Model Report COMPLETE Shell Tube

8/2/2019 Model Report COMPLETE Shell Tube

1/20

Shell and Tube Heat Exchanger, James Anstey

Heat Transfer in Shell and Tube Exchangers: A Further

Study of the Reliability of Current Theoretical Methods.

Submitted By : James Anstey (SID: 9506654)

Group 13 : Anne Claxton

Anna Schlunke

Date Performed : 23-3-99

Date Submitted : xx-4-99

Date Re-Submitted : x-5-99

1


2/20


Executive Summary:

The focus of this work is to take existing correlations between heat exchanger

design and heat transfer rate (for example Kerns or Bells methods) and test

their reliability and accuracy for the determination of overall heat transfer

coefficients and pressure drops. The overall heat transfer coefficient was

determined experimentally and subsequently compared to the sum of the

individual heat transfer coefficients for the tube and shell sides as calculated

theoretically (appropriate fouling resistances and wall thermal conductivity

were also taken into consideration for this summation).

The results obtained demonstrate that the calculation of the overall heat

transfer coefficients using Kerns method appears more reliable when there

exists a highly turbulent flow regime in the shell-side. It is postulated that this

effect may be due to the reduced contribution of the shell-side coefficient,

with fouling factors becoming increasingly dominant in the overall coefficient.

Conversely Bells method displays a better agreement with experimental

results with a lower shell-side Reynolds number. Hence it is concluded that

Bells method gives a more reliable shell-side heat transfer coefficient than

that obtained with Kerns. It was not possible to differentiate the accuracy of

the various fouling resistances due to error involved in calculating the overall

heat transfer coefficients arising from both the log mean temperature driving

force and the temperature correction factor. Errors ranged from 10 130 %,

averaging around 25 %.

There was a significant disagreement between the calculated overall

pressure drops for the shell side with Kerns and Bells methods when

compared to the experimental values. It has not been elucidated if this result

is an experimental artifact (due to equipment failure: for example nozzle

blockage) or a reflection on the performance of the two methodologies.

2


3/20


Table of Contents:

HEAT TRANSFER IN SHELL AND TUBE EXCHANGERS: A FURTHER STUDY OF THE

RELIABILITY OF CURRENT THEORETICAL METHODS..............................................................1

EXECUTIVE SUMMARY:...............................................................................................................................2

TABLEOF CONTENTS:................................................................................................................................3

INTRODUCTIONAND THEORETICAL BACKGROUND:..........................................................................................4

EXPERIMENTAL METHODOLOGY:..................................................................................................................8

RESULTS:...............................................................................................................................................10

DISCUSSION:...........................................................................................................................................13

Experimental Reliability.................................................................................................. ........ .......13

Evaluation of Theoretical Methods............................................................................................. ....14

CONCLUSION:..........................................................................................................................................17

REFERENCES:..........................................................................................................................................18

APPENDICES:...........................................................................................................................................19

3


4/20


Introduction and Theoretical Background:

Shell and tube heat exchangers are common in industrial practice. It is

necessary to test the reliability and accuracy of existing correlations between

heat exchanger design and heat transfer rate (for example Kerns or Bells

methods) for the determination of overall heat transfer coefficients and

pressure drops.

The calculation of individual heat transfer coefficients resulting from fluid flow

is possible due to the experimentally determined correlation between the

Nusselt (Nu), Reynolds (Re) and Prandtl (Pr) numbers. The Nusselt number

acts to define the heat transfer properties of the fluid which is proportional (not

linearly) to the fluid flow (as defined by the Reynolds number) and the heat

capacity of that fluid (the Prandtl number). For a non-viscous fluid (such as

water) this relationship is of the form:

baxNu .(Pr).(Re)=

For water the equation contains no correction for changes in viscosity with

temperature, as this effect is negligible over the temperature range

considered. The parameters a, b, x have been fitted experimentally to provide

a working relationship under constrained geometric parameters (for instance

the Sieder-Tate relationship for fluid flow in pipes). The values of Nu, Re, and

Pr are described by:

k

dhNu e

.=

edu ..Re =

k

Cp .Pr=

Where:

