Furnaces

1.Introduction:

Furnaces are used throughout the industry to provide the heat, using the
combustion of fuels. These fuels are solid, liquid or gaseous. Furnaces consist
essentially of an insulated, refractory lined chamber containing tubes. Tubes
carry the process fluid to be heated, and sizes are device for burning the fuel
in air to generate hot gases. A great variety of geometries and sizes are used,
and much of the skill employed in their design is based on experience.
However, all furnaces have in common the general feature of heat transfer
from hot gas source to a cold sink, and in the past few decades theoretical
models of increasing complexity and power have been developed to aid the
designer.[1,2,3]

2.Types of furnaces used in process plant[1-6]

An industrial furnace or direct fired heater is equipment used to provide heat

for a process or can serve as reactor which provides heats of reaction. Furnace
designs vary as to its function, heating duty, type of fuel and method of
introducing combustion air. However, most process furnaces have some
common features. Fuel flows into the burner and is burnt with air provided
from an air blower. There can be more than one burner in a particular furnace
which can be arranged in cells which heat a particular set of tubes. Burners
can also be floor mounted, wall mounted or roof mounted depending on
design. The flames heat up the tubes, which in turn heat the fluid inside in the
first part of the furnace known as the radiant section or firebox. In this
chamber where combustion takes place, the heat is transferred mainly by
radiation to tubes around the fire in the chamber. The heating fluid passes
through the tubes and is thus heated to the desired temperature. The gases
from the combustion are known as flue gas. After the flue gas leaves the
firebox, most furnace designs include a convection section where more heat
is recovered before venting to the atmosphere through the flue gas stack.
(HTF=Heat Transfer Fluid. Industries commonly use their furnaces to heat a
secondary fluid with special additives like anti-rust and high heat transfer
efficiency. This heated fluid is then circulated round the whole plant to heat
exchangers to be used wherever heat is needed instead of directly heating the
product line as the product or material may be volatile or prone to cracking at
the furnace temperature.)

The radiant section is where the tubes receive almost all its heat by radiation
from the flame. In a vertical, cylindrical furnace, the tubes are vertical. Tubes
can be vertical or horizontal, placed along the refractory wall, in the middle,
etc., or arranged in cells. Studs are used to hold the insulation together and
on the wall of the furnace. The tubes are a distance away from the insulation
so radiation can be reflected to the back of the tubes to maintain a uniform
tube wall temperature. Tube guides at the top, middle and bottom hold the
tubes in place. The convection section is located above the radiant section
where it is cooler to recover additional heat. Heat transfer takes place by
convection, and the tubes are finned to increase heat transfer. The first two
tube rows in the bottom of the convection section and at the top of the radiant
section is an area of bare tubes (without fins) and are known as the shield
section, so named because they are still exposed to plenty of radiation from
the firebox and they also act to shield the convection section tubes, which are
normally of less resistant material from the high temperatures in the firebox.
The area of the radiant section just before flue gas enters the shield section
and into the convection section called the bridge zone. Crossover is the term
used to describe the tube that connects from the convection section outlet to
the radiant section inlet. The crossover piping is normally located outside so
that the temperature can be monitored and the efficiency of the convection
section can be calculated.

In petrochemical industries, furnaces are used to heat petroleum feedstock

for fractionation, thermal cracking, and high-temperature processing. Usually,
these furnaces are fired by oil or gas. They have to be designed to ensure that
the fluid receives the correct amount of heat and has sufficient residence time
within hot zone. While at the same time excess temperatures have been
avoided. These excess temperatures lead to degeneration of the product or
damage to the furnace. The balance is achieved by appropriate disposition of
the tubes carrying the fluid within the furnace, and careful control of firing
rate and fluid flow Calculations are required to determine the fuel consumption
and the maximum temperatures of the tube and walls. Tube temperatures in
some plant may be as high as 900 °C, and combinations of high pressure
(e.g., 200 atm) and relatively high temperatures (e.g., 450 °C) are not
uncommon. Process heaters come in many shapes and sizes; Figures 3.1, 3.2
and 3.3 show typical arrangements.Fig.3.1 is a vertical cylindrical process
heater with a band of vertical tubes in the radiation zone and a bank of
horizontal tubes at the outlet that receive heat mainly by convection. The
latter may have fins attached to enhance heat transfer, except for the base of
the furnace and the flames are vertically oriented. Typical heat transfer rates
for the vertical tubes in the radiation zone are about 50 kW/m2, and the total
heat rating is usually in the range 3 to 60 MW.
Fig.3.2[1]shows an alternative arrangement, where the tubes are horizontal
and cover not only the vertical walls but also the sloping roof of the “cabin”.
Units of this type are used for a similar range of duty as is the aforementioned
vertical cylinder. Fig.3.3[1] shows the more unusual design for smaller heat
loads, where a single central wall of horizontal tubes is heated on both sides
by two sets of burners set in the base.

