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Process Engineering
Training ProgramMODULE 8
Application of Heat and Mass BalancesSection Content
1 Application of H eat Balances to Process, Evaluation
2 H eat Balances –Im perial U nits
3 Paper 12 –Heat Balances
4 H eat Transfer
5 H eat Transm ission
Presentations
MASS, HEAT AND ENERGY BALANCES
HEAT TRANSFER
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Blue Circle Cement
PROCESS ENGINEERING TRAINING
PROGRAM
Module 8
Section 1
Application of Heat Balances and Mass
Balances to Process, Evaluation
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Application of Heat Balances
to Process Evaluation
P LayneJ. A. Stringer
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1 INTRODUCTION
The purpose of the rotary kiln is to increase the temperature of the raw material so that the chemical reactions
leading to the formation of cement clinker can take place. The heat required to increase the temperature of the
feed and for the chemical reactions is generated by burning fuel.
It is clearly desirable on the grounds of cost to operate the kiln with as low a consumption of fuel as possibleconsistent with a high output of good quality clinker and to this end it is necessary to understand how the heat
generated by burning fuel is utilized.
Figure 15.1 shows the temperature of material and gas along a kiln and the five zones into which it is
conventional to divide the kiln. In the first two zones, the temperatures are relatively low and the processes
which the feed undergoes are mainly physical i.e. drying and preheating. In modern practice when the
moisture content of the feed is relatively low, these processes are carried out in a separate preheater. In thethird or calcining zone, chemical reactions start to take place, in particular the dissociation of calcium
carbonate. In this zone it will be noted the material temperature rises only slightly despite a big change in gas
temperature. In the fourth zone, the material is raised to around 1400 0 C at which the main clinker forming
reactions can occur. The burning of fuel is arranged so that the gas temperature is a maximum in this zone.
Finally ,in the fifth zone, the clinker is cooled by gas at a lower temperature. This process, of course, is largely
performed in a separate cooler.
The main quantities of heat involved in carrying out the processes in each of the five zones may be fairly
readily determined and hence the overall heat requirement of the kiln system can be obtained.
The relative length of each of the five zones is determined by several factors (e.g. difference in temperature of
gas and material, gas velocity, volume loading) whose relationship is by no means fully understood.
2 HEAT AND MASS BALANCES
The economic aspects of any system involving the utilization of fuel can generally be tied to the thermal
efficiency of the system. To determine this efficiency a heat balance has to be performed upon the system
under equilibrium conditions. In this balance the heat supplied to, and lost from the system are equated. This
balance takes no account of the internal modes of heat transfer but rather shows in the relative distribution of outgoing quantities what the input is required for.
Figure 15.2 illustrates some of the parameters considered in making a heat balance for a wet process kiln with
Fuller cooler. The dotted line encloses the system. Heat flows across the dotted line only are calculated; heat
h h h b l h b d i h ld i ld d il d f ll f h ili i
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When the heat balance has been constructed it should yield a detailed account of all sources of heat utilization
i.e. which functions use large amounts of the fuel, and which functions use a negligible amount of fuel. If
greater thermal efficiency can be achieved in the system it will show which items are worthy of greater
attention. In the wet process rotary kiln system a heat balance will show that virtually all the heat input is
utilized between
(a) the theoretical heat of reaction,
(b) vaporization of the slurry moisture,
(c) sensible heat of the exit gases,
(d) shell losses
3 CONSTRUCTION OF THE HEAT BALANCE
A list of kiln data is shown in Table 15.1 to illustrate the measurements which are required to perform a heat
balance, together with typical figures. The amount of data required depends somewhat upon the accuracy
required of the resulting balance; the relative merits of the additional data are discussed in the appropriate
sub-sections.
The base lines upon which the heat balance is performed are selected mainly for simplicity of calculation. The
quantities of heat involved are based upon lkg. of clinker and listed as kcal./kg. These may be converted to per
cent standard coal/clinker by dividing the kcal./kg by 70 (standard coal is a theoretical coal with a gross
calorific value of 7000 kcal./kg.). The quantities of sensible heat are calculated from a datum temperature
which can be taken as ambient or some similar fixed value (e.g. 200 C).
As an example, a heat balance on a wet process coal fired kiln will now be calculated. The relevant kiln data
and analyses of raw meal, clinker, and fuel are set out in Tables 15.1 and 15.2. The data available in practice
may be more or less than this amount, and it is thus not possible to completely standardise the procedure of
heat balance determination.
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3 1 PRELIMINARY CALCULATIONS
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3.1 PRELIMINARY CALCULATIONS
From the data in the tables, the first requirement is to calculate the undetermined solid mass flows.
The raw coal consumption is 0.251 kg./kg. of clinker. The coal moisture is 5%, thus the consumption of dry
coal will be
0.251 x( )
−
100
5100 = 0.238 kg./kg. of clinker
The ash content represents 15.3% of the dry coal, equivalent to 0.153 x 0.238 = 0.0364 kg./kg. of clinker. It is
assumed that all the ash is absorbed in the clinker, therefore, the clinker derived from raw meal = 1 - 0.0364 =
0.9636 kg./kg. of clinker.
The raw material also suffers a loss on ignition on passage through the kiln. Loss on ignition is determined by
placing a small weighed sample of material in a cool furnace and raising the temperature to 900o C over 1
hour. After 3 - 4 hours at between 850o - 950o C the sample is removed, cooled in a desiccator and reweighed.
The loss of weight determined represents mainly vapor from associated and combined water and carbon
dioxide from carbonate dissociation and organic matter combustion.
The raw meal suffers a loss on ignition of 35.28%, so that the quantity of raw meal required to produce this
0.9636 kg. of clinker =
( )( )28.36100
1009636.0
−×
= 1.52 kg
The raw meal further suffers a degree of dust loss, which is 0.06 kg./kg of clinker. The loss on ignition of the
partly decarbonated dust is 20.2%, equivalent to
0.06 x =( )
( )28.36100
2.20100
−−
= 0.075 kg. of dry meal/kg of clinker
The total raw meal required to produce lkg of clinker is therefore 1.52 + 0.75 = 1.595 kg. A slurry moisture of
39.2% will be equivalent therefore to
clinkerofwater/kgofkg1 02839.2x1.595
= 3 3 POTENTIAL HEAT IN COAL
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3.3 POTENTIAL HEAT IN COAL
Raw coal burnt per kg. of clinker is equivalent to 0. 238kg. of dry coal .
Gross calorific value of dry coal = 6750 kcal./kg. Heat supplied by burning coal,0.238 x 6750 = 1607 kcal./kg
of clinker.
It will be noted that the gross calorific value has been used in which it is assumed that the water vapor from
the combustion of the dry coal is condensed. In fact this water is carried out of the kiln as vapor and an
allowance has to be made for this in calculating the sensible heat of the exit gases.
3.4 POTENTIAL HEAT IN RAW MATERIALS
The dry raw meal contains 0.07% of combustible organic carbon equivalent to
1.595 x100
07.0= 0.0011 kg./kg. of clinker
Calorific value of carbon = 7828 Kcal./kg.
Heat supplied by burning carbon is 0.0011 x 7828 = 8.6 Kcal./kg. of clinker
3.5 SENSIBLE HEAT IN COAL
If the same quantity of heat is supplied to the same mass of different materials, and there are no chemical or
physical changes of state, the resulting temperature rises are not the same, but depend on the specific heat of
the material.
Supposing that a quantity of heat Q is supplied to a given mass of material m, leading to a rise in temperature
of the material from temperature 1t to 2t then
Q = m S ( 2t - 1t )
where S is the mean specific heat of the material over the temperature range 1t to 1t Some useful values of
specific heats are shown in Tables 15.3 and 15.4.
The sensible heat of a material is calculated in the above manner by calculating the heat contained in the
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TABLE15.2 FUEL, FEED, CLINKER AND DUST DATA
COAL CLINKER
Moisture 5.0% Insoluble Residue 0.21Calorific Value of Dry
Coal
6750
kcal/kg
Si02 21.63
Analysis of Dry Coal A1203 6.57
Ash 15 3% Fe203 2 78 The coal is fed to the mill at 20oC i e the datum temperature to yield a 2t - 1t value and hence sensible heat
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The coal is fed to the mill at 20 C, i.e. the datum temperature, to yield a 2t 1t value and hence sensible heat
value of zero in this case.
3.6 SENSIBLE HEAT IN COMBUSTION AIR
It is calculated later that the total air drawn into the system is 4,457 kg./kg. of clinker. Assuming this air is all
at 22oC, its sensible heat is 4.457(22-20)0.24 = 2.14 kcal./kg. of clinker.