=h heat transfer coefficient (W/m2.K)

=ed equivalent diameter (m)

=k thermal conductivity (W/m.K)

=u fluid velocity (m/s)

= fluid density (kg/m3

)= fluid viscosity (kg/m.s)

4


5/20


=pC heat capacity of the fluid (J/kg.K)

Kerns and Bells methods both use this general relationship between fluid

flow and heat transfer, but in addition define means of calculating appropriate

shell side fluid velocities. Hence it is possible to use the general relationshipfor heat transfer, modified by supplying specific dimensionless numbers

(specifically the Reynolds number) which are dependent on the arrangement

of the shell and tube exchanger. These two correlations differ by the means in

which each calculate the shell-side velocities and account for non-ideal heat

transfer; for instance Bells method includes correction factors for fluid leakage

and bypass in the heat exchanger, terms not present in the Kerns method

calculation. Sample calculations for both of these methods are presented inAppendix A, and the reader is referred to Coulson and Richardson Volume 6

for a thorough detailing of both procedures.

Now once the individual heat transfer coefficients have been calculated for the

shell and tube sides, and with the inclusion of appropriate fouling resistances

and wall conductivity and overall heat transfer coefficient can be derived.

o

o

osoi

i

it A

F

AhAA

F

AhUA++++=

.

1

..

11

Where:

=U overall heat transfer coefficient (W/m2.K)

=A overall heat transfer area (m2)

=th tube side heat transfer coefficient (W/m2.K)

=iA tube inside area (m2)

=iF inside fouling resistance (m2

.K/W)

= tube wall thickness (m)

= wall thermal conductivity (W/m.K)

=oA tube outside area (m2)

=sh shell side heat transfer coefficient (W/m2.K)

=oF outside fouling resistance (m2.K/W)

5


6/20


As the overall heat transfer coefficient can also be determined experimentally

it is possible to test the reliability of individually determined heat transfer

coefficients (from both Kerns and Bells methods) after their summation to

give an overall coefficient. The experimental overall heat transfer coefficient

can be calculated from the following formula:

mav TUAQ =

Where:

2/)( chav QQQ +=

cpcch TCmQQ = ..

=cm cold stream flow-rate (kg/s)

= cT change cold stream temperature (between inlet and outlet)

lmtm TFT = .

=tF temperature correction factor, a function of two dimensionless

temperature ratios R, S.

)(

)(tube

i

tube

o

shell

o

shell

i

TT

TTR

=

)()(

tube

i

shell

i

tube

i

tube

o

TTTTS

=

Ft can be read off temperature correction factor plots specific for the geometric

design of the heat exchanger.

)(

)(ln

)()(

tube

i

shell

o

tube

o

shell

i

tube

i

shell

o

tube

o

shell

i

lm

TT

TT

TTTTT

=

=shelliT inlet shell side fluid temperature

=shelloT outlet shell side fluid temperature

=tubeiT inlet tube side fluid temperature

=tubeoT outlet tube side fluid temperature

Hence by measuring the heat transfer of the exchanger under different flow

regimes (laminar to transitional to turbulent) the accuracy of the two methods

6


7/20


can be evaluated, particularly when the shell side coefficient is the dominant

resistance.

The shell-side pressure drop can be calculated with the following formula

(Kerns method):

2

.8

2

s

Be

sfs

u

l

L

d

DjP

=

Where:

=fj shell side friction factor

=sD diameter of the shell

=L length of shell

=Bl distance between baffles

=su shell-side fluid velocity

The shell-side pressure drop can also be estimated with Bells method, which

attempts to provide a more reasonable representation of the pressure drop by

summing the calculated pressure drops for individual parts of the exchanger.

The exchanger is broken up into three compartments: a) the end zones, b) the

flow across the tubes, and c) the window zones. Again the reader is referred

to Coulson and Richardson Volume 6 and Appendix A for a full description of

the calculations.