3.Furnace heat transfer[1-8]

A fuel-fired furnace consists of a gaseous heat source, a heat sink, and a

refractory enclosure, as illustrated diagrammatically in Fig.3.4.[1] Heat is
transferred to the heat sink by radiation and convection from the hot gases
and by reradiation from the refractory walls. In developing any model of the
process, it is necessary to consider two heat transfer phenomena:

 The heat emission from hot gases containing combustion products, i.e.
the heat source.
 The heat absorbed by the tubes, taking into account their geometrical
configuration and material properties (the heat sink), composed of
primary heat transfer from hot gases and secondary heat exchange with
the refractory walls.
3.1.Furnace heat balance

Heat is released in a fuel-fired furnace as a result of combustion, and the rate

of heat generation, Qf, is equal to the rate of combustion of fuel, Mf, multiplied
by its lower calorific value, Δhf:

Qf = Mf Δhf...............................(1)

The heat generated by the combustion process appears initially as sensible

heat in the steam of hot gases, consisting of combustion products and excess
air, passing through the furnace at a rate Mg. Part of this heat is transferred
to the heat sink at a rate Qg, part is lost through the furnace walls at a rate
Ql, and the remainder is carried out of the furnace through the exhaust stack
as the sensible heat of the partially cooled combustion products at a rate Qp.
As illustrated in Fig. 3.5[1] the heat balance for this process may be expressed
as:

Qf = Qg + Ql +Qp...............................(2)
If there were no heat sink and no losses, all the heat released by combustion
would go into heating the gases produced, which would then attain a
temperature, Tf, known as the adiabatic flame temperature. The adiabatic
flame temperature is, therefore given by:

Qf = Mgcpg (Tf-To)...............................(3)

Where To is the air inlet temperature and cpgis an appropriate average value
of the gas specific heat for the range To to Tf.

In a real furnace the gases do not attain the adiabatic flame temperature, due
to the heat sink and wall losses. For example, neglecting losses but allowing
for heat removal by the sink at a rate of Qg), the theoretical gas temperature,
Tg) is given by

Qf -Qg=Mgcpg Tg-To...............................(4)

Hence, combining equations (3) and (4)

This equation shows how the gas temperature, Tg is related to the rate of heat
transfer of the sink, Qg, by heat balance. However, Qg is also related to Tg by
the heat transfer characteristics of the hot gas and of the sink. A solution of
the problem requires a combination of these two sets of equations.
 Furnaces

3.2 Hot gases as heat source

The chemical composition of the gases produced by the combustion of

hydrocarbons depends upon the choice of fuel and the amount of excess air
employed above the stoichiometric requirements. In practice, excess air is
required to ensure complete combustion; typical values are 10% for gaseous
fuels, 15 to 20% for liquid fuels, and 20% for pulverized fuel, although lower
percentages can be achieved with efficient burners.

As we know, gaseous combustion products radiate heat when raised to

temperatures above their surroundings. When solid particles are present in
the furnace gas stream they become incandescent, radiating both heat and
light, so producing a glowing or luminous flame. Gaseous fuels burn with a
nonluminous flame, but liquid and solid fuels produce luminous flames due to
the presence of particles of carbonaceous material. For example, soot or coke
resulting from the incomplete combustion of the hydrocarbons and mineral
matter originally in the fuel. In general, solid fuel produces a more luminous
flame than does liquid fuel.
Carbon dioxide and water vapor are the main sources of radiation for
nonluminous flames, and the total emissivity εg of a volume of combustion
gases is dependent upon the temperature Tg and product of partial pressure
and effective path length PL . The total absorptivity of a gas also depends upon
its temperature and partial pressure path length product, but in addition upon
the temperature Ts of the source of the radiation that is being absorbed.[1,9,10]

3.3 Heat Sink

The rate at which heat is transferred by radiation from the hot gases to sink
depends not only upon the emissivity of the gas and emissivity of the sink
surface, but also upon the relative size of the sink. This is because the
unconverted refractory lining radiates back into the furnace heat that it has
received from the flame, and some of this is absorbed by the heat sink.

This compound effect is illustrated in Fig. 3.6, where two extreme cases are
shown. The diagram on the left represents the case in which the sink area is
very small, and that on the right represents the case in which the sink is very
large and completely covers the furnace walls.