TABLE 15.3
MEAN SPECIFfC HEATS OF UNDISSOCIATEO GASES
BETWEEN 20'C AND t'C
toC 02 N2 Air Co C02 H20 S02vapor
20 0.218 0.248 0.240 0.249 0.198 0.435 0.143
100 0,220 0.248 0.240 0.249 0.211 0.447 0.147
200 0.223 0.249 0.242 0.250 0.221 0.452 0.150
300 0.227 0.250 0.243 0.252 0.230 0.457 0.154400 0.230 0.252 0.246 0.254 0.238 0.463 0.157
500 0.234 0.254 0.248 0.257 0.246 0.471 0.161
600 0.237 0.256 0.250 0.259 0.252 0.478 0,164
700 0.240 0.258 0.253 0.262 0.258 0.486 0.167
800 0.243 0.261 0.256 0.265 0.263 0.495 0.170
900 0.245 0.264 0.258 0.268 0.268 0.502 0.173
1000 0.247 0.266 0.260 0.270 0.271 0.512
1100 0.249 0.268 0.263 0.273 0.275 0.519
1200 0.251 0.271 0.265 0.275 0.278 0.527
1300 0.253 0.272 0.267 0.277 0.281 0.532
1400 0.255 0.275 0.269 0.278 0.284 0.542
1500 0.256 0.276 0.271 0.280 0.286 0.547
1600 0.258 0.278 0.272 0.282 0.289 0.5531700 0.258 0.280 0.273 0.283 0.291 0.561
1800 0.260 0.281 0.274 0,285 0.293 0.567
1900 0.262 0.282 0.276 0.286 0,294 0.573
2000 0.263 0.284 0.277 0.287 0.296 0.578
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3.7 SENSIBLE HEAT IN RAW MATERIALS
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Slurry is fed to the kiln at 17oC, i.e. less than the datum temperature, therefore the sensible heat of the slurry
will be a negative value on the input side of the heat balance.
The specific heat of the dry raw material is taken as 02, (the specific heats of the main constituents are all
approximately 0.2).
Sensible heat in the dry raw material = 1.595(17 - 20)0.2 = -0.957 kcal./kg. of clinker.
Sensible heat of slurry moisture = 1.028(17 - 20)1 = -3.84 kcal./kg. of clinker. Total sensible heat of feed =
-4.041 kcal./kg. of clinker.
3.8 HEAT OUTPUT
The heat output is also the sum of various components; but these are of a rather more complex nature than the
input variables.
Some basic knowledge of heats of reaction, Dalton's Law, and dewpoint are useful, and brief details on each
of these can be found in Appendix 1.
3.9 THEORETICAL HEAT OF REACTION
The heat required to convert raw meal into clinker can be calculated from first principles using basic heat of
reaction data (Appendix 1, Table 15.6) : the composition of the raw meal is known. This method is illustrated
and the effects of different lime saturation factors, silica ratios, alumina ratios, free lime, coal ash absorption
and clay mineral type are discussed in Research Department Report SR-64/28/R-8.
Various formulae have been developed by zur Strassen(1957) and Crichtoi (1938) to permit more rapid
estimation of the theoretical heat. A formula of zur Strassen, which gives good agreement with calculations
from first principles, is used here:
Qt = 2.22A + 6.48Mc + 7.646Cc - 5.116S - 0.59F
where Qt is the theoretical heat in kcal./kg of clinker
A is the weight in g of Al2O3 per 100g. of clinker
Substituting in this formula data from Appendix 1, Table 15.6 gives
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Qt = 2.2 x 6.57 + 6.48 x 1.09 + 7.646 x 66.31
-5.116 x 21.63 - 0.59 x 2.78
= 417 kcal./kg. of clinker
In general theoretical heats of all clinker fall quite close to 420 kcal./kg, and this value can be adopted when
insufficient data is available to apply the above formula.
3.10 HEAT TO EVAPORATE WATER
The slurry moisture is equal to 1.028 kg./kg. of clinker. Incorporated in this figure is the moisture content of
the dust losses, equal to =× 028.1595.1
075.00.048 kg./kg of clinker. Treating the dust loss moisture separately this
leaves 1.028-0.048 = 0.98 kg./kg. of clinker of slurry moisture. It is assumed this water is evaporated at 20o C,
at which temperature the latent heat is 586 kcal./kg. Therefore the heat required for the evaporation of slurry
moisture is
0.98 x 586 = 574.3 kcal./kg. of clinker
The raw material contains 1.34% of combined water equal (deducting the dust loss component) to
100
34.152.1 ×= 0.0204 kg./kg. of clinker. The heat required to evaporate this water at 20oC is 0.0204 x 586 =
11.9 kcal./kg. of clinker.
(Note the heat of dissociation of combined water is included in the theoretical heat).
The percentage of moisture in the coal is 5.0%, equal to 0.251 x100
0.5 = 0.013 kg. of water/kg. of clinker.
The heat required to vaporize this moisture at 20oC = 0.013 x 586 = 7.59 kcal./kg. of clinker.
In calculating the heat input to the kiln, the gross calorific value of the coal was used, thereby implying that
the water vapor from the combustion of the hydrogen in the coal was condensed. In calculating the heat output
of the kiln, therefore, the latent heat of vaporization of this water has to be included. The amount of water in
3.12 COMBUSTION PRODUCTS
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The carbon in the fuel and raw material are burnt thus
C 02 CO2
+ →12kg. 32kg. 44kg.
(A small fraction of the carbon is burnt to CO and not CO2 this is allowed for later).
The hydrogen in the fuel is burnt thus
2H2 O2 2H2O
+ →4kg. 32kg. 36kg.
The sulphur in the fuel-is burnt this
S O2 SO2
+ →32kg. 32kg. 64kg.
On the basis of I kg. of clinker the fuel combustion should yield
0.238 x100
76 x
12
44 = 0.663kg. of carbon dioxide
0.238 x4
36
100
4.4× = 0.094kg of water vapor
44 0.7× = 0. 0257 kg. of carbon dioxide/kg. of raw meal
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1210× 0. 0257 kg. of carbon dioxide/kg. of raw meal
equivalent to .0257 x 1.595 = 0.0409 kg. of carbon dioxide/kg. of clinker.
A small part of this oxygen for combustion comes from the coal; per kg. of clinker this is
0. 238 x100
8.1= 0. 0043kg
The weight ratio of nitrogen to oxygen in air is 3.31 (assuming the nitrogen includes all the inert gas).
Therefore the weight of nitrogen in the air required for combustion is (0.57 + 0.0297 - 0.0043) x 3.31 = 1.971
kg./kg. of clinker.
There is also some nitrogen in the coal equal to
0.238 x100
0.9= 0.0021 kg./kg. of clinker
3.13 EXCESS AIR IN THE EXIT GASES
We must now consider the excess air in the exit gas (i.e. air in excess of the combustion requirements) as
shown in the exit gas analysis.
CO2 28.1% by volume
CO 0.1% by volumeO2 0.85% by volume
N2 (by difference) 70.95% by volume
Σ = 100.0
If the combustion had been complete the volume of CO would have burnt to an equal volume of CO2 by
combining with half its volume of O2 The gas analysis would have then been
CO2 28.2% by volume
O2 0.8% by volume
N 71 00% b l
The O2 content of 0.8% represents the excess air. The ratio by volume of nitrogen to oxygen in air is 3.76,
h f h i h i i h i i b i h
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therefore the N2 content representing the excess air is 0.8 x 3.76 = 3.1%, the remaining N2 being the
combustion-air and the coal. The N2 content being due to combustion air is
(71.0 - 3.1) =+
×0.00211.971
1.97167.8%
The percentage of excess air is, therefore
%6.410067.8
3.1=×
The weight of nitrogen in the excess air is
×100
4.61.971 = 0.0907 kg./kg. of clinker
and the weight of complimentary oxygen is
=31.3
0.09070.0274 kg./kg. of clinker
The total weight of air entering the kiln (i.e. combustion air plus excess air), per kg. of clinker is
Combustion air .595 + 1.971 + 2.566
Excess air 2.566 x 4.6/100 =0.118
Total 2.684
3.14 OTHER SOURCES OF WATER VAPOUR
The combustion of the fuel provides one source of water vapor, the other sources consisting of the feed, coal
moisture, and included water vapor in the combustion air.
h l i ff b h f d i k /k f li k
Some. of the feed leaves the kiln as dust which is only partially decarbonated. Loss on ignition of the dust is
20 2% compared with 36 3% of the feed
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20.2% compared with 36.3% of the feed.
Assuming the losses on ignition represent the degree of decarbonation, the percentage decarbonation of the
dust on a loss free basis is
%6.55100
3.36100
3.36
2.201002.20
3.361003.36
=×
−
−− −
Therefore the carbon dioxide evolved by the dust is
55.6 x (0.3487 + 0.0257) = 0.209 kg./kg. of dust
100
The dust loss of 6% on clinker is equivalent to 0.075 kg. of dry raw meal/kg. of clinker. Therefore the carbon
dioxide derived from the feed is
582.0209.0100
6100
2.5734.870.075).-(1.595 =×+
+ kg./kg clinker
(It has been assumed that the dust has been completely dried, i.e. slurry moisture and combined water have
been removed).
3.16 HEAT CONTENT
Summation of the constituent gas weights per kg. of clinker results in the following (in kg.).
H2O from feed 1.049
from combustion of coal 0.094
from coal moisture 0.013from water vapour in air 0.0133
Total 1.1693
SO2 from combustion of coal 0.0076
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O2 from excess air 0.0274
N2 from coal 0.0021
from combustion air 1.9710
from excess air 0.0907Σ
2 N= 2.0638
The heat required to raise these gases from 20oC to 212oC, a temperature difference of 192oC, is
(1.1693 x 0.452 x 192)+ (1.245 x 0.222 x 192)+(0.0076 x 0.15 x 192)+ (0.0274 x 0.223 x 192)+(2.0638 x
0.249 x 192) = 254.5 kcal./kg. of clinker.
Sensible heat of exit gases = 254.5 kcal./kg. clinker.
