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INTRODUCTION TOHEAT EXCHANGERS

1.1 Introduction

The need for heat transfer arises because it is a way to transfer energy from one media to

another. Some of the common applications requiring a transfer of energy in the form of

heat are heating a cooler fluid by using some hot fluid (e.g air preheating in gas turbine

power plants), reducing the temperature of hot fluid by using a cooler fluid (e.g cooling

water used in chillers), boiling a liquid using a hot fluid (e.g boiling of common water

from heavy water in steam generator of a nuclear reactor), and condensing a gaseous fluid

by using cooler fluid (e.g in condenser of a steam power plant).

A heat exchanger is a device that is used to transfer thermal energy (enthalpy) between two

or more fluids, between a solid surface and a fluid, or between solid particulates and a

fluid, at different temperatures and in thermal contact. n heat exchangers, there are usually

no external heat and wor! interactions.

1

Chapter 1



"eat exchangers are devices that facilitate the exchange of heat between two fluids that are

at different temperatures, while !eeping them from mixing with each other. "eat

exchangers are commonly used in practice in a wide range of applications, from heating

and air conditioning systems in a household, to chemical processing and power production

in large plants. "eat exchangers differ from mixing chambers in that they do not allow the

two fluids involved to mix.

"eat exchangers are manufactured in a variety of types and thus we shall start this chapter

with the classification of heat exchangers. Then we shall describe different flow

configurations of the heat exchangers. #e shall also mention some ma$or application areas

of heat exchangers. Towards the end of the chapter, we shall explain some of the basic

terminologies related to the shell and tube heat exchangers that is the main focus of this

sub$ect.

%ommon examples of heat exchangers are shell&and tube exchangers, automobile radiators,

condensers, evaporators, air preheaters, and cooling towers. f no phase change occurs in

any of the fluids in the exchanger, it is sometimes referred to as a sensible heat

echan!er. There could be internal thermal energy sources in the exchangers, such as in

electric heaters and nuclear fuel elements. %ombustion and chemical reaction may ta!e

place within the exchanger, such as in boilers, fired heaters, and fluidi'ed&bed exchangers.echanical devices may be used in some exchangers such as in scraped surface

exchangers, agitated vessels, and stirred tan! reactors. "eat transfer in the separating wall

of a recuperator generally ta!es place by conduction. "owever, in a heat pipe heat

exchanger, the heat pipe not only acts as a separating wall, but also facilitates the transfer

of heat by condensation, evaporation, and conduction of the wor!ing fluid inside the heat

pipe. n general, if the fluids are immiscible, the separating wall may be eliminated, and

the interface between the fluids replaces a heat transfer surface, as in a direct&contact heat

exchanger.

ot only are heat exchangers often used in the process, power, petroleum, transportation,

air&conditioning, refrigeration, cryogenic, heat recovery, alternative fuel, and

manufacturing industries, they also serve as !ey components of many industrial products

2



available in the mar!etplace. These exchangers can be classified in many different ways.

#e will classify them according to transfer processes, number of fluids, and heat transfer

mechanisms. %onventional heat exchangers are further classified according to construction

type and flow arrangements. Another arbitrary classification can be made, based on the

heat transfer surface area*volume ratio, into compact and non compact heat exchangers.

This classification is made because the type of equipment, fields of applications, and

design techniques generally differ. Additional ways to classify heat exchangers are by fluid

type (gas+gas, gas+liquid, liquid+liquid, gas two&phase, liquid two&phase, etc.), industry,

and so on, but we do not cover such classifications in this chapter.

1." Classi#ication o# heat echan!ers

ifferent heat exchanger applications require different types of hardware and different

configurations of heat transfer equipment. The attempt to match the heat transfer hardware

to the heat transfer requirements within the specified constraints has resulted in numerous

types of innovative heat exchanger designs.

There are different ways to classify the heat exchangers.

a) %lassification based on construction and function.

b) %lassification based on flow configuration.

c) %lassification based on interface between streams

d) %lassification based on type of temperature change pattern.

1.".1 Classi#ication based on construction and #unction

3



-ollowing are some of the main types of heat exchangers based on their construction and

equipment

/. ouble pipe heat exchanger

0. Shell and tube heat exchanger 1. 2late heat exchanger

3. 2late fin heat exchanger

4. %ompact heat exchanger

5. 6egenerative heat exchanger

7. Adiabatic wheel heat exchanger

8. 2hase change heat exchanger

DOU$%E &I&E HEAT EXCHANGER

t is the simplest type of heat exchangers, consisting of two concentric pipes of different

diameters. 9ne fluid in a double pipe heat exchanger flows through the smaller pipe while

the other fluid flows through the annular space between the two pipes. ouble pipe heat

exchangers have the lowest heat transfer surface area for a given length of the exchanger.

They have a very low pressure drop. This type of heat exchanger finds its application in a

variety of industries for purposes such as material processing, food preparation and air&

conditioning.

-igure /./ouble pipe heat exchanger

SHE%% AND TU$E HEAT EXCHANGER

4



Shell and tube heat exchanger is the most commonly type of heat used in industry today.

This is due to a number of advantages that they have over other types of heat exchangers.

They are relatively simple and have the ability to handle a large variety of wor!ing fluids.

Shell and Tube heat exchangers are typically used for high pressure applications with

pressures greater than 1: bar and temperatures greater than 05:;%.

Shell and tube heat exchangers consist of a series of tubes. 9ne set of these tubes contains

the fluid that must be either heated or cooled. The second fluid runs over the tubes that are

being heated or cooled so that it can either provide the heat or absorb the heat required. A

set of tubes is called the tube bundle and can be made up of several types of tubes< plain,

longitudinally finned, etc.

A shell and tube heat exchanger is a modification of double pipe heat exchanger. This is a

common form of construction, common and robust. "owever it is heavier than a double

pipe heat exchanger.

-igure /.0 Shell and tube heat exchanger

&%ATE HEAT EXCHANGER

5



The plate heat exchangers consist of a series of plates that are arranged one over the other

and connected together so as to provide strength to the assembly. They normally have flow

ports in all four corners and are clamped together in a frame that carries bushes or no''les

lined up with the plate ports and connected to the external pipe wor! that carries the two

liquid streams.

The plate heat exchanger is particularly suitable for heat recovery duties in the chemical,

petroleum, food, dairy, and brewing industries.

There are at least three different configurations that fall into the category of plate heat

exchangers, (a) 2late&and&frame or gas!eted plate exchanger, (b) Spiral plate heat

exchanger and (c) =amella (6amen) heat exchanger

-igure /.1 2late fin heat exchanger

&%ATE 'IN HEAT EXCHANGER

6



2late fin or matrix heat exchangers represent about the most compact form of heat transfer

surface, at least in the usual case that the fluids must be !ept separated. These exchangers

are constructed of multiple layers of matrix or sandwich&folded metal sheets, separated by

parting sheets.

This type of heat exchanger consists of alternate hot and cold passages in between parallel

plates and having fins on them to enhance the heat transfer process. -ins are used on one

side for only for liquid to gas heat transfer and on both sides for gas to gas heat transfer.

This type of heat exchangers is used commonly for waste heat recovery applications.

CO(&ACT HEAT EXCHANGER

This type of heat exchanger is designed specifically to reali'e a larger heat transfer surface

area per unit volume. The ratio of heat transfer surface area to volume is called the area

density. A heat exchanger is classified as compact heat exchanger if it has an area density

equal to or greater than 7:: m0 * m1. This type of heat exchanger finds application in car

radiators, glass&ceramic gas turbine heat exchangers and the regenerator of a Stirling

engine.

-igure /.3%ompact heat exchanger

REGENERATI)E HEAT EXCHANGER

7



n this type of heat exchanger, the heat (heat medium) from a process is used to warm the

fluids to be used in the process, and the same type of fluid is used on either side of the heat

exchanger (these heat exchangers can be either plate&and&frame or shell&and&tube

construction). These exchangers are used only for gases and not for liquids.

-igure /.4 6egenerative heat exchanger

ADIA$ATIC *HEE% HEAT EXCHANGER

8



The adiabatic heat exchanger uses an intermediate solid or liquid to serve as a heat transfer

medium. The intermediate solid passes alternately through the hot and cold fluid streams.

9n its pass through the hot fluid it absorbs thermal energy in the form of sensible resulting

in an increase in temperature of it. This thermal energy is returned to the cold fluid when

the wheel passes through it.

Two examples of this are adiabatic wheels, which consist of a large wheel with fine threads

rotating through the hot and cold fluids, and fluid heat exchangers.

&HASE CHANGE HEAT EXCHANGER

n addition to dealing with single phase applications, heat exchangers also find their application in dealing with two phase mixtures. 2hase change heat exchangers can either

be condenser type converting vapors to liquid or evaporator type vapori'ing liquid to

vapors.

1."." Classi#ication based on #lo+ con#i!uration

A ma$or characteristic of heat exchanger design is the relative flow configuration, which isthe set of geometric relationships between the streams. t must be emphasi'ed that the

configurations described represent ideali'ations of what truly occurs it is never possible,

in practice, to ma!e the flow patterns conform to the ideal.

>ased on the flow configuration, the heat exchangers can be classified as<

/. 2arallel -low

0. %ounter -low

1. %ross -low

3. %ross %ounter -low

4. ultipass Shell and Tube -low

&ARA%%E% '%O*

9



n parallel flow heat configuration, the two fluids flow parallel to each other, in the same

direction.

This type of arrangement can not ma!e effective use of temperature difference between the

two fluid streams. "owever, this arrangement gives more uniform wall temperaturedistribution than most of the other flow configurations. 2arallel flow arrangement is not

preferred in cases where efficiency is the factor of prime importance.

-igure /.5 2arallel flow configuration

COUNTER '%O*

n counter flow configuration, the two wor!ing fluids flow parallel to each other, but in the

opposite direction.

%ounter&flow exchangers are most efficient, in that they ma!e the best use of the available

temperature difference, and can obtain the highest change of temperature of each fluid.

-igure /.7 %ross flow configuration

CROSS '%O*

10



n this arrangement, the two fluids flow at right angles to each other. The cross flow

arrangement is shown schematically in the figure /.8. -rom efficiency point of view, this

configuration lies in between the parallel and counter flow arrangements. They are easier

to construct. An example of cross flow is the car radiator.

-igure /.8 %ross flow configuration

-igure /.? %ross counter flow configuration

CROSS COUNTER '%O*

Sometimes, real heat exchanger flow configurations conform approximately to the

ideali'ations shown in -ig. They are termed cross&counter&flow exchangers. Two&, three&,

11



and four&pass types are represented and, of course, the possible number of passes is

unlimited.

%ross&counter&flow exchangers can be regarded as compromises between the desiderata of

efficiency and ease of construction. The greater the number of passes, the closer is theapproach to counter&flow economy.

(U%TI&ASS SHE%% AND TU$E '%O*

2arallel&flow and counter&flow features may be combined within the same exchanger, as

when tubes double bac!, once or more, within a single shell and the same effect can be

achieved, with straight tubes, by the provision of suitably subdivided headers.

The @&tube, or hairpin, arrangement has the advantage of easy construction because only

one end of the shell needs to be perforated, not two.

-igure /./: ultipass shell and tube flow configuration

1."., Classi#ication based on inter#ace bet+een strea-s

The two wor!ing fluids in a heat exchanger interact with each other through some

interface. They are brought into contact in a variety of ways and hence the heat exchangers

can be classified accordingly.

12



The different types of fluid&interface types include<

/. 2lain tubes

0. -inned tubes

1. atrix arrangements3. -ilms

4. Sprays

1.". Classi#ication based on t/0e o# te-0erature chan!e 0attern

According to the pattern of temperature change, heat exchangers can be classified as<

/. Single phase heat exchangers

0. 2hase change heat exchangers

SING%E &HASE HEAT EXCHANGERS

n a single phase heat exchanger all the heat flows in the form of latent heat only. There is

no latent heat involved at any point. The wor!ing fluid leaves the exchanger in the same

phase as it had entered it. n this case there is an appreciable change in the temperatures of

the two streams. Temperature of cold stream rises and temperature of hot stream falls, the

two being approximately equal at the exit.

a$ority of the heat exchangers in used in practice are of single phase type.

&HASE CHANGE HEAT EXCHANGERS

Sometimes, it is required by the exchanger to change only the phase of the wor!ing fluid.

n this case latent heat is also involved which accompanies a change in phase of one of the

streams without causing an appreciable change in its temperature. This type of heat

exchangers is called as phase change heat exchangers.

13



xamples of phase change heat exchangers include condensers and evaporators or boiler.

1., A00lication Areas o# Heat Echan!ers

1.,.1 In General

"eat exchangers are widely used in<

• 2ower plants

• Steel factories

• Transformer stations

• Bas processing plants

• %hemical plants

• %argo*chemical tan!er ships

• %ruise ships

• ngines

• Steam and gas turbines

• Space heating

• 6efrigeration

• Air conditioning

• 2etrochemical plants

• 2etroleum refineries

• atural gas processing.

1.,." In Industr/

"eat exchangers are widely used in industry both for cooling and heating large scale

industrial processes.

"eat exchangers are used in many industries, some of which include<

• #aste water treatment

• 6efrigeration systems

• #ine&brewery industry

14



• 2etroleum industry

1.,., In Aircra#t

n commercial aircraft, heat exchangers are used to ta!e heat from the engineCs oil system

to heat cold fuel. This improves fuel efficiency, as well as reduces the possibility of

free'ing fuel.

n early 0::8, a >oeing 777 flying as >ritish Airways -light 18 crashed $ust short of the

runway. n an early&0::? >oeing&update sent to aircraft operators, the problem was

identified as specific to the 6olls&6oyce engine oil&fuel flow heat exchangers. 9ther heat

exchangers, on >oeing 777 aircraft powered by B or 2ratt and #hitney engines, are notaffected by the problem.

1.,. In Electronics

• n 2ersonal computers

• n transformers

• n amplifiers

• n converters

• n household appliances

15



-igure /.// Application areas of heat exchangers

16



$asic 'luid (echanics

And Heat Trans#er

".1 INTRODUCTION

"eat exchangers are flow devices, that is, they involve the flow of two wor!ing fluids relativeto some boundary. The transfer of heat ta!es place across this boundary. Therefore in dealing

with the heat exchanger design problems we should have !nowledge of interaction between

the fluids and surface, fluid and surface properties that affect this interaction, the basic

mechanisms by which transfer of heat ta!es place and the factors that can be controlled to

improve this heat transfer.

The scope of this chapter is a brief introduction of the basic principles of heat transfer, study

of fluid properties that affect the rate of heat transfer and the basic mechanisms of heattransfer in a heat exchanger. #e shall study method to calculate overall heat transfer

coefficient for a heat exchanger. Towards the end of the chapter we shall explain the concepts

of log mean temperature difference and T (mean design metal temperature), and derive

the expressions for effectiveness of a heat exchanger.

17

Chapter 2



"." THER(ODNA(ICS RE)IE*

t is not the purpose of this thesis to supply all the !nowledge of thermodynamics that a heat

exchanger designer will need, but rather to refresh the designerDs memory about the most

commonly needed concepts. Some of the basic definitions and terminologies that are

important from view point of our pro$ect are explained in the following paragraphs.

".".1 TE(&ERATURE

-or present purposes, temperature is that property of matter, differences of which are cause of

heat transfer. t is an intensive property. ts symbol in this boo! is T, and it is measured in

Eelvin (E) or degrees %elsius (;%).

Desi!n te-0erature

The temperature that a heat exchanger is designed to maintain (inside) or operate against

(outside) under the most extreme conditions.

(ini-u- desi!n -etal te-0erature

t is the lowest temperature at which a pressure vessel or a heat exchanger can be operated at

full design pressure without impact testing of its component parts. Some users have a standard

value for T that has been chosen as the lowest temperature conditions at the site.

