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 oH (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

vapOH0u ∆hxHh2

⋅−= (3-1)

OH2x 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

uiiu hxh ⋅∑= (3-2)

ix being the combustible proportion of gas and uih 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 adϑ results from the energy balance for the adiabatic

combustion chamber in accordance with Figure 3-2

dissGadpGGLpLLffuf hMcMcM)ch(M ∆⋅+ϑ⋅⋅=ϑ⋅⋅+ϑ⋅+ &&&& . (3-3)

Energy is inserted with the mass flow of fuel and air. The enthalpy ffc ϑ⋅ fed in with the fuel

can be disregarded compared with the heating value uh . 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

...M~h~∆

xM~h~∆

xM~h~∆

x∆hOH

OHOH

H

HH

CO

COCOdiss

2

2

2+⋅+⋅+⋅= (3-4)

i∆h being the dissociation enthalpies of the reactions such as

22 O21COCO +→

222 O21HOH +→

HOHOH 2 +→

OOO 2 +→

and so forth. In Eq. (3-3) is cf und cpL the specific heat capacity of fuel and air respectively and pGc 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

( ) ( )LGpGpLG cdc∆hG

L

ϑ−ϑ⋅=ϑ⋅ϑ= ∫ϑ

ϑ

. (3-6)

Consequently the following applies

( ) TdTcTT

1c

G

L

T

T

p

LG

pG ⋅−

= ∫ . (3-7)

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

00pp TTTcTc ⋅= (3-8)

Thus the following results as the mean value of a gas component

( )( ) 1TT

1)TT(

1n

1

Tc

Tc

0

1n0

0p

p

−

−⋅

+=

+

(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

piiiG

G

piiGpG cx~1

cxc ⋅ρ⋅∑⋅ρ

=⋅∑= . (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

fL MLλM && ⋅⋅= (3-11)

and

( )Lλ1MMMM fLfG ⋅+=+= &&&& . (3-12)

With these two equations the following results from the energy balance (3-3) for the adiabatic combustion temperature

( ) L

pG

pL

pG

diss

pG

uad c

c

L1

L

c

h

cL1

hϑ⋅⋅

⋅λ+

⋅λ+

∆−

⋅⋅λ+=ϑ . (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 LpLcLλ ϑ⋅⋅⋅ is only

approximately 1 to 3 % of the heating value. Then

( ) pGpL cLλ1cLλ ⋅⋅+≈⋅⋅ (3-14)

can be approximately set. Therefore the following ensues for the adiabatic temperature

L

pG

diss

pG

uad

c

h

c)L1(

hϑ+

∆−

⋅⋅λ+≈ϑ . (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

eGpGGLpLLuf QcMcMhM &&&& +ϑ⋅⋅=ϑ⋅⋅+⋅ (3-16)

eQ& being the heat flow of loss to environment. Using the approximation (3-14) the following

results for the temperature of the gas

( ) L

pG

feuG

cLλ1

MQhϑ+

⋅⋅+

−=ϑ

&&

. (3-17)

If an efficiency of apparatus

u

feua

h

MQh &&−=η (3-18)

is introduced, the following ensues for the temperature

( ) L

pG

auG cLλ1

ηhϑ+

⋅⋅+

⋅=ϑ . (3-19)

If the process gas emits the effective heat flow Q& , then the energy balance is

( ) fgpfgfeLpLfuf cLλ1MQQcLλMhM ϑ⋅⋅⋅+⋅++=ϑ⋅⋅⋅⋅+⋅ &&&&& (3-20)

fgϑ then being the flue gas temperature. For the flue gas temperature the following is obtained

from the above using equation (3-14)

( ) L

pfgf

euffg

cLλ1M

QQhMϑ+

⋅⋅+⋅

−−⋅=ϑ

&

&&&

. (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

heat flow Q& of the process to be carried out

( ) ( ) uefgpfg

euf

/hcLλ11

QQhM

ϑ−ϑ⋅⋅⋅+−

+=⋅

&&& (3-22)

when ϑe is the environmental air temperature. The specific energy demand related to the product flow M& is applied to compare processes

( ) ( ) uefgpfg

euf

/hcLλ11

MQh

M

hM

ϑ−ϑ⋅⋅⋅+−

+∆=

⋅ &&

&

&

(3-23)

h∆ being the product’s specific change of enthalpy in accordance with

hMQ ∆⋅⋅⋅⋅==== && . (3-24)