3.17 COOLER EXAUST AIR
931 kg./min of air is exhausted from the cooler at 115o
C. I kg. of clinker is made every 0.0019 min. Theweight of air/kg. of clinker is therefore 931 x 0.0019 = 1.773 kg./kg. of clinker.
The sensible heat contained in this air is 1.773 x (115 - 20) x 0.241 = 40.6 kcal./kg. of clinker. With a rotary or
planetary cooler, this item would not occur.
The total air drawn into the kiln and cooler per kg. of clinker, (in kg.) is
Combustion Air 2.566
Excess Air 0.118
Cooler Exhaust Air 1.773
4.457 kg.
This figure has been used in section 3.6 to calculate the sensible heat of air entering the system.
3.18 SENSIBLE HEAT OF CLINKER
The determination of the shell losses from kilns, coolers etc. is a difficult problem.
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From the outer surface of the kiln shell heat is transferred to the surroundings by two means. Radiation takes
place according to an equation of the form
4
3
4
2r TTAq −αε=
where 2T and 3T are the absolute temperatures of the shell and the surroundings respectively, ε is theemissivity of the surface and γ is a constant. Convection takes place according to an equation of the form
( )32c tthAq −=
where 2t and 3t are the temperature of the shell and the surroundings respectively and h is a coefficient whosevalue depends on a number of factors including the dimensions of the kiln and the air velocity over the
kiln.
By measuring the temperature and emissivity along a kiln shell the heat loss can be estimated using formulae
of the form of equations noted above. Numerous measurements have to be made as there is a very large
variation in the temperatures at various points on the shell. The temperature at any particular point depends on
the corresponding temperatures in the kiln, the type and thickness of the brickwork and the thickness of anycoating. The shell loss from a modern kiln is of the order of 4070 kcal./hr.m 2 of surface, though a very wide
variation is to be expected from this value.
Measurements have also to be made of cooler, preheater, coal mill and connecting ducting temperatures as
there is a substantial, though relatively smaller, shell loss from these as well.
It will be evident from the above equation that the shell loss depends on the temperature conditions in the kiln
and the kiln geometry. On the whole the temperature conditions in a kiln do not vary much with output. (There
is, however, a tendency for temperature to rise with output), In consequence the shell loss remains
substantially constant whatever the output. In this way the shell loss differs from for example, the exit gas loss
and the clinker loss which increase with output.
For the purpose of the heat balance, the total shell loss of the system is taken as 1.11 x 10 5 kcal./min. This isequivalent to 1.11 x
510 x 0.0019 = 210.9 kcal./kg. of clinker.
3.20 HEAT LOST IN MAKING DUST
Th d l i kil i id bl i i d i i d i i h f diffi l k
The percentage decarbonation has been estimated as 55.6% equivalent to 0.209 kg. of carbon dioxide per kg.
f d t A i thi b di id t f th di i ti f l i b t th i ht f
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of dust. Assuming this carbon dioxide to come from the dissociation of calcium carbonate, the weight of
calcium carbonate dissociated is
0.06 x 0.209 x44
100 = 0.029 kg./kg. of clinker
At 20oC, the heat of dissociation of calcium carbonate is 422 kcal./kg. hence the heat required to partially
decarbonate the dust is .029 x 422 = 12.24 kcal./kg. of clinker.
The heat loss associated with the dust is, therefore, 2.42 + 12.24 =14.66 kcal./kg. of clinker.
Also associated with the dust is the heat required to dry its slurry moisture and combined water.
The slurry moisture as shown in section 3.10 is equal to 0.048 kg./kg. of clinker.
The heat required for the evaporation of this moisture at 20oC (again using a latent heat of 586 kcal./kg.) is
0.048 x 586 = 28.13 kcal./kg. of clinker.
The combined water (1.34%) amounts to 0.075 x100
34.1 = 0.001 kg./kg of clinker.
The heat required to evaporate this water at 20oC is 0.001 x 586 = 0.59 kcal./ kg. of clinker.
The total heat required for evaporation of water associated with the dust is therefore 28.13 + 0.58 = 28.72
kcal./kg. of clinker.
The total heat loss associated with the dust is therefore 14.66 + 28.72 = 43.38 kcal./kg. of clinker.
It will be noted that the heat required to vaporize and heat up to the exit gas temperature the water in that part
of the feed lost as dust and also the sensible heat of the carbon dioxide evolved by the dust have been
estimated earlier. It is, of course, possible to consider those heat quantities under the heading of heat lost in
making dust.
On some works dust is returned to the kiln. Where this happens calculations should be based on the net dust
loss (i.e. total dust loss. minus that returned), the returned dust being considered as part of the feed.
3.21 HEAT LOST BY INCOMPLETE COMBUSTION
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The presence of carbon monoxide in the exit gas indicates that combustion of the carbon in the fuel (or raw
meal) has not been complete and this represents a loss of heat.
The weight of carbon monoxide is calculated from the exit gas analysis
% by volume % by volume
after elimination of CO
CO2 28.1 28.2
CO 0.1
O2 0.85 0.8
This 0.8% was shown in section 3.13 to represent 0.0274 kg. of oxygen/kg. of clinker. Therefore the oxygen
required to combine with the carbon monoxide present is
0.0274 x8.0
0.8)-(0.85= 0.0017 kg./lg. of clinker
Carbon monoxide reacts with oxygen thus
2CO + O2 → 2CO2
(56kg.) (32kg.) (88kg.)
Therefore the weight of carbon monoxide combining with 0.0017kg. of oxygen is
0.0017 x32
56 = 0.003kg
The heat lost in burning carbon to carbon monoxide instead of carbon dioxide is 2417 kcal./kg of carbon
monoxide. The heat lost by incomplete combustion is therefore 0.003 x 2417 = 7.25 kcal./kg of clinker.
TABLE 15.5
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HEAT BALANCE
HEAT INPUT kcal./kg. of % of heat input
Clinker Coal
Combustion 1607.0 99.59
Sensible Heat 0.0 0
Feed
Combustion of Organic Matter 8.60 0.53Sensible Heat - 4.04 - 0.25
Air,
Sensible Heat 2.13 0.13
TOTAL 1613.69 100.00
HEAT OUTPUT
Theoretical Heat 417.00 25.84
Evaporation of Water
Heat to vaporize slurry moisture 574.30 35.59
Heat to vaporize combined water in feed 11.90 0.74
Heat to vaporize coal moisture 7.59 0.47
Heat to vaporize water from combustion 54.9 3.41
Sensible Heat in Exhaust Gases
Sensible Heat of Exit Gases 254.5 15.77
Sensible Heat of Exhaust Air from Cooler 40 60 2 52 3.22 HEAT UNACCOUNTED FOR
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All the various items in the heat balance have now been calculated, and are summarized in Table 15.5. In this
particular case the heat unaccounted for is 28.8 kcal./kg. of clinker, only 1.8% of the total heat input.
In making any heat balance, there is likely to be some heat unaccounted for. The relative size of this factor
gives some measure of the accuracy of the balance and the data on which it is based. However, it has to be
remembered that an error in one item may be cancelled out by errors in other items, resulting in a misleadingly
small out of balance.
Although inaccurate data or the failure to consider certain factors are the most likely causes of a large heat
unaccounted for, the possibility of unsteady conditions at the time of making measurements should also be
taken into account, For example, it will be readily appreciated that after lighting up a cold kiln the heat input
will exceed the heat output until steady conditions are reached.
In certain instances, the determination of all the items (and in particular the shell loss) in the heat balance may
not be possible and these items are then included as heat unaccounted for.
4 USES OF THE HEAT BALANCE
4.1 SIMPLIFICATION OF THE HEAT BALANCE
Calculation of a heat balance along the lines described above is lengthy and tedious, and may require data
which is not always available. Certain simplifications may be justified, however, without too much
approximation.
On the heat input side of the balance it is reasonable to treat the burning of the fuel as the sole source, as the
other inputs rarely exceed 1% of the total.
On the heat output side of the balance the quantities are more evenly divided. As indicated in section 3.9 it is
reasonable to assume a value of 420 kcal./kg. of clinker for the theoretical heat. The heat required to vaporize
the slurry moisture represents the major constituent on the output side, but can fairly readily be calculated. The
heat to vaporize the combined water in the feed and coal moisture can only be ignored if the relevantcontributions in the raw meal and coal compositions are also small, i.e. < 2%, and < 20% respectively. The
sensible heat in the exit gases represents the most tedious part of the calculation, but is also one of the major
constituents in the balance. The sensible heat of clinker can be calculated very readily. The shell loss cannot
be calculated with any accuracy without numerous surface temperature measurements. In general the shell loss
If suitable data is available, either first hand or by reasonable approximation then this type of calculation can
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be programmed. By using a computer it is possible to reproduce the results of the above heat balance within a
matter of seconds. This method also has much greater flexibility as it is also possible to vary some of the input
data and predict their likely effects upon fuel economy.
A computer program has been developed by Eng. R & D, Barnstone on similar lines to the above method to
construct a kiln and cooler heat balance.
By introducing a suitable loop into the program it is possible without introducing large errors to investigate the
effects of selected input variables upon the heat requirements of the kiln. The variables investigated using this
technique are slurry moisture, back end temperature, back end oxygen, dust losses, and shell losses. The
results of these variations are plotted graphically in Fig. 15.3 (a) - (e), and discussed below based on the
sample calculation.
