Chapter 1 H-EX

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Heat Exchangers Selection & Design

CHAPTER ONEHEAT TRANSFER FUNDAMENTALS

Chapter 1 – Heat Transfer FundamentalsEnppi Copyright © Enppi 2007

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HEAT TRANSFER FUNDAMENTALS

1.1 Introduction

In the majority of chemical processes, heat is either given out or absorbed. And in a very wide range of chemical plant; fluids must often be either heated or cooled. Thus, in furnaces, evaporators, distillation units, driers and reaction vessels one of the major problems is that of transferring heat at the desired rate.

1.2 Heat Transfer Mechanisms

Alternatively, it may be necessary to prevent the loss of heat from a hot vessel or steam pipe. The control of the flow of heat in the desired manner forms one of the most important sections of chemical engineering. Provided that a temperature difference exists between two parts of a system, heat transfer will take place in one or more of three different ways.

Conduction Radiation Convection

In practice, the overall mechanism of heat transfer is usually a combination of all three possibilities. The temperature level at which the heat transfer takes place and the conditions under which the heat is transferred determine the share which each of the above mentioned mechanisms has in the final result.

These mechanisms are, however, not involving mass transfer. Evaporation and condensation are important heat transfer phenomena which involve mass transfer.


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Generally, heat transfer occurs whenever regions of different temperatures can communicate and heat flows from the high temperature region to the low temperature region. Equilibrium is achieved when the temperatures of the regions are equal. Equilibrium is, therefore, dependent on the temperature and independent on the heat content of the regions.

1.2.1 Conduction

Conduction is defined as the transfer of heat from one part of a body to another part of the same body or from one body to a second body in direct contact with the first one, without any appreciable displacement of the particles of the body or bodies.

All physical states of matter (solids, liquids and gases) are able to conduct heat to some degree. Solids may either be good conductors (e.g. the metals) or poor conductors ("insulators", such as non-metal elements, cork, asbestos, etc...), whereas gases and liquids are, as a rule, very poor heat conductors.

Steady state conduction of heat through a homogeneous solid one dimensional body is represented mathematically by the following equation, which is known as Fourier's law:

Where,q = the rate of heat transferA = the area through which the heat flows, taken at a right

angle to the direction of flow.

= the temperature gradient along the line of heat flow since the temperature decreases in the direction offlow, the sign of this term is negative.


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K = a constant, known as the thermal conductivity, the value of which depends on the composition of the material through which the heat flows and on the temperature level at which the flow takes place.

The effect of the temperature level on the value of k is generally small.

Figure 1.1 – One dimensional conduction through a plane wall

Materials which are good conductors of electricity are also good heat conductors {copper: K = approx. 220 BTU/(hr.ft2)(°F/ft}. Electrical insulators are also heat insulators, the k for cork being only 0.025 BTU/(hr.ft2)(°F/ft).


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For most of the metals the temperature coefficient of k is negative (aluminum and brass are exceptions), while for most insulators it is positive. Practically all non-metallic liquids have thermal conductivities, which fall between 0.05 and 0.150 BTU/ (hr.)(°F)(ft.). The values for water and a few salt solutions are somewhat higher. The temperature coefficient of k for liquids is negative, except that of water.

All gases have very low thermal conductivities {0.005-0.18 BTU/(hr.ft2) (F/ft)} and usually show a positive temperature coefficient.

Before Fourier's law can be applied to the solution of a practical problem, it must be integrated. The result of the integration will depend, of course, entirely upon the shape of the object that conducts the heat. However, only a few forms are commonly found in practical cases and only a few of these have any use in the petroleum refinery. Some of the most common conduction equations are tabulated in Table 1.1 and an indication is given of their (limited) application in the refinery.

The customary assumption in applying these equations is that the thermal conductivity k remains constant. In cases where a wide variation exists the arithmetic average can be use, provided the variation with temperature is approximately linear.


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The units in which the various terms in the equations are expressed may be either of the metric or the British system, but should be consistent.

Plane walls:

Conduction through a homogeneous plane surface, e.g. a furnace wall.

Cylindrical walls:

Conduction through insulation on piping. Conduction through heat exchangers, metal tubes walls separating one fluid from another at different temperatures.

Composition plane walls:

Conduction through two or more plane walls of different composition in series.