The temperature at which a vessel is %harvy impact tested is called test minimum design

metal temperature.

"."." &RESSURE

2ressure is the force that the material or more specifically a fluid exerts on its surroundings,

normal to its surface, per unit area of that surface. ts units are ewton per square meter

(*m0).

Desi!n 0ressure

18



The pressure used in the design of a vessel component together with the coincident design

metal temperature, for the purpose of determining the minimum permissible thic!ness or

physical characteristics of the different 'ones of the vessel. #hen applicable, static head shall

be added to the design pressure to determine the thic!ness of any specific 'one of the vessel.

Test 0ressure

t is the pressure at which hydrostatic test of a pressure vessel is carried out. ormally it is /.4

times of the highest pressure encountered in service.

"."., DENSIT

ensity of a fluid is the mass of the fluid per unit volume its units are !ilograms per cubic

meter (!*m1).

".". S&ECI'IC INTERNA% ENERG

The specific internal energy u of a material is the extensive property which changes as a

consequence of heat and wor! transfers in accordance with the linear relationship

#here m stands for the mass of the material, F signifies an increase, G is the symbol for the

heat transferred to the material, and # is the external wor! done by it during the transaction.

The units of u are $oules per !ilogram (H*!g).

".".2 S&ECI'IC ENTHA%&

The specific enthalpy h of a material is the extensive property that is related to the specific

internal energy @, to the pressure 2, and the density I by the relationship<

=i!e @, h is usually a function of two variables, for example, pressure and temperature its

units are $oules per !ilogram (H*!g).

19



".".3 S0eci#ic Heat Ca0acit/

n general, cv and c p for any particular substance are functions of temperature and pressure.

"owever, are often slowly varying properties and, over the range of temperatures li!ely to be

encountered in a heat exchanger, the variations can frequently be neglected.

>ecause steady flows, to which c p is more relevant than cv are so prevalent in heat exchanger

practice, the symbol c is sometimes used without subscript, to stand for the constant&pressure

specific heat capacity, c p.

"., HEAT TRANS'ER

"eat is a form of energy that is transferred from one body at a higher temperature to another

body at a lower temperature by the virtue of temperature difference between them.

"eat transfer can be defined as a branch of science which deals with the transformation of

energy from one form into other forms, and the laws and principles governing these energy

transformations.

(ECHANIS(S O' HEAT TRANS'ER

There are five different ways of heat transfer to be found in industrial applications.

• %onduction

• %onvection

• >oiling

• %ondensation

• 6adiation

".,.1 CONDUCTION

%onduction is a process in which heat is transferred by the physical contacts between the

particles. n conduction, regions with higher molecular energy will pass their energy to

regions with low molecular energy through direct molecular collisions. n metals, free

electrons moving within the structure also transfer heat through conduction.

20



-ourierCs law is also called the law of conduction. t is an empirical law based on

observations.

-igure 0./ %onduction through a plane surface

t states that the time rate of heat flow, dG*dt, through a homogeneous solid is directly

proportional to the area, A, of the section at right angles to the direction of heat flow, and to

the temperature difference along the path of heat flow, dT*dx i.e.

"ere ! is the constant of proportionality !nown as thermal conductivity of the material.

".,." CON)ECTION

%onvection heat transfer can be defined as the transport of heat from one point to another if a

flowing fluid as a result of macroscopic motion of fluid particles and the heat being carried as

internal energy.

%onvection is the transfer of heat by the actual movement of the warmed matter. t is thetransfer of heat energy in a gas or liquid by movement of currents. (t can also happen in some

solids, li!e sand.) The heat moves with the fluid.

%onvection is one of the ma$or modes of heat transfer and mass transfer. %onvective heat and

mass transfer ta!e place through both diffusion, the random >rownian motion of individual

21



particles in the fluid, and advection, in which matter or heat is transported by the larger&scale

motion of currents in the fluid. n the context of heat and mass transfer, the term JconvectionJ

is used to refer to the sum of advective and diffusive transfer.

".,., RADIATION

All the matter constantly radiates energy in the form of electromagnetic waves. The amount of

energy radiated depends strongly on the absolute temperature of the material and to some

extent on the surface characteristics ob the body. The magnitude of energy transferred by a

particular surface is governed by Stephen and >olt'mann law. This law states that the amount

of energy radiated by a body is directly proportional to the fourth power of absolute

temperature.

At normal temperatures, radiation heat transfer is relatively less significant conduction and

convection, though there are a few areas where it can ma!e significant contributions e.g the

loss of heat from non insulated steam lines. At higher temperatures it becomes significant

however, such temperatures are seldom encountered in heat exchanger applications.

". '%O* $OUNDAR %AER

-luids flowing past solid bodies adhere to them, so a region of variable velocity is built up

between the surface and free stream as shown in the fig. This variable velocity region is called boundary layer. The boundary layer is usually very thin in comparison to the overall

dimensions of the body immersed in fluid. Thic!ness of boundary layer is denoted by 4. The

boundary layer thic!ness is arbitrarily defined as

t is the approximate distance from the surface to a point at which the fluid achieves free

stream velocity.

The dimensional functional equation of boundary layer thic!ness on a flat surface is

#here

22



vm K free stream velocity

I K density of fluid in !g*m1

L K dynamic viscosity in !g*m.s

x K length along the surface at which boundary layer thic!ness is being evaluated

"..1 SING%E &HASE '%O*

A single phase flow is the flow of a fluid in a single phase, i.e flow as either a liquid or a gas.

At no point in the path of flow a two phase mixture is formed.

Single phase flow must be characteri'ed by both the geometry of the duct through which the

flow occurs and by the flow regime of the fluid as it goes through the duct. There are two basically different types of duct geometry< constant cross&section, in which the area available

for flow to the fluid has both the same shape and the same area at each point along the duct,

and varying cross&section, in which the shape and*or the area of the duct vary with length,

usually in a regular and repeated way.

The type of flow in a duct can also be characteri'ed by the flow regime that is, laminar flow,

turbulent flow, or some transition state having characteristics of both of the limiting regimes.

All of the exact definitions of laminar flow are very complex, and illustration (-ig. 0.3) ismuch more useful.

-igure 0.3 A comparison of laminar and turbulent flow

23



".." T*O &HASE '%O*

n the present context, two&phase flow will usually refer to the simultaneous flow of a liquid

and a gas or vapor through a duct.

Such a flow occurs when a vapor is being condensed or a liquid is being vapori'ed less

commonly, a two&phase flow may involve a gas&liquid mixture (such as air and water) flowing

together and being heated or cooled without any appreciable change of phase.

The actual two&phase flow configuration, or regime, existing in a conduit in a given case

depends upon the relative and absolute quantities and the physical properties of the fluids

flowing, the geometric configuration of the conduit, and the !ind of heat transfer process

involved, if any.

#e may view the flow regime as a consequence of the interaction of two forces, gravity and

vapor shear, acting in different directions. At low vapor flow rates, gravity dominates and one

obtains stratified, slug&plug, or bubble flow depending upon the relative amount of liquid

present. At high vapor velocities, vapor shear dominates, giving rise to wavy, annular, or

annular&mist flows.

The analysis of heat transfer to or from a two&phase flow is quite complex, involving

properties, quantities, and fluid mechanics of both phases. The design correlations resultingfrom these analyses are also sub$ect to greater error than those for single phase heat transfer.

".2 Ther-al $oundar/ %a/er

f the wall temperature tw is different from the fluid stream temperature tm, there exists a

thermal boundary layer of thic!ness Mt, different from thic!ness of flow boundary layer M. This

thermal boundary layer plays an important role in determination of convective heat transfer

coefficient.

24



'unda-entals o# Shell and

Tube Heat Echan!ers

,.1 Introduction

A shell and tube heat exchanger is a tubular vessel housing a set of tubes (called the tube

bundle) containing a fluid at some temperature and immersed in a different fluid at some other

temperature. The transfer of heat ta!es place between the two wor!ing fluids due to the

difference of temperature between them. The fluid flow inside the tubes is said to be Ntube

sideO fluid and the fluid flow external to the tubes is said to be Nshell sideO

Shell and tube heat exchangers in their various constructional modifications are probably themost widespread and commonly used basic heat exchanger configuration used in process

industries. They are used in the process industries, in conventional and nuclear power stations

as condensers, steam generators in pressuri'ed water reactor power plants, and feed water

25

Chapter 3



heaters, as they are proposed of many alternative energy applications as ocean, thermal and

geothermal they are also used in some air conditioning and refrigeration systems.

The reasons for this general acceptance are several. The shell and tube heat exchanger

provides a relatively large ratio of heat transfer surface area to volume and weight. t providesthis surface in a form that is relatively easier to manufacture in a wide range of si'es and that

is mechanically rugged enough to withstand normal shop fabrication stresses, shipping and

field erection stresses and normal service operating conditions. There are several

modifications of the basic from that can be used for special services. The shell and tube

exchangers can be easily cleaned and those components most sub$ect to failure + gas!ets and

tubes + can be easily replaced. -inally, good design methods exist, and the expertise and good

shop facilities for successful design of shell and tube heat exchangers are available throughout

the world.

'i!ure ,.1 An example of a fixed tubesheet shell and tube heat exchanger

26



The simplest type of shell and tube heat exchanger is shown in -igure 1./, where warm

!erosene enters the shell on its top side. The !erosene flow path is guided between the tubes

by baffle plates and it exits at the bottom shell side no''le, cooled to the desired temperature.

The tube bundle is supported between two tubesheets with baffle supports placed at intervals

to support the brace and tubes. The tube side flow enters the tube bundle on bottom left side

and exits on top left side with a hori'ontal baffle plate separating the two tube side flows. This

type of arrangement is called a /&0 exchanger, one shell&side pass and two tube&side passes.

-igure 1.0 shows a reboiler in which isobutene vapor is generated by heating liquid isobutene.

This type of reboiler is called a N!ettleO type reboiler because of the excess area above the

tube bundle that is provided for vapor separation.

'i!ure ,." A @&tube !ettle type reboiler

n another type of reboiler where shell and tube exchanger is mounted vertically alongside a

process tower. "ere the heat energy of steam is used to separate the propane and propylene

liquid into a gas liquid two phase mixture. This type of arrangement is common in gas

27



processing industry. The supports of such an exchanger should be designed carefully, because

of the tube thermal expansions.

,." Classi#ication o# shell and tube heat echan!ers

Shell and tube heat exchangers can be classified based on one of the following criteria<

A. %lassification based on construction

>. %lassification based on service

%. %lassification based on shell configuration

. %lassification based on TA classes

,.".1 Classi#ication based on construction

-ixed tubesheet ST"s

@&tube ST"s

-loating head ST"s

'ied tube STHE

A fixed&tubesheet heat exchanger has straight tubes that are secured at both ends to tubesheets

welded to the shell. The construction may have removable channel covers (e.g., A=),

bonnet&type channel covers (e.g., >), or integral tubesheets (e.g., ).

Ad5anta!es

The principal advantage of the fixed tubesheet construction is its low cost because of

its simple construction. n fact, the fixed tubesheet is the least expensive construction

type, as long as no expansion $oint is required.

The tubes can be cleaned mechanically after removal of the channel cover or bonnet.

=ea!age of the shell side fluid is minimi'ed since there are no flanged $oints.

They require fewer gas!ets than other configurations.

28



Disad5anta!es

A disadvantage of this design is that since the bundle is fixed to the shell and cannot

be removed, the outsides of the tubes cannot be cleaned mechanically. Thus, its

application is limited to clean services on the shell side. "owever, if a satisfactorychemical cleaning program can be employed, fixed&tubesheet construction may be

selected for fouling services on the shell side.

n the event of a large differential temperature between the tubes and the shell, the

tubesheets will be unable to absorb the differential stress, thereby ma!ing it necessary

to incorporate an expansion $oint. This ta!es away the advantage of low cost to a

significant extent.

aximum temperature difference between fluids is approximately 0::o- with out the

inclusion of an expansion $oint.

'i!ure ,., A fixed tubesheet shell and tube heat exchanger

U6tube STHE

As the name implies, the tubes of a @&tube heat exchanger are bent in the shape of a @. There

is only one tubesheet in a @ tube heat exchanger. "owever, the lower cost for the single

tubesheet is offset by the additional costs incurred for the bending of the tubes and the

29



somewhat larger shell diameter (due to the minimum @&bend radius), ma!ing the cost of a @&

tube heat exchanger comparable to that of a fixed tubesheet exchanger.

Ad5anta!es

The advantage of a @&tube heat exchanger is that because one end is free, the bundle

can expand or contract in response to stress differentials.

The outsides of the tubes can be cleaned, as the tube bundle can be removed.

=ower cost than a fixed tub or floating head type exchanger

nternal gas!eted $oint is eliminated.

Tube bundle is removable and replaceable.

Disad5anta!es

The disadvantage of the @&tube construction is that the insides of the tubes cannot be

cleaned effectively, since the @&bends would require flexible& end drill shafts for

cleaning.

@&tube heat exchangers can not be used for services with a dirty fluid inside tubes.

The @ Shaped tubes reduce the number of tubes that can be installed

ndividual tubes are not replaceable.

'i!ure ,. A @&tube shell and tube heat exchanger

30



'loatin! head STHE

The floating&head heat exchanger is the most versatile type of ST", and also the costliest. n

this design, one tubesheet is fixed relative to the shell, and the other is free to NfloatO within

the shell. This permits free expansion of the tube bundle, as well as cleaning of both the

insides and outsides of the tubes. Thus, floating&head ST"s can be used for services where

both the shell side and the tube side fluids are dirty P ma!ing this the standard construction

type used in dirty services, such as in petroleum refineries.

Ad5anta!es

Ability to handle dirty fluids and high differential temperatures

>oth head and tubes can be cleaned.

ndividual tubes can be removed and replaced

Disad5anta!es

%ost more than fixed tube heat exchangers

ore gas!ets than fixed tube heat exchangers which can cause lea!age.

T/0es o# #loatin! head construction

There are various types of floating& head construction. The two most common are

i. 2ull&through with bac!ing device (TA S)

ii. 2ull through (TA T).

31



,."." Classi#ication based on ser5ice

>ased on their function, shell and tube heat exchangers can be classified one of the following

types<

Reboiler + it is a type of heat exchanger that transfers heat to a liquid to produce a two phasegas + liquid mixture used in a distillation column.

Ther-osi0hon Reboiler + it is a type of heat exchanger that provides natural circulation of

the boiling fluid by a static liquid head.

'orced circulation reboiler + a reboiler in which a pump is used to force the liquid through

the heat exchanger (reboiler) into the distillation column.

Condenser + a heat exchanger that condenses the vapors of a liquid by removing heat fromthem.

&artial condenser + it is a heat exchanger designed in such a way that it only partially

condenses a gas to provide heat to another medium to satisfy a process condition. The residual

gas is recirculated through a heater and is recycled. A common application of partial

condenser on the distillation column is using excess steam to heat up a process fluid.

'inal condenser & it is an exchanger in which all the gas is condensed and all the heat is

transferred to the other medium.

Stea- !enerator + it is a heat exchanger that generates steam, such as a boiler, to provide

energy for the process requirements. The most classic example is the old steam locomotive,

which is a shell and tube heat exchanger Nmounted on wheelsO with the steam used to power

the locomotive. (This unit is a fired vessel and its design is not governed by AS section

Q ivision).

Qapori'er + it is an exchanger that fully or partially vapori'es a liquid.

Chiller + it is an exchanger in which a process medium is cooled by operating a refrigerant,

or by cooling and heating with little or no phase change.