4.2.1 SLURRY MOISTURE
Variation in slurry moisture content has a marked effect upon heat input in that a reduction of 0.5% in slurry
moisture yielded a saving of about 1% in coal consumption. By the use of suitable additives greater reductions
may be obtained in slurry moisture, and hence coal consumption. It is therefore important to run at the lowest practicable slurry moisture content in the interests of fuel economy.
4.2.2 BACK END TEMPERATURE
Back end temperature reduction also produces a significant effect upon heat requirement. A reduction of 10oC
in back end temperature resulted in a fuel saving of about 1%. Some limitations may be encountered with for example dewpoint (leading to corrosion), but again small reductions can produce appreciable savings.
4. 2. 3 DUST LOSSES
A large source of fuel wastage is seen in the effects of dust loss. If in the sample heat balance the dust loss
were doubled, the fuel requirement would rise by a factor of about 6 ½ %. On some kilns dust losses of theorder of 24%, four times the sample value, are obtained representing an enormous waste of fuel. The dust
removed also provides a large disposal problem, as it is rarely in the case/of a wet process returned to the kiln
(by e.g. insufflation at the kiln hood).
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4.24 SHELL LOSSES
Sh ll l t f i l l ti f th h t l i b t 13% i thi R d ti i h ll
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Shell losses represent a fairly large proportion of the heat losses, i,e. about 13% in this case. Reduction in shell
losses could only be gained by improving the insulation of the kiln lining which is rarely possible. If however
improved insulation were possible, then a reduction of say 25% in shell loss could yield a saving of heat input
of about 3%.
4.2.5 BACK END OXYGEN
Back end oxygen content, as shown on Fig, 15.3 (e), has a significant but less drastic effect upon heat
requirements than the above variables. Accurate control of the back end oxygen is still a very effective method
of saving fuel, as a reduction from say 2.5% to 0.5% can save about 1% of fuel consumption. It is therefore
important to meter the back end oxygen content as accurately as possible, and work at the lowest practicable
value.
It is not possible to apply this type of treatment with sufficient accuracy to a practical system as it considers
the effects of one variable isolation. In practice changes in one input variable would affect others, e.g. changes
in slurry moisture would result in changed values of back end temperature, dust loss, etc. The heat balance
does however highlight the order of savings which may be achieved by small improvements in the more
significant variables, i.e. slurry moisture, back end temperature, and dust loss. As fuel represents a major
proportion of production cost even small improvements in fuel efficiency can be very worthwhile.
5 REFERENCES
Crichton, D.C., 1938, Rotary Kiln Heat Balance by Equations. A.p.C.M. Ltd, Research Dept. 6 pp.
zur Strassen, H., 1957. The Theoretical Heat Requirements for Cement Burning. Zement - Kalk - Gips, 10.1., p 1-12.
APPENDIX I - HEAT OF REACTION, DALTON'S LAW, AND DEWPOINT
1 HEAT OF REACTION
In order to carry out certain chemical reactions it is necessary to supply heat. These reactions are said to be
endothermic. An important example in this context is the dissociation of calcium carbonate.
(i.e. the products of the reaction are assumed to be brought to the initial temperature of the reactants) at some
arbitrary reference temperature (e.g. 0oC, 20
oC). Table 15.6 contains the heats of reaction at 20
oC of the main
ti i i th t i l i th kil It h ld b i t d th t th ti d t il
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reactions occurring in the material in the kiln, It should be appreciated that these reactions do not necessarily
take place at the reference temperature of 20oC.
The heat of reaction at some other temperature, t, can be found from the data in Table 15.6 by assuming the
reactants are brought from t to 20o
C then react and the products are taken from 20o
C to t.
2 DALTON'S LAW-OF PARTIAL PRESSURE
This law states that the pressure exerted by a mixture of non-reaction gas is equal to the sum of pressures
which each gas would exert if it alone occupied the total volume of the mixture at the same temperature i.e.
PV = V (P1 + P2 + P3 . . . .) etc. where P and V are the pressures of the mixture and P1, P2, P3, etc. are the partial pressures of the individual gases,
In this context the law finds an important application in connection with the dewpoint of gases; this is dealt
with in the next section.
The partial pressure of carbon dioxide in kiln gases determines the conditions at which the decarbonation
reactions occur (see Figure 15.4). For any particular temperature there is a partial pressure of carbon dioxide
below which dissociation occurs.. -
CaCO3 → CaO + CO2
and above which the reverse reaction takes place:
CaO + CO2 → CaCO3
3 DEWPOINT OF A GAS
Consider a gas in which the partial pressure of water vapor is P w . On cooling the gas temperature is reached
where the water vapor begins to condense. This temperature is the dewpoint of the gas and it varies with P was shown in Figure 15.5. P w is equal to 1 atmosphere (760mm. Hg) at the boiling point of water.
The dewpoint temperature of a gas can be calculated from the weight composition as illustrated.
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Blue Circle Cement
PROCESS ENGINEERING TRAINING
PROGRAM
Module 8
Section 2
Heat Balances – Imper ial Units
PAPER NO.5
HEAT BALANCES
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HEAT BALANCES
1. Introduction
2. Objectives of the Heat Balance
3. Internal Heat Exchange
4. Control Volume
5. Units
6. Mass Balance
7. Reference Temperature
8. Sensible Heat
9. Heat of Reaction
10. Combustion of Coal
11. Latent Heat
12. Heat of Clinker Formation (Theoretical Heat)
13. Shell Losses
HEAT BALANCES
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(BTU/lb UNITS)
1. INTRODUCTION
The purpose of the rotary kiln is to increase the temperature of the raw material so that the chemical reactionsleading to the formation of cement clinker can take place. The heat required to increase the temperature of the
feed and for the chemical reactions is generated by burning fuel.
The plant operator is interested in the economic aspects of kiln fuel utilization. For a given kiln system this is
governed by the thermal efficiency at which the system is being operated. Clearly it is desirable on the grounds
of cost to operate the kiln at the lowest possible fuel consumption. But this must be consistent with the highest practicable output of acceptable quality clinker.
2. OBJECTIVES OF THE HEAT BALANCE
The heat balance equates the heat supplied to - consumed in – and lost from the kiln system under equilibrium
(steady normal operating) conditions, as shown schematically in Fig.l. Consideration of the heat balance
enables the following objectives to be met:
a) To account for the energy actually used
b) To monitor plant performance regularly
c) To evaluate the effects of changes in materials, plant and process operations on fuel consumption
d) To decide where to give priority in the works improvement plan to reduce fuel consumption
e) To provide data for improved plant design, i.e: refurbishment, modification, new plant
f) To achieve the basic objectives of kiln operation, i.e. maximum output of acceptable clinker at
lowest possible fuel consumption.
3. INTERNAL HEAT EXCHANGE
Fig.2 shows the temperature of material and gas along a kiln and the five zones into which it is conventional
to divide the kiln. In the first two zones, the temperatures are relatively low and the processes which the feed
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undergoes are mainly physical, i.e. drying and preheating. In modern practice these processes are carried out in
a separate preheater. In the third zone, chemical reactions start to take place, in particular the dissociation of
calcium carbonate (calcining or decarbonation). In preheater kilns about 30% and in precalciner kilns up to
95% of this process occurs in the preheater system. In this zone, it will be noted that the material temperature
rises only slightly despite a big change in gas temperature. In the fourth zone, the material is raised to above1400°C at which temperature the main clinker-forming reactions occur. The burning of fuel is arranged so that
the gas temperature is a maximum in this zone. Finally, in the fifth zone, the clinker is cooled by gas at a
lower temperature. This process, of course, is largely completed in a separate cooler.
The main quantities of heat involved in carrying out the processes in each of the five zones can be readily
determined, and hence the overall heat requirement of the kiln system can be obtained.
The relative length of each of the five zones is determined by several factors (e.g. difference in temperature of
gas and material, gas velocity, volume loading), and there is considerable overlapping of the processes.
It is the external heat exchange factors with which we are primarily concerned in the heat balance, and the
principles to be discussed in this paper are listed in Fig.3.
4. CONTROL VOLUME
4.1 Concept of Control Volume
The control volume is the system enclosed by external boundaries across which the heat flows occur. The heat
balance is concerned with these cross boundary flows which must be measured/calculated. If is these heat
flows that the operator aims to control as much as possible.
Fig.4 shows the control volume for a wet process kiln with grate cooler. Feed and fuel and primary and
secondary air enter the system. Clinker and flue dust, kiln exhaust gases and cooler exhaust air leave the
system. Some heat is also lost from the kiln and cooler shells.
Where a preheater is installed, inleaking air and preheater shell losses must also be considered (Fig.5). If there
is a precalciner, coal will also enter the system at the preheater.
With rotary and planetary coolers there will be no cooler exhaust air to consider.
5. UNITS
5 1 C ti l U it
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5.1 Conventional Units
The normal convention is to use to the Système International d'Unitès (SI) units for the heat flow - kilocalorie
(kcal) to produce one unit - kilogramme (kg) of clinker.
i.e. kcal/kg clinker
It is important to understand the difference between net and gross bases of expressing these units. The term
kcal/kg clinker implies net basis, which is normally used for comparisons. The significance of net and gross
units will be discussed later.
