BURNING RATES IN INCINERATORS PART I

A SIMPLE RELATION BETWEEN TOTAL, VOLUMETRIC AND AREA FIRING RATES

R. H. ESS E NHIGH

Pennsylvania State University University Par k, Pennsylvania

ABSTRACT

A simple relation is derived between the area firing rate, FA (lb/ sq ft hr), the total firing rate or incinerator capac­ity, F (lb/hr), and the average volumetric reaction rate, Rv (lb/cu ft hr). It has the form

_ 2/3 1/3 1/3 FA = c.Rv .F = K.F

where c is an incinerator factor that depends on the pro­portional dimensions of the combustion chamber and has a value near unity. K is a waste factor that varies with the waste type and the incinerator factor.

This equation has essentially the same form as an em­pirical semi-logarithmic equation used in practice. Com­parison of the two has enabled the calculation of com­bustion intensities for different waste types. The combus­tion intensity for a waste with 10 percent moisture is about 38,500 Btu/cu ft hr, but this drops to 1,400 Btu/cu ft hr (a factor of 20 difference) as the moisture rises to 85 per­cent. This influence of moisture is greater than was ex­pected; possible reasons for this are discussed in Part II.

NOMENCLATURE

a ratio of W to H A grate area (sq ft)

b ratio of L to H B heating value of fuel (Btu/lb)

87

firing rate or incinerator capacity (lb/hr)

area firing rate (lb/sq ft hr)

combustion chamber height (ft)

combustion intensity (Btu/cu ft hr atm)

waste factor (equation 2.12) logarithmic waste factor (equation 1.1) length of incinerator

P pressure in combustion chamber (atm)

R proportionality factor for (equation 2.13) R V = average reaction rate (lb/hr cu ft)

Vc combustion chamber volume (cu ft)

W combustion chamber width (ft)

INTRODUCTION

Of all the problems involved in incineration one of the more obscure is that concerned with determining the maxi­mum duty or capacity of an incinerator. The units in which duty is measured or specilled are the same as for any other furnace or combustion chamber. They are cus­tomarily either combustion intensity, I (Btu/cu ft hr), or furnace firing rate, F (lb/hr: frequently known simply as furnace capacity). In grate fired systems it is also and more frequently given on the basis of unit area of grate surface, either as Btu heat release rate per unit area, or as pounds-per-hour rate-of-Ioading of fuel per unit area, FA.

The problem is that there are limits to the maximum allowable values of I, F, or FA ' but for a solid fuel bed there is no method yet available for estimating these from first principles, in con trast to pulverized coal and oil flames where the requirement is that the largest coal par­ticle or oil drop must burn out during its transit through the combustion chamber. This requires a match of the transit and the burning times, and was used by Rosin [1] as the basis for his combustion intensity equation which, as shown recently [2] , gives correct order of magnitude values for combustion intensities computed from burning times.

For solid bed systems the maximum duty still has to be determined empirically because of the lack of knowledge of burning times, particularly in the overbed combustion. For coal it was found after many years experience [3] that combustion intensities in excess of 35,000 Btu per cu ft hr generally caused trouble by flame impingement on the boiler tubes because the combustion volume was then too small for the attempted firing rate. This value is seen to be on the low side compared with intensities obtained with some other fuels (Table 1) though it is typical of pulverized coal boilers. The same intensity is also sug­gested by the Building Research Advisory Board [4] as an upper limit for incinerators on a semi-continuous rating, though a figure almost half that (18,000) is suggested for intermittent operation. This is for refuse consisting of 80 percent rubbish and 20 percent garbage and given [4]

somewhat confusingly both as 4500 Btu/lb and 6000 Btu/ lb [The former figure would be more appropriate to the "classic" 50/50 ratio].

Somewhat lower combustion intensities (25,000 Btu/hr cu ft) are suggested by the I.I.A. [5] but their recommendations are given in a more comprehensive form in terms of total and area capacity, F and FA ' They divided all wastes into seven types (Table 2). The last three are "special" and the first four, as argued elsewhere [6], are in essence the same "basic" material of 10,000 Btu/lb on a dry inert-free (D.I.F.) basis but otherwise with increasing percentages of moisture. In domestic and municipal incineration we are concerned primarily with waste types 0 to 3 alone.

Variations of capacity and loading rate for the four waste types of interest were extensively studied some years ago [7, 8] and the results obtained reduced [5] to tabular form (reproduced as Table 3) and the empirical expression

FA = KL.log F (1)

88

where KL is a "waste factor" of value 13 for Types 0 and 1, 10 for Type 2, and 8 for Type 3. The loading rates in Table 3 are of interest, ranging from 16 to 39 lb/sq ft hr at which upper value they are com parable [3] with coal rates on stoker-fired furnaces (but with higher calorific value fuel).

