3. Energy Conversion
3.1 Heating values
The chemical enthalpy is converted into heat by the oxidation of the carbon and hydrogen
contained in the fuel. If, in accordance with Figure 3-1, the gas is cooled to 0 °C after
combustion, then the resulting water is present as liquid. The enthalpy converted in the
process is denoted as gross heating value H o (earlier designation upper heating value). After
the combustion the gas is drawn off with temperatures above dew point so that the water is
vaporous. As a result the condensation enthalpy is not converted into heat. Then the converted
chemical enthalpy of the fuel is denoted as net heating value hu (earlier designation lower
heating value). Both values are thus differentiated only by the proportion of the condensation
enthalpy
h u = H 0 − x H 2 O ⋅ ∆h vap
(3-1)
x H 2 O being the proportion of water in the gas.
Table 3-1 lists the gross heating values and the net heating values for typical fuels. The values
for the fossil fuels represent average values for Germany [3.1]. Hydrogen possesses the
highest heating value in relation to the mass. Here the difference between gross heating value
and heating value is the largest. This difference is the greatest in the case of the fossil fuels; in
natural gas 10%. In natural gas the heating value depends comparatively more greatly on the
composition. If this is known, then the heating value can be calculated using
h u = ∑ x i ⋅ h ui
(3-2)
x i being the combustible proportion of gas and h ui its heating value. As a rule the proportions
are CH4, H2 and CO. Table 3-1 lists their heating values.
In solid and liquid fuels the chemical bond type of the components is not known so that the
heating value must always be determined experimentally. If the heating value would be
calculated according to Eq. (3-2) from the C- and H mass fraction of the composition given in
Table 2-1, so too high heating value results. Especially, if oxygen is included already in the
fuel, as it is the case for example in methanol, then considerably higher values result. The
heating values of liquid fuels vary by ± 3 % depending on the reference given. The different
densities of liquid fuels have to be taken into account because they are saled in volume (litre)
and not in mass (kg). As a consequence a litre of Diesel fuels contains about 14 % more
energy than a litre of Otto fuel.
For black coal the heating value depends on the composition, especially on the amount of
volatile matter, and can vary by ± 8 % from the given mean value. Raw lignite coal has a low
heating value because of the high content of liquid water. Lignite dust, which has been dried,
has consequently a higher value. This value is lower than that for black coals because of the
content of oxygen (see table 2-1).
The heating value of woods depends on their kind and amount of water. In the table only
approximate values can be given. Remarkable is the low heating value related to volume.
Therefore, the energy transport is not so econonomic than that for coal and oil.
The higher the heating value of fuels the higher is also their air demand. Figure 3-2 shows the
heating value and the air demand for a lot of combustible matter. It can be seen that
approximately a linear correlation exists. More and more fuels are used which are separated
from residuals and waste. Their composition is mostly known. However, the heating value
can be determined and herewith the air demand can be estimated according Figure 3-2.
Heating values and energy consumption often given in different units. The transfer of these
units is summarized in Table 3-2.
As briefly described in part, the crude fuel must be treated for use after its extraction from the
earth. The treatment demands energy. If the energy for the transport and storage is added on,
the so-called supply energy results. This is compiled for some fuels in Table 3-3. Other
sources specify partly slightly deviating values (±1% of the percentage of the heating value).
Such supply energies are necessary to calculate the cumulative energy required in the scope of
eco-studies. For natural gas and crude oil approximately 10% of the heating value and for
bituminous coal 5% is therefore required for provision.
3.2 Combustion Gas Temperatures
3.2.1 Designations
The gas after combustion is designated as combustion gas and the temperatur as combustion
temperature respectively (Figure 3-3). In an adiabatic chamber the highest temperature is
obtained. For temperatures above 1800 °C it has to be considered that in reason of equilibrium
the conversion is not complete. Than it is differed between the adiabatic combustion
temperature with and without dissociation of gas components. If heat is emitted during the
combustion, for example through loss owing to non-adiabatic walls, then the temperature of
the gas flowing out of the combustion chamber is called process gas temperature. The gas
released into the environment after completely used is designated as flue gas and the