For the rating of firing plants the pyrotechnical efficiency

uf

ef

hM

QQ

⋅

+=η

&

&&

(3-25)

is introduced, which produces the ratio of the emitted heat to fuel energy consumption. Using equation (3-22) the following is obtained

( ) ( )u

efgpfgf

h

cLλ11

ϑ−ϑ⋅⋅⋅+−=η . (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

uf

ovhM

Q

⋅=η

&

&

(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

afov η⋅η=η (3-28)

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

fuel flow with and without heat recovery is denoted with fM& or f0M& respectively, the

following can be defined as the efficiency of energy saving

uf0

uf

hM

hM1E

⋅

⋅−=

&

&

. (3-29)

Using the fuel consumption according to equation (3-22) the following is obtained from this

( ) ( )( ) ( )efgpfgu

effgpffgu

cLλ1h

cLλ1h1E

ϑ−ϑ⋅⋅⋅+−

ϑ−ϑ⋅⋅⋅+−−= (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

( )( )

( )( )effgpLL

fgffgpfgG

effgpLL

eLppLLR cM

cM

cM

cM

ϑ−ϑ⋅⋅

ϑ−ϑ⋅⋅=

ϑ−ϑ⋅⋅

ϑ−ϑ⋅⋅=η

&

&

&

&

(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)

( ) ( )

( ) ( )( )

⋅⋅λ+

⋅⋅λ⋅η−⋅ϑ−ϑ⋅⋅⋅λ+−

ϑ−ϑ⋅⋅⋅λ+−−=

pfg

pLReffgpfgu

effgpfgu

cL1

cL1cL1h

cL1h1E (3-32)

and with the pyrotechnical efficiency in accordance with equation (3-26)

( )( )

⋅⋅λ+

⋅⋅λη−⋅η−−

η−=

pfg

pLRf

f

cL1

cL111

1E (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 21.0x~ LO2

> or 23.0x LO2> . 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)

( ) uefgpfg

LO

uf

/hcx

Oλ11

QhM

2

ϑ−ϑ⋅⋅

⋅+−

=⋅&

& . (3-34)

If the relative efficiency of energy saving is defined in turn as

uf0

uf

hM

hM1E

⋅

⋅−=

&

&

(3-35)

uf0 hM ⋅& being the fuel demand related to the O2 concentration of the ambient air 23.0x LeO2= ,

then the following ensues from the two equations above

( )

( )efgpfg

LO

u

efgpfg

LeO

u

cx

Oλ1h

cx

Oλ1h

1E

2

2

ϑ−ϑ⋅⋅

⋅+−

ϑ−ϑ⋅⋅

⋅+−

−= (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

ff00 cMC ⋅= & (3-37)

f0M& being the necessary fuel flow and fc the price of the fuel. In the case of operation with O2

enrichment the costs

22 OOff cMcMC ⋅+⋅= && (3-38)

are incurred, 2OM& being the O2 mass flow introduced and

2Oc the price of the oxygen. The

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

LeO

LeOLO

LOf

O

2

22

2

2

x1

xx

x

Oλ

M

M

−

−⋅

⋅=

&

&

. (3-39)

If a cost saving is defined analogously to the fuel saving

0

CC

C1E −= (3-40)

then, using the equations (3-31) to (3-34) and the fuel demand in accordance with equation (3-30), the following ensues

f

O

LeO

LeOLO

LO

Cc

c

x1

xx

x

OλE)(1EE 2

2

22

2

⋅−

−⋅

⋅⋅−−= . (3-41)

This equation shows that the cost saving does not depend on the individual prices but on the price ratio. Owing to 0c

2O > the cost saving is always smaller than the energy saving. Only in

the ideal case 0c2O = 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 ( )1x

2O =L

. The cost saving decreases

linearly with rising price ratio. Below the line 0E C = 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 0E C = , the maximum price ratio, up to which an

O2 enrichment is still economical, amounts to

LeOfgpfg

u

LeO

maxf

O

2

22

x

Oλ1

c

h

1x

1

c

c

⋅−−

⋅

−

=

ϑ

. (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

( )( )dewOH

fgOH

con

2

2

x

x1η

ϑ

ϑ−= (3-43)

is introduced, ( )dewOH2x ϑ 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

( )( )

( )

( )fgOH

dewOH

dewOH

fgOH

con

2

2

2

2

pp

pp

p

p1η

ϑ

ϑ

ϑ

ϑ

−

−⋅−= (3-44)

using the equilibrium steam pressure of the water vapor eqp 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

u

u0con

h

hHηE

−⋅= (3-46)