5.2 USA Units
In the USA the units used are based on a mix of the British thermal unit (Btu) and the American short ton (T)
systems.
i.e. mBtu/T(m = 1 million)
where 1 kcal/kg = 3.6 x 10 3− mBtu/T
or 1 mBtu/T = 277.78 kcal/kg
6. MASS BALANCE
A prerequisite for making the heat balance is a knowledge of the various quantities of gases and solidsentering or leaving the system (control volume). A mass balance has, therefore, to be performed prior to
calculation of the heat supplies or losses in the heat balance. The data required will consist of rates of raw
meal, fuel and air entering the system, which should equal the rates of clinker, dust and flue and exhaust gases
leaving the system. (Fig.7).
Again, it is essential that the mass balance is made under steady state conditions. The mass balance will
actually be partly measured and partly calculated, and it is the measured parameters that must be atequilibrium.
When equilibrium exists, the mass flow into the system in unit time will equal the mass flow from the system
(Fig.8).
7. REFERENCE TEMPERATURE
For determining the heat balance it is necessary to define a reference or datum temperature on which all
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For determining the heat balance, it is necessary to define a reference or datum temperature on which all
quantities of sensible heat are based. An obvious reference temperature could be 32°F, but more commonly a
temperature nearer to ambient is used for convenience. In the UK a reference temperature (t ref ) of 20°C
(68°F) is used. In tropical areas a higher temperature, 25 (77°F) or 30°C (86°F) may be defined.
8. SENSIBLE HEAT
8.1 Heat v Temperature
If the same quantity of heat is supplied to the same mass of different materials and there are no chemical or
physical changes of state, the resulting temperature rises are not the same, but depend on the specific heats of
'he materials. The heat contained by the material giving rise to its temperature is its sensible heat.
Suppose 'that a quantity of heat Q is supplied to a given mass of material m, leading to a rise in temperature
of the material from Lemperature t° 1 to t° 2 then:
Q = mS (t° 2 - t°1 )where S is the mean specific heat of the material over the temperature range t° 1 to t° 2 .
The sensible heat of each material is calculated in the above manner by calculating the heat contained in the
material above a datum temperature.
e.g. Consider a grate cooler exhaust of 4 lb air at 390°F per lb of clinker produced, reference temperature
68°F:
Q = ms (t ref - 1t )( 1t - t ref )
= 4-x 0.242 (390-68)
Q = 311.7 BTU/lb clinker
8.2 Specific Heat
Intermediate values can be interpolated, most easily by plotting a SH/temperature curve over the appropriate
range.
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e.g. mean SH of clinker between 68°F and 660°F from Fig.9 is 0.210 by interpolation.
8.2.3 Calculated Values
It is possible to calculate the mean SH between any two temperatures using the data in the tables as follows:
SH t 2 -t 3 = ( )23
12211331
tt
)t-(t t-tSH-)t-(t t-tSH
−
e.g. Oxygen
SH 68°F to 212°F = 0.220
SH 68°F to 392°F = 0.223
SH 212°F to 392°F = 0.223100-200
20)-(1000.220-20)-(200
= 0.2254
All heat quantities (Q) associated with sensible heat can be calculated knowing mass (m), temp (t xo
) andmean SH ( x
oref
o tSt − ).
9. HEAT OF REACTION
In order to carry out certain chemical reactions, it is necessary to supply heat. These reactions are said to be
endothermic. An important example in this context is the dissociation of calcium carbonate.
CaCO 3 → CaO + CO 2 (886.7 BTU/lb clinker)
In other reactions, however, heat is evolved and these are said to be exothermic. The combustion of coal or oi
arbitrary reference temperature (e.g. 32°F, 68°F). Table 3 contains the heats of reaction at 68°F of the main
reactions occurring in the material in the kiln. It should be appreciated that these reactions do not necessarily
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take place at the reference temperature of 68°F.
The heat of reaction at some other temperature, to, can be found from the data in Table 3 by assuming the
reactants are brought from t°C to 68°F, then react and the products are taken from 68°F to t°
10. COMBUSTION OF COAL
10.1 Calorific Value
When coal is combusted in air the combustion products include water vapor from the hydrogen in the coal.
The calorific value (CV) of coal as determined is the gross value. The water vapor from the dry coal
combustion is condensed in the test apparatus, giving up ILS latent heat which 'is included in the water bath
measurement of the heat evolved (Fig.10). Hence the CV test gives the "higher heating value" or gross CV of
the coal.
In the kiln system, the water vapor from coal combustion is discharged to atmosphere via the stack.
Condensation occurs in the atmosphere and the latent heat is then given up outside the control volume. Hence
only the "lower heating value" or net CV of the coal is utilized.
The net CV of the coal can be calculated from the measured gross CV if the hydrogen content is known, i.e:
CV net = CV gross - LHV100
H9M 2+ BTU/lb
where M = % moisture in coal (wet basis)
H = % hydrogen in coal (dry basis)
LHV = latent heat 1= 1056 BTU/lb
For typical UK kiln coals the gross to net factor is approximately 0.96. (For heavy fuel oil it is 0.94 and for
For a coal fired wet process kiln the heat supplied by the coal is calculated as follows (similarly for other kiln
processes):
l /lb
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Dry coal CV = 12150 BTU/lb gross
Coal moisture = 5%
As-fired coal consumption = 25.1%
Net CV = 12150 x 0.96 = 11664 BTU/lb
Dry coal cons. = 25.1 x100
5-100= 23.8%
(0.238 lb coal/lb clinker)
Heat input = 0.238 x 11664 = 2776 BTU/lb
The term “2776 BTU/lb" implies the net or actual fuel consumption.
10.3 Combustion Products from Coal
The combustibles in coal are carbon, hydrogen and sulfur. The reaction for the combustion of carbon (C) in
oxygen ( 2O ) to give carbon dioxide (C 2O ) is as follows:
C + 2O → C 2O
12 lb + 32 1 b → 44 lb
where the weights represent the relative proportions of the reactants and product from their atomic weights.
For the wet process kiln with 0.238 lb coal per lb clinker and 76% C in the coal:
C 2O from coal combustion = 0.23812
44
100
76××
Referring back to Section 10.2, it must be understood that in the absence of a suitable excess of oxygen, someof the carbon will burn to carbon monoxide (CO) only, in which case some of the potential heat input will be
lost. This CO loss must be calculated in the heat balance.
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10.4 Heat From Organic Carbon in Raw Meal
Some raw meals can have a significant amount of organic carbon present, which contributes to the heat input.
Although normally relatively small at up to about 10 kcal/kg, in the case of an oil shale for example, the heat
input may be large (Rawang Works oil shale gives about 270 BTU/lb of total heat input of 1440 BTU/lb
clinker).
11. LATENT HEAT
When water is heated, its temperature rises to 212°F, this involves the sensible heat between ref t and 212°F.
Further heating does not cause further temperature rise, but converts the water to steam (water vapor) without
increasing the temperature. This is the latent (not sensible) heat of vaporization (LHV) of water, i.e. the heat
required to accomplish the physical change of state from liquid to gas.
The calculation can be made considering the LHV of water at the reference temperature and the mean SH of water vapor from ref
ot and the exit gas temperature. Alternatively the calculation can use the mean SH of water
between the reference temperature and 212°F, the LIHIV o-F water at 212°F and the mean SH of water vapour
between 212°F and the exit gas temperature. For convenience we use the former calculation.
e.g. ref ot = 68°F
LHV68°F = 1052.8 BTU/Ib H O2
SH68°F-414°F of WV = 0.4526
BET = 414°F
0.98 lb slurry H O2
/lb clinker
Q LHV68°F = 0.98 x 1052.8 = 1031.7 BTU/lb clinker
Q SH/WV68-414°F = 0.98 x 0.4526 (414-68)
12.1 Calculation of Theoretical Heat
The heat required to convert the raw meal to clinker is termed the theoretical heat. Regardless of the relative
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efficiency of the kiln system, this heat must be supplied to produce the Bogue clinker compounds. It can be
calculated from first principles by using basic heat of reaction data (Table 3) if the composition of the raw
meal is known. However, the required data is seldom available, and the calculation is tedious.
Various formulae have been developed to permit more rapid estimation of the theoretical heat. A formula by
zur Strassen (1957) which gives good agreement with basic calculations is:
Q th = 4.002A t + 11.683M c + 13.786C c - 9.224S - 1.054 (F + Mn) BTU/lb clinker
where Q th = theoretical heat of clinker formation
A t = lb Al 32 O ex clay per 1001b clinker
M c C c = lb mgO and CaO ex MgC 3O and CaC 3O per 1001b clinker respectively
S, (F+Mn) = % Si 2O and % (FFe 2 3O + Mn 2 3O ) in loss free clinker
As an approximation, zur Strassen's formula can be simplified for application to typical high grade limestone
and shale raw mixes as follows:
Q th = 4.002A + 11.683M + 13.786C - 9.224S - 1.064F BTU/lb clinker
where A, M, C, S and F are the % A1 32 O , MgO, CaO, Si 2O and Fe 2 3O in the clinker.
i.e. clinker: A1 32 O 6.57%, MgO 1.09%, CaO 66.31%, S 2O 21.63%, Fe 32 O 2.78%
Q th = 4.002 x 6.57 + 11.683 x 1.09 + 13.786 x 66.31 - 9.224 x 21.63 - 1.064 x 2.78
∴Theoretical heat = 751 BTU/lb clinker
Generally, theoretical heat values for OPC (Type I) clinker range from about 720 to 755 BTU/lb clinker. The
latter value is usually taken in the absence of full data. However, the theoretical heat depends on raw meal
b) montmorillonite 725.8 BTU/1b
c ) illite 723 1 BTU/lb
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c ) illite 723.1 BTU/lb
It can be seen that kaolinite minerals give theoretical heat approaching 755 BTU/1b, but montmorillonite an
illite minerals are much easier to combine.