All this information, though quite comprehensive, is still incomplete. The use either of lor of F has certain value in different situations, but neither alone gives a complete picture of the incinerator boundary limitations, and use of one without the other can be misleading. How­ever, a simple relationship exists between the three quan­tities that is easily derived, and the purpose of this paper is to present the derivation together with some appro­priate comment.

THE BURNING RATE EQUATION

Combustion Chamb er Mod el

To derive the burning rate equation that relates I, F, and FA ' we assume that the combustion chamber of any incinerator can be represented as equivalent to a rectangu­lar box of height H, width W, and length L. The width and length can then be represented as multiples of the height, thus

W = aH (2)

L = bH (3)

For the grate area A, and the combustion volume Vc we can then write

2 (Area) A = WL = (a b)H

3 (Volume) Vc = HWL = (a b )H

(4)

(5)

The quantities a and b are ratios and their ranges of values are of importance. The Building Research Ad­visory Board [4] recommend the ratio of length to width ( b/a) to lie between one and two so (ab) lies between a 2 and 2a2• For a value of a, the true height may be about equal to the width (a=l), but the effective height due to combustion in the flue above or in a secondary chamber alongside could be twice this (i.e., roughly equal to the length), so a would be about 1/2. The quantity (a b) could therefore lie between 0.25 and 2.

TABLE 1 TABLE OF COMPARISONS OF COMBUSTION INTENSITIES

OBTAINED WITH DIFFERENT FUELS

Combustion Intensity Fuel Type

Btu/hr cu ft atm Gas Liquid Solid

4 x 109 Mullins theo-retical upper limit

109

108 Longwell bomb (80% combustion) (special research Liquid fuel reactor) rockets

107 Premixed gas Ramjet burners (intensity defined on flame Gas turbines volume). using pressure

atomized oil. Solid fuel rockets

106 Premixed or P.F. (pulverized. turbulent dif- Medium fuel oils fuel) (Experimental fusion gas flames (pressure and for M.H.D.). Also with intensity air atomized). cyclone burners defined on furnace alone (excluding

lOs volume. Heavy fuel oils radiant chamber). (Air and steam atomized).

Household oil 104 burners

P.F. and stoker firing (industrial).

103

102 All fuels - for drying and baking ovens.

NOTE: The industrial furnace operations can be taken as being at one atm. The gas turbines are normally pressurized operation.

89

Classification of Wastes Type Description

*0 Trash

*1 Rubbish

*2 Refuse

*3 Garbage

4 Animal solids and

•

organic wastes

5 Gaseous, liquid or semi-liquid wastes

6 Se mi-solid and solid wastes

TABLE 2 (5)

CLASSIFICATION OF WASTES TO BE INCINERATED

Principal Components

Highly combustible waste, paper, wood, carboard cartons, including up to 10% treated papers, plastic or rubber scraps ; commercial and industrial sources

Combustible waste, paper, cartons, rags, wood scraps, combustible floor sweepings; domestic, commercial, and industrial sources

Rubbish and garbage; residential sources

Animal and vegetable wastes, restaurants, hotels, markets; institutional, commercial, and club sources

Carcasses, organs, solid organic wastes; hospital, laboratory, abattoirs, animal pounds, and similar sources

Industrial process wastes

Combustibles requiring hearth, retort, or grate burning equipment

Approximate Composition % by Weight

Trash 100%

Rubbish 80% Garbage 20%

Rubbish 50% Garbage 50%

Garbage 65% Rubbish 35%

100% Animal and Human Tissue

Variable

Variable

Moisture Content

%

10%

25%

50%

70%

85%

Dependent on pre-dominant components

Dependent on pre­dominant

Incom bustible Solids %

5%

10%

7%

5%

5%

Variable according to wastes survey

Variable according to wastes

components survey

Btu Value/lb

of Refuse as Fired

8500

6500

4300

2500

1000

Variable according to wastes survey

Variable according to wastes survey

Btu of Aux. Fuel

Per Lb of Waste

to be included in

Combustion

Calculations

o

o

o

1500

3000 .

Variable according to wastes survey

Variable according to wastes survey

Recommended Min Btu/hr

Burner Input per lb Waste

o

o

1500

3000

8000 ( 5000 Primary) (3000 Secondary)

Variable according to wastes survey

Variable according to wastes survey

*The above flgures on moisture content, ash, and Btu as fired have been determined by analysis of many samples. They are recommended for use in

computing heat release, burning rate, velocity, and other details of incinerator designs. Any design based on these calculations can accommodate • • •

mmor variations.