accompanying temperature as flue gas temperature. In accordance with Figure 3-3 the
combustion with heat emission can be carried out in one or two apparatuse connected in a
series. If the gas contains dust after combustion, for example in the case of solid fuels or dust
generating products, then it is designated as a smoke gas. Only after cleaning, then it is called
a flue gas.
3.2.2 Adiabatic Combustion Temperature
The combustion in an adiabatic chamber gives the highest temperatures of the gas. This
adiabatic combustion temperature ϑad results from the energy balance for the adiabatic
combustion chamber in accordance with Figure 3-2
& (h + c ⋅ ϑ ) + M
& ⋅c ⋅ϑ = M
& ⋅c ⋅ϑ + M
& ⋅ ∆h .
M
f
u
f
f
L
pL
L
G
pG
ad
G
diss
(3-3)
Energy is inserted with the mass flow of fuel and air. The enthalpy c f ⋅ ϑf fed in with the fuel
can be disregarded compared with the heating value h u . Exceptions are only hot lean gases.
Energy flows out with the mass of the combustion gas and with dissociation enthalpy of the
not complete oxidized components. The following applies to the dissociation enthalpy
∆h diss
~
~
~
∆h H 2
∆h CO
∆h OH
= x CO ⋅ ~
+ xH2 ⋅ ~
+ x OH ⋅ ~
+ ...
M CO
MH2
M OH
(3-4)
∆h i being the dissociation enthalpies of the reactions such as
CO 2 → CO + 1 2 O 2
H 2O → H 2 + 1 2 O2
H 2 O → OH + H
O2 → O + O
and so forth.
In Eq. (3-3) is cf und cpL the specific heat capacity of fuel and air respectively and c pG is the
mean spec. heat capacity of the combustion gas.
The specific heat capacity is temperature dependent. Hence, corresponding with the definition
of the enthalpy, a mean value must be introduced in the balancing between the air and gas
temperatures
ϑG
∆h LG = ∫ c p (ϑ) ⋅ dϑ = cpG ⋅ (ϑG − ϑL ) .
(3-6)
ϑL
Consequently the following applies
cpG
1
=
TG − TL
TG
∫ c (T ) ⋅ dT .
p
(3-7)
TL
Absolute temperatures being applied for the sake of expediency. The temperature dependence
of the specific heat capacity of a gas component can in fact be approximated very well by the
power function [Müller, 1968]
n
c p (T ) = c p (T0 ) ⋅ (T T0 )
(3-8)
Thus the following results as the mean value of a gas component
c p (T )
c p (T0 )
=
1 (T T0 ) n +1 − 1
⋅
n +1
T T0 − 1
(3-9)
The mean specific heat capacity of the gas mixture is obtained from sum of the mass related
specific heat capacity of the individual components
cpG = ∑ x iG ⋅ cpi =
1
⋅∑~
x iG ⋅ ρ i ⋅ c pi .
ρG
(3-10)
Table 3-4 lists the specific heat capacities with the accompanying exponents n and the
densities for the most important gas components. Figure 3-4 shows the temperature
dependence of the specific heat capacity of the combustion gas for typical fuels.
The following applies to the mass flows
& =λ⋅L⋅M
&
M
L
f
(3-11)
and
& =M
& +M
& =M
& (1 + λ ⋅ L ) .
M
G
f
L
f
(3-12)
With these two equations the following results from the energy balance (3-3) for the adiabatic
combustion temperature
ϑad =
hu
∆h diss
λ ⋅ L c pL
−
+
⋅
⋅ ϑL .
(1 + λ ⋅ L) ⋅ cpG
cpG
1 + λ ⋅ L cpG
(3-13)
Figure 3-5 shows the adiabatic combustion temperature and the accompanying concentrations
in the combustion with air preheated to 800 °C. From this it is obvious that the maximum
adiabatic combustion temperature is not produced at stoichiometric combustion (λ = 1) but
when combustion is hypostoichiometric with approximately λ = 0.9. In this case the converted
enthalpy is in fact lower than λ = 1; the air demand L is lower as well. The various
components reach their maximum concentrations at different excess air numbers.
Figure 3-6 specifies the influence of the dissociation on the adiabatic combustion temperature.
The dissociation is not taken into account in the upper temperature profile. Therefore only the
homogeneous water gas reaction equation is taken into account in the area of
hypostoichiometric combustion. In this case the maximum value results when λ = 1. The
dissociation of CO2 and H2O is taken into account in the average curve. In the lower curve
additionally the dissociation of O2 and H2 is also taken into account. It is obvious from the
figure that approximately above temperatures of 1800 °C the dissociation exerts an influence
and that the dissociation of O2 and H2 can still be disregarded up to temperatures of
approximately 2300 °C.
If the air is only slightly preheated, then the enthalpy of the air λ ⋅ L ⋅ c pL ⋅ ϑL is only
approximately 1 to 3 % of the heating value. Then
λ ⋅ L ⋅ c pL ≈ (1 + λ ⋅ L ) ⋅ c pG
(3-14)
can be approximately set. Therefore the following ensues for the adiabatic temperature
ϑad ≈
hu
∆h diss
−
+ ϑL .
(1 + λ ⋅ L) ⋅ cpG
cpG
(3-15)
The adiabatic temperature is all the lower, the higher the excess air number is, and all the
higher, the higher the air preheating and the higher the O2 content of the combustion air and
the lower the air demand thus is.
Figure 3-7 shows the adiabatic temperature for typical fuels. An adiabatic temperature only
slightly higher than in natural gas is produced by fuel oil. By comparison coal possesses lower