From the theory presented above it is possible to estimate the values for

individual heat transfer coefficients, and subsequently calculate an overall

heat transfer coefficient for the shell and tube exchanger. Pressure drops for

both shell and tube sides can also be estimated using the Kern and Bell

correlations. Both the pressure drops and the heat transfer coefficient can be

compared to those calculated from experimental results.

7


8/20


Experimental Methodology:

Experimental work was performed on a 96 tube heat exchanger; with eight

tube passes for one shell pass, and with 34 baffle plates (20 % baffle cut).

Temperatures of the tube and shell flow were measured at point of entry and

exit. The flow rate and pressure drops of both the shell and tubes were also

measured.

Figure 1: Overall schematic of the shell-tube exchanger set-up.

The tube arrangement is square pitch with bundle diameter of 190 mm and

heat transfer length of 178 cm. Each tube is made of drawn copper with an

inside diameter of 7.1 mm and wall thickness of 1.2 mm. The shell contains

34 baffles spaced 50.8 mm apart and has an internal diameter of 195 mm.

Flow-rates and temperatures were allowed to equilibrate for 20 minutes after

each change in condition.

8

Hot Water

Cooling

Tower

12 tubes per

pass, 8 passesShell in

Shell out

Tube in

Tube out


9/20


Table 1: Experimental conditions for operation of the shell and tube HX.

Run Fshell (kg/min) Ftube (kg/min) Thot tank (C) Tcold tank (C)1 42.3 2.5 40 20

2 42.3 10.6 40 20

3 41.3 23.4 40 204 41.0 39.3 40 20

5 41.3 29.6 40 20

6 41.0 49.6 40 20

7 29.6 7.2 40 20

8 25.7 16.6 40 20

9 27.8 21.2 40 20

10 28.5 36.6 40 20

11 27.4 29.7 40 20

12 28.1 44.2 40 20

13 28.3 28.6 60 20

9


10/20


Results:

All raw data can be found in appendix A. Figure 2 shows that, for all but two

runs, the heat gained by the cold stream was within experimental

uncertainties of that lost by the hot stream, confirming the energy balance for

these data and hence the reliability of the results.

y = -1.0592x

0

20000

40000

60000

-60000 -40000 -20000 0

Heat Loss Hot Stream (W)

HeatG

ainColdStream

(W)

Figure 2: Plot of the shell-side heat loss against the tube-side heat gain.

Gradient of the line is the heat balance. X-errors bars are calculated by the

maximum heat loss to the surroundings at steady-state. Y-error bars are

negligible as they represent the possible temperature deviation between the

inlet and outlet of the tubes (less than 1 % error).

Propagation of error calculations, shown in Table 2, demonstrate the strong

sensitivity of the temperature correction factor (Ft) and the log mean

temperature difference (Delta Tlm) to temperature fluctuations of 0.2 degrees

Celsius and flow-rate oscillations of 0.5 L/min.

Figure 3 shows that the agreement between theory and experiment in the low

heat transfer range is poor for both Bells and Kerns methods, but that. Bell's

method is much better at higher heat-transfer coefficients.

Figure 4 demonstrates that low heat transfer occurs for tube-side laminar flow.

10


11/20


Table 2: Propagation of error to the log mean temperature and the

temperature correction factor.

Run Err Ft Err Delta Tlm Total Err

1 13 40 49

2 8 7 9

3 6 9 12

4 5 25 34

5 6 11 18

6 5 104 133

7 8 7 9

8 7 9 14

9 6 17 23

10 6 23 32

11 6 44 5812 5 14 22

13 3 30 40

0

100

200

300

400

500

600

700

800

900

1000

0 200 400 600 800 1000 1200

Experimental U (W/m2.K)

EstimatedU(W/m2.K)

Figure 3: Plot of all calculated vs experimentally determined heat transfer

coefficients. Error bars are included for Bells and Kerns methods with the

maximum fouling. Derivation of experimental error is attached in appendix C.