90

TABLE 3 [5)

MAXIMUM BURNING RATE IN LBs/sa FT/HR OF VARIOUS TYPE WASTES

Burning rates are calculated as follows:

Maximum burning rate in lbs per sq ft per hr for types #0, #1, #2 and #3 wastes, using factors as noted in the formula

Br = Factor for type waste x log of capa�ity/hr #0 Waste Factor 1 3 #1 Waste Factor 1 3 #2 Waste Factor 1 0 #3 Waste Factor 8

Br = Max. burning rate in lbslsq ft/hr

I.E: - Assume incinerator capacity of 1 00 lbs/hr for type #0 waste

Br = 13 (Factor for #0 waste) x log 1 00 (capacity/hr) = 1 3x2 = 26 lbslsq ft/hr ----------------------------------------------------------.---------------------

Capacity lbs/hr

100

200

300

400

500

600

700

800

900

1000

•

Logarithm

2.00

2.30

2.48

2.60

2.70

2.78

2.85

2.90

2.95

3.00

#0 Waste* Factor 1 3

26

30

32

34

35

36

37

38

38

39

#1 Waste* #2 Waste Factor 1 3 Factor 1 0

26 20

30 23

32 25

34 26

35 27

36 28

37 28

38

38

39

29

30

30

#3 Waste Factor 8

1 6

1 8

20

21

22

22

23

23

24

24

#4 Waste** No Factor

10

12

1 4

15

1 6

17

18

18

1 8

1 8

*The density of the mixture and therefore the burning rate in lbslsq ft of Type 0 Waste, or Type 1 Waste is affected if the trash or rubbish mixture contains more than 10% by weight of catalogues, magazines, or packaged papers.

**The maximum burning rate in lbslsq ft/hr for Type 4 Waste depends to a great extent on the size of of the largest animal to be incinerated. Therefore, whenever the largest animal to be incinerated exceeds 113 the hourly capacity of the incinerator, use a rating of 10 lbslsq ftlhr for the design of the incinerator.

91

Definitions

We now introduce the two definitions for I and FA.

Com bustion Intensity (I) is given by

I = FBI VeP Btu/cu ft hr atm (6)

where B is Btu per lb; P is the absolute pressure in atmos­pheres, and P = 1 for incinerators. The other symbols are already defined (see Nomenclature). Substituting for Ve by equation (5), and rearranging (with P = 1)

F = (I /B) (ab)H3

(7)

Area Firing Rate (FA) is given by

(8)

Substituting for A by equation (4) and rearranging

2 F = (a b)H .FA (9)

Burning Rate Equation

The incinerator height, H, in equations (7) and (9) can be eliminated giving the burning rate equation

(10)

This can be written in the more convenient form

FA = K.F1/3 (11)

where K is a "waste factor" for a given incinerator. This factor depends primarily on the calorific value of the par­ticular waste and the allowable combustion intensity that can be achieved with that waste.

Empirical Relation

The basic similarity between equations (1) and (11) is evident. This can be made more explicit by considering the relation

Fl/3 = R.log F (12)

where R ranges from 2.3 to 3.3 as F rises from 100 to 1000 (lb/hr), but it can be written as (3.0 ± 0.3) for the range in F of 300 to 1000.

Substituting for F in equation (11) by equation (12) gives equation (1) with the "logarithmic waste factor" given by

92

R.K R (IIB)213 / ( ab )1/3

cR (l/B)2/3

(13)

where c = ( ab f l /3 and can be called the incinerator factor. Using the values of KL from Table 3, I can be estimated. The values obtained have some interesting features and are discussed below. In particular the ratio (liB) has sig­nificance as the average volumetric reaction rate R v' given by

RV = FI Ve = (fiB) lblhr cu ft

APPROXIMATE VALUES OF

COMBUSTION INTENSITY

(14 )

Equation (13) can be used to estimate f for the dif­ferent types of waste using the experimental values of KL if we select appropriate values for R and c or (a b). For R, the best value seems to be 3.0 according to the data given in the previous section. For (ab), we have already concluded (under Combustion Chamber Model) that it should lie between 0.25 and 2. The value of [l/(ab) 1 can therefore range from 0.5 to 4 and its cube root (c) can lie between 0.794 and 1.59. This generates an overall multi­plying factor for calculating the ratio (liB) of 0.42 to 0.21.

Applying these factors to the Type 0 waste (Trash) to estimate I gives the two figures 108,000 and 38,000 Btulcu ft hr respectively. Comparing these with the values cited in the Introduction we may conclude that the 0.21 multiplying factor is the appropriate one, giving a value of 1.59 for the Incinerator Factor (c) , and implying that the incinerator used to obtain the data in Table 3 was equivalent to one of roughly square cross-section and of height about twice its side.

Using these factors of R = 3, and of 0.21 for the over­all multiplying factor, Table 4 lists the estimated values of the waste factor, K, and the combustion intensities, I. Since the combustion intensities are computed from values of KL given as integers, and in view of the other approximations involved, the errors in I are probably at least 10 percent. In computing these values the heats of combustion, B, have been adjusted to a common basis of 5 percent inert. Type 4 waste has also been included, with a K waste factor of 2 obtained directly from the Table 3 data by plotting FA against the cube root of F.