adiabatic temperatures. Lean gases such as top gas produce only relative low adiabatic
temperatures. Thus these gases ignite and burn relatively poor, which is the reason why air is
often preheated in these cases.
Figure 3-8 represents the influence of the air preheating on the adiabatic combustion
temperature, again using the example of natural gas. The higher the temperature, the smaller
is the influence of the preheating air on the adiabatic combustion temperature, since larger
proportions dissociate.
Finally Figure 3-9 represents the influence of the O2 enrichment of the air. The adiabatic
combustion temperature can already be increased considerably by relatively low oxygen
enrichments.
3.2.3 Non-adiabatic Temperature and Flue Gas Temperature
Heat losses across wall are always present in real combustion chambers. Normally
combustion processes have excess air numbers higher than 1.1 and heat loss. Therefore the
temperature of the gas is so low that dissociation can be neglected. The energy balance is as
&
& ⋅h + M
& ⋅c ⋅ϑ = M
& ⋅c ⋅ϑ + Q
M
f
u
L
pL
L
G
pG
G
e
(3-16)
& being the heat flow of loss to environment. Using the approximation (3-14) the following
Q
e
results for the temperature of the gas
ϑG =
& M
&
hu − Q
e
f
+ϑ .
(1 + λ ⋅ L) ⋅ cpG L
(3-17)
If an efficiency of apparatus
ηa =
& M
&
hu − Q
e
f
hu
(3-18)
is introduced, the following ensues for the temperature
ϑG =
h u ⋅ ηa
+ϑ .
(1 + λ ⋅ L ) ⋅ cpG L
(3-19)
& , then the energy balance is
If the process gas emits the effective heat flow Q
& +Q
& +M
& ⋅h + M
& ⋅λ⋅L⋅c ⋅ϑ = Q
& ⋅ (1 + λ ⋅ L ) ⋅ c ⋅ ϑ
M
f
u
f
pL
L
e
f
pfg
fg
(3-20)
ϑfg then being the flue gas temperature. For the flue gas temperature the following is obtained
from the above using equation (3-14)
ϑfg =
& −Q
&
& ⋅h −Q
M
f
u
e
+ ϑL .
&
M f ⋅ (1 + λ ⋅ L ) ⋅ cpfg
(3-21)
The level of the flue gas temperature thus depends on the heat emission and consequently on
the type of process.
3.3 Fuel Demand
3.3.1 Pyrotechnical Efficiency
From the energy balance (3-20), the following results as the fuel demand for the necessary
& of the process to be carried out
heat flow Q
& ⋅h =
M
f
u
& +Q
&
Q
e
1 − (1 + λ ⋅ L ) ⋅ c pfg ⋅ (ϑfg − ϑe )/h u
(3-22)
when ϑe is the environmental air temperature. The specific energy demand related to the
& is applied to compare processes
product flow M
& M
& ⋅h
&
M
∆h + Q
f
u
e
=
&
M
1 − (1 + λ ⋅ L ) ⋅ cpfg ⋅ (ϑfg − ϑe )/h u
(3-23)
∆h being the product’s specific change of enthalpy in accordance with
& =M
& ⋅ ∆h .
Q
(3-24)
For the rating of firing plants the pyrotechnical efficiency
ηf =
& +Q
&
Q
e
& ⋅h
M
f
(3-25)
u
is introduced, which produces the ratio of the emitted heat to fuel energy consumption. Using
equation (3-22) the following is obtained
ηf = 1 −
(1 + λ ⋅ L )⋅ cpfg ⋅ (ϑfg − ϑe )
hu
.
(3-26)
Figure 3-10 represents this efficiency for the two fuels, natural gas and heating oil. It is
obvious that the efficiency is all the higher, the lower the flue gas temperature is and the more
the excess air number approaches the stoichiometric value. When flue gas temperatures and
excess air numbers are equal, the fuel oil has in fact a somewhat higher pyrotechnical
efficiency, in practice however, due to the acid dew point, higher flue gas temperatures must
be maintained in fuel oil firings than in natural gas firings.
The overall efficiency
ηov =
&
Q
& ⋅h
M
f
u
(3-27)
is introduced for the rating of the proportion of the utilized heat to the expended fuel. Using
equation (3-18) the following then ensues for the overall efficiency
(3-28)
ηov = ηf ⋅ ηa
This is thus smaller than the pyrotechnical efficiency.
3.3.2 Heat Recovery from Flue Gas
In many processes of high-temperature technology the combustion gases leave the kiln with
temperatures far above 200 °C. Therefore, Figure 3-11 presents the pyrotechnical efficiency
for temperatures up to 1000 °C. It is clear that the efficiencies drop to approximately 40%.
Figure 3-12 presents in principle, heat recovery from the heated gas reduces the specific
energy consumption, in which the air for the combustion in a recuperator is preheated. If the
& or M
& respectively, the
fuel flow with and without heat recovery is denoted with M
f
f0
following can be defined as the efficiency of energy saving
E =1−
& ⋅h
M
f
u
.
&
M f0 ⋅ h u
(3-29)
Using the fuel consumption according to equation (3-22) the following is obtained from this
E = 1−
h u − (1 + λ ⋅ L ) ⋅ c pffg ⋅ (ϑffg − ϑe )
h u − (1 + λ ⋅ L ) ⋅ c pfg ⋅ (ϑfg − ϑe )
(3-30)
The level of the air preheating and therefore of the temperature reduction of the combustion
gas depends on the quality of the recuperator. For its specification, the efficiency
& ⋅ c ⋅ (ϑ − ϑ ) M
& ⋅ c ⋅ (ϑ − ϑ )
M
Lp
e
ffg
fg
ηR = & L pL
= & G pfg
M L ⋅ c pL ⋅ (ϑffg − ϑe ) M L ⋅ c pL ⋅ (ϑffg − ϑe )
(3-31)
is defined which is the enthalpy emission of the combustion gas in the recuperator in relation
to the inlet enthalpy. Thus the following results from equation (3-30)
E = 1−
h u − (1 + λ ⋅ L ) ⋅ cpfg ⋅ (ϑffg − ϑe )

