re = Reynolds number of the shell side fluid. All other variables are described in the previous section. The following equations may be useful in your analysis of the heat exchanger. The 1st law of thermo: ( ) ( )& &mC T Q mC Tp Shell p Tube

∆ ∆= =

The design equation for a shell-and-tube heat exchanger: Q = U As FT ∆TLM

A combination of the two previous equations ∆TLM =⋅

=⋅

QUA F

mC TUA FT

p

T

& ∆

Shell Side Pressure Drop For the case of fluid flow across tubes, the following equation can be used to approximate the pressure drop due to friction.

− =⋅

⋅

∆P

B f N Gg

o r s

c o

2 2'ρ

Bo = Correction factor to account for friction due to reversal in direction of flow, recrossing of tubes, and variation in cross section. When the flow is across unbaffled tubes, it can be taken as roughly 1.0; otherwise it can be taken as the number of tube crosses. The number of tube crosses is equal to the number of baffles in the exchanger plus 1. f’ = A special friction factor for shell-side flow (see below). Gs = Mass flux of fluid, (mass/time⋅free area) Free area is explained later in this section. Nr = The number of rows of tubes across which shell fluid flows. Since the shell has a circular cross-sectional area, a square area must be approximated to determine the number of rows in the exchanger. To do this, set up the given number of tubes into a square grid. For example, if given 15 tubes, you can approximate using a 4x4 grid. The length of the grid must equal the width of the grid; (ie: it must be a perfect square). See the example in Figure 5. gc = Gravitational conversion factor (necessary when English units are used) ρo = Density of the shell-side fluid at the bulk temperature. The friction factor f’ is a function of the Reynolds number of the flowing fluid and of the arrangement of the tubes. When 2000 < Re < 40,000 the friction factor can be approximated as follows:

f bD G

oo s

f

'.

=

−

µ

0 15

Do = Outside diameter of tube (length) µf = Shell-side fluid viscosity (pressure⋅time) For staggered tubes, bo = 0.23 + 0.11 (xT - 1)1.08

For tubes in line, ( )

bx

xo

L

T xL

= +− +

0 0440 08

1 0 431 13.

..

.

Where: xT = The ratio of tube center-to-center distance (i.e. pitch) transverse to flow to tube diameter, xL = The ratio of pitch parallel to flow to tube diameter.

4 x 4 grid, ≈ 15 tubes

Figure 5

Both quantities (xT and xL ) are dimensionless. The heat exchangers in SB-92 contain staggered tubes. Free area is simply the area available for flow through the shell. This means that the area occupied by tubes must be subtracted from the total area of the shell. In the diagram below, the free area is represented by the unshaded portion of the heat exchanger.

Figure 6: Side Cross Sectional View of Heat Exchanger 1

Pitch = Center to Center Distance Between Tubes Clearance = Center to Center Distance minus Outside Diameter of Tube

Spacing of Baffles = Distance between Sets of Baffles, from center to center

Tube

Center to Center Distance Between Tubes

Shell Inside Diameter

Outside Diameter of Tube

Clearance

Spacing of BafflesBaffle Baffle

Bibliography 1. Felder, Richard M., Rousseau, Ronald W., Elementary Principles of Chemical Processes, 2nd Edition, John Wiley and Sons, Inc., NY, NY (1986), pp. 615-624. 2. McCabe, Warren L., Smith, Julian C., and Harriott, Peter, Unit Operations in Chemical Engineering, 5th Edition, McGraw-Hill Book Company, NY, NY (1993), Section 3. 3. Perry, John H., Chilton, Cecil H., and Kirkpatrick, Sidney D., Perry’s Chemical Engineers’ Handbook, 4th Edition, McGraw-Hill Book Company, NY, NY (1963), Chapter 10 4. Peters, Max S., and Timmerhaus, Klaus D., Plant Design and Economics for Chemical Engineers, 4th Edition, McGraw-Hill Book Company, NY, NY (1991), Chapters 14 and 15. 5. Welty, James R., Wicks, Charles E., and Wilson, Robert E., Fundamentals of Momentum, Heat, and Mass Transfer, 3rd Edition, John Wiley and Sons, Inc., NY, NY (1984), Chapters 19, 20, and 22. 6. Geankoplis, Christie J., Transport Processes and Unit Operations, 3rd Edition, Prentice-Hall, Inc., NJ (1993), Chapter 4.