The computed combustion intensities in Table 4 show a much wider variation than is suggested by the values quoted in the Introduction and they bring out more clear-

TABLE 4 ESTIMATED VALUES OF WASTE FACTOR (K)

AND OF COMBUSTION INTENSITIES (I)

Waste Type 0 1 2 3 4

Logarithmic Waste 13 13 10 8 Factor (KL)

Ash % (A) 5 5 5 5 5 Moisture % (M) 10 25 50 70 85 Heat of Combustion 8500 7000 4500 2500 1000 (B) Btu/lb

Auxiliary fuel 1500 3000 Btu/lb to

8000 Average Volumetric 4.53 4.53 3.06 2.17 1.41 reaction rate eii v) lb/hr cu ft

Waste Factor (K) 4.33 4.33 3.33 2.67 2.0 Combustion 38,500 31,750 13,750 5,425 1,405 Intensity (I) Btu/cu ft hr

ly than anything the overriding influence of moisture on the incinerator behavior. Probable reasons for this in­fluence are 'discussed in Part II.

CONCLUSIONS

1) The simple analysis of incinerator behavior pre­sented in this paper leads to the following relation be­tween incinerator capacity, F (lb/hr), and the grate load­ing or area firing rate, FA (lb/sq ft hr)

2) The "waste factor" K is given by

K = c(I/B)2/3 = c.R/1

3

where I is the combustion intensity (Btu/cu ft hr), B is the calorific value of the waste (Btullb), Rv is the average volumetric reaction rate (lb/hr cu ft), and c is a dimen­sionless Incinerator Factor that depends on the relative proportions of the incinerator.

3) The equation obtained between FA and F has a similar form to the following semi-logarithmic equation obtained empirically from experiment.

93

This is obtainable from the derived equation by substitu­tion of (R log F) for F1/3, which substitution holds to within ± 10 percent over the range 300 to 1000 lb/hr capacity.

4) The theoretical waste factor, K, is then related to the logarithmic waste factor KL, determined experimen­tally, by the relation

213 cR(I/B)

5) With appropriate values adopted for the constan ts c, R, and B, the experimental values of KL were used to calculate the corresponding values of combustion intensity, I, for the five waste types, 0 to 4. The values of I were found to vary by a factor of 20 for a change in moisture from 10 percent to 85 percent.

6) This range in combustion intensity is unexpectedly wide and is only partly offset by the auxiliary fuel require­ments of the wastes types 3 and 4. Moisture has long been known to have a significant influence on the incinerator capacity but the magnitude of its influence on combustion intensity was not suspected. It is obviously of prime im­portance to determine the reasons for this effect that are considered in Part II of this paper.

REFERENCES

[1] Rosin, P.O., Braunkohle, Vol. 24, 1925, p. 241; Proc.

Internat. Conf. on Bituminous Coal, Vol. 1, 1925, p. 838.

[2] Essenhigh, R. H., Ind. Eng. Chern., Vol. 59, 1967, p. 52.

[3] de Lorenzi, Otto, Ed., Combustion Engineering, first

edition, Combustion Engineering Co., Inc., 1948, �h. 9, p. 20.

[4] Ziel, P. H., "Apartment House Incinerators,:' Building

Research Advisory Board Technical Study for Federal Housing

Administration, National Academy of Sciences, National Research

Council Publication No. 1280, 1965.

[5] I.I.A. Incinerator Standards, May, 1966, Incinerator

Institute of America, New York.

[6] Essenhigh, R. H., and Gelernter, G., "Systematic Ap­

praisal of Incinerator Research Requirements," Preprint No. 37C.

Presented at A.!, Chern. E. National Meeting, November, 1967.

[7] Rose, A. H., and Crabaugh, H. R., "Incinerator Design

Standards: Research Findings," publications of the Los Angeles

County Air Pollution Control District No. 60.

[8] Williamson, J. E., MacKnight, R. J., and Chass, R. L.,

"Multiple-Chamber Incinerator Design Standards for Los Angeles

County," Publications of the Los Angeles County Air Pollution

Control District, October, 1960.

PART II THE INFLUENCE OF MOISTURE ON THE

COMBUSTION INTENSITY

ABSTRACT

The influence of moisture in reducing incinerator capacity is attributed to the extra thermal load it pro­vides on the flame which so reduces the average flame temperature that the average burning rate of the waste is significantly decreased. The actual change in flame temperature is quite small but the effect is greatly magni­fied by the high temperature coefficient of the reaction. Analysis of published experimental data gave an activation energy of 22 kcal, which is consistent with combustion of smoke. When moisture reduces the flame temperature the burning time increases, and the input of air and fuel (waste) have to be reduced to increase the stay time to match the burning time.