0H 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

( )LOMetOx 2xL1MM ⋅+⋅= && (3-52)

and

( ) LOMetLNMetG 22xL1MxLMM ⋅⋅−⋅+⋅⋅⋅= λλ &&& , (3-53)

whereby LN2

x and LO2x 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 Oxide O L h∆ MetM~

meltϑ melth∆ c )1(ad =λϑ

Met

O

kg

kg2

Met

air

kg

kg

Metkg

MJ

kmol

kg C°

Oxidekg

kJ Kkg

kJ

Oxide ⋅

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: Burning of metals As energy balance is valid

( ) adpGGmeltadOxOxLLLMet cMhcMcMhM ϑ⋅⋅+∆+ϑ⋅⋅=ϑ⋅⋅+∆⋅ &&&& . (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

( )

( ) ( ) GLOOxLO

meltLOad

cLxcxL1

hxL1h

22

2

⋅⋅−λ+⋅⋅+

∆⋅⋅+−∆=ϑ . (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.

Fig. 3-1: Determination of Heating Value

0

5

10

15

20

0 10 20 30 40 50

Sto

ch

iom

etr

ic A

ir D

em

an

d

Blast furnace gas

Coke oven gas

CO

PapersTextilies

Landfill gas

Wood

Methanol

Gum & Leather

Biogas

Pulverised lignite

Alcohol

Plastics

CokeCoal

Anthracite

Carbon

Car tyres

Natural gas L

Fuel oil S

Benzene

Fuel oil EL

Propane

Natural gas H

L = 0,33 • [kg L /MJ] hu

Gasoline

Heating value hu in MJ/kg

Fig. 3-2: Correlation between heating value and air demand

0 °C Fuel

0 °C Air

HO

Dry combustion gas 0 °C

Liquid water 0 °C

Complete Combustion with 1>λ

Reaction Chamber

Fig. 3-3: Temperature of Combustion Gas

Adiabatic Firing Chamber

Fuel FM&

Air LL ,M ϑ&

Combustion gas

GM&

Adiabatic temperature

adϑ

Non-adiabatic Firing Chamber

Furnace/Heating

Fuel FM&

Air LL ,M ϑ&

Combustion

gas GM&

Temperature

Gϑ

Flue gas GM&

Flue gas temperature

fgϑ

Q&

eQ&

Furnace/Heating

Fuel FM&

Air LL ,M ϑ&

Q&

Flue gas GM&

Temperature fgϑ

eQ&

Furnace/heating

Solid Fuel

M&

Air LL ,M ϑ&

Smoke gas

Purification

Flue gas

eQ&

0,95

1,00

1,05

1,10

1,15

1,20

1,25

1,30

0 200 400 600 800 1000 1200 1400 1600

Gas temperature [°C]

Mean s

pecific

heat

capacity [kJ/(

kg K

)]

Natural gas type L

Fuel oil (light)

Blast furnace gas

Antracite

λ = 1.0

λ = 1.2

Fig. 3-4: Mean specific heat capacity

1,E-04

1,E-03

1,E-02

1,E-01

1,E+00

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

Mola

r C

oncentr

ation

1800

1850

1900

1950

2000

2050

2100

2150

2200

2250

2300

Adia

batic g

as tem

pera

tur

[°C

]

Natural gas type L

Air: 0.21% O2

Air preheating: 800 °C

O2

H2O

CO2

H2

COϑϑϑϑ

N2

O

H

OH

Fig. 3-5: Temperature and concentration at combustion of natural gas type L

Anthracite

1800

1900

2000

2100

2200

2300

2400

2500

2600

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

Adia

batic g

as tem

pera

ture

[°C

]

Natural gas type L

Air: 0,21 Vol% O2

Air preheating: 800 °C

CO2, H2O, O2, N2

CO2, H2O, O2, N2, CO, H2

CO2, H2O, O2, N2, CO, H2, O, H, OH

Gas components concidered:

CO2, H2O, H2,

CO, N2

Fig. 3-6: Compairison of adiabat gas temperature with and without dissociation

1200

1300

1400

1500

1600

1700

1800

1900

2000

2100

2200

1 1,2 1,4 1,6 1,8 2

Excess air number

Gas tem

pera

ture

[°C

]