Composite cylindrical walls: Conduction through two insulating layers of different material on a large cylindrical vessel

Table 1.1 – Steady state conduction evaluations


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1.2.2 Convection

Convection is one of the most mechanisms by which heat is transferred in industrial equipment. As was mentioned before, in most practical cases heat transfer takes place by a combination of radiation, conduction and convection, but as a rule convection plays the most important part.

Convection may be caused by currents which are the result of differences in density at various points in a medium owing to temperature.Differences and is then known as natural convection. When some kind of mechanical agitation is employed, the convection is known as forced convection.

A practical example of natural convection is the heating of a tank filled with oil with the aid of a steam coil at the bottom of the tank. Forced convection takes place, for instance, when the contents of a steam heated tank are circulated by means of the pumps.

As will be seen when dealing with the practical applications of heat transfer, the type of flow of the fluids between which heat is transferred is very important. It is well known that a fluid can be transported either in stream line flow (viscous or laminar flow) or in turbulent How, depending upon the value of the Reynolds number represented by the following mathematical expression:

Where,Re = Reynolds number D = Diameter of the conduitv = linear velocity of the fluidρ = density of the fluid at flowing conditionsG = mass velocity


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η = absolute viscosity at flowing conditionsy = kinamatic viscosity

It should be pointed out that the Reynolds number is dimensionless and consequently has the same numerical value as long as the units in which D, v, ρ, y and η are expressed are consistent.

When the value of the Reynolds number, expressed in consistent units is well below 2100, the fluid flows in stream line flow (Laminar flow)

Each infinitesimally thin layer of fluid moves through the pipeline of conduit as a coaxial cylinder.

At Reynolds number between (2100-10000) the flow in transition region.

At Reynolds numbers above 10000 the parallel flow changes to a whirling motion (turbulent flow) and only a very thin layer adjacent to the wall of the conduit remains unmixed with the rest of the fluid (see figure 1 .2).

It has been found that as the turbulence increases the thickness of the non-turbulent fluid film adjacent to the wall of the conduit decreases. Studies of heat transfer to fluids flowing within conduits have shown that the rate of heat transfer is a function, of the thickness of the non-turbulent fluid film, which is directly related to the Reynolds No. of the fluid. This non-turbulent fluid film is the major resistance to the flow of heat by convection from the wall to the main body of fluid. When considering the factors which affect the thickness of this film it will be seen that it is a function of physical properties of the fluid and the condition under which it flows.


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Figure 1.2 – Types of fluid flow


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1.2.2.1 Film coefficient of Transfer by Convection

If a fluid flows through a pipe which is heated on the outside, the rate of heat transfer by convection from the inside of the tube wall to the main body of the fluid depends upon a coefficient generally referred to as the film coefficient. The rate of heat transfer can be mathematically represented by the following equation:

Where,q = rate of heat transfer, BTU/hr A = area through which heat is transferred, sq. ft.h = film coefficient, BTU/ (hr) (sq.ft.) (°F)t = temperature difference between the inner surface of

the tube and the main body of the fluid, °F

Nusselt Number

Prandtl Number

Reynolds Number Re


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The value of h depends on a number of factors chiefly associated with the physical properties of the fluid and the conditions under which it is flowing. A few of the factors that affect the value of the film coefficient are:

Viscosity of the fluid, Density of the fluid, Velocity of the fluid, Thermal conductivity of the fluid, Specific heat of the fluid, Degree of turbulence of the fluid, Shape of the tube wall, and Position of the tube.

1.2.2.2 Overall Coefficient of Heat Transfer

Practically in all industrial heat transfer equipment heat is exchanged between two fluids separated by a metal wall, and mostly the flow inside and outside the tube is turbulent. In Figure 1.3, the temperature gradient is shown when heat is transferred from a fluid flowing inside a tube to a tube flowing outside the tube. It will be clear that in such a case the transfer of heat takes place by conduction and convection and that the rate of transfer is affected by the following factors:

The non-turbulent or viscous fluid film on the outside of the tube. The thickness and thermal conductivity of the dirt and/or scale layer

on the outside of the tube. The thickness and thermal conductivity of the tube wall. The thickness and thermal conductivity of the dirt and/or scale layer

on the inside wall of the tube. The non-turbulent or viscous fluid film on the inside of the tube.