NOMENCLATURE

A% ash percentage (=5%)

B calorific value of waste (Btu/lb)

Bo calorific value of dry waste (Btu/lb)

C concen tration

cf = concentration of fuel

cg = concentration of oxidizer (oxygen)

cp specific heat (Btu/lb of)

E activation energy (kcal/mole)

E% excess air percentage

f factor defined by equation (24) F = firing rate (lb/hr)

Fo firing rate of dry waste (lb/hr)

hg evaporation enthalpy of water

Hw total wall loss (Btu/hr)

Hwo wall loss when firing dry waste (Btu/hr)

94

1 combustion intensity (Btu/cu ft hr)

10 combustion intensity when firing dry waste (Btu/cu ft hr)

] factor defined by equation (10)

j' = j factor modified for auxiliary fuel (equation 11)

k kinetic constant for waste (lb/hr cu ft)

ko kinetic constant for combustible (lb/hr cu ft)

m moisture fraction = (M/100)

M% moisture percentage

Rv average reaction rate (lb/hr cu ft)

Rvo average reaction rate of dry waste (lb/hr cu ft)

Tb boiling temperature of water tR) Tf flame temperature (OR) Tfo flame temperature of dry waste (R) To surroundings temperature (R) V reaction rate factor in equation (2.2) (lb/hr cu ft)

Vo reaction rate factor firing dry waste (lb/hr cu ft)

W moisture weight ratio = M/(0.95-m)

W' moisture weight ratio adjusted for auxiliary fuel

Po air density at s.t.p. (lb/cu ft)

INTRODUCTION

There are several ways in which moisture can influence the combustion intensity in an incinerator. The most obvious is by straight dilution. The presence of evapor­ated moisture increases the gas volume so that the con­centrations of the fuel (smoke, volatiles, etc.) and the oxygen are reduced. At the same time the increased volume of gas decreases the residence time in the combus­tion chamber so that, either combustion is completed

utside the chamber, or else the residence time is in-

creased again by reducing the air input which in turn must be balanced by reducing the overall combustion rate. The presence of moisture also provides an extra thermal load so that the flame temperature will drop. In general, as shown by calculations given elsewhere on coal [1) , the moisture has to be at a very high level before the extra thermal load becomes appreciable, but relatively small changes in flame temperature can have a big effect on the rate of reaction if the activation energy of the process is high; and this affects the burning time. Finally, the moisture may interfere directly (chemically) with the progress of the reaction, though this is thought to be unlikely.

This summation of possibilities ignores the real split of the reaction into a solid bed Zone (I) and an overbed combustion Zone (II), as described in a previous paper (Part I: (6)). This is a split that will have to be taken into account for more detailed computations in the future, but for our purposes here the continued use of the approximation of an overall combustion intensity, also used for the equations and values discussed in Part I, involves only a relatively small and still tolerable increase in the overall error (+ 20 percent may be a fair estimate).

With this proviso as a basis, this paper assesses the rela­tive importance of the four factors listed above in so far as their influence on the combustion intensity due to moisture is concerned.

THE INFLUENCE OF REACTIVITY

•

The factors listed in the Introduction can be quantified and separated by making use of the overall reactivity or

-

average volumetric reaction rate, Rv (lb/hr cu ft). This is defined by equation (14) of Part I as

-

Rv = (l/B) (lb/hr cu ft) (12.13) (1)

-

The mean volumetric reaction rate, Rv' depends on a variety of factors such as the concentrations of the fuel and the oxidant, some intrinsic "reactivity factor", and a temperature function. The "fuel" involved is an immense­ly complex mixture of gases, tars, volatile vapors, "smoke", carbon particles, etc., but as a first approximation we may assumed that there exists some "global" activation energy,

-

E, that can be assigned to the reaction system. Rv can therefore be written

-

(2)

95

where U contains the intrinsic reactivity factors and Tf is the average flame temperature.

The calorific value of the fuel, B, depends on th� mois­ture content. If the calorific value of the D.I.F. material is BoBtu/lb, then a waste of A% ash and containingM% moisture has a calorific value given by

B = Bo (1 - (A+M)/100) Btu/lb waste (3)

Bo is quoted in the Part I Introduction as 10,000 Btu/lb A is taken in Table 4 (Part I) as 5 percent.

Using the above information, equation (1) can be •

rewrItten as

l=Bo (0.95-m)Uexp(-E/RTf) (4)

where m = M/I00. The problem now is to determine U and Tf as functions

of W or m.

HEAT AND MASS BALANCE

The flame temperature, Tf, may be estimated by means of a heat and mass balance on the incinerator. In prin­ciple this is quite simple to set up since all the heat of combustion must go either into the sensible heat of the stack gases or the wall loss, Hw (Btu/hr). Two com­plications to be considered are the magnitude of the un­known wall loss and the effect of supplementary fuel.