32



'i!ure ,.3 TA shell configuration

33



,., Construction details #or shell and tube heat echan!ers

t is essential for the designer to have a good wor!ing !nowledge of the mechanical features

of ST"s and how they influence thermal design. The principal components of an ST" are<

• Shell

• Shell cover

• Tubes

• %hannel

• %hannel cover

• Tubesheet

• >affles

• o''les.

• Tie&rods and spacers

• mpingement plate

• 2ass partition plates

• =ongitudinal baffle

• Supports

• -oundation

34



'i!ure ,.7 omenclature of shell and tube heat exchanger components

37



,.,.1 Shell

The shell is simply the container for the shell&side fluid. The shell normally has a circular

cross section and is commonly made by<

6olling a metal plate of the appropriate dimensions into a cylinder and weldingthe longitudinal $oint (these are called Jrolled shellsJ).

Small diameter shells (up to around 03 inches in diameter) can be made by cutting

pipe of the desired diameter to the correct length (Jpipe shellsJ).

The roundness of the shell is important in fixing the maximum diameter of the baffles

that can be inserted and therefore the effect of shell&to&baffle lea!age. 2ipe shells are

more nearly round than rolled shells unless particular care is ta!en in rolling, n order to

minimi'e out&of&roundness, small shells are occasionally expanded over a mandrel in

extreme cases, the shell is cast and then bored out on a boring mill.

n large exchangers, the shell is made out of low carbon steel wherever possible for

reasons of economy, though other alloys can be and are used when corrosion or high

temperature strength demands must be met.

,.,." Tubes

The tubes are the basic component of the shell and tube exchanger, providing the heat

transfer surface between one fluid flowing inside the tube and the other fluid flowing

across the outside of the tubes.

Tubes should be able to withstand the following<

a. 9perating temperature and pressure on both sides.

b. Thermal stresses due to differential thermal expansion between the shell and the

tube bundles.

c. %orrosive nature of both shell side and tube side fluid.

Classi#ication o# tubes

38



The tubes may be classified according to one or more of the following<

eans of fabricating tubes

a. #elded tubes

b. Seamless tubes Shape of tubes

a. Straight tubes

b. @&tubes

Structure of tubes

a. 2lain (bare) tubes

b. xtended surface (singly finned) tubes

c. %orrugated (doubly finned) tubes&lain or bare tubes

2lain or bare tubes are most common in shell and tube design. These tubes come in two

basic types<

a. Solid wall construction

b. uplex construction

The solid wall tube is what the name implies, a simple tube of solid wall construction.

The duplex design consists of a tube within a tube in which the outer tube is mechanically

drawn over the inner tube.

'inned tubes

xtended or enhanced surface tubes are used when one fluid has a substantially lower

heat transfer coefficient than the other fluid. oubly enhanced tubes, with enhancement

both inside and outside, are available that can reduce the si'e and cost of the exchanger.

xtended surfaces, (finned tubes) provide two to four times as much heat transfer area onthe outside as the corresponding bare tube, and this area ratio helps to offset a lower

outside heat transfer coefficient.

Shell and tube heat exchangers employ low finned tubes to increase the surface area on

shell side when the shell side heat transfer coefficient is low compared to the tube side

39



coefficient. The low finned tubes generally have helical or annular fins on individual

tubes with fin height slightly less than /.4?mm.

Corru!ated tubes

A corrugated tube has both inside and outside heat transfer enhancement. t may be a

finned tube which has integral inside turbulators as well as extended outside surface or

tubing which has outside surfaces designed to promote nucleate boiling.

Tube -aterial

Tube metal is usually low alloy steel, low carbon steel, stainless steel, copper, admiralty,

cupronic!el, inconel, aluminum (in the form of alloy), or titanium. 9ther materials can

also be specified for specific applications.

Tube si8e

Tube si'e is specified by its outside diameter and wall thic!ness.

Tube dia-eter

Tube diameter is its outside diameter. Selection of a specific diameter tube is made on

specific requirements. -rom the heat transfer point of view, smaller diameter tubes yield

higher heat transfer coefficient and result in a compact heat exchanger. =arge diameter

tubes on the other hand are easier to clean, more rugged and are necessary when the

allowable tube side pressure drop is small. Almost all heat exchanger tubes fall within the

range of 1*3in (0:mm) to 0in (4:.8mm).

Tube +all thic9ness

Tube wall thic!ness is generally specified by the >irmingham wire gauge (>#B). Tube

wall thic!ness must be chec!ed against the internal and external pressure separately, or maximum pressure differential across the wall. "owever in some cases the pressure is not

the governing factor in determining the wall thic!ness. xcept when pressure governs,

the wall thic!ness is selected on following basis.

/. 2roviding an adequate margin against corrosion.

40



0. -retting aid wear due to flow induced vibrations.

1. Axial strength. 2articularly in fixed tubesheet exchangers.

3. Standardi'ed dimensions.

4. %ost

Tube count

To design a shell and tube heat exchanger, one must !now the total number of tubes that

can fit into a shell of given inside diameter. This is !nown as tube count. A mathematical

approach using number theory is suggested to predict the tube count present tube count

for various combinations of tube layout parameters. This method eliminates the

disadvantage of drawing the tube layout pattern and can accommodate any pattern.

The tube count depends on the flow rate of fluid and the available pressure drop. Thenumber of tubes is selected such that tube side velocity for water and similar liquids

range from 1 to 8 ft*sec (:.?&0.3 m*s) and the shell side velocity ranges from0 to 4 ft*sec

(:.5&/.4 m*s). The lower velocity limit is desired to fouling, the higher velocity is limited

to avoid erosion& corrosion on tube side, and impingement attac! and flow induced

vibrations on shell side. #hen send, silt and particulates are present, the velocity is !ept

high enough to prevent settling down.

Tube 0itch

Tube pitch is defined as the shortest distance between two ad$acent tubes. esigners

prefer to employ the minimum recommended tube pitch, because it leads to the smallest

shell diameter for a given number of tubes. "owever, in exceptional circumstances, the

tube pitch may be increased to a higher value, for example, to reduce shell side pressure

drop. n most shell and tube heat exchangers, the minimum ratio of tube pitch to tube

outside diameter is never less than /.04.

Tube la/out

There are four tube layout patterns,

Triangular (1:;),

6otated triangular (5:;),

41



Square (?:;)

6otated square (34;).

A triangular (or rotated triangular) pattern will accommodate more tubes than a square (or

rotated square) pattern. -urthermore, a triangular pattern produces high turbulence and

therefore a high heat&transfer coefficient. "owever, at the typical tube pitch of /.04 times

the tube 9.., it does not permit mechanical cleaning of tubes, since access lanes are not

available. %onsequently, a triangular layout is limited to clean shell side services.

-or dirty shell side services, a square layout is typically employed. "owever, since this is

an in&line pattern, it produces lower turbulence. Thus, when the shell side 6eynolds

number is low (R 0,:::), it is usually advantageous to employ a rotated square pattern.

'i!ure ,.7 Tube layout pattern

,.,., $a##les

>affles are used to support tubes, enable a desirable velocity to be maintained for the

shell side fluid, and prevent failure of tubes due to flow&induced vibration.

Classi#ication o# ba##les

The baffles are classified into following main categories<

42



/. Transverse baffles

a. 2late baffles

i. Segmental baffles

ii. is! and doughnut baffles

iii. 9rifice baffles

b. 6od baffles

0. =ongitudinal baffles

Se!-ental ba##les

Segmented baffles may be single&segmental, double&segmental, or triple&segmental as

shown in the figure 1.8.

'i!ure ,.: Single, double and triple segmented baffles

The most common baffle shape is the single segmental. The segment sheared off must be

less than half of the diameter in order to insure that ad$acent baffles overlap at least one

full tube row. -or liquid flows on the shell side, a baffle cut of 0: to 04 percent of thediameter is common for low pressure gas flows, 3: to 34 percent (i.e., close to the

maximum allowable cut) is more common, in order to minimi'e pressure drop.

The main features of double and triple segmented baffles include<

43



/. The flow on the shell side is split into two or more streams as per the number of

baffle segments, namely, double, triple, multiple etc. hence the danger of shell

side flow induced vibrations is minimum.

0. The baffle spacing should not be too small otherwise it results in a more parallel

flow with significant low stagnant areas.

Dis9 and dou!hnut ba##les

The dis! and doughnut baffle is made up of alternate Ndis!O and NdoughnutO baffles. This

baffle design provides a lower pressure drop as compared to a single segmental baffle for

the same unsupported tube span.

Ori#ice ba##les

n an orifice baffle, the tube&to&baffle&hole distance is large so that it acts as an orifice for

the shell side flow.Rod ba##les

The rod baffles consist of rods that run through a series of circular rings as shown in the

figure. 9n this type of arrangement, the rods brea! up thus damping the vibrations. The

rods also reduce turbulence to below resonant levels of the natural frequency of the tubes

and hence reduce fluid elastic vibrations.

%on!itudinal ba##les

=ongitudinal baffles divide the shell into two or more sections, providing ultipass on

the shell side. This type of baffles should not be used unless the baffle is welded to the

shell and tubesheet.

44



'i!ure ,.; ifferent types of plate baffles

45



'i!ure ,.; 6od baffles

$a##le s0acin!

>affle spacing is the centerline&to&centerline distance between ad$acent baffles. t is the

most vital parameter in ST" design.

The TA standards specify the minimum baffle spacing as one&fifth of the shell inside

diameter or 0 in., whichever is greater. %loser spacing will result in poor bundle

penetration by the shell side fluid and difficulty in mechanically cleaning the outsides of the tubes. -urthermore, a low baffle spacing results in a poor stream distribution as will

be explained later.

The maximum baffle spacing is the shell inside diameter. "igher baffle spacing will lead

to predominantly longitudinal flow, which is less efficient than cross&flow, and large

46



unsupported tube spans, which will ma!e the exchanger prone to tube failure due to flow&

induced vibration.

$a##le cut

>affle cut is the height of the segment that is cut in each baffle to permit the Shell side

fluid to flow across the baffle. This is expressed as a percentage of the shell inside

diameter. Although this, too, is an important parameter for ST" design, its effect is less

profound than that of baffle spacing. >affle cut can vary between /4 and 34 of the

shell inside diameter.

'i!ure ,.1< >affle %ut

,.,. Tube sheet

a tubesheet is an important component of a heat exchanger. t is the principal barrier

between the shell side and tube side flows. 2roper design of a tubesheet is important for

safety and reliability of heat exchanger. The sheets are mostly circular with uniform

pattern of drilled holes.

Classi#ication o# tube sheets

Tube sheets come in two basic types/. Single tube sheet

0. ouble tube sheet

The double tubesheet can further be categori'ed into two categories<

47



a. %onventional double tubesheet design, in which two individual tubesheets are

placed side by side at each end of the tubes.

b. ntegral double tubesheet design, in which a single plate is first drilled and then

grooved midway between the faces.

Single tubesheets are much more common than double tubesheets because of process

applications and economy.

Tube to tubesheet attach-ents

Tubes are attached to the tube sheets by one of the following methods<

6olling

#elding

6olling and welding

xplosive welding

>ra'ing

xpansion of tubes into tubesheets is most widely used and is satisfactory for many uses.

"owever, when stresses are higher, or where pressures are such that significant lea!age

can occur, or where the contamination between the fluids is not permitted, the tubes are

welded to the tubesheet.

,.,.2 Tube bundle

A tube bundle is an assembly of tubes, baffles, tubesheets, spacers, tie rods and

longitudinal baffles, if any. Spacers and tie rods are required for maintaining the space

between baffles.

,.,.3 Channel Co5ers

The channel covers are round plates that bolt to the channel flanges and can be removed

for tube inspection without disturbing the tube&side piping. n smaller heat exchangers,

bonnets with flanged no''les or threaded connections for the tube&side piping are often

used instead of channels and channel covers.

,.,.7 &ass 0artition 0late

A pass partition plate or a pass divider is needed in one channel or bonnet for an

exchanger having two tube&side passes, and they are needed in both channels or bonnets

48



for an exchanger having more than two passes. f the channels or bonnets are cast, the

dividers are integrally cast and then faced to give a smooth bearing surface on the gas!et

between the divider and the tube sheet. f the channels are rolled from plate or built up

from pipe, the dividers are welded in place.

The arrangement of the dividers in multiple&pass exchangers is somewhat arbitrary, the

usual intent being to provide nearly the same number of tubes in each pass, to minimi'e

the number of tubes lost from the tube count, to minimi'e the pressure difference across

any one pass divider (to minimi'e lea!age and therefore the violation of the T

derivation), to provide adequate bearing surface for the gas!et and to minimi'e

fabrication complexity and cost.

There are some limitations on how the different types of heat exchangers can be partitioned to provide various numbers of passes. These are summari'ed in the following

lines<

/. -or fixed tubesheet exchanger, any practical number of passes, even or odd, can

be used. -or ultipass arrangements, partitions are to be built into both front and

rear heads.

0. -or @&tube exchangers, minimum two passes are required. Any practical even

number of tubes can be obtained by building partition plates in the front head.1. #ith pull through floating head (T head) type and split bac!ing ring exchanger (S

head), any practical even number of passes is possible. -or single pass operation,

however, a pac!ed $oint must be installed on the floating head (2 type). #ith this

arrangement only one or two passes are possible. #ith externally sealed floating

tubesheet (# type), there is no practical tube pass limitation.

3. Two phase flow on the tube side, whether boiling or condensing, is best !ept with

a single pass or in @&tubes to avoid uneven distribution and hence uneven heattransfer.

49



'i!ure ,.11 Typical tube pass layouts

50



,.,.: I-0in!e-ent 0late

The inlet no''le often has an impingement plate set $ust below to divert the incoming

fluid $et from impacting directly at high velocity on the top row of tubes. Such impact can

cause erosion, cavitations, and*or vibration.

'i!ure ,.1" mpingement plate

n order to put the impingement plate in and still leave enough flow area between the

shell and plate for the flow to discharge without excessive pressure loss, it may be

necessary to omit some tubes from the full circle pattern. 9ther more complex

arrangements to distribute the entering flow, such as a slotted distributor plate and an

enlarged annular distributor section, are occasionally employed.

,.,.; Tube6Side Channels and No88les

Tube&side channels and no''les simply control the flow of the tube&side fluid into and out

of the tubes of the exchanger. Since the tube&side fluid is generally the more corrosive,

these channels and no''les will often be made out of alloy materials (compatible with the

tubes and tube sheets, of course). They may be clad instead of solid alloy.

51Chapter 4



(aintenance o# shell

And tube heat echan!er

.1 Introduction

The structural integrity of a heat exchanger depends on proper mechanical design arrived

at after detailed stress analysis !eeping in view all the static, dynamic, transient and steady

loads. "eat transfer efficiency and fabrication cost of a heat exchanger are directly

influenced by proper and functional mechanical design. Therefore an optimum mechanicaldesign of various components of a heat exchanger is of paramount importance.