λ ⋅ L ⋅ c pL 

h u − (1 + λ ⋅ L ) ⋅ cpfg ⋅ (ϑffg − ϑe )⋅ 1 − ηR ⋅


(
)
1
+
λ
⋅
L
⋅
c
pfg 

(3-32)
and with the pyrotechnical efficiency in accordance with equation (3-26)
E = 1−
ηf

λ ⋅ L ⋅ c pL 

1 − (1 − ηf ) ⋅ 1 − ηR

(1 + λ ⋅ L ) ⋅ cpfg 

(3-33)
Figure 3-12 represents this efficiency of energy saving. It is obvious from this that particularly
in low pyrotechnical efficiencies much energy can be saved by heat recovery. In a
pyrotechnical efficiency of 0.5 for example and a recuperator efficiency of likewise only 0.5 a
relative energy saving of approximately 35% is produced.
The efficiency of energy saving is offset though by the investment costs. These are still
relatively inexpensive up to air preheating temperatures of approximately 600 °C, since they
then can still be constructed out of steel. If the combustion gas permits a considerably greater
preheating of the air, then as a rule regenerators made of ceramic materials are introduced
here. It should be noted that air preheating can be problematic with flue gases which contain a
high proportion of dust or liquid metal oxides (adherence on the walls) or trace gases which
act corrosively.
3.3.3 O2 Enrichment of Air
As Figure 3-13 schematically depicts, a further possibility for the reduction of the specific
energy consumption exists in the oxygen enrichment of the combustion air. The air from the
environment is mixed with pure oxygen so that the combustion air possesses an O2
concentration ~
x O 2 L > 0.21 or x O 2 L > 0.23 . In accordance with equation (2-2) and (2-6)
respectively, the air demand and consequently also the flue gas flow sink in this way, as a
result of which the flue gas losses are reduced.
From equation (3-20) the following is obtained for the fuel demand using equation (2-6)
& ⋅h =
M
f
u
&
Q
 λ ⋅O 
 ⋅ c ⋅ (ϑfg − ϑe )/h u
1 − 1 +
 x O L  pfg

2

.
(3-34)
If the relative efficiency of energy saving is defined in turn as
E =1−
& ⋅h
M
f
u
&
M f0 ⋅ h u
(3-35)
& ⋅ h being the fuel demand related to the O2 concentration of the ambient air x
M
f0
u
O 2 Le = 0.23 ,
then the following ensues from the two equations above

λ ⋅ O 
h u − 1 +
⋅ c ⋅ (ϑfg − ϑe )
 x O Le  pfg

2

E = 1−
 λ⋅O 
 ⋅ c ⋅ (ϑfg − ϑe )
h u − 1 +
 x O L  pfg

2

(3-36)
Figure 3-14 shows this relative efficiency of energy saving as a function of the O2 enrichment
of the air using the example of fuel natural gas. It is obvious that the efficiency of energy
saving is all the greater, the higher the flue gas temperature is and the greater the excess air
number deviates from one. It is especially apparent from the representation that slight oxygen
enrichments are already sufficient to achieve a relatively high fuel saving and that a further
enrichment only slightly increases the fuel saving.
The fuel costs saved are offset by the oxygen costs. The current costs are thus compared with
one another for the economic assessment of the O2 enrichment. In the operation without O2
enrichment the costs result in
& ⋅c
C0 = M
f0
f
(3-37)
& being the necessary fuel flow and c the price of the fuel. In the case of operation with O2
M
f0
f
enrichment the costs
& ⋅c + M
& ⋅c
C=M
f
f
O2
O2
(3-38)
& being the O2 mass flow introduced and c the price of the oxygen. The
are incurred, M
O2
O2
investment costs for the installation of the O2 enrichment are comparatively low and can be
allowed for the additional oxygen price. The level of the O2 flow depends on the O2
enrichment in accordance with
&
M
λ ⋅ O x O 2 L − x O 2 Le
O2
.
=
⋅
&
x
1
−
x
M
O2L
O 2 Le
f
(3-39)
If a cost saving is defined analogously to the fuel saving
EC =1−
C
C0
(3-40)
then, using the equations (3-31) to (3-34) and the fuel demand in accordance with equation (330), the following ensues
E C = E − (1 − E) ⋅
λ ⋅ O x O 2 L − x O 2 Le c O 2
⋅
⋅
.
x O2L
1 − x O 2 Le
cf
(3-41)
This equation shows that the cost saving does not depend on the individual prices but on the
price ratio. Owing to c O 2 > 0 the cost saving is always smaller than the energy saving. Only in
the ideal case c O 2 = 0 are both equally large. Figure 3-15 depicts the relative cost saving as a
function of the price ratio with the flue gas temperature as parameter and to be precise using
the example of natural gas with maximum O2 enrichment x O 2 L = 1 . The cost saving decreases
(
)
linearly with rising price ratio. Below the line E C = 0 the O2 enrichment leads to an increase
of the costs. At present the price ratio of oxygen to fuel is approximately in the range 0.2.
According to that a cost saving is obtained only in processes with flue gas temperatures
approximately above 700 °C.
From the equations (3-36) and (3-31) with E C = 0 , the maximum price ratio, up to which an
O2 enrichment is still economical, amounts to
1
 c O2