12.3 Effect of LSF
Kaolinite, SR 2.3 AR 2.4 HFO firing
a) LSF 89% 732.8 BTU/lb
b) LSF 94% 754.7 BTU/Ib
It can be seen that reducing the LSF significantly reduces the theoretical heat.
112.1 Effect of Coal-Ash Absorption
Kaolinite, LSF 94%, SR 2.3, AR 2.4 Coal firing (15% ash)
a) Ash absorbed 3.75% 745.7 BTU/1b
b) Ash absorbed 7.5% 736.9 BTU/Ib
It can be seen that coal ash acts as a mineraliser, making combination easier.
LSF 84% SR 2.0 AR 0.7 676.6 BTU/Ib
As would be expected the theoretical heat of Type IV clinker is very low.
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12.6 Burnability
Theoretical heat should not be confused with burnability. The latter includes raw meal fineness and
homogeneity, mineralisers, free lime level etc.
13. SHELL LOSSES
Heat is transferred from the outer surfaces of the kiln (and cooler etc) shell to the surroundings by two means.
Most of the heat is lost by radiation (Fig.11a). Radiation takes place according to the equation:
Q r = ( )4
3
4
2 TTA −εσ
Where Q r = heat lost in BTU/h by radiation
A = area of shell in ft²
T 2 T 3 = absolute temperature (t°F + 460) of shell and surroundings respectively
ε = surface emissivity - rough steel equals 98% of black body at 930°F (ε can be measured)
σ = Stefan's constant 0.173 x 10 8− BTU/ft²h(°R )4
Some heat is lost by convection (Fig 11a). Convection takes place according to the equation:
Qc= 0.13 CA (t
2 - t
3) 1.25
where Qc = heat lost in BTU/h by convection
t 2 t 3 = temperatures of shell and surroundings respectively
The determination of the shell losses from kilns, coolers, etc is a difficult problem. The shell loss from a
modern BCI operated kiln is of the order of 4070 kcal/h×m² of surface, although a very wide variation is to beexpected from this value. For a moderate to large wet process kiln this would give a shell loss value of the
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order of 210 kcal/kg clinker. For a conventional suspension preheater kiln the shell loss would be about 90
kcal/kg clinker.
It is evident from above that the shell loss depends on the temperature conditions in the kiln and the kilngeometry. On the whole, the temperature conditions in a kiln do not vary much with output. In consequence,
the shell loss remains substantially constant whatever the output. However, as shown in Fig.11b, radiation
losses increase exponentially with shell temperature. Hence the importance of good refractory, coating and
firing conditions for fuel economy.
14. HEAT UNACCOUNTED FOR
In making any heat balance, there is usually some heat unaccounted for. The relative size of this factor gives
some measure of the accuracy of the balance and the data on which it is based. However, it has to be
remembered that an error in one item may be cancelled out by errors in other items, resulting in a misleadingly
small heat unaccounted for value.
Although inaccurate data or the failure to consider certain factors are the most' likely causes of a large heat
unaccounted for, the possibility of unsteady conditions at the time of making measurements should also be
considered. For example, it will be readily appreciated that, after lighting up a cold kiln, the heat input will
exceed the heat output until steady conditions are reached as the system absorbs heat.
In certain instances, the determination of all the items (in particular the shell loss) in the heat balance may not
be possible and these items are then included as heat unaccounted for.
15. USES OF THE HEAT BALANCE
15.1 Simplification of the Heat Balance
Calculation of a heat balance along the lines described above is lengthy and tedious, and may require datawhich are not always available. Certain simplifications may be justified, however, without too much
approximation.
On the heat input side of the balance it is reasonable to treat the burning of the fuel as the sole heat source as
as about. 1500 BTU/hrft² of surface, which may decrease with increasing kiln size. Small wet process kilnsmay, however, have shell losses as high as 20% of the heat input and this value probably gives rise to the
greatest inaccuracies. If the dust loss is not known, the assumption of 5% on clinker and 30% decarbonisation
is possibly a fair approximation, from which the heat loss can be calculated. Finally, the heat loss due to
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p y pp y
incomplete combustion may be ignored if the % CO in the exit gas is small, i.e. less than 0.2%.
15.2 Programmed Heat Balance
If suitable data are available, either first hand or by reasonable approximation, then this type of calculation can
be programmed. By using a computer, it is possible to reproduce the results of the heat balance within a matter
of seconds. This method also has much greater flexibility as it is possible to vary some of the input data and
predict their likely effects upon fuel economy.
15.3 Significance of Variables
By introducing a suitable loop into the program, it is possible to investigate the effects of selected input
variables upon the heat requirements of the kiln without introducing large errors. For example, variables
investigated using this technique were slurry moisture, back end temperature, back end oxygen, dust losses
and shell losses. The results of these variations were plotted graphically in Fig.12 (a) - (e) and are discussed below, based on the example heat balance for a wet process kiln.
15.3.1 Slurry Moisture
Variation in slurry moisture content has a significant effect on heat input. A reduction of 0.5% in slurry
moisture yields a saving of about 1% in coal consumption. By the use of suitable additives, greater reductionsmay be obtained in slurry moisture and hence, coal consumption. It is therefore important to run at the lowest
practicable slurry moisture content in the interests of fuel economy.
15.3.2 Back End Temperature
Reduction in back end temperature also produces a significant effect upon heat requirement. A reduction of
50°F i b k d t t lt i f l i f b t 1% S li it ti b t d ith
the kiln (by insufflation at the kiln hood) or by dust scoops on the kiln shell, thereby reducing fuelconsumption.
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15.3.4 Shell Losses
Shell losses represent a fairly large proportion of the heat loss, i.e. about 13% in the example. Reduction in
shell losses can only be gained by improving the insulation of the kiln lining which is often not possible.
However, if improved insulation is possible, then a reduction of say 25% in shell loss could yield a fuel savin
oil about 3%.
15.3.5 Back-end Oxygen
Back-end oxygen content has a less significant effect on heat requirements than the above variables. Accurate
control of the back-end oxygen is still an effective method of saving fuel however, as a reduction from say
3.5% to 1.5% can save about 1% of fuel consumption. It is therefore important to monitor and control the
back-end oxygen content as accurately as possible at the optimum practicable value (1.5 - 2.0%).
15.3.6 Interaction of Variables
It is not possible to apply this type of study to a practical system with sufficient accuracy as it considers the
effects of one variable in isolation. In practice, changes in one input variable affect others, e.g. changes in
slurry moisture will result in changed values of back-end temperature, dust loss, etc. The isolated variable
approach does, however, highlight the order of savings which may be achieved by small improvements in the
more significant variables, i.e. slurry moisture, back-end temperature and dust loss etc. As fuel represents a
major proportion of production cost, even small improvements in fuel efficiency are worthwhile.
16. CONCLUSION
The essence of the heat balance is that the high fuel consuming items become apparent. Changes in fuel
consumption can be ascribed to particular changes in the process and remedial/improvement action decided.
Priorities for improvements can be established. As a works improvement plan progresses, the heat balance
will show the real savings being achieved. The simple presentation enables all members of the managementteam to follow the progress being made and to participate in the optimization of fuel consumption.
References
TABLE I
MEAN SPECIFIC HEATS OF UNDISSOCIATED GASES BETWEEN 68-F AND t-
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t°F O2 N2 Air CO CO2 H2O
Vapor
SO2
68 0.218 0.248 0.240 0.249 0.198 0.435 0.143
212 0.220 0.248 0.240 0.249 0.211 0.447 0.147
392 0.223 0.249 0.242 0.250 0.221 0.452 0.150
572 0.227 0.250 0.243 0.252 0.230 0.457 0.154
752 0.230 0.252 0.246 0.254 0.238 0.463 0.157
932 0.234 0.254 0.248 0.257 0.246 0.471 0.1611112 0.237 0.256 0.250 0.259 0.252 0.478 0.164
1292 0.240 0.258 0.253 0.262 0.258 0.486 0.167
1472 0.243 0.261 0.256 0.265 0.263 0.495 0.170
1652 0.245 0.264 0.258 0.268 0.268 0.502 0.173
1832 0.247 0.266 0.260 0.270 0.271 0.512
2012 0.249 0.268 0.263 0.273 0.275 0.519
2192 0.251 0.271 0.265 0.275 0.278 0.527
2372 0.253 0.272 0.267 0.277 0.281 0.532
2552 0.255 0.275 0.269 0.278 0.284 0.542
2732 0.256 0.276 0.271 0.280 0.286 0.547
2912 0.258 0.278 0.272 0.282 0.289 0.5533092 0.258 0.280 0.273 0.283 0.291 0.561
3272 0.260 0.281 0.274 0.285 0.293 0.567
3452 0.262 0.282 0.276 0.286 0.294 0.573
3632 0.263 0.284 0.277 0.287 0.296 0.578
Above 2732°F dissociation must be taken into account
Data for O2, N2, Air, CO, CO2, H2O Vapor from Spiers : Technical Data on Fuel, 1962
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TABLE 3 - HEATS OF REACTION AT 68°F
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FIG.8 GAS FLOWING THROUGH A SYSTEM
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Heat Loss vs Surface Temp
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0
2000
4000
6000
8000
10000
12000
0 200 400
H e a t L o s s ( k c a l / m 2 / h )
Strong Wind (10 C)
Strong Wind (20 C)
Strong Wind (30 C)
Med Wind (10 C)
Med Wind (20 C)
Med Wind (30 C)
Still Wind (10 C)
Still Wind (20 C)
Still Wind (30 C)
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APPENDIX I
FUNDAMENTALS OF HEAT BALANCES
1. Preliminary Considerations
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In making a heat balance, the total heat supplied to the system is equated to the total heat leaving the system
under equilibrium conditions. This makes no particular allowance for the internal heat exchanges occurring,
but shows how the heat used may be divided from a consideration of the heat input and output quantities.