Basic Balance

At a firing rate F lb/hr the total heat input is FB Btu/hr. Equating this to the sensible heat in the stack gases plus the wall loss leads to an equation with the firing rate, F, appearing in every term but the wall loss. Dividing through by F gives a balance on the basis of one lb of waste

B = [(I-m) + (po B/100) (1 + E/I00)) cp (Tr To)

+ [hg + 2cp (Tf -Tb) ) (m) + (Hw/F) (5)

This simple balance is based on the common assumption that the specific heat (cp) of the total mass of fuel (with ash) and air is the same as that of the same mass of com­bustion products. The heat in the moisture is the evap­oration enthalpy (hg) plus the sensible heat above the boiling point, T b' with the specific heat of the moisture taken as twice that of the combustion products (= 0.5 for cp = 0.25).

•

Substituting for B gives approximately [for the ratio 0.05/(0.95-m) assumed small)

(6) + [ hg +2cp( Tr Tb)) [m/(0.95-m)) +Hw/F(0.95-m)

If the material is dry this becomes

Bo = [1+(poBo/100)(1+E/100)) cp( Tfo- To)+Hw/0.95Fo

(7)

Elimination of Wall Loss

The wall loss can be taken into account in one of two ways. The first is by direct calculation. The second is by its elimination. So far as direct calculation is concerned, this would be very much a matter of guess work. The range of possibilities can be reduced somewhat by using known ranges of the heat utilization factor defined by Thring [2) and used in furnace analysis by MacLellan [3). The full details of this type of analysis are out of place here though available in the reference cited. However, certain assumptions and conclusions of the analysis can be utilized. One conclusion is that wall losses for refrac­tory lined furnaces are typically in the range of 10 to 20 percent. Use of this value in equation (7) gives a flame temperature in the region of 2000 F for 300 percent excess air (as suggested [4) of Part I). This seems realistic.

In the absence of any other method of estimating the wall loss, this way would be acceptable. However, a better way may be the elimination of the loss term. Inspection of the two loss terms in equations (6) and (7) shows that Hw is divided by the rate of input of combustible alone. As this drops and the moisture rises the flame tempera­ture drops, and so must Hw' As a first approximation Hw is likely to be roughly proportional to the actual thermal input, BF, or [BoF(0.95-m)). (Hw/FB) is then approximately constant so subtracting equation (7) from (6) would eliminate the loss terms. Performing this sub­traction gives

where W is the weight ratio of moisture, Ib/lb, fuel =

m/(0.95-m) Rewriting this in terms of Tf we have

(8)

96

where ] = 1/[l+(poBo/100)(1+E/100)) (10)

These can be evaluated if Tfo is evaluated from equation (7) making some reasonable assumption about the ratio (Hw o/0.95 FoBo)' This is considered below.

Effect of Supplementary Fuel

In the case of wastes of Types 3 and 4 considerable supplementary fuel is supplied: Evaluation of this con­tribution is a little difficult as it alters a number of factors simultaneously. Primarily it increases the Btu input, but it does so without increasing the total gas volume as much as would be the case if the increased Btu input came in the waste. This is because the supplementary fuel is fired near stoichiometric whereas the waste is fired with high excess arr.

So far as the heat balances are concerned the effect of supplementary fuel is clear. In equations (6) and (7) a quantity B' for the supplementary Btu input should be added to B . Then on the R.H.S. of each equation the o , gas volume should be increased by (poB /100). By sub-traction to obtain equation (8) the extra B' terms on the L.H.S. will cancel out again and the overall effect will be replacement of the] term [equation 10] by a]' given by

This can be regarded as equivalent to a reduction of the true moisture content to an effective content W', given by

W' = (J '/J).W (12)

Strictly, there should be a further correction to the maxi­mum flame temperature for the dry material, Tfo' but the correction is small and it appears only in a small correction term.

Approximate Values

The equations given above can be substantially simpli­fied by evaluating the constants. Values adopted for the coefficients are as follows cp = 0.25, Po = 0.05 lb/cu ft, Bo = 10,000 Btu/lb, E% = 250. These give a value for] of 0.054.

The boiling point of water, Tb, is 672 Rj the evapora­tion enthalpy, h , can be taken as 1150 Btu/lb. The flame temperature, Tf! ' can be calculated from equation (9) by assuming 15 percent wall loss so Tfo = 2300 R. Inserting these values equation (11) can be written

( TiTfo) = (1 - 0.0765W)/(1 + 0.108W) (13)

Substituting for W by the moisture fraction, m, then gives

(TfITfo) = (1 - 1.13m)/(I-0.94m) (14)

REACTIVITY FACTORS

The reactivity factor is contained in V, given in equa­tion (2). This equation can be made more explicit by taking V = Vo and I = 10 at m = 0 from which we get

(15 )

The only component of the R.H.S. of this equation not expressed or expressible in terms of m is the ratio (VIVo)'

To elucidate this ratio we now have to make assump­tions about the nature of the reaction. The most reason­able assumption is that the component, V, is proportional to the product of the fuel and oxidant concentrations, cf and cg.