 c
 f

 =

 max
x O 2 Le
−1
hu
λ⋅O
−1−
c pfg ⋅ ϑ fg
x O 2 Le
.
(3-42)
This price ratio depends therefore only on the flue gas temperature, the fuel and the excess air
number; on the other hand it does not depend on the level of the O2 enrichment. Figure 3-16
shows this maximum price ratio as a function of the flue gas temperature with an excess air
number of 1.3.
As a rule an O2 enrichment is not worthwhile at current prices. A heat recovery from the flue
gas will be more economical. An O2 enrichment can however be economical for other
reasons, for example if by this means a production increase can be achieved in an existing
plant or if additional costs in the flue gas cleaning can be saved in the case of very dirty flue
gases such as from waste incineration.
3.4 Domestic Firings
Domestic firings are characterized by very low process temperatures, which are specified by
the return temperature of the heating water recirculation loop. The pyrotechnical efficiency
can be increased and the gross heating value can be used to reduce the energy consumption of
private households.
3.4.1 Pyrotechnical Efficiency
In Germany once again a higher value for the pyrotechnical efficiency of heating systems is
stipulated starting in the year 1998 for energy saving in private households. According to the
size of the system the efficiencies must be above 89 to 91%. As a rule in systems the air is
sucked in through the injector effect of the escaping fuel. In this way excess air numbers in
the magnitude of three result so that in accordance with Figure 3-9 the required efficiency
cannot be maintained. Modern systems therefore have a controlled air inlet in order to set the
lowest possible excess air numbers, as a rule around 1.2. With an additional slightly reduced
exhaust temperature modern (conventional) heating systems achieve a pyrotechnical
efficiency of approximately 95%. The condensate problems which might occur here are gone
throught the chimneys.
3.4.2 Gross Heating Value Use
In view of the low temperature level of the process heat, gross heating value use can save fuel
energy in heating engineering. Here a portion of the condensation enthalpy of the water vapor
in the flue gas is used. The humidity of the flue gas was already explained with Figure 2-9.
Figure 2-10 represents the dew point temperature of the flue gas. According to that in the case
of natural gas the flue gas must be cooled under 60 °C and in the case of fuel oil even under
50 °C before the steam condenses. Since natural gas moreover still possesses the higher
proportion of water vapor the gross heating value use is worthwhile as a rule only with this
fuel.
The more the flue gas is cooled, the more condenses as a result. For the assessment of the
gross heating value use the condensation rate
η con = 1 −
x H 2 O (ϑfg )
x H 2 O (ϑdew )
(3-43)
is introduced, x H 2 O (ϑdew ) being the flue gas humidity in accordance with Figure 2-9 at the
dew point temperature. Using equation (2-14) the following results from this
η con = 1 −
p H 2 O (ϑfg ) p − p H 2 O (ϑdew )
⋅
p H 2 O (ϑdew ) p − p H 2 O (ϑfg )
(3-44)
using the equilibrium steam pressure of the water vapor p eq according to equation (2-53).
Figure 3-17 presents the rate of condensation for natural gas as a function of the flue gas
temperature with various excess air numbers. The lower the excess air number is, the more
condenses.
The energy saving amounts to
E = η con ⋅
H0 − h u
hu
(3-46)
H 0 being the gross heating value. In comparison with the other fossil fuels the difference from
the heating value is the greatest in the case of natural gas and in accordance with Table 3-1
amounts to 10.5%. At a maximum heating temperature of 40 °C with a return temperature of
the heating water of 30 °C, a cooling of the flue gas is possible up to approximately 40 °C.
According to Figure 3-17 the gross heating value use then amounts to 60%. In accordance
with Figure 3-9, the pyrotechnical efficiency amounts to 99% at this flue gas temperature. The
total pyrotechnical efficiency in the gross heating value us can consequently reach values of