52



FACTORS AFFECTING PERFORMANCE OF HEAT

EXCHANGERS

For efective heat transer, the heat exchange syste sho!"# $e

c"ean an# hea"thy% & the eta" s!races are o!"e# or corro#e#,

proper t!r$!"ence is not intro#!ce# or heat #issipation, coo"ing'!i# itse" is not co"# eno!gh to a$sor$ #esire# heat or the 'o( o

'!i#s is not s!)cient eno!gh, the heat #!ty o the exchanger

(o!"# re#!ce% *his #rop in heat #!ty is re'ecte# as #eteriorate#

perorance o the heat exchange e+!ipent%

a-or actors re#!cing heat exchangers. perorance are/

i% Fo!"ingii% Corrosion an# eaages

iii% ca"ingiv% F"!i# *eperat!re

v% igh ∆

vi% o( F"!i# e"ocity an# estricte# F"o(Fouling:

eposition o inso"!$"e, poro!s an# "oose ateria", present in

(ater, at the s!race o heat exchange e+!ipent is ca""e#

fouling%

*hese ateria"s inc"!#e partic!"ate atter ro air, igrate#

corrosion pro#!ct, si"t a""oys an# san#, organic containants

oi"s, $io"ogica" atter, extraneo!s ateria" "eaves, t(igs :

(oo#%

Affects<erorance #eteriorations o heat exchangers is

experience# #!e to o""o(ing actors;

estricte# coo"ing (ater 'o(%

eat exchanger t!$es are p"!gge# $y 'ocs re#!cing heattranser area%

Fo!"ing initiates an# propagates !n#er #eposit corrosion,(hich threatens e+!ipent hea"th%

53



"!#ge #eposition in coo"ing (ater $asin that re<contri$!tes perio#ic c"eaning%

Cleaning:

Fo!"e# s!races co!"# $e c"ean $oth echanica""y an#

cheica""y% o(ever, the o#e o c"eaning is s!$-ecte# to thecharacteristics an# extent o o!"ing%

Mechanical (Physical) Tea!"en!:

Fi"tration o s!spen#e# so"i#s o ae<!p (ater is carrie#o!t thro!gh si#e strea ="ters% > 80? are reove#conse+!ent"y at 5<8 cyc"es o concentration%

eposits are physica""y (ipe# o!t as (e"" (ith scrapers,$r!shes, $a""s an# (ater -ets%

Che"ical Tea!"en!:

ynthetic po"yers ca""e# #ispersants are !se# to #ispersethe o!"ants% *hese inc"!#e# po"yacry"ate, po"yaretes,partia""y hy#ro"y@e# po"yacry"ai#es an# their copo"yers

Aat!ra" #ispersants, s!ch as tannirs, "ig!in s!"orate, an#car$oxyethy"e ce""!"ose are a"so !se# $!t are "esserefective than synthetic #ispersants%

*he a-or so!rces o organic o!"ing are oi"s an# $io"ogica"

species% o(ever, the ost #etrienta" o!"ing is the

$io"ogica" o!"ing #!e to its pec!"iar o!"ing an# corrosion

characteristics%

#iological $ouling:

The presence and growth of lining organic matter is referred to as >iofouling.Bio<o!"ing intereres (ith the 'o( o (ater thro!gh heat

exchangers an# other con#itions% *his inhi$its heat transer

an# contri$!tes to !n#er<#eposit corrosion an# genera"

#eterioration o the entire coo"ing syste%

eca"c!"ating coo"ing (ater syste are i#ea" inc!$ators or

prooting the gro(th an# pro"ieration o icroorganis #!e

54



to sat!rate# oxygen, expos!re to s!n"ight, aintaine#

teperat!re 30DC an# p 6<9% *he $!i"#<!p o a $io="

is initiate# (ith the a#sorption o organic ateria" on the

eta" s!race ro the $!" (ater% *he icroorganiss

attach to the s!race an# gro( thro!gh the assii"ation o n!trients%

Bio<=" re#!ces heat transer $eca!se o its ins!"ating

properties% *he sot e"astic ripp"e s!race a$sor$s inetic

energy ro the 'o(ing (ater an# increase# p!ping energy

is re+!ire# to overcoe the rictiona" resistance o the ="%

*ho!gh the $io<="s are 95<98? (ater, they pro#!ce

signi=cant press!re #rop%

*here are 03 a-or c"asses o icroorganis, (hich areassociate# (ith re<circ!"ating coo"ing (ater syste;

i% E"gaeii% F!ngiiii% BacteriaAlgae:

E"gae range ro !nice""!"ar sing"e ce"" p"ants to !"ti<

ce""!"ar species% *he "atter inc"!#e #iverse ors an#

shapes, inc"!#ing s"iy asses, copose# o severa" ce""sor "ong stan#s ="aents o a"gae% E"" a"gae contain co"o!r

pigents, the ost iportant o (hich is ch"orophy""% E"gae

!s!a""y 'o!rish on (et s!races s!ch as coo"ing to(er

"!$er, ist e"iinators, screens an# #istri$!tion trays,

(hich are expose# to oxygen an# s!n"ight%

E"gae severe"y corro#e eta" s!races% arge s"ie ass

contri$!tes to crevice corrosion an# pitting% assive gro(th

a"so inhi$its proper (ater #istri$!tion $y p"!gging screens,

restricting 'o(, an# interering (ith p!p s!ction%

Fungi:

55



F!ngi are sii"ar to a"gae $!t #o not contain ch"orophy""%

a-or !ngi are o"#s an# yeast% *hey re+!ire oist!re an#

air $!t not s!n"ight% *hey 'o!rish on (ater n!trients s!ch as

$acteria an# a"gae, to (hich they are attache#% o"# !ngi

are ="aento!s in or, $!t yeasts are !nice""!"ar% Certainspecies o !ngi cons!e (oo# coponents, ca!sing

serio!s s!race #eterioration an# interna" #ecay o (oo# rot%

#ac!eia:

Bacteria are !nice""!"ar icroscopic p"ant "ie organiss

sii"ar to a"gae $!t "ac ch"orophy""% *hey exist in three

$asis ors;

i% o#<hape# Baci""!sii% pherica" Cocc!siii% pira" piri""!sater or (et environent, high in organic content is s!ita$"e or

the pro"ieration o $acteria" s"ie% !ch shines signi=cant"y

re#!ce heat transer e)ciency an# aggravate !n#er #eposit

corrosion% Eero$ic $acteria" 'o!rish in oxygen environent (here

as Enaero$ic $acteria" gro( in the a$sence o oxygen% Gn#er

#eposit corrosion 'o!rishes (ith heavy $io<o!"ing%

Ion %e&osi!ing 'ac!eia oxi#i@e (ater so"!$"e erro!s ionFe2 into inso"!$"e erric oxi#e Fe2H3, (hich #eposits on

the insi#e o the piping, re#!ce 'o( an# aggravate crevice

corrosion%

Shine $o"ing 'ac!eia or #ense, sticy $ioasses that

ipe#e (ater 'o( an# s!stain the gro(th o other

organiss, contri$!ting to o!"ing, there$y%

Coosion:

*he #eterioration o eta" or its properties ca!se# $y the

reaction (ith its s!rro!n#ings environent is tere# as

corrosion%

56



For corrosion reactions to occ!r in (ater services, a potentia"

#iference sho!"# occ!r $et(een eta" an# s!rro!n#ing

environent an# a"so $et(een #iferent areas on the s!race%

*his ca!ses the passage o e"ectrica" c!rrent thro!gh the

eta" ro the area o "o( potentia" to high potentia"%

Ty&es o$ Coosion:

*here are t(o ain types o corrosions;

1% Cheica" corrosion2% I"ectro<cheica" corrosion

Che"ical coosion invo"ves a cheica" reaction $et(eenthe eta" s!race an# its s!rro!n#ings (itho!t any

transportation o e"ectrons%

F"o( o e"ectrons #!e to re#!ction J oxi#ation reaction an#

potentia" #iference across the eta"s. s!race is the pec!"iar

characteristic o corrosion type no(n as elec!o che"ical

coosion%

ost coon ors o corrosion that have $een o$serve#

heat transer e+!ipent are o""o(ing;

i% Kenera" L Gnior corrosionii% Ka"vanic corrosioniii% Irosion corrosioniv% Crevice corrosion concentration ce""sv% itting corrosion

*he aci# $y<pro#!cts o soe $acteria a"so corro#e the heat

exchange eta"s% Eongst the is s!"phate re#!cing

$acteria no(n as SRBs% *hey convert #isso"ve# s!"ph!r

copo!n#s H4<2 to hy#rogen s!"phi#e 2% Car$on stee",

stain"ess stee" an# copper $ase# a""oys are severe"y corro#e#

$y 2% es!"ovi$rio #es!"!ricans is the ost prevai"ing

s!"phate re#!cing $acteria, (hich ain"y exists !n#er

#eposits that are #evoi# o oxygen%

57



*he or o corrosion attac on car$on stee", $y these

$acteria, is +!ite #istractive/ it is recogni@a$"e $y the sooth,

#isc shape# concentric rings ore# on the eta" s!race%

10H+ + SO 4-2 + 4Fe 4Fe+2 + H2S +

4H2O

H2S + Fe+2 FeS + 2H+

The formation of blac! iron sulphide deposits, accompanied by an odor of rotten egg, is the peculiar characteristic of attac! by S6>s.

*he aero$ic s!"ph!r $acteria, *hio$aci""!s oxi#i@es s!"ph!r,

s!"phi#es an# s!"phates in to s!"phaic aci#% oca"i@e# p

#epression is experience at "ocations (here these organiss

contact the eta"% evera" genera" thinning o stee"s is

o$serve#, conse+!ent"y%

Ni!i$ying 'ac!eial oxi#i@e aonia into nitrate, (hich

#ecreases p%

NH3 + CO2 HNO3 + H2O

epai# genera" thinning o stee"s an# copper $ase# a""oys

occ!rs% *he nitrate $ase# corrosion inhi$itors a"so $ecoe in

efective #!e to their oxi#ation into nitrate $y this specie o

$acteria%

Aec!s o$ Te"&ea!ue on Coosion:

Corrosion is an e"ectrocheica" phenoenon% &t is not

s!rprising that an increase in teperat!re (i"" ca!se an

increase in corrosion rates% *eperat!re p"ays a #!a" ro"e

(ith respect to oxygen corrosion Fig<1% &n open recirc!"ating

coo"ing (ater systes, corrosion rates increase "inear"y (ith

teperat!re !p to a axi! va"!e% Beyon# this point, therates #ecrease $eca!se o re#!ce# oxygen so"!$i"ity at the

!ch higher teperat!res% For c"ose# systes in (hich

oxygen cannot escape, corrosion rates increase stea#i"y (ith

teperat!re%

58



En !n!s!a" teperat!re efect, no(n as thero<ga"vanic

attac, can occ!r (ith copper a""oy% *eperat!re #iferences

o at "east 65DC $et(een the en#s o copper con#!its (i""

ca!se the co"# en# to $e catho#ic to the hot en#% Copper ions

(i"" #isso"ve corro#e at the hot en# an# igrate to the co"#en#% Et the catho#e, copper ions (i"" p"ate o!t, $!t at the

ano#e, the s!race (i"" $ecoe ro!gh an# (i"" pit%

Scale e&osi!ion:

#ater&formed deposits commonly referred to as scale, can be defined as a

crystalline growth of an adherent layer (barrier) of insoluble salt or oxide on a heat

exchanger surface. The rate of formation is a complicated function of many

variables including temperature, concentration of scale&forming species, p", water

quality, and hydrodynamic conditions.

The normal solubility of scales increase with temperature, but a few, such as

calcium carbonate and calcium sulfate, have the opposite trend. @nfortunately, these

scales are commonly found in cooling water systems. n the hottest areas, calcium

carbonate and calcium sulfate will precipitate and form a thic! barrier deposit.

Calciu- carbonate is perhaps the most common scale found in cooling water

systems. %alcium and bicarbonate al!alinity are both needed to form this extremelytenacious scale (al!alinity is the concentration of "%91

&, %910& and 9"& ions present

in the water). An increase in heat and*or p" will cause the bicarbonate ion to

decompose to carbon dioxide and calcium carbonate.

Ca(HCO3 )2 CaCO3 + CO2 + H 2O

The greatest concentration of %a%91 will occur at the hottest areas along the heat

transfer surfaces.

any methods have been proposed to predict the formation of calcium carbonate.

"owever, they are all based upon the thermodynamic equilibria of carbonic acid

and al!alinity corrected for temperature and dissolved solids (ionic strength).

59



Calciu- sul#ate can exist in various forms in cooling water systems, the most

common being gypsum (%aS93.0"09). The hemihydrate and anhydrite forms are

much less common. Their solubility, as a function of temperature, is shown in

-ig.&0. Bypsum is more soluble than calcium carbonate by at least a factor of 4:.

This phenomenon provides the basis for sulfuric acid addition to control %a%91 in

recirculating cooling water systems. The normal upper limit for calcium and sulfate

concentrations in the absence of an inhibitor is expressed by<

[Ca2+ ] x [SO 42- ] = 500000

here the $racete# va"!es are the ioni! !on!en"#a"ions

expresse# in i""igra per "iter pp%

Calciu- 0hos0hate =Ca,=&O>"> scale has become more common in recirculatingcooling water systems. The increases in p", calcium concentration, and amount of

phosphate common to many accepted chemical treatments has increased the

potential for calcium phosphate deposits on heat transfer surfaces. 9ther water

sources also have contributed to increased levels of phosphate. Surface ma!eup

waters containing agricultural runoff and sewage plant effluents can have high

levels of orthophosphate ions.

*he so"!$i"ity o ca"ci! phosphate #ecreases as pincreases% &t has inia" teperat!re #epen#ency ro 25D

to 75DC% *hese #eposits are !s!a""y aorpho!s an#

event!a""y transor to the ore crysta""ine hy#roxyapatite

Ca5H43H% Beca!se o the "o( so"!$i"ity o ca"ci!

phosphate a$o!t 10<30, #eposits can or easi"y in

(aters containing 5 gL o orthophosphate ions an# 300

gL o ca"ci! ions at p 7 to 7%5% *he sca"e<oring

ten#ency o ca"ci! phosphate is a cop"ex !nction o p,

ca"ci! har#ness, orthophosphate concentration, ionic

strength, an# teperat!re% C!rrent"y, there are no r!"e<o<

th!$ re"ationships $et(een these varia$"es% E"so, in the

a$sence o any orthophosphate #eposit, the orthophosphate

ions can contri$!te to the corrosion inhi$ition o car$on stee"%

60



Calciu" silica!e (%aSi91) and magnesium silicate (gSi91) scales tend to

develop under more al!aline cooling water conditions, in which the p" is

approximately 8.4 or greater. These scales are very tenacious, dense, and difficult to

remove from heat transfer surfaces. Although the solubility of silica (Si90)

increases with p", the solubility of the al!aline silicates decreases as p" increases.

An upper limit for the silica concentration is /4: mg*= as Si9 0 in most recirculating

waters, although other factors affect this limit. (a!nesiu- silicate can precipitate

on heat transfer surfaces with magnesium concentrations as low as 4: mg*= and /4:

mg*= Si90. A rule&of&thumb JpseudosolubilityJ product of g0, (mg*l as %a%91)

and Si90, (mg*l as Si90 ) less than 14,::: has been developed. The addition of

chemical treatment as a preventative measure is essentially nonexistent. The most

effective method of control is to !eep the silica concentration in the

recirculating cooling water below the /4: mg*= limit.

Flui% Te"&ea!ue:

Temperature difference is the driving force by which heat is transferred from

a source to a receiver.

#hen the two fluids travel in opposite directions along a pipe, they are in

counter flow. #hereas fluids traveling in the same direction are in parallel *

co&current flow. The temperature of the inner pipe fluid in either case varies

according to one curve as it proceeds along the length of the pipe, and the

temperature of the annulus fluid varies according to another. The temperature

difference at any length from the origin where = K : is the vertical distance

between the two curves. The flow pattern and curves are attached

High Pessue o&:

*he 'o( o a"" '!i#s is $ase# on t(o paraeters%

• otentia" or 'o(

• esistance to the 'o(

61



isturbing anyone of these two parameters upsets the flow of the fluids. As the

systemDs pressure drop increases, the resistance to flow increases and consequently,

the flow is restricted. The pressure drop could be due to mechanical failure or

damages in the system such as bro!en baffles, twisting of equipment that leads to

fluid channeling, bro!en plug or gate of valves etc.