(16 )

so (17)

The constant, k, is a basic kinetic constant of propor­tionality for the reaction and, for concentrations ex­pressed in ratios, k has dimensions of lblhr cu ft. It should be, strictly, the reactivity constant for the combustible fraction of the waste. However, it is clear from equation (1) that Rv' as computed, is an average reaction rate of total waste, not just of combustible, since this is the quan­tity required experimentally. Similarly, equation (2) gives V for the waste, not the combustible, and equation (16) does likewise for k. For zero moisture ko is the kinetic constant for the combustible. The kinetic con­stant for the wet waste, k, is therefore computed for a real quantity of combustible that is less than the real quantity of waste. If, therefore, k was recalculated on the basis of lblhr of combustible instead of total waste its value would be decreased. The correction factor is there­fore the opposite to that for B [equation (3)], thus

ko = k[I-(A+M)/I00] (18)

When ko is based on zero moisture and 5 percent ash, as for Vo and 10 defined above, equation (18) becomes

(kolk) = (1 - 1.05m) (19)

97

This is a factor that exactly corrects for the change in B by equation (3) due to dilution by moisture.

The two concentration ratios can be determined on the following basis. Assume that a certain fuel and oxidant concentration exists in unit volume of air and combustion products at a temperature Tfo' If now moisture is intro­duced the volume will expand because of the extra volume occupied by the moisture, and simultaneously contract because of the drop in temperature. If Co is the concen­tration of either component in lblcu ft, then the equiva­lent, dry, gas volume at Tf containing this weight of solid would be (TfITfo) cu ft.

To this must be added the volume occupied by the moisture. For every lb of fuel containing M% of moisture the cold volume of combustion and excess air is [(BII00) (1 + EII00)] cu ft. At the same time a weight m lb of moisture is evaporated. Treating this as a perfect gas then this would occupy 20 m cu ft. This gives a factor increase of

1 + 20m/(BII00) (1 + EII00) (20)

and evaluating for Band E gives

1 + 0.05m/(1 -1.05m) = (1- m)/(I-1.05m) (21)

The concentration ratio is therefore given by

clco = (1-1.05m)/(I- m) (TtfTfo) (22)

If the concentration factor holds true for both fuel and oxidant then the ratio has to be squared to give the correct factor in (VIVo). The final expression for ( IIIo) therefore becomes

1110 = f.exp [(-EIRTfo) (0.19m)/(1 -1.13m)] (23)

where

2 2 j = [(I-1.05m) (1-0.94m)]/[(I-m) (1-1.13m)]

EVALUATION

(24 )

In the evaluation of equation (23) using the data tabu­lated in Table 4 of Part I the pre-exponential factor, j, was found to be quite insensitive to the moisture fraction, m. This was a conclusion anticipated from inspection of equation (24) but it was confirmed by calculation. The factor ranged from 1 to 1.5 as m increased from 0 percent

•

to an effective value of 78 percent [after correction for the effect of auxiliary fuel by equation (14)]. In com­parison,I dropped from a value of 45,000 for 10, obtained by extrapolation, to 5,640 (after correction for auxiliary fuel), a factor of about 8. Unexpectedly, the two factors are actually working in opposite directions.

It was clear from this assessment that the principal variation in 1 was due to the exponential factor. To test this, equation (23) was rewritten in the form

1/1n (jIoII) = (RTfoI0.19E) [(11m) -1.13] (25)

Fig. 1 shows the data plotted according to this form. The graph is consistent with this equation, even to the zero ordinate at a positive fInite value of (l/m). There is some discrepancy in the value of the intercept. The predicted value, from equation (25), is 1.13, and the value obtained from the graph is about half this. However, a discrepancy of a factor of 2 in an intercept is generally tolerable, par­ticularly where so many approximations are involved.

Since the form of the equation is clearly correct the graph can be used to estimate the global activation energy

--......

0 -.... -

'" 0 -......

...

'0 l! :::I -.,

>

Waste Type

n l I l ,, ____ �43�2� ____ �1� ____________________ �O

II ,..

24

•

•

O���� ____ � ____ � ____ � ____ � o 2 4 6 • 10

Values of (1/m)

FIG. 1 PLOT OF RECIPROCAL OF LOG (flo/I) AGAINST RECIPROCAL OF m, THE MOISTURE FRACTION, TO TEST EQUATION (25), AND TO DETERMINE THE ACTIVATION ENERGY OF THE OVERALL REACTION.