105% (in relation to the heating value). Compared with modern heating systems with
pyrotechnical efficiencies of up to 94%, an energy saving of 11% is consequently possible.
This saving consists therefore of up to 6% from the gross heating value use and of up to 5%
reduction of the flue gas losses.
The fuel costs saved are in turn offset by higher investment costs, since the gross heating
value boilers are technically more complex and larger heating surfaces are necessary in view
of the lower heating temperatures. The technology of heating engineering will be dealt with in
the relevant chapter.
In houses erected until now the heating system is designed for higher flow and return
temperatures of the water recirculation loop than 40 or 30 °C respectively. In older systems
the flow and return temperatures amount to 70 to 50 °C. When these heating system is
replaced with gross heating value heating the condensation heat is consequently lower than
6% specified above, which makes the economic feasibility worse. By comparison the heating
system in new buildings is designed for the low water temperatures without considerable
additional costs, an underfloor heating being very suitable. In gross heating value heating an
installation on the roof presents itself, as a result of which the costs for the chimney are saved.
3.5
Burning of metals
Not only fossil fuels but also a multiplicity of further materials can be oxidized and therewith
burned. However most of these materials occur not naturally and are relatively expensive.
Therefore their oxidation remains limited to special cases. In this section as example the
burning of some metals is treated. In the form of dust these can react and burn very well.
In fig. 3-21 the mass flows are represented for an adiabatic reaction. As combustion products
result a metallic oxide, which is present liquid due to the very high combustion temperature,
and a gas, which consists of nitrogen and for excess air of surplus oxygen. To the mass flows
applies
(
)
& =M
&
M
Ox
Met ⋅ 1 + L ⋅ x O 2L
(3-52)
and
& =M
&
&
M
G
Met ⋅ λ ⋅ L ⋅ x N 2 L + M Met ⋅ (λ − 1) ⋅ L ⋅ x O 2L ,
(3-53)
whereby x N 2 L and x O 2 L are the mass concentrations of nitrogen and oxygen in air. The
oxygen and air requirement can be computed with the Eg. (2-3) and (2-5) given in section 2-2.
In the table 3-6 these two values for the burning of the four metals chrome, aluminum,
magnesium and iron are specified. By comparison with the tables 2-3 and 2-5 it is evident
that metals have a very small air requirement.
Metal
Cr
Al
Mg
Fe
Oxide
Cr2O3
Al2O3
MgO
Fe3O4
O
L
∆h
~
M Met
kg O2
kg Met
kg air
kg Met
MJ
kg Met
kg
kmol
0.46
0.89
0.67
0.38
2.0
3.9
2.9
1.7
11.0
31.0
25.0
6.7
52
27
24
56
ϑmelt
∆h melt
°C
kJ
kg Oxide
kg Oxide ⋅ K
853
1089
1946
595
0.86
1.23
1.34
0.88
2330
2054
2832
1597
ϑad (λ = 1)
c
kJ
°C
3379
4782
4655
2334
Table 3-6: Burning of metals
As energy balance is valid
&
&
&
&
M
Met ⋅ ∆h + M L ⋅ c L ⋅ ϑ L = M Ox ⋅ (c Ox ⋅ ϑad + ∆h melt ) + M G ⋅ cpG ⋅ ϑad .
(3-54)
With the metal reaction enthalpy ∆h is supplied. The enthalpy supplied with air is negligible.
With the metallic oxide also melting enthalpy is exhausted. The specific thermal capacity cOx
of the metallic oxides is represented in fig. 3-22. The mean specific thermal capacity of the
gas is computed with Eq. (3-10). With the Eqs. (3-52) and (3-53) follow for the adiabatic
burning temperature
ϑad =
(
)⋅ c
)
∆h − 1 + L ⋅ x O2L ⋅ ∆h melt
(1 + L ⋅ x
O2L
Ox
(
)
+ λ − x O2L ⋅ L ⋅ cG
.
(3-55)
This temperature is specified for a stoichiometric reaction in table 3-6 with the associated
enthalpy. One recognizes that the burning temperature is not only much more higher than the
melting temperature but also very much higher than the combustion temperature of the fossil
fuels. The burning temperature is so high despite the low reaction enthalpy relatively low
opposite that of the fossil fuels, since the oxygene requirement is so small. Due to their high
temperature the metallic oxides shine very brightly. Therefore these are used for fireworks.
HO
0 °C Fuel
Dry combustion gas 0 °C
Reaction Chamber