In the case of refractory surface, assuming no heat loses, is in equilibrium

with the gases and reradiates all the heat falling upon it. The total radiation
flux within the enclosure is equal to that emitted by a blackbody at
temperature Tg . Under these circumstances the heat flux to the sink is
independent of the gas emissivity, depending only on the emissivity of the
sink itself. The rate of heat transfer to a very small sink at temperature T 1 is
therefore

QgA1-->0 = A1ε1σ(Tg4-T14)....................(6)

In the second case,where the sink covers the whole of the interior of the
furnace, the situation is analogous to the exchange between two parallel party
reflecting surfaces. It was already known that the rate of heat transfer is given
by

Intermediate situations can be estimated by using the equation for the simple
case when the sink and the refractory are intimately mixed (Hottel and
Sarofim, 1967). This is called the speckled surface equation and is quite
adequate for preliminary estimates of furnace performance. It gives
Where C is the ratio of the sink area to the total area, i.e. A1/At.

Fig. 3.6 shows an example of the way of the effective emissivity (the term in
the curly braces in Equation 8) varies with C. The example assumes a gas
emissivity is close to that of the gas, εg of 0.3 and a sink emissivity, ε1 , 0f
0.85, the latter being typical of tube surfaces. For large values of C the
effective emissivity is close to that of gas, εg , and is intensive to the value of
the sink emissivity, ε1 . For this reason the emissivity of tube surfaces in the
fire tube boilers, where the sink entirely encloses the hot gas stream, may
often be taken as unity for calculation purposes.

Fig:3.6[1]
Fig. 3.6 Effect of heat sink area on effective emissivity. (a) small heat sink
area; (b) large heat sink area; (c) blackbody analogous to (d) exchange
between reflecting surfaces;

Fig:3.7

Fig (3.7) an example(εg, ε1) speckled surface equation.[1]

εc=(1/(1/ε1+C(1/ εg)-1)),C=A1/At

3.4 Effect of tube geometry on the heat sink characteristics

So far the heat sink has been treated as a plain surface. In practice, however,
it consists of one or more banks of tubes usually mounted close to the
refractory wall, as shown diagrammatically in Fig. 3.7. Normally there is a
space between the tubes and consequently some of the radiation from the hot
gases is not intercepted and impinges on the refractory wall behind the tubes.
Most of this heat is reradiated and part contributes to the heat flow to the
sink. This is a complex situation and complete formal analysis is very difficult.
Because of mutual shielding effects of adjacent tubes, the radiation heat flux
varies circumferentially around the tubes, as shown diagrammatically in Fig.
3.8.[1] The surface of the tube facing inward (position 1 in the figure) receives
maximum heat flux because it is subject to radiation from a total angle of
180°. Point 2 receives radiation from a smaller angle and point 3 only from a
very narrow beam; beyond this point there is an area of the tube that receives
no direct radiation from the hot gases. There is, of course, an additional
component of heat flux, mainly on the back of the tubes, due to reradiation,
but this is much smaller in magnitude.

The ratio of peak to mean heat flux is a function of tube pitch to diameter
ratio, B, as shown in Fig.3.9[1] for three typically configurations. This factor is
important in assessing the permissible heat rating of a furnace, because it is
the peak heat flux, which is usually the limiting factor. A simplification of this
complex situation was proposed by Hottel in which the heat sink is defined as
an equivalent plain surface having an area equal to that covered by the tubes,
as shown in Fig. 3.10, and an effective emissivity, eeff, which would give the
same radiative heat transfer as the tube bank.

The first step in calculating the equivalent emissivity of the plain surface is to
determine the fraction, F, of radiation intercepted by the tubes. The equation
for F is based on optical path geometry, namely,

F = 1-(1/B){(B2-1)1/2-cos-1(1/B)}..............(9)

This function is plotted in Fig.3.11[1] for a single and a double row of tubes.

The interception factor, F,can then be used in calculating the effective

emissivity of the tube bank, including radiation from an adiabatic refractory
backing,as:

εeff= 1/{(1/F(2-F)) + ((B/π)(1/ε1-1))}..................(10)

Effective emissivity based on this equation is plotted in Fig. 3.12[1] as a
function of tube pitch to diameter ratio for a tube material emissivity of 0.85.
It is clear from the form of the equation and the shape of the curve that tube
spacing has a very powerful effect. This is partly due to the fact that the actual
tube surface area per unit of total projected area, A, is proportional to 1/B, a
fact reflected in the reduction in the fraction, F, of radiation intercepted, which
plays a predominant role in determining eeff. The foregoing equations apply
to true banks adjacent to the refractory wall. A similar approach can be made
to the case of a centrally mounted tube bank, but here a different form of
equivalent plain area has to be used. Procedures for this type of furnace
geometry are outlined in the Heat Exchanger Design Handbook (Truelove,
1983).
4. Furnace models

The full mathematical description of practical furnaces is exceedingly complex,

combining aerodynamics, chemical reactions, and heat transfer, and computer
programs are necessary for detailed solutions. Advanced methods of
calculation may be divided into zone methods and flux methods.