A prerequisite of making the heat balance is the calculation of the various quantities of gases, liquid and solids
entering or leaving the system. The total weight of feed, fuel and air entering the system will equal the total
weight of the clinker, dust, air and gases leaving the system. Likewise the weight of any component (e.g car-
bon, CaO) in the material streams entering the kiln will equal the weight of the same component in thematerial streams leaving the kiln.
2. Heat Supplied to the Kiln
The heat supplied to the kiln may be considered to come almost entirely from the fuel, although the raw
materials may contain a small percentage of organic material which contributes some heat to the system when
it burns. If the material feeds are above the datum temperature a small quantity of sensible heat will also beshown on this side of the heat balance.
3. Heat Expenditure
The ways in which heat is used in the kiln and the various heat losses may be divided as follows:
a) Theoretical Heat The net total of heat required for the various chemical reactions, i.e dissociation of carbonates, formation of silicates and aluminates in the burning zone and the removal of combined water
from clay minerals. It is assumed that the reactions take place at the datum temperature.
b) Heat Lost in Exhaust Gases
i) The water in the feed is evaporated and heated to the exit gas temperature.
ii) The CO2 from the dissociation of carbonates is heated to the exit gas temperature.
iii) The gases from the combustion of fuel and organic matter in the feed are discharged at the exit gas
vi) The air used for combustion contains a small quantity of water vapor which is heated to the exit gastemperature (in addition water may be sprayed into the cooler).
vii) Excess hot air is exhausted from a Fuller (grate) type cooler.
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c) Heat Lost in Clinker
Shell Loss There are losses through the kiln shell and hood and the walls of the kiln, cooler, preheater
and coal mill by radiation and convection.
d) Dust Loss The dust carried out of the kiln is heated to the exit gas temperature and may have partially
reacted.
e) Heat Lost by Incomplete Combustion Any carbon monoxide present due to imperfect combustionrepresents a loss of heat.
4. Basis and Datum Temperature
In a heat balance on a kiln it is simplest to make calculations on the basis of a given weight of clinker, usually
1 kg or 11b. Heat quantities are expressed as kilocalories or British thermal units respectively. Hence the unitsused will be kcal/kg and Btu/lb respectively.
The heat quantities are calculated from a datum temperature. This can be taken as the atmospheric temperature
or some similar fixed temperature (e.g. 60°F, 20°C).
HEAT BALANCE
WET CHAINED KILN WITH GRATE COOLER (BTU/lb UNITS)
1. INTRODUCTION
It is clearly desirable on the grounds of cost to operate the kiln with as low a consumption of fuel as possible
consistent with a high output of good quality clinker and, to this end, it is necessary to understand how the
heat generated by burning fuel is utilized. This requires the construction of a heat balance.
b) Vaporization of the slurry moisture
c) Sensible heat of the exit gases
d) Shell losses
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The base lines upon which the heat balance is performed are selected mainly for simplicity of calculation. The
quantities of heat involved are based upon 1 lb of clinker and listed as BTU/lb. The quantities of sensible heatare calculated from the datum temperature (68°F).
CONSTRUCTION OF THE HEAT BALANCE
As an example, a heat balance on a wet process coal fired kiln will now be calculated. The relevant kiln data
and analyses of raw meal, clinker and fuel are set out in Tables 1 and 2. (The data available in practice may be
less than this amount, and it is thus not possible to completely standardize the procedure of heat balance
determination.)
3.1 Preliminary Calculations
From the data in the tables, the first requirement is to calculate the undetermined solid mass flows.
The clinker output is 34.72T/h.
The raw coal consumption is 0.251 lb/lb of clinker. The coal moisture is 5%, thus the consumption of dry coal
will be:
0.251 x100
5)-(100= 0.238 lb/lb of clinker
Hence, coal moisture = 0.013 lb/lb of clinker
The ash content represents 15.3% of the dry coal, equivalent to 0.153 x .238 = 0.0364 lb/lb of clinker. It is
assumed that all the ash is absorbed in the clinker. Therefore, the clinker derived from raw meal is:
1 -0.0364.= 0.9636 lb/lb of clinker
The ra material also s ffers a loss on ignition on passage thro gh the kiln Loss on ignition is determined b
36.28-100
100x0.9636= 1.512 lb
The raw meal further suffers a degree of dust loss, which is 0.06 lb/lb of clinker. The loss on ignition of the
partly decarbonated dust is 20.2%, equivalent to:
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p y , q
( )( )
075.028.361002.2010006.0 =
−−× lb lb dry meal/lb of clinker
the total raw meal required to produce 1 1b of clinker is, therefore, 1.512 + 0.075 = 1.587 lb. A slurry
moisture of 39.2% will be equivaliant, therefore, to:
39.2)-(100
39.2x1.587= 1.023 lb of water/lb of clinker
3.2 Heat input
The total heat input is calculated by summing the various components containing both sensible and potentialheat. In this example, we must consider any sensible heat contained in the fuel, combustion air and raw
materials, plus the potential heats contained in the fuel and raw material.
3.3 Potential Heat in Coal
Raw coal burnt per lb of clinker is equivalent to 0.238 lb of dry coal.
Gross calorific value of dry coal = 12170 BTU/lb. Heat supplied by burning coal:
0.238 x 12170 = 2896 BTU/lb of clinker (gross)
It will be noted that the gross calorific value has been used in which it is assumed that the water vapor from
the combustion of the dry coal is condensed. In fact, this water is carried out of the kiln as vapor and an
allowance has to be made for this in calculating the sensible heat of the exit gases.
3.5 Sensible Heat in Coal
The coal is fed to the mill at 68°F (the datum temperature) to yield a nil 12 tt − value and hence a sensibleheat value of zero in this case:
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0.238 x (68 – 68) 0.23 = nil
3.6 Sensible Heat in Combustion Air
It is calculated later (Section 3.17) that the total air drawn into the system is 4.438 lb/lb of clinker. Assuming
this air is all at 72°F, its sensible heat is:
4.438 (72-68) 0.24 = 4.26 BTU/lb of clinker
3.7 Sensible Heat in Raw Materials
Slurry is fed to the kiln at 63°F, i.e. less than the datum temperature. Therefore, the sensible heat of the slurry
will be a negative value on the input side of the heat balance.
The specific heat of the dry raw material is taken as 0.2 (the specific heats of the main constituents are all
approximately 0.2).
Sensible heat in the dry raw material =
1.587 (63-68) 0.2 = -1.587 BTU/lb of clinker
Sensible heat of slurry moisture
1.023 (63-68) 1 = -5.115 BTU/lb of clinker
Total sensible heat of feed = -6.702 BTU/lb of clinker
3.8 Heat Output
A derivation of zur Strassen's formula can give a good approximation for the theoretical heat using the clinker oxide values:
Q th = 4.002A.+ 11.683M + 13.786C - 9.2245S - 1.064F
where A M C S and F are the weight % of the clinker oxides i e:
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where A, M, C, S and F are the weight % of the clinker oxides, i.e:
Q th = 4.002 x 6.57 + 11.683 x 1.09 + 13.786 x 66.31 - 9.224 x 21.63 - 1.064 x 2.73
= 752.0 BTU/lb of clinker
3.10 Heat to Evaporate Water
The slurry moisture is equal to 1.023 lb/lb of clinker. Incorporated in this figure is the moisture content of the
dust losses, equal to:
1.587
0.075x 1.023 = 0.048 lb/lb of clinker
Treating the dust loss moisture separately, this leaves 1.023 -0.048 = 0.98 lb/lb of clinker of slurry moisture. Itis assumed that this water is evaporated at 68°F, at which temperature the latent heat is 1056 BTU/lb.
Therefore, the heat required for the evaporation of slurry moisture is:
0.98 x 1056 = 1035 BTU/lb of clinker
The raw material contains 1.34% of combined water equal (deducting the dust loss component) equal to:
100
1.34x1.512= 0.0203 lb/lb of clinker
The heat required to evaporate this water at 68°F is:
0.0203 x 1056 = 21.4 BTU/lb of clinker
(Note the heat of dissociation of combined water is included in the theoretical heat).
The percentage of moisture in the coal is 5.0%, equal to:
In calculating the heat input to the kiln, the gross calorific value of the coal was used, thereby implying thatthe water vapor from the combustion of the hydrogen in the coal was condensed. In calculating the heat output
of the kiln, therefore, the latent heat of Vaporization of this water has to be included. The amount of water in
the combustion products is 0.094 lb/lb clinker (see Section 3.12). therefore, heat to evaporate water in
combustion products is:
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0.094 x 1056 = 99.3 BTU/lb of clinker
3.11 Sensible Heat of Exit Gases
To calculate the sensible heat lost by the exit gases, the total masses of the constituent gases have first to be
calculated, via appropriate mass balances.