0 °C Air
Liquid water 0 °C
Complete Combustion with λ > 1
Fig. 3-1:
Determination of Heating Value
20
Propane
Stochiometric Air Demand
Natural gas H
Fuel oil S
Gasoline
Natural gas L
Coke oven gas
Carbon
15
Fuel oil EL
Benzene
Anthracite
Alcohol
10
Car tyres
Coal
Coke
Biogas
Methanol
Landfill gas
Plastics
Pulverised lignite
5
CO
Wood
Textilies
Papers
Blast furnace gas
Gum & Leather
L = 0,33 • [kg L /MJ] hu
0
0
10
20
30
Heating value hu in MJ/kg
Fig. 3-2:
Correlation between heating value and air demand
40
50
&
Fuel M
F
Adiabatic Firing
Chamber
& ,ϑ
Air M
L
L
&
Q
e
&
Fuel M
F
Non-adiabatic
Firing Chamber
Combustion
&
gas M
G
Combustion gas
&
M
G
Adiabatic temperature
ϑad
Furnace/Heating
&
Flue gas M
G
&
Q
Temperature
ϑG
& ,ϑ
Air M
L
L
Flue gas
temperature
ϑfg
&
Q
e
&
Fuel M
F
Furnace/Heating
&
Q
& ,ϑ
Air M
L
L
&
Flue gas M
G
Temperature ϑfg
&
Q
e
Solid Fuel
&
M
Furnace/heating
& ,ϑ
Air M
L
L
Fig. 3-3: Temperature of Combustion Gas
Smoke gas
Flue gas
Purification
Mean specific heat capacity [kJ/(kg K)]
1,30
λ = 1.0
1,25
1,20
Natural gas type L
Fuel oil (light)
Antracite
Anthracite
Blast furnace gas
1,15
1,10
λ = 1.2
1,05
1,00
0,95
0
Fig. 3-4:
200
400
600
800
1000
Gas temperature [°C]
1200
1400
1600
Mean specific heat capacity
1,E+00
2300
N2
Molar Concentration
H2O
1,E-01
2200
CO2
2150
O2
CO
2100
ϑ
OH
H2
1,E-02
H
2050
2000
O
1,E-03
1950
Natural gas type L
Air: 0.21% O2
Air preheating: 800 °C
1900
1850
1,E-04
1800
0,7 0,8 0,9
1
1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9
Excess air number
Fig. 3-5: Temperature and concentration at combustion of natural gas type L
2
Adiabatic gas temperatur [°C]
2250
Adiabatic gas temperature [°C]
2600
CO2, H2O, H2,
CO, N2
2500
Gas components concidered:
CO2, H2O, O2, N2
2400
CO2, H2O, O2, N2, CO, H2
2300
CO2, H2O, O2, N2, CO, H2, O, H, OH
2200
2100
2000
Natural gas type L
Air: 0,21 Vol% O2
Air preheating: 800 °C
1900
1800
0,6
0,7 0,8
0,9
1
1,1
1,2
1,3
1,4 1,5
1,6
1,7 1,8
1,9
2
Excess air number λ
Fig. 3-6:
Compairison of adiabat gas temperature with and without dissociation
2200
2100
Gas temperature [°C]
2000
1900
1800
CO
1700
H2
1600
Gas flame coal
Fuel oil light
Natural gas type L
Antracite
coal
Anthracite
coal
1500
1400
Blast furnace gas
1300
Brown coal
1200
1
1,2
1,4
1,6
Excess air number
Fig. 3-7:
Adiabatic flame temperature with dissociation
1,8
2
2300
ϑair
2200
Temperature [°C]
800 °C
2100
600 °C
2000
400 °C
1900
200 °C
1800
1700
0 °C
1600
0,7
0,8
0,9
1
1,1
1,2
1,3
1,4
Excess air number
Influence of air preheating on gas temperature
Temperature [°C]
2400
0,3
2300
Adiabatic combustion of
natural gas type L, λ = 1.1
0,25
2200
H2O
0,2
ϑ
2100
0,15
2000
0,1
CO2
1900
0,05
O2
1800
0,21
CO H
2
0,26
0,31
Concentration of O2 in air
Fig. 3-9:
Influence of O2 enrichment
0,36
0
0,41
Concentration
Fig. 3-8:
1
Natural gas type L
Fuel oil (light)
0,99
Firing efficiency
0,98
0,97
0,96
0,95
0,94
λ=1
λ = 1,2
λ = 1,5
0,93
0,92
λ=2
0,91
0,9
0
20
40
60
80
100
120
140
160
180
200
220
240
Temperature difference between flue gas and combustion air [K]
Fig. 3-10: Firing efficiency
1
0,9
Firing efficiency
0,8
0,7
λ=1
0,6
λ = 1,2
0,5
λ = 1,5
Natural gas type L
0,4
λ=2
0,3
0,2
0
200
400
600
800
Temperature difference between flue gas and combustion air [K]
Fig. 3-11: Firing efficiency for natural gas type L
1000
.
Qe
Ambient Air ϑe
.
Q
Fuel
Flue gas
.
ϑfg, MG
Firing
Flue Gas
ϑffG
.
Preheated Air ϑLp, ML
Fig. 3-12: Firing plant with heat recovery from flue gas
1
ηf
Relelative energy saving
0,1
0,8
0,2
0,3
0,6
0,4
0,5
0,4
0,6
0,7
0,2
0,8
0,9
0
0
0,2
0,4
0,6
Efficiency of recuperator ηR
Fig. 3-13: Relative energy saving by air preheating
0,8
1
Furnace
flue gas
.
Q
ϑAO
Ambient air
ϑL
Fuel
Heat
exchanger
Heat
exchanger
ϑAL
Flue gas
.
Mg,ϑA
.
Preheated air ϑLV, ML
.
Preheated fuel ϑBV, MB
ϑ
ϑAO
ϑLV
Flue gas
ϑAL
ϑBV
Air
Flue gas
Fuel
ϑL
ϑA
Flow length
Fig. 3-14: Firing plant with heat recovery by air and fuel preheating
1
0,9
ηRL = 0,8 ηRB = 0,8
ηRL = 0,8 ηRB = 0
λ = 1,1
Rel. energy saving E
0,8
0,7
0,6
ηf
0,5
0,4
0,4
0,3
0,2
0,6
0,1
0,8
0
0
1
2
3
Air demand L
Fig. 3-15: Relative energy saving by air and fuel preheating