H2

CO

Gas flame coal

Fuel oil light

Natural gas type L

Brown coalBlast furnace gas

Antracite coal

Fig. 3-7: Adiabatic flame temperature with dissociation

Anthracite coal

1600

1700

1800

1900

2000

2100

2200

2300

0,7 0,8 0,9 1 1,1 1,2 1,3 1,4

Excess air number

Tem

pera

ture

[°C

]

ϑair

800 °C

600 °C

400 °C

200 °C

0 °C

Fig. 3-8: Influence of air preheating on gas temperature

1800

1900

2000

2100

2200

2300

2400

0,21 0,26 0,31 0,36 0,41

Concentration of O2 in air

Tem

pera

ture

[°C

]

0

0,05

0,1

0,15

0,2

0,25

0,3

Concentr

ationH2O

CO2

O2

COH2

ϑ

Adiabatic combustion of

natural gas type L, λ = 1.1

Fig. 3-9: Influence of O2 enrichment

0,9

0,91

0,92

0,93

0,94

0,95

0,96

0,97

0,98

0,99

1

0 20 40 60 80 100 120 140 160 180 200 220 240

Temperature difference between flue gas and combustion air [K]

Fir

ing e

ffic

iency

Natural gas type L

Fuel oil (light)

λ = 1

λ = 1,2

λ = 1,5

λ = 2

Fig. 3-10: Firing efficiency

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 200 400 600 800 1000

Temperature difference between flue gas and combustion air [K]

Firin

g e

ffic

ien

cy

λ = 1

λ = 1,2

λ = 1,5

λ = 2

Natural gas type L

Fig. 3-11: Firing efficiency for natural gas type L

Preheated Air , MϑLp L

Fuel Firing

ϑffG

Ambient Air ϑe

Q.

Qe

.

Flue gas

, Mϑfg G

.Flue Gas

.

Fig. 3-12: Firing plant with heat recovery from flue gas

0

0,2

0,4

0,6

0,8

1

0 0,2 0,4 0,6 0,8 1

Efficiency of recuperator ηR

Rele

lative e

nerg

y s

avin

g

ηηηηf

0,2

0,1

0,3

0,4

0,5

0,6

0,7

0,8

0,9

Fig. 3-13: Relative energy saving by air preheating

Furnaceflue gas

ϑAO

Ambient air

ϑL

Flue gas

Preheated air , MϑLV L

.

Q.

. Mg, Aϑ

Preheated fuel , MϑBV B

.

Heatexchanger ϑAL

Fuel

Heatexchanger

Fuel

ϑAL

ϑ

ϑL

AirFlue gasϑBV

Flue gas

ϑA

ϑAO

ϑLV

Flow length Fig. 3-14: Firing plant with heat recovery by air and fuel preheating

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 1 2 3 4 5

Air demand L

Rel. e

nerg

y s

avin

g E

ηRL = 0,8 ηRB = 0,8

ηRL = 0,8 ηRB = 0

λ = 1,1

ηηηηf

0,4

0,6

0,8

Fig. 3-15: Relative energy saving by air and fuel preheating

FuelQ.

Flue Gas

Ambient Air x

Oxygen CombustionAir x

O Le2

O L2 Fig. 3-16: Oxygene enrichment of combustion air

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Oxygen content in enriched air [m3

O2/m3

air]

Rela

tive fuel savin

g

Flue gas temperature

800°C

600°C

400°C

Natural gas type L

λ = 1.1

λ = 1.3

1000°C

1200°C

1400°C

1600°C

Fig. 3-17: Influence of oxygene enrichment

-0,25

0

0,25

0,5

0,75

1

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4

Price relation oxygen / fuel

Rela

tive c

ost savin

gs

Natural gas type L

λ = 1.3

Flue gas temperature

1600°C

1400°C

1200°C

1000°C

800°C

600°C

400°C

Fig. 3-18: Relative cost savings

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

500 600 700 800 900 1000 1100 1200 1300 1400 1500

Flue gas temperature [°C]

Lim

it p

rice r

ela

tion

Excess air number λ = 1.3 Antracite

Natural gas

type L

Fuel oil light

Fig. 3-19: Limit price relation

Anthracite

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 5 10 15 20 25 30 35 40 45 50 55 60

Flue gas temperature [°C]

Condensation d

egre

e η

co

n

λλλλ

1.1

1.21.3

Fuel oil light

1.1

1.2

1.3

Natural gas

type L

Fig. 3-20: Condensation degree

0,80

0,82

0,84

0,86

0,88

0,90

0,92

0,94

0,96

0,98

1,00

30 50 70 90 110 130 150

Gas temperature [°C]