-ouling and deposition may also raise the system pressure drop. TubesD plugging

due to dirt accumulation in tubes, deposition of corrosion products and fouling in

piping are few examples due to which system pressure increases. Scaling also

imparts additional pressure drop by restricting the fluid flow.

*o+ Flui% ,eloci!y An% Res!ic!e% Flo+:

Along with temperature difference, heat transfer is also enhanced by fluid

turbulence. f the velocity of fluids is lower than a bear minimum and flow is

restricted, not only the effectiveness of heat dissipation is affected, but other

problems such as fouling and corrosion are introduced into the system due to fluid

stagnation.

#hen water travels slowly through a tube, dirt and slime resulting from micro&

organic action adheres to the tubes, which would be carried away if there were

greater turbulence. As a standard practice, the use of cooling water at velocities less

than 1 fps (feet*sec) should be avoided, although in certain localities minimumvelocities as high as 3 fps are required for continued operation.

The mechanical design involves the design of pressure retaining and non pressure retaining

components and equipments to withstand the design loads and the deterioration in service

so that the equipment will wor! satisfactorily and reliably throughout its service life. A

selected heat exchanger must satisfy the process requirements with the allowable pressure

drop until the next scheduled maintenance of the plant. The basic logical structure of

design of a shell and tube heat exchanger is given in the following figure 3./.

62



Main!enance Poce%ue o$ Shell an% Tu'e Hea!

E-changes:

For peroring aintenance activity on heat exchanger (e cano""o( these steps%

/. -or performing any type of activity first step is wor! permit.0. solate the heat exchanger 1. 6emove channel head cover, channel head3. 6emove -loating head cover, floating head4. 2ull out bundle5. %lean the bundle with the help of rotary lances or flexible lances

7. %lean the bundle from out side and shell from inside with the help of hydro $etting

gun8. nspect by inspection?. >ox up heat exchanger by following opening steps/:. "ydro test the exchanger on /.4 percent of design pressure//. 6emove blinds/0. "and over to operations.

Cleaning o$ Hea! E-change Tu'e #un%le:

/. echanical %leaning0. %hemical %leaning1. Self %leaning

Mechanical Cleaning:

&n echanica" c"eaning y#ro -etting achines are !se# or &nterna"

c"eaning o t!$es otary "ances an# 'exi$"e "ances are !se# an# or

externa" c"eaning o t!$es $!n#"e y#ro -etting g!ns are !se#%

E.ui&"en! ae /se% $o Mechanical Cleaning:

Hy%o 0e!!ing Machine:

63



*!$e c"eaning proce#!res or she"" an# t!$e heat exchangers are

perore# of<"ine, the ost re+!ent"y chosen an# astest etho#

$eing echanica" c"eaning% Eong other of<"ine etho#s is the !se o

very high<press!re (ater $!t, since the -et can on"y $e ove# a"ong

the t!$e s"o("y, the tie taen to c"ean a heat exchanger can $ecoe

exten#e#% Kreat care !st $e taen to avoi# #aaging any t!$e sheet

or t!$e coatings (hich ay $e present/ other(ise the s!ccess!"

reova" o o!"ing #eposits ay $ecoe associate# (ith ne( t!$e

"eas or increase# t!$e sheet corrosion, (hich are on"y revea"e# ater

the !nit has $een $ro!ght $ac on<"ine

Eccessories;

K!nning, or K!n Metting, invo"ves the !se o a -etting g!n, a porta$"e

co$ination o operator.s contro" va"ve, "ance an# no@@"e/ nora""y

rese$"ing a g!n in arrangeent vario!s no@@"es ay $e !se#;

64



6ota$et no''le< used for larger areas has good cutting effect and broad

span Straight $et no''le (or pin no''le)< used for shot gunning and cutting. -an $et no''le< used for broad areas, but because of a limited cutting

effect, is suitable only for washing.

Bunning may be used for large or external surfaces, for example tube bundle faces, tan!

walls, structural steel and valves. Shot gunning is the term used for blasting deposits out of the

end of a pipe or tube, prior to flex&lancing or pipe&cleaning. #hen gunning, the hand&held no''le

can be directed virtually in all planes of operation. The lance man is not shielded from the

reflected high&pressure stream. Also, if the barrel is too short, there is potential for the operator to

stri!e his feet with the high&pressure water.

1. Rotar/ %ance

The apparatus receives hot pressuri'ed water and sprays the water downwardly onto the

surface to be cleaned through a rotating manifold of spray no''les. The manifold is

mounted within a push able cart or chassis, similar to a lawnmower chassis, for rotational

movement in a plane parallel with the surface to be cleaned. o''les of the spray

manifold are tilted at an angle such that water sprayed from the no''les provides an

65



angular momentum to the manifold. The apparatus is also provided with a mechanism for

raising or lowering the height of the no''les above the surface and for setting a minimum

selected height.

H&NHA*E G*& EAC&AK H&*&HAI

*his "ancing syste (as #esigne# to efective"y c"ean t!$es in heat

exchangers an# evaporators% &t is !se# (ith rigi# "ance an# no@@"e tip%

*he (ater exits thro!gh sa"" ori=ces in no@@"e tip as high ve"ocity

(ater -ets that are capa$"e o !np"!gging an# reoving sca"e in t!$es%

Eir or hy#ra!"ic otors s!pp"y rotation an# ee# po(er%

ince the "ance are contin!o!s"y rotate#, a e(er n!$er o "arger,ore po(er!" -et are !se# to cop"ete"y c"ean the insi#e o the t!$es%

arger -ets (i"" a"so penetrates to!gher #eposits ore efective"y then

any sa""er, non rotating -ets% otation o the tip a"so aes this too"

efective or po"ishing t!$e (a""s% Ao@@"e tips (ith c!tting e#ges can

a"so $e !se# to co$ine the a#vantages o echanica" c!tting (ith

(ater $"asting% *he po(ere# ee# a""o(s a"" the -et po(er to $e !se# in

attacing the ateria" ahea# o the tip%

Che"ical Cleaning: ynthetic po"yers ca""e# #ispersants are !se# to #isperse the

o!" ants% *hese inc"!#e# po"yacry"ate, po"yerases, partia""y

hy#ro"y@e# po"yacry"ai#es an# their copo"yers

Aat!ra" #ispersants, s!ch as tannirs, "ig!in s!focate, an#

car$oxyethy"e ce""!"ose are a"so !se# $!t are "esser efective

than synthetic #ispersants%

*he a-or so!rces o organic o!"ing are oi"s an# $io"ogica"

species% o(ever, the ost #etrienta" o!"ing is the $io"ogica"

o!"ing #!e to its pec!"iar o!"ing an# corrosion characteristics%

66



Sel$ cleaning

S"s are often used in the heating of fluids which contain solids and thus have a

tendency to foul the inside of the heat exchanger. The low pressure drop gives the S" its

ability to handle fouling easier. The S" uses a Nself cleaningO mechanism, wherebyfouled surfaces cause a locali'ed increase in fluid velocity, thus increasing the drag (or

fluid friction) on the fouled surface, thus helping to dislodge the bloc!age and !eep the

heat exchanger clean. JThe internal walls that ma!e up the heat transfer surface are often

rather thic!, which ma!es the S" very robust, and able to last a long time in demanding

environments.J They are also easily cleaned, opening out li!e an oven where any build up

of foul ant can be removed by pressure washing. Self&%leaning #ater filters are used to

!eep the system clean and running without the need to shot down or replace cartridges

and bags.

(echanical Desi!n o# shell

and tube heat echan!er

67

Chapter 5



-low diagram< echanical esign of shell and tube heat exchanger

68



'i!ure .1 >asic logical structures for process heat exchanger design

n this chapter we will restrict ourselves to the mechanical design of heat exchanger i.e we

will study only the final level of the above given diagram. The series of steps within the

dotted rectangle are concerned with process design and are generally the function of a

process or a chemical engineer.

69



." 'unda-ental re?uire-ents o# -echanical desi!n

A certain minimum amount of information is required for mechanical design of a shell and

tube heat exchanger. These requirements have been listed below<

/. Thermohydraulic deign details in the form of TA or an equivalent specification

sheet.

0. TA class (6, %, >), type of TA shell (shell types are specified in chapter 1)

and channels* heads.

1. Shell side and tube side passes.

3. umber, type, si'e and layout of tubes.

4. esign temperatures and pressures.

5. xternal pressure if the requirement is to design under external pressure or under

internal vacuum.

7. iameter and length of shell channel* head, and its configuration.

8. #orst case coincident conditions of temperature and pressure.

?. o''le, wind, seismic loads and impact loads (including water hammer if any).

/:. Superimposed loads due to insulation, piping and stac!ed units etc.

//. %orrosion properties of the fluids and the environment in which the unit will be

installed and the expected service life. This in turn will determine the corrosion

allowance or help in better material selection.

/0. aterials of construction, except tube material, which is already decided at thermal

design stage.

/1. -ouling characteristics of the streams to be handled by the exchanger.

/3. -low rates to si'e the no''les and determine whether the impingement protection is

required or not.

70



/4. Special restrictions imposed by the purchaser on available space, piping layout,

location of supports, types of material and servicing conditions etc.

., Contents o# -echanical desi!n

The designer of a heat exchanger has to ma!e many decisions during the design process.

"e has to select between alternative options or choose a method from different possible

ways. n general one has to ma!e the following decisions<

/. #hat design standards are to be followed in designing of any given components&

TA, AS Section Q ivision , >S 44::, S<0840&/?5?, S9*S&05?3,

The pressure vessel code (Hapan), B9ST (@SS6), %9A2, S%T (-rance).

0. #hat type of connections are to be made (welded, flanged or pac!ed) at front head,

tube sheet and rear head.

1. #hat types of weld $oints are to be made at what specific locations&butt welds, lap

welds.

3. #hich type of welding is to be done at different locations&TB welding SA#,

B etc.

4. #hat types of flanged $oints are to be selected&loose type of flanges, integral type

flanges, optional type flanges.

5. #hat types of gas!ets are to be used&ring type gas!ets or full face gas!ets.

7. #hat types of closures are to be used at ends&elliptical, hemispherical, torispherical

or conical.

8. #hat combination of loads will govern the pressure parts design&shell side

pressure, tube side pressure, differential thermal expansion, self weight, mechanical

vibrations and seismic vibrations.

?. Type and style of openings.

/:. etails of vent and drain designs.

71



//. inimum bend radii for @&tubes.

/0. #hether to use an expansion $oint or not. f yes then what type of $oint is to be

selectedU

uring the process of mechanical design, the following parameters are decided !eeping in

view the loadings and the performance of the exchanger.

/. Shell thic!ness

0. Shell flange and channel flange design.

1. ished end calculations.

3. esign of openings and no''les.

4. Tubesheet thic!ness.

5. Shell longitudinal stress and bending stress.

7. Tube longitudinal stress, both inside and outside the periphery.

8. %hannel longitudinal stress and bending stress for given loading conditions.

?. Tube&to&tubesheet $oint load.

/:. -lat cover thic!ness

//. esign of supports.

. (echanical desi!n 0rocedure

The mechanical design of a heat exchanger can be divided into the following main steps<

• dentify all the applied loadings.

• etermine the stresses induced in the material as the result of applied load.

72



• etermine the codes and standards to be used in design process.

• Select materials of construction.

•

%ompute pressure parts thic!ness and reinforcements.

• Select appropriate welding details.

• esign non pressure parts.

• esign saddles and other supporting elements.

• Specify inspection methods and carry out inspection accordingly.

..1 A00lied loadin!s

The mechanical design of heat exchangers begins with consideration of the service loads

and a determination of their values. =oads may be subdivided into two categories,

depending on their cause and on their variation with time.

n the first category, the following types should be considered<

• istributed mechanical load, for example, internal or external pressure.

• echanical load concentrated on a small area, for example, self&weight loading applied

at a column or saddle support or load applied at an anchor by a pipe.

• Thermal loading caused by differential expansion of the shell&and&tube bundle, by the

thermal expansion of the heat exchanger on its supports, by temperature gradients

through the thic!ness of a plate or shell, or by differences between thermal expansion

coefficients in the $unction between two elements.

n the second category shoc! loads that may occur in an accident&for example, thermal

shoc! due to direct impingement of cold fluid on a hot surface are included. These loads

73



may be maintained throughout the whole life of the heat exchanger, change only a few

times, or undergo a cyclic variation.

.." Stress anal/sis

Stress analysis is the determination of the relationship between the external forces applied

to the vessel and the corresponding stresses produced in the vessel.

9nce the loads normally occurring in service and those anticipated in possible accidents

are characteri'ed, the next step is to find the stress distribution, assuming elastic behavior.

As in the case of loads, elastic stresses may be subdivided into several categories,

depending on both their origin and the effect they have on the strength of the structure.

The AS >oiler and 2ressure Qessel %ode categori'e the stresses into a number of

groups in accordance with detailed rules that are not always unequivocal. A simple

classification is the following<

T/0e 1 stress

Stress distributed uniformly through the thic!ness caused by internal or external pressure&

in general, any stress not limited by a displacement and capable of causing widespreadyielding and ultimately plastic collapse of the structure. The pressure&induced stress in a

cylindrical shell is a typical example.

T/0e II stress

>ending stress caused by mechanical loading. The bending stress in a tube plate, under the

effect of the difference in pressure between the tube side and the shell side is an example of

this stress, whose value may be permitted to exceed the yield point of the material without producing plastic collapse of the plate.

74



T/0e III stress

Stresses caused by constraints at $unctions or by thermal loading. =imited by displacement,

these stresses cannot by themselves bring about ultimate plastic collapse.

T/0e I) stress

The previous stresses affect a wide area. A type Q stress, on the other hand, is

concentrated in the immediate vicinity of a notch, a sharp reentrant corner, a threaded

connection, and so on. Such notch&type stress raisers need be considered only when the

material used is brittle or when cyclic variations of the load can lead to fatigue failure.

n some design codes, stresses are classified into five types. These are<

• 2rimary membrane stress, 2m

• 2rimary bending stress, 2 b

• =ocal membrane stress, 2=

• Secondary stress, G

• 2ea! stress, -

&ri-ar/ -e-brane stress@ &-

The component of primary stress (a stress developed by the imposed loading that is

necessary to satisfy the laws of equilibrium) that is obtained by averaging the stress

distribution across the thic!ness of the pressure vessel is referred to as the primary

membrane stress. xamples of primary membrane stress are<

• %ircumferential (hoop) and longitudinal (meridian) stress due to internal or external

pressures.

• Stress due to vessel weight.

• =ongitudinal stress due to bending of hori'ontal vessel over the supports.

75



• embrane stresses in the no''le wall within the area of reinforcement due to pressure

or external loads.

• Stresses caused by wind and seismic forces.

&ri-ar/ bendin! stress@ &b

n contrast to cylindrical shells, certain structural shapes cannot resist external loading

without bending, and the resultant stress produced is called primary bending stress.

2rimary bending stress is capable of causing permanent distortion or collapse of the vessel.

Some examples of primary bending stress are<

>ending stress due to pressure in a flat cover.

>ending stress in the crown of the torispherical head due to internal pressure.

%ocal -e-brane stress@ &%

=ocal (primary) membrane stress is produced by either pressure load alone or by other

mechanical loads. t has some self limiting characteristics.

Secondar/ stress@

Secondary stress is a normal or shear stress arising because of the constraint of ad$acent

material or by self constraint of the structure.

Secondary stresses can be divided into two ma$or categories,

/. =oad actuated secondary stresses

0. Temperature actuated secondary stresses

&ea9 stress@ '

76



2ea! stresses are the additional stresses due to stress concentration in highly locali'ed

areas. They are caused by both mechanical and thermal loads and they apply to both

limiting and non limiting loads.