4
5
Fuel
.
Q
Flue Gas
Ambient Air xO2Le
Oxygen
Combustion
Air xO L
2
Fig. 3-16: Oxygene enrichment of combustion air
Natural gas type L
λ = 1.1
λ = 1.3
1,0
0,9
Flue gas temperature
Relative fuel saving
0,8
1600°C
0,7
1400°C
0,6
0,5
1200°C
0,4
1000°C
0,3
800°C
600°C
0,2
400°C
0,1
0,0
0,2
0,3
0,4
0,5
0,6
0,7
Oxygen content in enriched air [m
Fig. 3-17: Influence of oxygene enrichment
0,8
3
3
O2/m air]
0,9
1
1
Flue gas temperature
1600°C
Relative cost savings
0,75
Natural gas type L
λ = 1.3
1400°C
0,5
1200°C
1000°C
0,25
800°C
600°C
0
400°C
-0,25
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
Price relation oxygen / fuel
Fig. 3-18: Relative cost savings
0,8
0,7
Excess air number λ = 1.3
Antracite
Anthracite
Natural gas
type L
Limit price relation
0,6
0,5
Fuel oil light
0,4
0,3
0,2
0,1
0,0
500
600
700
800
900
1000
1100
1200
Flue gas temperature [°C]
Fig. 3-19: Limit price relation
1300
1400
1500
1
Condensation degree ηcon
0,9
0,8
0,7
0,6
Natural gas
type L
1.1
1.2
1.3
0,5
0,4
0,3
1.1
1.2
1.3
λ
Fuel oil light
0,2
0,1
0
0
5
10
15
20
25
30
35
40
45
50
55
Flue gas temperature [°C]
Fig. 3-20: Condensation degree
1,00
0,98
0,96
Efficiency
0,94
0,92
Fuel oil light
λ
0,90
0,88
1,5
0,86
0,84
Natural gas type L
1,5
1,2
1,2
1,0
1,0
0,82
0,80
30
50
70
90
110
130
Gas temperature [°C]
Fig. 3-21: Efficiency of combustion plants with gross heating value as reference
150
60
M Met , ∆h
M Oxid , ϑ Schm , ∆h ad
M L , ϑL
M g , ϑad
Fig. 3-22: Mass flow in metal combustion
Spezific heat capacity [kJ/kg K]
2,0
1,8
1,6
MgO
1,4
Al2O3
1,2
Fe3O4
1,0
Cr2O3
0,8
0,6
0
500
1000
1500
2000
2500
Temperature [K]
Fig. 3-23: Spezific heat capacity of metal oxids
3000
3500
4000
Fuel
ρ
kg/m3
iN.
0.090
1.25
0.718
2.01
0.83
0.79
0.51
1.25 – 1.35
0.92 – 0.98
850
950
840
730
812
806
2000
1300
1000
1200
1000
700
Hydrogen
Carbon monoxide
Methane
Propane
Natural gas L
Natural gas H
Cokeoven gas
Top gas
Biogas
Light oil
Heavy oil
Diesel oil
Petrol
Methanol
Ethanol
Graphite
Coal
Coke
Raw lignite
Lignite dust
Wood (dry)
Net heating value
MJ/m3
10.8
12.6
35.9
93.2
31.8
37.4
17.5
3.3 – 3.7
18 - 21
16.2
21.6
38,6
28,7
19 - 22
12 - 15
MJ/kg
120
10.1
50.0
46.4
38.3
47.3
34.3
2.4 – 2.8
18 - 23
42.7
41.0
42.7
43.5
19.9
26.8
33.8
29.7
28.7
8.5
19 - 22
17 - 21
Upper heating value
MJ/m3
12.8
12.6
39.8
101.2
35.2
41.3
19.7
3.3 – 3.7
20 - 24
-
MJ/kg
142
10.1
55.4
50.3
42.4
52.3
38.6
2.5 – 2.8
20 – 25
45.4
43.3
45.4
46.5
22.7
29.7
33.8
31.7
28.9
10.5
18 - 22
Table 3-1: Reference values for heating values of fuels
Fuel
Natural Gas
Light Oil
Heavy Oil
Coal
Coke
Lignite
Electricity without distribution
Electricity with distribution
Treatment Demand Energy
In MJ/kg
In % from heating value
4.6
13
4.7
11
4.1
10
2.1
7
6.0
21
0.3
3
0.33 kWhel/kWhprim
0.315 kWhel/kWhprim
Table 3-3: Treatment Demand Energy for Fossil Fuel according to Ffe [1.2] and Mauch
[1.1]
Gas
NO2
O2
CO2
H2O
CO
H2
cp
KJ/(kgK)
n
-
1.00
0.90
0.84
1.75
1.00
14.20
0.11
0.15
0.30
0.20
0.12
0.05
~
M
kg/kmol
28.0
32.0
44.0
18.0
28.0
2.0
ρi
kg/m3
1.234
1.410
1.939
0.793
1.234
0.088
Table 3-4: Specific heat capacity and density at 273 K and 1 bar
Heating power
in kW
4 – 25
25 –50
> 50
until 1983
up 1983
up 1988
up 1998
15
14
13
14
13
12
12
11
10
11
10
9
Table 3-5: Limit values in % for loss of flue gas for oil and gas heating according to
installation year
1 Kilojoule (kJ)
1 Kilocalorie (kcal)
1 Kilowatt hour (kWh)
1 kg coal equivalent
(SKE)
1 kg Crude oil equivalent
(RÖE)
1 m3 Natural Gas
Table 3-2:
kJ
kcal
4,1868
3 600
29 308
0,2388
860
7000
41 868
31 736
m3
Natural
Gas
0,000278 0,000034 0,000024 0,000032
0,001163 0,000143 0,0001
0,00013
0,123
0,086
0,113
8,14
0,7
0,923
kWh
kg SKE
kg RÖE
10 000
11,63
1,428
-
1,319
7 580
8,816
1,083
0,758
-
Conversions for energy units
Metal Oxid
O
L
∆h
~
M Met
ϑ Melt
∆h Melt
c
ϑ ad (λ = 1)
kg O2
kg Met
kg Air
kg Met
MJ
kg Met
kg
kmol
°C
kJ
kg Oxid
kJ
kg Oxid ⋅ K
°C
Cr
Cr2O3
0.46
2.0
11.0
52
2330
853
0.86
3379
Al
Al2O3
0.89
3.9
31.0
27
2054
1089
1.23
4782
Mg
MgO
0.67
2.9
25.0
24
2832
1946
1.34
4655
Fe
Fe3O4
0.38
1.7
6.7
56
1597
595
0.88
2334
Table 3-6: For calculation of metal combustion