Effic

iency

λλλλ

1,01,2

1,5

1,01,2

1,5

Fuel oil light

Natural gas type L

Fig. 3-21: Efficiency of combustion plants with gross heating value as reference

M M

MM , ϑ

, ϑ, h∆ , h∆

, ϑ

Met Oxid

g

Schm ad

adL L Fig. 3-22: Mass flow in metal combustion

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

0 500 1000 1500 2000 2500 3000 3500 4000

Temperature [K]

Spezific

heat capacity [kJ/k

g K

]

Fe3O4

Cr2O3

Al2O3

MgO

Fig. 3-23: Spezific heat capacity of metal oxids

Fuel

ρ

Net heating value

Upper heating value

kg/m3 iN.

MJ/m3 MJ/kg MJ/m3 MJ/kg

Hydrogen Carbon monoxide Methane Propane

0.090 1.25 0.718

2.01

10.8 12.6 35.9

93.2

120 10.1 50.0

46.4

12.8 12.6 39.8

101.2

142 10.1 55.4 50.3

Natural gas L Natural gas H Cokeoven gas Top gas Biogas

0.83 0.79 0.51

1.25 – 1.35 0.92 – 0.98

31.8 37.4 17.5 3.3 – 3.7

18 - 21

38.3 47.3 34.3 2.4 – 2.8 18 - 23

35.2 41.3 19.7 3.3 – 3.7 20 - 24

42.4 52.3 38.6 2.5 – 2.8 20 – 25

Light oil Heavy oil Diesel oil Petrol Methanol Ethanol

850 950 840 730

812 806

- - - -

16.2 21.6

42.7 41.0 42.7 43.5 19.9 26.8

- - - - - -

45.4 43.3 45.4 46.5 22.7 29.7

Graphite Coal Coke Raw lignite Lignite dust Wood (dry)

2000 1300 1000 1200

1000 700

- 38,6 28,7 -

19 - 22 12 - 15

33.8 29.7 28.7 8.5

19 - 22 17 - 21

- - - -

- -

33.8 31.7 28.9 10.5

- 18 - 22

Table 3-1: Reference values for heating values of fuels

Fuel Treatment Demand Energy In MJ/kg In % from heating value

Natural Gas Light Oil Heavy Oil Coal Coke Lignite Electricity without distribution Electricity with distribution

4.6 4.7 4.1 2.1 6.0 0.3

0.33 kWhel/kWhprim

0.315 kWhel/kWhprim

13 11 10 7 21 3

Table 3-3: Treatment Demand Energy for Fossil Fuel according to Ffe [1.2] and Mauch [1.1]

Gas cp

KJ/(kgK) n -

iρ

kg/m3

M~

kg/kmol

NO2 O2 CO2 H2O CO H2

1.00 0.90 0.84 1.75 1.00 14.20

0.11 0.15 0.30 0.20 0.12 0.05

1.234 1.410 1.939 0.793 1.234 0.088

28.0 32.0 44.0 18.0 28.0 2.0

Table 3-4: Specific heat capacity and density at 273 K and 1 bar

Heating power in kW

until 1983 up 1983 up 1988 up 1998

4 – 25 15 14 12 11 25 –50 14 13 11 10 > 50 13 12 10 9

Table 3-5: Limit values in % for loss of flue gas for oil and gas heating according to

installation year

kJ kcal kWh kg SKE kg RÖE m3 Natural

Gas 1 Kilojoule (kJ) - 0,2388 0,000278 0,000034 0,000024 0,000032 1 Kilocalorie (kcal) 4,1868 - 0,001163 0,000143 0,0001 0,00013 1 Kilowatt hour (kWh) 3 600 860 - 0,123 0,086 0,113 1 kg coal equivalent (SKE)

29 308 7000 8,14 - 0,7 0,923

1 kg Crude oil equivalent (RÖE)

41 868 10 000 11,63 1,428 - 1,319

1 m3 Natural Gas 31 736 7 580 8,816 1,083 0,758 - Table 3-2: Conversions for energy units

Metal Oxid O L h∆ MetM~

Meltϑ Melth∆ c ( )1ad =λϑ

Met

2O

kg

kg

Met

Air

kg

kg

Metkg

MJ

kmol

kg C°

Oxidkg

kJ

Kkg

kJ

Oxid ⋅ 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