Some examples of pea! stresses are

• Thermal stresses in a cladding or a weld

• Thermal stresses in a wall due to sudden thermal shoc!.

• Stress at a local structural discontinuity.

.., Desi!n standards

The pressure parts of a shell&and&tube heat exchanger are designed in accordance with a

pressure vessel design codes. ifferent countries of the world have different design codes

for pressure vessel and heat exchanger design. Some of the codes are accepted

internationally. These standards are made by different organi'ations wor!ing around the

globe. The following table lists the national standards for different countries.

TE(A

A pressure vessel design code alone cannot be expected to deal with all the special features

of shell&and&tube heat exchangers. To give guidance and protection to designers,

fabricators, and purchasers ali!e, a supplementary code is desirable that provides minimum

standards for design, materials, thic!nesses, corrosion allowances, fabrication, tolerances,

testing, inspection, installation, operation, maintenance, and guarantees for shell&and&tube

heat exchangers.

Table .1B National desi!n standards #or un#ired 0ressure 5essels

77



National Standard Countr/

AS section Q, ivision @SA

>SS 44:: @E

S%T -rance

A.. er!blatter Bermany

A%% taly

Stoomwen'en utch

S9*S&05?3 nternational

S< 0804&/?5? etherlands

B9ST @SS6 HS > 8031 Hapan

9ne universally accepted code that does this is the Standards of Tubular xchanger

anufacturers Association, !nown as TA. Although TA is designed specifically to

supplement the AS >oiler and 2ressure Qessel %ode, Section Q, ivision /, a large

portion of it may be used to supplement other pressure vessel codes if required. TA is

applicable to shell&and&tube heat exchangers with the following limitations<

• Shell diameter not exceeding / 403 mm

• 2ressure not exceeding 0 / *m0

• 2roduct< shell diameter V pressure not exceeding /: 4:: (mm V *m0)

AS(E $oiler and &ressure )essel Code Section )III

This code gives minimum requirements for the design, fabrication, inspection, andcertification of vessels with design pressures between /.:1 bar g (/4 psig) and 0:5 bar g (1

::: psig). The code consists off three divisions, namely ivision , ivision , and

ivision . ivision is normally used for most of the cases in heat exchanger design,

however ivision is preferred for high stress applications.

78



$S 22<<

This recently introduced code replaces >S /4:: and >S /4/4 and is intended to unify the

@.E. requirements for ail pressure vessels. aterials other than those listed in the code

may be used by agreement between purchaser and manufacturer provided that they arecovered by a written specification as comprehensive as the >S specification for the

equivalent material and that the design stresses are determined in a manner consistent to

>S.

A. D. (er9blatter

The A. . er!blatter # series of specifications lists acceptable materials that can be used

for a specific design. "owever other materials may be authori'ed with the agreement of theinspecting authority. n the latter case the # specifications give requirements that must be

satisfied.

These regulations are in the form of data sheets covering different aspects of vessel design

and construction, and are produced by a group of associations. 6evisions are made from

time to time to !eep up with advances in the !nowledge. Some aspects of vessel and

exchanger design are not covered, and the method is agreed upon by the purchaser,

inspecting authority, and designer. The code references used refer to the /?77 edition of A.

. er!blatter.

.. (aterial Selection

The selection of materials of construction for heat exchangers is in many instances

influenced by the design of the equipment. =ess often the properties of the required

material dictate the type of design that can be used. The need for economy in material on

the one hand, and for efficient heat transfer on the other, requires that when metals are used

the heat exchange ta!es place across relatively thin sections, and this in turn means that the

selected material must have sufficient corrosion resistance to operate for a reasonable time

without perforation.

79



The design codes and standards discussed in Sec. 3.3.1 list materials that may be used in

heat exchangers. 9ther materials may be used sub$ect to agreement between purchaser,

inspecting authority, and the manufacturer in general, design codes and standards specify

minimum qualities of materials.

General Considerations

This is a brief information guide for a vessel engineer who must be familiar with

commonly used construction materials to be able to specify them correctly on engineering

drawings or in material specifications for a particular $ob.

The selection of construction materials for %ode pressure vessels has to be made from

%ode approved material specifications. A metallurgical engineer usually specifies the mosteconomical materials of low first cost and for low future maintenance cost that will be

satisfactory under operating conditions and will meet other requirements.

There are many factors supported by experience and laboratory test results that must be

considered in selecting the most suitable materials. They include the following<

• %orrosion resistance in the service corrosive environment,

• Strength requirements for design temperature and pressure,

• %ost,

• 6eady mar!et availability,

• -abricability,

• Guality of future maintenance.

Benerally, process equipment is designed for a certain minimum service life under specific

operating conditions. >ased on a corrosion rate in mils (:.::/ in.) per year (2W) a total

corrosion allowance is established which is added to the calculated required thic!ness.

Typical design lives are given below for several types of petrochemical equipment.

80



20 yearsB -ractionating towers, reactors, high&pressure heat&exchanger shells, and other

ma$or equipment, which is hard to replace.

10-15 years< %arbon&steel drums, removable reactor parts, and alloy or carbon&steel tower

internals.

5-10 years: %arbon&steel piping, heat&exchanger tube bundles, and various process column

internals.

The selected material must be suitable for services of different levels of severity from the

standpoint of pressure, temperature, corrosive environments, cyclic or steady operations,

etc. 9bviously, a number of divisions is possible. "owever, since the choice of material for

a vessel depends primarily on the service environment, it would seem practical to classifyconstruction materials according to service< non&corrosive, with corrosion rates negligible

or very low and definitely established (for carbon steel, a maximum of QX in. total

otherwise an alternative material with a better corrosion resistance is used) or corrosive,

requiring special materials other than carbon steels low&alloy steels.

Non6Corrosi5e Ser5ice

n addition to corrosion resistance, the fundamental material selection criteria are designtemperature and design pressure.

n the range of cryogenic temperatures (from &304 ;- to &/4: ;-) carbon and low alloy

steels are brittle and austenitic stainless steels or non&ferrous metals li!e aluminum alloys

that do not exhibit loss of the impact strength at very low temperatures must be employed.

(-or a cryogenic engineer the dividing line between the cryogenic and low temperatures is

usually &03: ;-, below which temperature only so&called permanent gases remain in the

gaseous state. This distinction is not of practical significance here.) The temperature range

at which a material changes gradually from ductile to brittle is called the transition

temperature and is readily determined from %harpy impact tests conducted over a range of

temperatures. The designer of %ode low&temperature equipment must base his

computations on the %ode approved properties of the material at room temperature.

81



"owever, for some %ode materials (@=T 01) the higher yield and tensile strengths of alloys

at very low temperatures can be used to reduce weight and cost where possible. >ecause of

the low reactivity of most chemicals al very low temperatures, corrosion problems are few.

At low temperatures (from &/4: ;- to 10 ;- the %ode upper limit is &0: ;-) low&alloyand fine&grain carbon steels tested for notch toughness are found to perform satisfactorily.

n the range of intermediate temperatures (from 11 ;- to about 8:: ;-) low&carbon

steels are sufficient. @p to about 8:: ;- they behave essentially in an elastic manner that

is, the structure returns to its original dimensions when applied forces are removed and

maximum stress is below the yield point. The design allowable stress is based on the yield

strength or the ultimate strength obtained from short time rupture tests, supplemented by

fatigue or impact tests, where fluctuating or shoc! stresses are involved.

At elevated temperatures (above 8:: ;-) mar!ed changes in mechanical properties occur in

steels. They begin to exhibit a drop in ultimate and yield strengths and cease to be elastic,

becoming partly plastic. @nder a constant load, there is a continuous increase in permanent

deformation, called creep. The creep rate is measured in percent of a unit length per unit

time. Actually, some creep begins at temperatures over 54: ;-, but it does not become an

important factor for carbon steels until temperatures over 8:: ;- are reached. The designallowable stress is then based on two criteria<

a. The deformation due to creep during the service lifetime must remain within

permissible limits, and

b. A rupture must not occur. The allowable stresses are obtained from long&term creep

tests and from stress rupture tests at elevated temperatures. -ew data, if any, are

available on high&temperature endurance limits.

Steels used in vessel construction for elevated temperatures can be classified into five

general types<

82



Carbon Steels

These vary in strength at temperatures below 54: ;- because of small differences in carbon

content, but they all have similar properties in the creep range. #here their use is not

limited by sulfur corrosion or hydrogen attac!, they usually represent the most economical

material for intermediate as well as for elevated temperatures at low pressures. ot only

are they relatively cheap per pound, they are also comparatively easy to fabricate. ach

additional alloying element increases the cost of the steel, and often the difficulty of

fabrication and welding as well. The final overall cost of a carbon steel vessel may be

much less than the cost of an alloy steel vessel.

Carbon6-ol/bdenu- steels

=ow chromium molybdenum alloy steels (up to 1%r&l o) and intermediate chromium&

molybdenum alloy steels (up to ?%rYl o), some of these can be used up to /0:: ;-,

where resistance to graphiti'ation and hydrogen attac! is required. These steels have better

creep&rupture properties and high temperature strength than carbon steels, and there is an

economy in using them for pressure vessels sub$ected to high pressure at temperatures over

54: ;-. -urthermore, these steels may be required to resist oxidation sulfidation, or

hydrogen attac!.

'erritic =strai!ht chr-iu-> stainless steels

These are used in sonic applications.

Austenitic stainless steels

These are the only steels assigned allowable stresses in the %ode for temperatures higher

than /0:: ;- up to /4:: ;-. A decrease in oxidation resistance limits their usefulness above

this temperature.

83



S0ecial hi!h6te-0erature6resistin! allo/s

These are used for temperatures above /4:: ;-. They include type 1/: stainless steels and

ncoloy.The following tables provide a list of materials that can be used in corrosive and

non corrosive environments<

Table ."B aterials of construction for non corrosive service

Table .,B aterials of construction for corrosive service

84



85



.2 General &rocedure #or (echanical Desi!n o# a Shell and Tube Heat

Echan!er

The process of design of a heat exchanger on the basis of complete stress analysis of all the

components is very complicated and a tedious practice. Therefore it is a common design

practice to follow some rules that have been specified in different design standards. The

rules given to si'e a particular component have an analytic basis. These rules have

generally been adapted as a result of experience over the years, and the analytic

bac!ground is sometimes hidden. The following section aims to explain the rules and

standards that are used in the design of various components of a shell and tube heat

exchanger.

.2.1 C/lindrical shell

The shell barrel must be straight and have no out&of&roundness, as a tightly fitting tube

bundle must be inserted in it. Standard pipe less than 34: mm in diameter is usually

available, and this will be used for the shell and head barrels instead of rolled plate.

epending on the fabricators roll capacity, at thic!nesses of the order of 8: mm and

greater or large thic!ness*diameter ratios, it may be necessary to use forged instead of

rolled barrels.

ost shell and head barrels greater than about 34: mm in inside diameter are rolled from

plate, and a complete shell barrel may comprise several smaller barrels, or stra!es,

welded together end to end. f there is any out&of&roundness, individual stra!es are

rerolled after welding the longitudinal seams. The longitudinal seams of ad$oining stra!es

are always staggered. The inside diameter of a rolled shell should not exceed the design

inside diameter by more than 1.0 mm (/*8 in) as determined by circumferential

measurement. All internal welds must be made flush.

-or internal pressure, the thic!ness of the shell is calculated from the hoop stress formula.

The equation is modified so that either internal or external cylindrical radius can be used.

The design formulae in the code are derived by equating the maximum membrane stress to

86



the allowable stress corrected for weld $oint efficiency. As per AS codes, the thic!ness

of cylinder wall should not be less than as computed by the following formulae<

Table .B AS code formulae for thin cylindrical shell to withstand internal pressure

(e-ber Thic9ness@ t (ai-u- internal

0ressure@ 0

%i-itation

%on!itudinal oints t K 26 * (S& :.52) 2 K Set * (6 :.5t)2RK :.184S

tRK :.4 6 Circu-#erential

ointst K 26o* (S :.32) 2 K 0St * (6 + :.3t)

2RK /.04S

tK :.46 In ter-s o# outside

radiust K 26o* (S :.32) 2 K St * (6o+ :.3t)

2RK :.184S

tRK :.4 6

-ollowing AS and TA standards govern the design of shell.

TE(A

inimum fabricated thic!ness 6%>&1./1

2ost weld heat treatment of %S channel 6%>&?./3

AS(E

inimum thic!ness of shell @B/5 (b)

nternal pressure thic!ness

t K 26* (S + :.52), @B07(c)

#here K weld $oint efficiency @w/0

Qacuum chec! (xternal pressure thic!ness) @B08

Tolerance on out&of&roundness @B8:

Bood practice regarding linings A22& -

%lad&shell design thic!ness @%=01

87



.2." Dished head

The analysis of hemispherical heads is straightforward, and all code rules are based on the

following equation<

L K 26 0 (/&Z) sin[ * 0t

-or ellipsoidal and torispherical heads, the analysis is more complex, and in recent years,

experimental and theoretical studies have examined the local stresses existing throughout

these heads. ished head channels are cheaper than those with bolted flat heads.

The thic!ness and maximum pressure for dished heads of different shapes are given in the

following table<

Table .2 AS formulae foe determination of dished heads

Head t/0e Thic9ness@ t (ai-u- internal

0ressure@ &

llipsoidal t K 2 * (0S + :.02) 2 K 0St * ( :.0t)Torispherical t K :.8842= * (S + :./2)s 2 K Set * (:.884= :./t)"emispherical t K 2= * (0S + :.02) 2 K 0Set * (= :.0t)%onical t K 2 * 0cos\ (S + :.52) 2 K 0Stcos\ * (

/.0tcos\)

-ollowing AS and TA standards govern the design of dished head<

TE(A

inimum fabricated thic!ness 6%>&1./1

>onnet inside depth for ultipass channels 6%>&?./0

2ost weld heat treatment of %.S. channels 6%>&?./3

AS(E

inimum thic!ness @B/5 (b)

nternal pressure thic!ness of semispherical,

0< / ellipsoidal and 5 torispherical @B10

nternal pressure thic!ness of other ellipsoidal

88



and torispherical heads @A3

Tolerance on shape @B8 /

Attachment welds to cylinder @#/1

Qacuum chec! @B 11

.2., 'lat head

#ith simple edge conditions, a flat plate under pressure is a straightforward bending

component. The $unction with the cylindrical shell is either welded or flanged, and this

$unction disturbs the simple stress distribution. The resultant stress&concentration factor is

accommodated in the code rules by a factor modifying the basic flat&plate formula. #ith

bolted heads an edge moment is added by the ad$acent flange bolting and a modifying

factor is again used.

The minimum thic!ness of flat head, cover and blind flanges shall be calculated by the

following relation<

t K d ] (%2*S)

-ollowing AS and TA standards govern the design of flat head<

TE(A

2artition groove considered as corrosion allowance 6%>&/.4/3

>olted channel cover thic!ness 6%>&?.0/

epth of partition groove 6%>&?.00

AS(E

Acceptable types of flat heads -ig. @B13

-lat head thic!ness @B13(c) (0)

Thic!ness at edge gas!et groove @B 13 (d)

6einforcement of opening @B 1?

.2. 'loatin! head co-0onents

The floating head is composed of three components<

89



/. The floating head cover&a dished or flat head

0. The floating head flange&attached to the cover

1. The bac!ing ring&usually split to allow withdrawal of the tube bundle

esign of floating head is governed by the following AS and TA standards.