Diamonds Kerns method (minimum fouling), squares Kerns method

(maximum fouling), triangles Bells method (minimum fouling), crosses

Bells method (maximum fouling).

11


12/20


200

300

400

500

600

700

800

0 5000 10000 15000

Tube-side Reynolds' Number

EstimatedOHTC(W/m2.K)

Figure 4: Plot of the Reynolds number across the tube-side against the

overall heat transfer coefficient (calculated using Bells method minimum

fouling). Squares 50 % flow shell-side, diamonds 100 % flow shell-side.

12


13/20


Discussion:

Experimental Reliability

The temperature fluctuations in the steady-state regime are estimated as 0.2

degrees Celsius, and flow-rate oscillations at 0.5 L/min. Initially the maximum

heat loss to the surroundings was calculated for the heat exchanger operating

in a steady-state regime. This value was obtained by measuring the

temperature drop the hot flow with zero cold flow through the tube-side. A

value of 1452 W was obtained, although this value itself comprises significant

error from the small change in temperature (error of 70 %). The reliability of

the other experimental results can be seen with a heat balance between the

shell and tube flows.

tpt

sps

TCm

TCmeHeatBalanc

=

..

..

Where:

=sm flow-rate of shell-side

=tm flow-rate of tube-side

=pC heat capacity

= sT inlet outlet temperature for shell-side

= tT inlet outlet temperature for tube-side

Under ideal steady-state conditions (where heat loss to the surroundings is

negligible) the heat loss from the shell side should equal the heat gain in the

tube flow. Figure 2 demonstrates that most of the experimental values are in

fact at steady-state, with the gradient of the linear regression (which is in fact

the heat balance) equal to 1 and lying within the error range of almost all

points. Although the heat balance may be valid, the calculation of the overall

heat transfer coefficient in the low heat transfer regime can give rise to large

uncertainty as the changes in flow-rates and temperatures are small. In this

case values such as the log mean temperature difference and the

temperature correction factor can propagate a large error to the heat transfer

coefficient.

13


14/20


This result is seen in Table 2 where the calculated uncertainty in the

parameters S and R (defined in the introduction) can result in errors of up to

10% in the temperature correction factor. Such high error results from the

nature of the function (Ft) which displays a drop-off in the region of < 0.8,

hence small perturbations in the inlet and outlet temperatures can result in a

large change in the Ft value (drop-off). Note that the methodology for the

calculation of errors is presented in appendix C. The total calculated error for

the mean temperature difference across the heat exchanger is also presented

in Table 2, which includes error from both the log mean temperature and the

temperature correction factor. As the log mean temperature driving force

involves the difference of the inlet and outlet temperatures the small errors

become very significant. This is readily apparent when the inlet tube side and

shell side temperatures are very close as with the exit temperatures (as for

run 6).

Evaluation of Theoretical Methods

For the theoretical calculation of the overall heat transfer coefficients two sets

of reasonable fouling resistances were used to investigate the size of the

effect of these resistances on the final coefficient. These values were:

A) Inside tube fouling resistance = 1.75 104 (m2.K/W)

Outside tube fouling resistance = 1.75 104 (m2.K/W)

Wall Conductivity = 401 (W/m.K)*

B) Inside tube fouling resistance = 3.5 104 (m2.K/W) b

Outside tube fouling resistance = 1.75 104 (m2.K/W)

Wall Conductivity = 401 (W/m.K)*

() Treated cooling tower water (Hewitt pg 872)

(b) Treated cooling tower water (Hewitt pg 872)

() Closed loop treated water (Hewitt pg 872)

(*) Drawn copper at 300 K (Hewitt pg 1022)

Figure 3 clearly shows the poor agreement between theory and experiment in

the low heat transfer range, with both Bells and Kerns methods performing

14


15/20


poorly. In all runs the flow through the shell-side of the exchanger is turbulent

with the shell-side Reynolds number > 2000. Hence such a result suggests

that the heat transfer coefficient for the tube-side is in error when the flow in

the tubes is laminar. This is consistent with the deviation occurring for both

Bells and Kerns methods, as the same tube-side coefficient is used for the

calculation of the overall heat transfer coefficient. This study is particularly

concerned with a situation where the shell-side coefficient gives a significant

contribution to the overall heat transfer coefficient as this will more rigorously

test the theoretical methods employed. Figure 4 demonstrates that the low

heat transfer occurs when there exists a laminar flow through the tube-side.