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Figure 1.3 – Flow of heat through tube walls

At a given point the overall transfer of heat can be expressed by the following equation:

q =UA ΔT

Where,q = rate of heat transfer = q1= q = q outsideU = overall coefficient of heat transferA = wall area through which heat is transferredΔT = temperature difference between the two fluids


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Each of the above mentioned five factors affecting the overall coefficient of heat transfer can be considered as an individual resistance being part of the total resistance to heat transfer. These resistances are added in the same manner as electrical resistances, i.e. the reciprocal values of the coefficients (being resistance values) are added up to give an overall resistance:

Where,U = Overall heat transfer coefficientho = Film coefficient for the fluid outside the tube wallhi = Film coefficient for the fluid inside the tube wall(kw/Iw) = Conductance of heat through the tube wall(ko/Io) = Conductance of heat through the deposit on the

outside of the tubeK = Thermal conductivity of tube wall of depositI = Thickness of the tube or layer of deposit(Ai/Ao) = Ratio of inside to outside tube are used to

convert all coefficients to a common basis, namely on the outside area

In most practical cases the resistance of the tube wall is so low that it can usually be neglected without causing a serious error in the overall coefficients. The scale deposits and the film coefficient are the two major controlling resistances. In many cases when there are no scale deposits and one of the fluids has a very high film coefficient, the overall coefficient can be calculated with sufficient accuracy by calculating only the other (low) film coefficient. However, in a large number of cases the scale deposits are the major resistances to heat transfer.

1.2.2.3 Mean Temperature Difference (MTD)


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The basic equation of heat transfer can be expressed practically:q = UA ΔTm

Where ΔTm is the mean temperature difference between the two fluids. The other symbols have the same meaning as in equation.

The effect of relatively small temperature differences on the physical properties of most of the petroleum hydrocarbons is usually too small to cause large errors in the value of U, so that the overall coefficient of heat transfer can be assumed constant. When larger differences occur, it is sufficiently accurate for practical purposes to assume that most physical properties vary approximately linearly, so that arithmetic averages of the properties can be satisfactorily used in the calculation of an average value of U.

Consequently once the overall transfer coefficient is known, the only problem in evaluating heat transfer for petroleum products is the proper calculation of the temperature difference.

The direction of flow of the liquids exchanging heat influences the rate of heat transfer.

The two fluids exchanging heat in industrial equipment may flow either co-current (parallel) or in countercurrent. In almost all cases countercurrent flow is preferred, since in this way a more efficient recovery of heat is usually possible. In Figure 1.4 the change of temperature with the distance of flow is illustrated for several common flow arrangements.

In any of these cases the mean temperature difference may be calculated as the logarithmic mean temperature difference:


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In order to avoid errors when calculating the temperature differences, the temperatures (in case of concurrent flow) are usually tabulated as follows:

______________________________(T1 - t2) (T2 - t1)

Where T1 and T2 are the inlet and outlet temperatures of the hotter fluid and t1 and t2 those of the colder fluid. The values for (t1 - t2) and (T2 – t1) can then be substituted and the mean temperature difference (MTD) can be computed.

When the ratio of the larger to the smaller temperature differences is less than 2, little error (<4%) arises from the use of the arithmetic average.

However, most of the heat exchange equipment used in the petroleum industry is the shell and tube type. One of the fluids flows through the tubes and the other fluid flows around the tubes in the shell.

In order to improve the efficiency of the heat exchange without unduly increasing the size of the equipment, the fluids are usually forced, to flow through the tubes and the shell in several passes by special baffle arrangements. Consequently the direction of the flow is reversed several times, which results in a lower Tm than the value which is calculated from the terminal temperatures. Charts have been drawn up from which a correction factor for Tm can be rapidly computed. Figures 1.4A to 1.4D show a number of these Tm correction charts which are applicable to the type of exchange equipment commonly used in petroleum refineries.


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Figure 1.4 – Temperature difference for common flow

If the number of shell passes, equal the number of tube passes, the correction factor = 1.0. For all other cases F< 1.0. An exchanger with correction factor <0.8 can seldom be justified.

Example:

Lean oil is to be cooled from 410 °F to 155 °F by rich oil entering at 110 °F and leaving at 330 °F. Find Tm.

Solution:410 -------------»155

-------------»


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From equation (5) Tm = 61 °FRatio P= (330-110) / (410-110) =0.733& Ratio R= (410-155) / (330-110) = 1.16

The following results are obtained:

Figure 1.4A & B - correction factor < 0.5Figure 1.4C - correction factor < 0.74 Figure 1.4D - correction factor < 0.84

Selecting exchanger with 4 shell passes and 8 (or multiple) tube passes therefore corrected Tm = 0.84 x 61 = 51.2 °F

Exercise

State from the above example the following:1. What type of direction of flow of the liquids exchanging heat?2a. What is the maximum temperature could the rich oil be gained if the flow is concurrent? 2b. Otherwise what will be the minimum temperature could the lean oil be reached for the concurrent case?3. Which flow type is therefore preferred?