Zone methods are employed when the heat release pattern from the flame is
known. They start by dividing the furnace and its walls into discrete zones.
The effective exchange areas between zones are determined, and the
radiative heat transfer corresponding to the prescribed heat release pattern is
calculated. In flux methods, instead of dividing the space into zones the
radiation arriving at a point in the system is itself divided into a number of
characteristic directions, representing averages over a specified solid angle.
Flux methods are well suited for use in combination with modern methods of
prediction of fluid flow and mixing pattern. Simultaneous solutions of the
radiative heat transfer equations using flux methods and turbulent flow
models are feasible.

4.1 “Well Stirred” furnace model[1-16]

This is the simplest approach to the assessment of furnace performance. One

of the first versions is the method of Lobo and Evans (Lobo and Evans, 1939),
which was used in Process Heat Transfer (Kern, 1986). Subsequently an
improved version, expressed in nondimensional terms, which made the
calculations easier, was presented in the book Radiative Heat Transfer (Hottel
and Sarofim, 1967). These authors also introduced additional terms to allow
for incomplete mixing and wall losses. Their model, later reviewed by Hottel
(1974), still forms the basis of most simple calculation procedures (e.g.,
Truelove, 1983).

The furnace is modeled in three zones as shown, Fig.3.13[1] namely, the

central hot gas zone, the heat sink, and the refractory walls. The combustion
region and the space occupied by hot products of combustion are lumped
together in the central hot gas zone (hence the alternative title “lumped
model”), which transfers heat by radiation to the heat sink, here shown
diagrammatically as a tube bank, and to the refractory walls containing the
furnace.

The following simplifying assumptions are made:

 The hot gases are perfectly mixed and at a uniform temperature, Tg.
 The heat sink is gray and has a uniform temperature, T1.
 The refractory surface is radiatively adiabatic, that is to say it radiates
all the heat that is receives.

The “well stirred” furnace model is based on a combination of the balance

equation for the furnace (Equation 5), namely.

(Qf-Qg)/Qf=(Tg-To)/(Tf-To)..................................(11)

And the expression for heat transfer to the sink based on the“specked surface”
model (Equation 8),namely.

Qf= A1{1/((1/εeff) + C(1/εg-1))} σ (Tg4-T14)=gr σ

(Tg4-T14).....................(12)

Where, gr, the total heat transfer factor for radiation from gas to sink, is

gr= A1/{1/eeff+C(1/εg-
1)}....................................(13)

Note that εeff(Equation 10) has replaced ε1, because

the model is using the projected area, A1, of the tube
bank as illustrated in Fig. 3.10.
If the furnace contains a convectively heated section, the total heat transfer
factor can be modified to introduce both radiation and convection,as

Qg =gr σ(Tg4-T14) +αAc(Tg-T1)................................(14)

Where,gr = total heat transfer factor for radiation from the gas to the sink,
including reradiation from the refractory walls and multiple reflection.
α= convective heat transfer coefficient from the gas to the sink.

Ac = area of the sink subject to convective heat transfer.

Because the convective component is usually small compared with that of

radiation it may be submitted in the gr,term as follows.Let

αAc (Tg-T1)= (αAc/4σT3g1)σ(T4g-

T41)..........................(15)

where

Tg1≈(Tg+T1)/2........................................................
(16)

Then

Qg=grc σ(Tg4-
T14).....................................................(17)

where

grc=gr+(α Ac/4σT3g1)...............................................
..(18)

Fig. 13 Simple well stirred Furnace model

Equations (11) and (17) can be combined to give

(Qg/σ grc)+T41=T4f{1-(Qg(Tf-
To)/QfTf}4...........................(19)

It is convenient to apply this expression in a

nondimensional form involving the terms:
Q,g =Qg(Tf-To)/QfTf =reduced furnace density
..................(20)

D, =Qf/σ grc3f(Tf-To) =reduced firing

density......................(21)

T,1 =T1Tf =reduced sink

temperature................................(22)

Equation (19) then reduced to

Q,gD,+(T,1)4) =(1-
Q,g)4...................................................(23)

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