Therefore it is sufficient to evaluate the most reliable theoretical heat transfer

coefficients (those which lie within the error of the experimental values)

against the experimental values. Figure 3 clearly shows that Bells method

most successfully models overall heat transfer, with most calculated values

lying within the error of the experimental values. The actual fouling would

appear to be between the two extreme values taken, with the minimum and

maximum fouling Bells method lying on either side of the line representing

agreement between theory and experimental.

It is also apparent that Kerns method displays less error when the shell-side

heat transfer coefficient is not controlling the overall heat transfer (ie a high

shell-side fluid flux). Bells method displays a trend counter to this with an

improvement in the overall heat transfer coefficient as the shell-side becomes

more dominant. Such a trend suggests that Bells method can more

accurately evaluate the shell-side coefficient whereas the agreement seen

with Kerns method may arise only when fouling resistances provide a large

contribution to the overall heat transfer coefficient.

For the calculation of pressure drops across the shell-side of the exchanger

both methodologies significantly underestimate the value of the pressure

drop. For Bells method this is almost a factor of ten on all occasions, and with

Kerns method by a factor of five. With such a large discrepancy found

between the experimental values and the theoretical calculations it is

speculated that some of the error may be attributable to the experimental

value rather than across the board poor agreement. Equipment failure such

15


16/20


as nozzle blockage or anomalous pressure readings could account for this

increase in shell-side pressure.

16


17/20


Conclusion:

The overall heat transfer coefficient as determined using the two theoretical

methods were tested against the experimentally determined values; where the

experimental values were chosen in the high heat transfer regime and at

when the heat exchanger was operating under steady-state conditions

(determined through a heat balance). Bells method (minimum fouling)

provided the most reasonable agreement with the experimental results.

The calculated pressure drops for the shell-side were not in agreement with

experimental results by upwards of a factor of ten as calculated with Bells

method. This discrepancy may be experimental artefact, hence no evaluation

of either theoretical method was possible.

17


18/20


References:

1. Coulson and Richardson, Volumes 1 and 6

2. Kern, D Q, Process Heat Transfer McGraw Hill, 1950

3. Hewitt, Shires, Bott, Process Heat Transfer CRC Press, 1994

18


19/20


Appendices:

19


20/20


Appendix A

Table 1: Experimental values obtained for the overall heat transfer coefficient

and pressure drops across shell and tube-sides.

Run Number Qh/Qc Uoverall (W/m2.K)

Pshell (kPa) Ptube (kPa)1 1.62 109 12.04 -0.142 1.12 334 12.04 3.02

3 1.06 608 12.11 10.9

4 0.88 733 11.97 24.38

5 0.88 645 12.13 15.12

6 0.79 817 12.06 32.91

7 1.09 214 7.37 1.1

8 0.97 432 7.25 6.56

9 0.99 432 7.01 10.02

10 0.95 655 7.17 24.3

11 0.83 540 7.16 15.5312 0.86 658 7.46 31.91

13 1.05 590 7.18 15.62

Table 2: Calculated shell-side pressure drops using Kerns and Bells

methods.

Run 1 2 3 4 5 6 7 8 9 10 11 12

Kern (kPa) 2.3 2.3 2.2 2.2 2.2 2.2 1.5 1.4 1.3 1.4 1.3 1.3

Bell (kPa) 1.6 1.6 1.5 1.5 1.5 1.5 0.8 0.7 0.7 0.7 0.7 0.7

Date post:	06-Apr-2018
Category:	Documents
Upload:	abubacker-siddieq
View:	224 times
Download:	0 times

Model Report COMPLETE Shell Tube

Documents