TE(A

inimum inside depth of floating&head covers 6%>&?./0

2ost weld heat treatment of %S floating head covers 6%>&?./3

aterials and corrosion allowance 6%>&4./1

Tube bundle support plate at floating end 6%>&4./3

AS(E

ished head thic!ness, internal pressure @A5 and @B10ished head thic!ness, external pressure @B11

-lange ring thic!ness @A5

Split&bac!ing&ring thic!ness @A41

.2.2 Tubes

Tubes in fixed tube sheet exchangers are sub$ected to and loads as wells as an internal

and external pressure. =ongitudinal tensile stresses arte treated the same way as pressuretensile stresses, but longitudinal compresses stresses may cause the tube to buc!le as a

column. Tubes are also sub$ected to end loads which effect the tube end fixing. n

thic!ness calculation minimum tolerances should be ta!en into account.

-ollowing AS and TA standards govern the design of tubes<

TE(A

Standard length 6%>&0./

Standard diameter and thic!ness 6%>&0.0inimum thic!ness before forming @ bends 6%>&0.1/

=ongitudinal stress (fixed tubesheet) 6%>&7.01*3

Tube $oint loads 6%>&7.4

Tube maintenance &3

90



AS(E

Thic!ness for internal and external pressure @B1/

Tube end fitting A22. A

.2.3 Tubesheet

Tubes sheets are most complex exchanger component and /4 variables can be listed that

affect the loading. TA in /?3/ first gave rule for the design of @ and floating&"ead

tubesheets based on modified plate formulae. Although empirical, these formulae gave

satisfactory results and a form of them is still is used in current TA rule .An analytical

approach for @ and floating "ead tube was provided by Bardener by treating the tube sheet

as a modified solid plate.

-ollowing AS and TA standards govern the design of tubesheet<

TE(A

ffective thic!ness of tubesheet A./0

%lad tubesheets& A./00 and 7.?

Tube hole clearances 6%>&7.3

xpanded tube $oints 6%>&7.4

AS(E

-or tubesheet extended for edge bolting, the thic!ness at the

periphery can be chec!ed as for the outer edge of a flat plate, -ig. (i) @B13 (d)

Attachment weld between shell and tubesheet @#/1 (e)

Tube end fixing, the maximum end load is dependent on code

stress, c.s.a., and type and testing of expanded or welded $oint A22. A

.2.7 No88les

-or no''le design, the principal codes illustrate two approaches. The traditional method of

no''le reinforcement by area replacement is used by AS Q iv. /, in which the

cross&sectional area of the reinforcement equals the cross&sectional area of the metal

91



removed from the shell. This reinforcement is added as a pad, a thic!ened branch, or a

thic!ened shell.

A limited amount of plastic deformation in local areas is accepted during initial operating

cycles, but a residual stress distribution is established and the subsequent behavior iscompletely elastic. This sha!edown behavior is achieved by limiting the maximum stress

in the no''le. -or branches in spherical shells this maximum is set at 0.04 times the

allowable stress in the non reinforced shell. -or branches in cylindrical shells the allowable

stress concentration factor is calculated from the estimated sha!edown factor for the no''le

geometry.

esign of no''les is governed by the following AS and TA standards<

TE(A

Beneral requirements 6%>&?./Qent and drain connections 6%>&?.1/2ressure and temperature connections 6%>&?.10/1Split flange design 6%>&?.4 o''le loadings 6%>&?.5

AS(E

Beneral requirements @B15aximum no''le diameter in cylinder using compensationrules is one half of shell diameter up to / 403 mm @B15 (b) (/)aximum no''le diameter in heads is one&half of shell diameter @B15 (b)(0)6ecommendations for large no''les @A7

=arge no''les require proof test @Bl:l6einforcement area required @B17 (b)=imits of reinforcement @B3:6einforcement of multiple openings (i.e., pitch R 0 V av) @B30inimum no''le nec! thic!ness @B34

.2.: Su00orts

Supports for heat exchangers are usually of two types<

• Saddle supports for hori'ontal units, one fixed and one sliding, with support angle

usually greater than /0:;.

• Support feet for vertical units

92



esign of supports is governed by the following AS standards<

AS(E

Bood practice regarding supports. App. Baterial for supports @B5 (b)=oads to be considered @B 00-itment of supports @B 80

.2.; 'lan!es

-lange design is perhaps the most complicated and tedious process in the designing of a

shell and tube heat exchanger. n design practice one can select a standard flange from the

available options or one may completely design a new flange.

There are three types of flanges, namely, loose, integral, or optional. The type of flangesto be used may depend on the availability of material, design conditions, the process

fluids, or manufacturing costs. -or example, a carbon steel loose&type flange having a lap

$oint could be used with a stainless steel shell.

-langes and bolting for external $oints shall be in accordance with %ode design rules,

sub$ect to the limitations set forth in the following paragraphs.

TE(A

inimum bolt si'e 6//./, %//./, >//./>olt circle layout 6%>&/.0

inimum recommended wrench and nut clearances 6%>&//.1

AS(E

6ules for bolted flange connections with ring type gas!ets App. 0

>asic gas!et seating width @A&3?.0

Bas!et and flange material selection @A&40

.2.1< Non 0ressure 0arts

esign of non pressure parts is mostly ta!en into consideration by TA and there are

no hard and fast rules specified by AS in this regard.

-ollowing are some of the standards that govern the design of such non pressure parts.

These standards are according to TA /?78 dition.

93



Transverse baffles 6&3./

=ongitudinal baffles 6&3.30

Support plates 6&3.1, 6&3.3

Tie rods and spacers 6&3.7/

mpingement plates 6&3.5

.3 Heat echan!er s0eci#ications sheet

>y established practice, a ma$ority of shell&and&tube exchangers are designed by the

manufacturers from specification sheets supplied by the user and partially filed out by the

designer. A typical such specification sheet, ta!en from ST heat exchangers company, is

reproduced in -ig. 3.0. @nfortunately, the information transferred from the user to thedesigner and fabricator by these forms almost never contains sufficient information for a

really complete design, and the details of who is really responsible for what are rather

confused.

9n the other hand, the user often imposes unnecessary constraints, such as specified tube

diameter and tube length, shell type and baffle type, and other design parameters, which

at closer examination are found to be rather arbitrary and prevent an optimum or a

NgoodO design. Specification of the maximum permissible pressure drop is probably themost sensitive of the entries, as it for all practical purposes fixes the design by inherent

implications. evertheless, this crucial value is often based on rather arbitrary criteria.

Similarly fouling resistances are specified from experience values or are based on TA

Standards for lac! of any better sources.

94



'i!ure ." Sample heat exchanger data sheet

95



The frequent practice of using high fouling resistances as safety factors is dangerous, as

the amount of safety gained is relative and can be determined only after all the resistances

have been established. #ith the exception of very common fluids, the specification of

physical properties, especially for fluid mixtures, is not only a most time&consuming

chore, but also is sub$ect to potentially great errors as sources of data are scarce. ore

often than not, crudely estimated values are used in the absence of better answers.

Thus the practices and usage of the specification sheets is a rather sensitive problem, and

the designer should ma!e sure that input of sufficient detail but without unnecessary

restrictions is available.

The recent trend, especially with large user companies, is to perform the thermohydraulic

design themselves and to let the manufacturer design the details of constructionalelements. This has the advantage that the user has more direct access to various aspects of

the process, chec!s for operation at other&than&normal conditions, usually a better supply

of physical properties data, and, last but not least, access to large, sophisticated computer

programs. >ut close cooperation between the user and the manufacturers remains a very

crucial element.

96



Desi!n Calculations

2.1 Introduction

This design example is for a shell and tube heat exchanger. The heat exchanger has a

fixed tubesheet on one side and a floating head on the other side. The measurements and

calculations are in S units. The design conforms to the standards of TA 0::7 edition

and AS >oiler and 2ressure Qessel %ode, Section Q, ivision , 0::7 edition.

2.1.1 S0eci#ications

xchanger type TA AHS

TA class 6

esign pressure shell side 0::: !2a

esign pressure tube side 4:: !2a

esign temperature shell side /::o%

esign temperature tube side /4o%

%orrosion allowance shell side 1 mm

%orrosion allowance tube side 1 mm

97

Chapter 5



Shell inside diameter 514 mm

%hannel inside diameter 514 mm

Shell inlet no''le nominal pipe si'e 0:1 mm

Shell outlet no''les nominal pipe si'e /40 mmTube side inlet no''le nominal pipe si'e 1:4 mm

Tube side no''le outlet nominal pipe si'e 1:4 mm

umber of tubes 358

Tube outside diameter /?.:4 mm

Tube wall thic!ness (/3 >#B) 0.// mm

Tube length 3.:5mm

Tube pitch 01.8/0 mm

Tube pattern 1:o

umber of tube passes 3

umber of baffle segments ?

>affle spacing 18: mm

>affle cut 04

mpingement protection none

#eld examination spot

2.1." (aterial s0eci#ication

Co-0onent 'or- S0eci#ication

Shell 2late SA&4 /4&7:

%hannel 2late SA&4 /4&7:

%hannel cover 2late SA&4 /4&7:

Shell cover cylinder 2late SA&4 /4&7:

Shell cover formed end 2late SA&4 /4&7:

98



Shell flanges -orgings SA&/:4

%hannel flanges 2late SA&4 /4&7:

Shell cover flange 2late SA&4 /4&7:

-loating head cover flange 2late SA&4 /4&7:2ass partition plate 2late SA&4 /4&7:

Tubesheets 2late SA&4 /4&7:

Tubes Seamless tube SA&0/:&Al

Shell side no''le 2ipe SA&/:5&>

Tube side no''le 2ipe SA&/:5&>

>olts >ar SA&/?1&>7

2.1., Order o# calculation

-or a heat exchanger with a floating tubesheet, assuming that the tube layout is !nown, it

is advisable to design the floating&head cover first. This will confirm if there is sufficient

space within the shell and outer tube limit circle diameter to fit the required gas!et. The

shell, channel, and shell cover cylinder thic!nesses may then be calculated. The

remaining components may then be designed at random. -or this design, the selected tube

wall thic!ness is chec!ed, followed by the design of the flanges and end enclosures. The

tubesheet and no''les calculations complete the calculations for components sub$ected to

pressure. -inally, the dimensions of the non pressure components are determined.

The units used for pressure are !2a, and for material stresses are 2a as specified in the

AS nomenclature (/ 2ascal K / newton per square meter).

99



2." 'loatin! Head

2.".1 'lan!e and dish

-rom AS @A&5, the minimum dish thic!ness is the greater of the tube&side or shell&side requirements.

'or internal 0ressure

t

#here,

2 K 2t K 4:: !2a,

6 K dish corroded inside radius

S K maximum allowable stress K /0/ 2a.

Assume

Shell&to&floating tubesheet radial clearance K 4 mm

Bas!et width, K /1 mm (TA minimum K /0.7 mm)

Then the flange corroded inside diameter, >

#here,

i K Shell internal diameter

V K 6adial clearance between flange and shell K -lange width

The flange uncorroded inside diameter is

100



Assume the dish uncorroded inside radius is :.74 V 4?1 K 334 mm

Then

So,

tfhd K

'ro- TE(A R6,.1,

inimum allowable corroded plate thic!ness is 5.14 mm. Assume that tfhd K 7 mm

'or eternal 0ressure

According to AS @B&11(c), the procedure for design based on external pressure is asfellows.

Step 1: Assume a head thic!ness t of 7 mm and calculate the value of factor A<

A

101



Steps 2, 3: nter -ig. %S&0 at A value of :.::/?4 and move vertically to material line for 7::;-. ove hori'ontally to the right and read > value of /34:: lbf*in0. ultiply thisvalue with 5.8?4 to convert it into !2a.

Step 4: The maximum allowable external wor!ing pressure for the assumed headthic!ness of 7 mm is<

2a

This value is less than the shell side design pressure so assume a higher value of thic!ness and repeat the procedure.

Assume t K ? mm

AK

-or this value of A,

102



K /:38:3

ow,

2a

Since 2a of 0/:4 !2a is greater than the external design pressure 2 of 0::: !2a, theassumed head thic!ness of ? mm is be satisfactory.

So the dish uncorroded thic!ness can be found as

Tfhd

T#hd

ish uncorroded inside radius is

103



2."." 'lan!e desi!n

The flange thic!ness is the greatest thic!ness of that required for gas!et seating, tube side pressure, shell side pressure or from geometric considerations to allow for the sufficient

crossover flow area. The positioning of dish cover relative to the flange centroid is animportant part of design calculations. There are several methods for this purpose onewhich is being used here is presented below.

/. %alculate the flange thic!ness required for gas!et seating.0. %alculate the gas!et thic!ness required for the crossover flow area.1. @se the greater thic!ness of the two of the above and position the outer edge of

the flange of the dish at the bac! of the flange.3. %alculate the loads and moments exerted on the flange by the tube side and shell

side pressure.4. f the flange is overstressed, hold the dish position and equal increments to bothsides of the flange until an acceptable thic!ness has been achieved.

The general equation for flange thic!ness is given by AS @A&5, where

n this equation,

- K

H K

(-or internal pressure)

(-or external pressure)

(-or gas!et seating)

'or !as9et seatin!

104



So,

, and

This gives,

Substituting the values in the expression for H<

H K

ow,

So,

t K 45.5 mm

t 27 -- =a00ro>

'or #lo+ crosso5er area

-or flow cross over area, from TA 6& 8./0

There are 358 tubes, /?.:4 mm 9 and 0./ mm wall thic!ness arranged in four passes.

-low area per pass K

105



-low area per tube per pass K /?.:4 + 0 X 0.//)0

According to TA 6&8./0, the total required crossover area is

f the effect of pass partition plate is neglected, the area available under the dish for crossover per pass is

The depth of flange required for crossover flow area per pass is

'or eternal 0ressure

- K

K

106



K 8

H K

K

K 455.50 mm0

ow,

t :.,: --

'or internal 0ressure

- K

K

H K

107



K

K 3/4.53 mm0

Since

So,

t "".: --

So we will consider the greatest value of thic!ness. This value is for gas!et seating. i.e<

t 27 --

2."., Gas9et and boltin! conditions

-or this design, flange design is as fellows<

Bas!et material< soft steel $ac!et asbestos filled

504 mm 9 x 4?? mm x1, with pass partition webs /: mm wide,

K /1 mm

bo K *0.

K 5.4 mm

-or bo ^ 5.14 mm

108



b K 5.304 mm

-rom table 0&4./,

m K 1.74 mm

y K 40.3 2a

K

K

K 5.08 X 5.304 X 5/0./4 X 1.74 X 4::

K 35,114

K :.784 X (5/0./4) 0 X 4::

K /37,:8/

K /73,:8/ 35,114

K /?1,3/5

109



K :.784 X (5/0./4) 0 X 0:::

K488,100

Am K Breater of A/ K #m/ * S b or A0 K #m0 * Sa

K greater of /?1,3/5 * /70 or 537,34? * /70

K 1753 mm0

>olt specifications< 03 0: bolts.

A b K 03 X 0/3.8?