3.12 Combustion Products
The carbon in the fuel and raw material are burnt thus:
C O2 C O2
+ →12 lb 32 lb 44 lb
(A small fraction of the carbon is burnt to CO and not C O2. This is allowed for later).
The hydrogen in the fuel is burnt thus:
2H2 O2 2H2O+ →
4 lb 32 lb 36 lb
The sulfur in the fuel is burnt thus:
S O2 S O2
+ →32 lb 32 lb 64 lb
On the basis of 1 lb of clinker the fuel combustion should yield:
0.238 x32
64
100
6.1 × = 0.0076 lb of sulfur dioxide
The oxygen required for combustion per lb of clinker is:
326132443276
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lb57.032
32
100
6.1238.0
4
32
100
4.4238.0
12
32
100
76238.0
=××+××+××
The 0.7% organic carbon in the raw meal is also burnt, consuming:
0187.012
32
100
7.0=× lb of oxygen/lb of raw meal, equal to:
0.0187 x 1.587 = 0.0297 lb of oxygen/lb of clinker, to give:
0257.012
44
100
7.0=× lb of carbon dioxide/lb of raw meal, i.e:
0.0257 x 1.587 = 0.0408 lb of carbon dioxide/lb of clinker A small part of this oxygen for
combustion comes from the coal; per lb of clinker, this is:
lb0043.0100
8.1283.0 =×
The weight ratio of nitrogen to oxygen in air is 3.31 (assuming the nitrogen includes all the inert gas).
Therefore, the weight of nitrogen in the air required for combustion is:
(0.57 + 0.0297 - 0.0043) x 3.31 = 1.971 lb/lb of clinker.
There is also some nitrogen in the coal equal to:
0.238 0021.0100
9.0=× lb/lb of clinker
CO2 29.1% by volume
CO 0.1% by volume
O2 0.85% by volume
N2 (by difference) 70.95% by volume
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100.0
If the combustion had been complete, the volume of CO would have burnt to an equal volume of CO2 by
combining with half its volume of O2. The gas analysis would have then been:
CO2 23.2% by volume
O2 0.9% by volume
N2 71.00% by volume
100.0
(The slight contraction in volume and the resulting correction which should be made to bring the analysis back
to 100% basis has been neglected - the error is insignificant at low CO contents).
The O2 content of 0.8% represents the excess air. The ratio by volume of nitrogen to oxygen in air is 3.76.
Therefore the N2 content representing the excess air is:
0.8 x 3.76 = 3.01%
the remaining N2 being the combustion air and the coal.
The N2 content being due to combustion air is:
(71.0 - 3.01) %9.67
0021.0971.1
971.1=
+
×
The percentage of excess air is therefore:
and the weight of complimentary oxygen is:
3.31
0.0867= 0.0262 lb/lb of clinker
The total weight of air entering the kiln (i.e. combustion air plus excess air) per lb of clinker is:
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Combustion Air 0.595 + 1.971 = 2.566
Excess Air 2.566 x 4.4/100 = 0.113
Total Air 2.566 + 0.113 = 2.679
(Also cooler exhaust air, Section 3.17)
3.14 Other Sources of Water Vapor
The combustion of the fuel provides one source of water vapor, the other sources consisting of the feed, coal
moisture and included water vapor in the combustion air.
The total water vapor given off by the feed is:
lb/lb of clinker
0.020 = 1.043
The air entering the kiln will contain some water vapor. In this country, the average weight of water per lb of
dry air is of the order of 0.005 lb. On this basis, the quantity of water vapor per lb of clinker is:
2.679 x 0.005 = 0.0134 lb
3.15 Other Sources of Carbon Dioxide
Some of the feed leaves the kiln as dust which is only partially decarbonated. Loss on ignition of the dust is20.2% compared with 36.3% of the feed.
Assuming the losses on ignition represent the degree of decarbonation, the percentage decarbonation of the
d t l f b i i
Therefore, the carbon dioxide evolved by the dust is:
100
55.6x (0.3487 + 0.0257) = 0.208 lb/lb of dust
The dust loss of 6% on clinker is equivalent to 0 075 lb of dry raw meal/lb of clinker Therefore the carbon
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The dust loss of 6% on clinker is equivalent to 0 .075 lb of dry raw meal/lb of clinker. Therefore, the carbon
dioxide derived from the feed is:
(1.587 - 0.075) 578.0208.0100
6
100
2.57)(34.87=×+
+ lb/lb clinker
(It has been assumed that the dust has been completely dried, i.e. slurry moisture and combined water have
been removed).
3.16 Heat Content
Summation of the constituent gas weights per lb of clinker results in the following (in lb):
H2O from feed (free + combined) 1.043 )
)
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)
from combustion of coal 0.094 ) ) 1.1634
from coal moisture 0.013 )
)
from water vapor in air 0.0134 )
CO2 from feed 0.582 )
) 1.24
from combustion of coal 0.663 )
SO2 from combustion of coal 0.0076
O2 from excess air 0.0262
N2 from coal 0.0021 )
)
from combustion air 1.9710 ) 2.0598
)from excess air 0.0867 )
The heat required to raise these gases from 68°F to 414°F, a temperature difference of 346°F, is:
(1.1634 x 0.452 x 346)+(1.245 x 0.222 x 346)+(0.0076 x 0.15 x 346)+ (0.0262 x 0.223 x 346)+(2.0598 x
0.249 x 346) = 457.4 BTU/lb of clinker, i.e:
Sensible heat of exit gases = 457.4 BTU/lb clinker
Combustion Air 2.566
Excess Air 0.113
Cooler Exhaust Air 1.769
4 438 lb
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4.438 lb
This figure has been used in Section 3.6 to calculate the sensible heat of air entering the system.
3.18 Sensible Heat of Clinker
The clinker leaves the cooler at 255°F. The sensible heat in the clinker/lb of clinker is:
1 x (255 - 68) 0.188 = 35.2 BTU/lb of clinker.
3.19 Shell Loss
Heat is transferred from the outer surface of the kiln shell, to the surroundings by two means.
Radiation takes place according to an equation of the form:
q r = ( )4
3
4
2 TTA −εσ
where A is the area, T2 and T3 are the absolute temperatures of the shell and the surroundings respectively, εis the measured emissivity of the surface and σ is the Stefan Boltzmann constant (0.173 – 10-8 BTU/hrft²R 4)
Convection takes place according to an equation of the form:
q c = hA ( )32 tt − 1.25
where t2 and t3 are the temperature of the shell and the surroundings respectively and In is a coefficient whosevalue depends on a number of factors including the dimensions of the kiln and the air velocity over the kiln.
By measuring the temperature and emissivity along a kiln shell, the heat loss can be estimated using formulae
Measurements have also to be made of cooler, preheater, coal mill and connecting ducting temperatures asthere is a substantial, though relatively smaller, shell loss from these as well.
For the purpose of this heat 5 balance, the total shell loss of the system is taken as 4.41 x 105 BTU/min. This
is equivalent to:
4 41 x 105 x 0 00086 = 379 3 BTU/lb of clinker
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4.41 x 10 x 0.00086 = 379.3 BTU/lb of clinker
3.20 Heat Loss in Making Dust
It is difficult to make an accurate estimate of the heat loss associated with the dust. The usual method is to
assume the dust is partially decarbonated dry raw meal. In this example, the degree of decarbonation is
estimated on the basis of the loss on ignition of the dust.
The dust loss is 0.06 lb/lb of clinker. The dust leaves the system at the exit gas temperature of 414°F.
Assuming a specific heat of 0.21 (i.e. as for CaCO3), the sensible heat loss is:
0.06 x (414 - 68) 0.21 = 4.36 BTU/lb of clinker
The percentage decarbonation has been estimated as 55.6% equivalent to 0.209 lb of carbon dioxide per lb of
dust. Assuming this carbon dioxide to come from the dissociation of calcium carbonate, the weight of calcium
carbonate dissociated is:
0.06 x 0.209 x44
100= 0.029 lb/lb of clinker
At 68°F, the heat of dissociation of calcium carbonate is 760 BTU/lb. Hence, the heat required to partiallydecarbonate the dust is:
0.029 x 760 = 22.04 BTU/lb of clinker
The heat loss associated with the dust is, therefore:
4.36 + 22.04 = 26.4 BTU/lb of clinker
Also associated with the dust is the heat required to dry its slurry moisture and combined water.
The combined water (1.34%) amounts to:
0.075 x100
1.34= 0.001 lb/lb of clinker
The heat required to evaporate this water at 68°F is:
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0.001 x 1056 = 1.056 BTU/lb of clinker
The total heat required for evaporation of water associated with the dust is, therefore:
50.69 + 0.59 = 51.28 BTU/lb of clinker
The total heat loss associated with the dust is, therefore:
26.40 + 51.28 = 77.68 BTU/lb of clinker
It will be noted that the heat required to vaporize and heat up to the exit gas temperature the water in that part
of the feed lost as dust and also the sensible heat of the carbon dioxide evolved by the dust have been
estimated earlier. It is, of course, possible to consider those heat quantities under the heading of heat lost in
making dust.
On some works,
Recommended