1.2.2.4 Economic Approach Temperature

When considering the principles underlying heat transfer it will be clear that heat exchanging fluids can never reach the same temperature at either of the exchange terminals (Figure 1.4). A certain temperature difference will always exist, which is known as the "approach temperature".

From a view point of maximum heat exchange a small approach temperature is desirable. However, as the approach temperature decreases, Tm (the MTD) decreases also, with the result that a larger heat exchange area is required (other conditions remaining the same).


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From an economic point of view there is an optimum approach temperature below which the increased recovery of heat no longer compensates for the increased heat transfer area to be installed.

This optimum figure can be determined on the basis of the cost per unit area of exchange surface, the value of the heat removed and assumptions regarding amortization of the heat exchange equipment. It has been found in practice (particularly for coolers in which products have to be cooled to the lowest possible temperatures attainable with cooling water) that in a large number of cases an approach temperature of 10 °F is economically attractive.

The customary practice is to design coolers and certain condensers for 1.0 °F approach temperature. For heat exchange between hydrocarbons, involving a large transfer area, the economic approach temperature may be considerably higher (30 °F). In such cases, it is advisable to carry out some approximate calculations, which are simplified by using charts published in the literature (Standards of Tubular Exchangers Manufacturers Association: TEMA standards).

1.2.2.5 Calculation of the Overall Heat Transfer Coefficient

As mentioned before, the overall heat transfer coefficient depends upon five factors, being the film coefficients for the fluids flowing inside and outside the tubes and the tube wall resistance. A complete discussion of the methods used for computing film resistances in all cases encountered in a refinery is far beyond the scope of this course. Different methods must be applied in individual cases, depending on whether the fluids are flowing with or without change of state and whether the hotter fluid flows inside or around the tubes.

In order to facilitate the calculations, graphical correlations have been derived and may be found in the literature. The film coefficients obtained by these graphical methods apply to clean surfaces, and for the calculation of the overall heat transfer coefficient the fouling resistance


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has to be incorporated. Usually the fouling resistances or fouling factors are given in terms of resistance to heat transfer instead of conductance.

Where,ro = Fouling resistance on the outside of the tubingri = Fouling resistance on the inside of the tubingrw = Resistance of the tube wall

1.2.3 Radiation

Heat radiation follows the same general laws as light, but it has a much longer wave length than light waves. Radiant heat is, therefore, reflected or absorbed by surfaces upon which it falls, the degree of reflection or absorption depending on the nature of the body. It has been found that dark surfaces absorb a large percentage of radiant heat, while light colored or shiny bodies reflect radiant heat.

Furthermore, experiments and theoretical considerations have shown that a body which readily absorbs radiant heat is also a good emitter of heat waves. The two factors governing the absorption and emission of heat are the nature of the body and its temperature. For theoretical purposes the concept of the perfect black body has been developed, which refers to a hypothetical body which absorbs all radiation incidents upon it and which is the perfect radiator of thermal energy.

Actually, no such body exists, but a number of real materials come close to being perfect black bodies. The ratio of the emissive power of a given body to that of a perfect black body is referred to as the emissivity.


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Furnace walls, tubes and most of the common construction materials have emissivities in the neighbourhood of 0.9 (black body = 1.0).

Stefan-Boltzman law:

Where,q = rate of radiant heat transfer emitted or absorbed σ = Stephan-Boltzman constant, which has the following

values in the different systems

=

A = area of the body T = absolute temperature of the bodyε = the emissivity of the bodyWhen considering the transfer of heat by radiation in any practical

case, it will be evident that the net rate of heat transfer is equal to the rate at which a body emits thermal radiation, minus the rate at which it re-absorbs the fraction of its thermal radiation which is reflected by surrounding surfaces and minus the rate at which it absorbs radiation emitted by the surroundings.

Thus the net rate of heat transfer is dependent not only upon the temperature and emissivity of the body, but also upon the temperature and emissivity of the surroundings.

For the case of an isothermal surface completely enclosed by another isothermal surface being separated by a non-absorbing medium, the net rate of radiant heat transfer can be represented as follows:


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Where,q and σ = same as in previousAe = effective areaFe = a factor to allow for the emissivities of the two surfaces.


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Chapter 1 H-EX