K 4/47 mm0

K :.4 (1,753 4,/47) X /70

K 757,0:5

Bas!et width chec!,

^ TA minimum width, 9r min/ or min0

TA minimum width K /0.7 mm

K 4,/47 X /70 * 5.08 X 5/0./4 X 1.74

K 3.3 mm

K 488,100 * 5.08 X 5/0./4 X 40.3

K 0.? mm

110



K

K 3/.33 degree

Bas!et inside diameter, > K 4?? mm

>olt circle diameter, % K 55: mm

Bas!et outside diameter, A K 7:0 mm

The moments involved in gas!et design are summari'ed in the form of tables below<Tube side o0eratin! conditionsB

=oad =ever arm, mm oment, &m" K :.784 X >0 X 2t K :.784 X (4??) 0 X 4:: K/3:,88?

h K :.4 (>% & >) K :.4 (55: & 4??) K 1:.4 mm

K "X h

K /3:,88? X 1:.4 K 3,0?4&m

"B K #m/ + " K "p K 35,114

hB K :.4 (>% & B) K :.4 (55: + 5/0./4) K 01.?4 mm

B K "B X hB

K 35,114 X 01.?4 K /,//:&m

"T K " + " K /37,:8/ + /3:,80? K 5,040

hT K :.4 (h hB) K :.4 (1:.4 01.?4) K 07.004 mm

T K "T X hT K 5,040 X 07.004 K /7:&m

"r K " cot _/ K /3:,88? cot (3/.33) K /4?,4/4

hr K 0:.: mm r K "r X hr K /4?,4/4 X 0:.: K &1/?:&mmo K 0,184&m

Shell side o0eratin! conditionsB

=oad, =ever arm, mm oment, &mm" K :.784 X >0 X 2s K :.784 X (4??) 0 X 0::: K 451,7/7

h K h + hB

K 1:.4 + 01.?4 K 5.44 mm

K " X h K 451,7/7 X5.44 K 1,5?:&mm

"T K "e + "

K /4?,4/4 + /3:,88? K 04,::4

h K "T + "B

K 07.004 + 01.?4 K 1.074 mm

T K "T X h K 04,::4 X 1.074 K 80&mm

"r K " cot _/ hr K 0:.: mm r K "r X hr

111



K /3:,80? X cot (3/.33) K 518,:4?

K 518,:4? X 0:.: K &/0,75/&mo K &8,?8?&m

Gas9et seatin!B

=oad, =ever arm, mm oment, &mm"B K # K 757,0:5

hB K 01.?4 mm a K "B X hB

K 757,0:5 X 01.?4 K /8,173&mo K /8,173&m

2.". 'loatin! head bac9in! de5ice desi!n

The bac!ing device clamps the floating cover to the tubesheet. There are various types of floating head, the one being used here is a single split ring type designed to AS @B41(a). The split ring is designed as if it were a solid flange without splits, using a value of 0:: of the greater of a or o.

n this case since a is greater than o, the effective thic!ness is therefore,

Shape constant, E K A * > K /./70

So from AS -igure @A&4/./

W K /0.1/

ow

a K /8,173&m

S K Sfa K/0/2a

> K 4?? mm

112



Substituting these values in the expression for floating head thic!ness,

t#hb 7;.< --

2., C/lindrical shell

The minimum, allowable thic!ness for cylindrical shell is the minimum of TA or AS requirements.

The minimum uncorroded thic!ness NtO is the greater thic!ness as obtained from theformulae in AS @B&07.

-or circumferential stress (longitudinal $oints),

t

-or longitudinal stress (circumferential $oints),

t

#here,

2 K esign pressure for shell side K 0::: ! pa

6 i K nside radius of vessel K 514 mm

S K Allowable material stress at design temperature K /0/2a

K #eld $oint efficiency K :.84

-or circumferential stress

t K

113



K

t 1< --

-or longitudinal stress

t K

t 3.12 --

-or external pressure,

Assume t K /: mm

Then,

A K

K

K mm


> K /58:: lbf*in0

K /58:: X 5.8?4

K //4,815 !2a

ow,

2a K

114



K

K 1417 !2a

Since this value of pressure is more than shell side pressure, a thic!ness of /: mm is safe.

2. Shell co5er =dished head>

The minimum allowable thic!ness for shell cover is the maximum value of TA andAS requirements. Shell cover used in this design is a 0</ ellipsoidal head. Accordingto AS @B&10, the minimum required thic!ness at the thinnest point is shall be thegreater of the thic!nesses calculated by the formula for ellipsoidal head and the formulafor hemispherical heads divided by the $oint efficiency of the head to shell $oint.

llipsoidal head formula,

t K

#here,

2 K Shell side design pressure K Shell cover cylinder diameter 0 X corrosion allowance

K 7/8 0 X 1 K 703 mm

S K

K :.84 X /0/ K /:0.842a

K #eld $oint efficiency K /.:Then,

t K

K

t 7.<2 --

115



"emispherical head formula,

t K

#here,

=e K *0 K 150 mm

K :.84

Then,

t K

K

t .12 --

According to AS @B&10, we will have to divide this thic!ness by weld $ointefficiency before using it in design calculations. So,

t K 3./4 * :.84

t .:: --

So we will use the higher value, i.e t K 7.:4 mm

Assuming a thinning allowance of /0.4 and including the corrosion allowance, theminimum required thic!ness comes out to be,

t K 7.:4 :./04 X 7.:4 1.::

t 1<.;, --

-rom TA 6&1.0, the minimum required thic!ness comes to be,t K ?.41 mm

Therefore rounding off to the nearest decimal, the plate thic!ness is // mm.

116



2.2 Channel co5er

The channel cover is a flat plate, bolted to the channel at its front end. ts effectivethic!ness is the maximum of AS or TA requirements.

-rom AS @B&13, for the given operating conditions,

t K B

#here,

t K effective channel cover thic!ness

%c K dimensionless factor K :.1

2 K esign pressure tube side K 4:: !2a

S K aximum allowable stress K /0/2a K Hoint efficiency# K >olt load for gas!et loading K 511,8:3#m/ K >olt load under operating conditions K 010,7:/ &mhB K radial distance from location of gas!et load reaction to the bolt circle K 7:5B K iameter at point of location of gas!et load reactiond b K ominal bolt diameter K 0:.: mmA b K Actual total cross sectional area of bolts K 5.:/7 mm0

Substituting the values of variables in the above expression we get the value of cover plate thic!ness,

t K

K

"7.3 --

-or gas!et seating, 2 K :

So,

117



t K

K

t 1;.; --

-rom TA 6&8.0/

t K

K

tK 40.5 mm

The gas!et has a compression factor m R 1.:. Therefore the thic!ness obtained by TAformula can be reduced by 0:. "ence,

t K :.8 X 40.5

t ".1 --

The thic!ness calculated by TA formula is greater than the thic!ness calculated byAS formula, so the effective thic!ness is 30./ mm. The cover overall thic!nessrounded off to nearest decimal, including the gas!et recess groove depth of 4 mm willtherefore be,

t : --

2.3 Tubes

Tube thic!ness is determined by using internal pressure formula as specified in AS@B&1/. #all thic!ness is specified in TA 6&0.0/.

t K

#here,

118



2t K Tube side pressure K 4::!2a

6v K Tube inside radius K 7.3/4 mm

S K aximum allowable stress K /0/ 2a

K Hoint efficiency K /.:

Then using the internal pressure formula,

t K

t <.<,1 --

-or external pressure, using the rules in AS @B&08,

Assume tube wall thic!ness, t K 0.// mm

Then,

AK

K

K


> K /7,0:: lbf*in0

K /70:: X 5.8?4

K //8,4?3 !2a

ow for the tube, the two pressures 2a/ and 2a0 will be calculated, the minimum of whichwill give the maximum allowable pressure.

2a/ K

119



K

K /8,5/:!2a

2a0 K

#here,

S is lesser of two times the maximum allowable stress value (/:1 2a) or :.?times the material yield strength (044 2a)

S K the lesser of 0 V /:1 K 0:5 2a9r

:.? V 044 K 00?.4 2a

Therefore S K 0:5 2a.

2a0 K

K 3:,471 !2a

The maximum allowable external pressure for the tube wall is therefore /8 5/: !2a,which is much greater than tube operating pressure of 4:: !2a. "ence a tube wallthic!ness of 0.// mm will be satisfactory for both the tube&side and shell&side design pressures.

t ".11 --

2.7 Tubesheets

This heat exchanger contains two tubesheets, one of which is fixed and the other is

stationary. >oth the tubesheets are considered gas!eted without edge bolting. Theeffective thic!ness is determined from TA 6&7.

2.7.1 Stationar/ tubesheet

The effective thic!ness of stationary tubesheet is the greater of that required for bendingor shear.

120



According to TA 6&7./10, thic!ness formula for bending is given by<

t K

Shear thic!ness is specified by TA 6&7./11,

t K

#here,

2 K Breater of shell side or tube side design pressure K 0:::!2aB K ean diameter of the gas!et at the stationary tubesheet K 578.08 mm

- K A constant K /.:S K aximum allowable stress K /0/2ado K Tube outside diameter K /?.:4 mm p K Tube pitch K 01.8/ mm

n this case only bending will be the governing parameter as

2*S R /.5(/&do*p)0

So putting the values in bending formula,

t K

t ,.3 --

The stationary tube sheet will have a raised face of 4mm thic!ness on each side for fittingthe gas!ets. The minimum overall thic!ness rounded off to the nearest decimal istherefore,

t K 31.5 0 X 4

t 2 --

2.7." 'loatin! tubesheet

The effective thic!ness of the floating tubesheet will be the same as the effectivethic!ness of fixed tubesheet because the parameters 2, S, - and B have the same value for both the cases. The only difference between the two is that floating tubesheet will have araised face of 4mm thic!ness on only one side of it.

121



2.: No88les and rein#orce-ents

2.:.1 No88les

The no''le wall thic!ness is calculated by using AS @B&15 or TA 6&?. The no''lewill be of seamless pipe. Assuming that there are no external loads, from AS @B&34,

the wall thic!ness of the no''le may not be less than the smaller of the following.

/. The required thic!ness of the shell or the head to which the no''le is attached pluscorrosion allowance provided in the shell ad$acent to the no''le.

0. The minimum thic!ness of standard wall pipe plus corrosion allowance on theno''le.

The formula used to calculate no''le thic!ness is the formula for internal pressure,

t K

A summary of wall thic!ness calculations for all the no''les is given in the followingtable<

Tube side Shell sidenlet * outlet nlet 9utlet nlet 9utlet umber of no''les / / / 0 ominal si'e 1:4 1:4 0:1 /402 K esign pressure, !2a 4:: 4:: 0::: 0:::6 K %orroded inside radiusof mating shell or head, mm

10:.4 10:.4 10:.4 10:.4

S K aximum allowablestress, 2a /0/ /0/ /0/ /0/ K Hoint efficiency / / / /c Kcorrosion allowance, mm 1 1 1 1t corrosion allowance, mm 3.11 3.11 8.1/ 8.1/Standard wall thic!ness, mm ?.41 ?.41 8./8 7.//Standard wallthic!nessX:.784 corrosionallowance, mm

//.13 //.13 /:./4 ?.00

in. allowable thic!ness,mm

3.11 3.11 8.1/ 8.1/

2ipe nominal thic!ness, mm 5.41 5.41 /:.1/ /:.?72ipe schedule 0: 0: 5: 8:

2.:." No88le rein#orce-ents

#hen a hole has been cut in a shell or head to accommodate a no''le, reinforcementsmay be required to compensate for the metal that has been removed. The reinforcementmay be in the form of<

122



/. A forged nec! no''le, AS @B&3:0. 6einforcing plate

The limits of reinforcement are given by the following relation,

tr K

And

trn K

#here,2 K esign pressure6n K o''le inside radius6 K ating vessel inside radius

S K Qessel allowable stress K /0/2aSn K o''le allowable stress K /:12a K Hoint efficiency K /.:

2.; Non 0ressure 0arts

2.;.1 Trans5erse ba##les

The baffle cut design is governed by TA 6&3./. t defines the baffle cut as thesegmental opening height expressed as a percentage of the shell inside diameter. Themaximum baffle to shell clearance is defines in TA 6&3.1. inimum baffle thic!ness

is specified in TA 6&3.3/.AS does not give any codes about the design of transverse baffles

The summary of baffle design calculations is given below<>affle diameter K 51:.44 mminimum baffle thic!ness K 3.75 mm>affle cut K 04>affle to shell radial clearance K 0.004 mm umber of baffles K ?

2.;." %on!itudinal ba##les=ongitudinal baffles are required to separate the fluid between passes. Thic!ness of longitudinal baffles is specifies by TA 6&3.30. The value is calculated to be 5.14 mm.

2.;., Su00ort 0lates

Support plates are used to reduce the effect of the combined weights of the head cover and tubesheet on the tubes in the hori'ontally mounted heat exchangers. According to

123



TA 6&3.1 and 6&3.3, support plates have same thic!ness and diameter as that of thetransverse baffles. The maximum unsupported tube length is specified in TA 6&3.40.

There is one support plate, 51/ mm 9 x 4 mm thic! in this heat exchanger.

2.;. Tie rods and s0acersesign of tie rods and spacers is governed by TA 6&3.7/, and it is summari'ed below< umber of tie rods< 5iameter of rods< /: mm=ength of tie rods< 1,83: mm

2.;.2 Saddle su00orts

either AS nor TA gives a design method for the design of saddle supports.

2.1< Su--ar/ o# -ain di-ensions

%omponent nsidediameter, mm

9utsidediameter, mm

Thic!ness,mm

=ength,mm

-romt head cover 8:3.: 38.:-ront head barrel 514.: 544.: /:.: 53:.:Shell barrel 514.: 544.: /:.: 1504Shell cover s!irt 7/8.: 73:.: //.: 014Shell cover dish 7/8.: 73:.: //.: 03:Tubes (358) /5.? /?.: 0./ 3:5:Shell no''le S/ /?8.4 0/?./ /:.1 /8:Shell no''le S0 /35.1 /58.1 //.: /8:

Shell no''le S1 /35.1 /58.1 //.: /8:%hannel no''le T/ 1//./ 101.8 5.3 /8:%hannel no''le T0 1//./ 101.8 5.3 /8:Stationary tubesheet 5?4.: 43.:-loating tubesheet 504.: 43.:>affles (?) 51/.: 4.:Support plate 51/.: 4.:Tie rods (5) /: 183:%over bolts front (08) 0: /4:Shell bolts front (08) 0: /74Shell bolts rear (08) 0: 0/:

-loating head bolts (03) 0: 03:

124



Re#erences

$oo9s

(echanical Desi!n O# &rocess S/ste-sF, Qol 0, by scope A. Eeith, Bulf publishing

company, "ouston, Texas, /??4

Heat Echan!er Desi!n Handboo9F, by Euppan, arcell e!!er nc. ew Wor!,

/?83

Heat Echan!ers Selection@ Ratin! And Ther-al Deis!nF@ by Sadi! Ea!ac and

"ongtan =iu, 0nd edition, 0::0.

&rocess Heat Trans#erF by . G. Eern, /?54

A Heat Trans#er Tetboo9F, by Hohn ". =ienhard Q * Hohn ". =ienhard Q, 1rd edition,

0::1.

"<<7 AS(E $oiler And &ressure )essel Code Section )III Di5ision IF@ by The

American Society of echanical ngineers Three 2ar! Avenue, ew Wor!, W /::/5&

4??:

125



Standards O# The Tubular Echan!er (anu#acturers AssociationO, by Tubular

xchanger anufacturers Association, %. 04 orth >roadway Tarrytown, ew Wor!

/:4?/, ?th edition, 0::7.

Heat Echan!er Desi!n Handboo9F@ by . >rian Spalding and H. Tabore!,

"emisphere 2ublishing %orporation, S> 9&8?/ /5&/04&0

O0ti-u- Desi!n O# Shell6And6Tube Heat Echan!erF , by =il$ana ar!ovs!a, Qera

es!oY6admila Eipri$anova, Ale!sandar Bri'o, SS 14: + :/15

Heat echan!ers Cha0ter 11F@ by Eevin . 6afferty, 2.. Bene %ulver Beo&"eat%enter Elamath -alls, 9regon ?75:/

E##ecti5el/ desi!n shell6and6tube heat echan!ersF@ by American nstitute of

%hemical ngineers, -ebruary /??8.

Heat and -ass trans#erF@ by Wounus %angel

*or9ed ea-0les in En!ineerin! Ther-od/na-icsF@ by H. # "arris, Assistant

lecturer in echanical ngineering, >righton Technical %ollege ngland.

126



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