•

98

of the reaction, E. According to equation (25) the slope of Fig. 1 should be

slope = 2.3Tfo/0.19E (26)

The slope has a value of 1.4. The flame temperature, Tfo ' was estimated above as 2300 R. This corresponds to about 1280 K. The calculation therefore gives us

E = 22,000 cal/mole (27)

DISCUSSION

The results of the evaluation above are clear cut. It is obvious that the factor dominating the incinerator capacity as the moisture increases is the highly temperature­sensitive reactivity of the material, due to the high activa­tion energy of the reaction. The influence of the moisture is parametric and is predominantly due to the "ballasting" action that drops the flame temperature; this drop in flame temperature in turn drops the reactivity because of the'major change in value of the Arrhenius factor (-EIRT). The influence of all the other factors listed in the Intro­duction such as dilution, decreased stay time, etc, is quite negligible.

In purely operational terms the reduced rate of reaction in the presence of moisture simply means that the gases, vapors, tars, and smoke take longer to burn. To refit the flame inside the combustion chamber when moisture is present, the stay time or transit time has to be reduced and this requires reduction of the air supply. With this reduced, the firing rate also has to be reduced to maintain the required fuel air ratio .

This suggests one possible way in which moisture could be taken into account in incinerator design. If the waste could be dried before charging into the combustion cham­ber in such a way that moisture was evaporated without signifIcant decomposition of the waste, the incinerator capacity could be directly increased because it would be burning drier waste. The moisture could then be charged to the combustion chamber through an effluent burner, either over the bed or into the exit gases as they leave the incinerator. It is even possible that they could be used for attemperating so that a higher combustion intensity could be maintained but with attemperation of the gas temperature by the moisture so that any risk of damage to the bri�kwork was not increased. This latter problem presupposes substantially reduced excess air and better

• • mlxmg.

However, other than use of attemperation, it is now clear that incinerator capacity is dominated by the re­activity of the smoke and other gases. The activation energy obtained, of 22 kcal, is known to be typical of solid carbon and coal combustion when the particles are small enough. This is equally true for pulverized coal particles [4] and for sub micron carbon particles formed in situ by cracking of the fuel gas [5]. There is currently some argument as to whether the activation energy repre­sents an adsorption or desorption step. This writer be­lieves, for reasons given elsewhere [6], that it is a desorp­tion energy and the reaction is therefore close to zero order. If that is so then, given good overfire mixing of secondary air and smoke, the principal factor controlling the flame length or burning time is the flame temperature and this is where reduction of the excess air is of greatest value.

This, in fact, points up one of two debatable elements of incinerator design. It is generally assumed, because wastes are often of low calorific value, that it is desirable to have all refractory lining for the walls. Unfortunately, this makes incinerator operation very inflexible. If the flame temperature could be increased then the burning time would be reduced so the incinerator capacity could be increased. Unfortunately, a reasonably dry waste may then produce so hot a flame that the refractories become endangered. However, if the walls are artificially cooled a small increase in wall loss will hardly affect the flame temperature, particularly if this can be offset by a further reduction of excess air.

The point behind this is that an increase in combustion intensity does not necessarily mean a change in flame temperature. If the combustion intensity is increased a reasonably constant flame temperature can be maintained if only the thermal load can be increased. This was first demonstrated by an analysis of furnace behavior by Thring and Reber [7] (see also Thring [2)) and extended recent­ly by MacLellan [3). The conclusion from this is that

•

some form of variable load would be advantageous as an alternative to moisture as a means of controlling flame temperatures. A simple way of doing this is a partly water cooled wall. This could be disadvantageous for the bed itself but is not necessarily so for the overbed flame. A valid objection to this would be on grounds of .-cost, but this is overcome if the heated water can be put to use. In other words, the incinerator should also function as a boiler. Such an idea is by no means new, as the long European use of waste fuels in central power stations can show.

99

The second debatable element of design is the general method of use of supplementary fuel. This does two things. It raises the temperature but reduces the oxygen concentration. If the burner is properly designed this can be advantageous in igniting gases because the reduced oxygen concentration is generally more than offset by the greatly increased reactivity due to the higher tem­perature. Nevertheless there are problems. If the excess air goes through the burner itself then the burner flame temperature may be drastically reduced and there could even be stability problems. If the extra air is already mixed with the smoke then there is a mixing problem involving how to get the smoke and flame gases to mix fast enough. This particular aspect of the problem was pointed up recently by Crouse and Waid [8) in a fume combustion problem.

For igniting a solid bed, a direct flame is the most common method, but this too suffers from a number of disadvantages. The ideal is a highly concentrated flame that will heat a small area to a high temperature so that reaction will start when the flame is removed. The ignit­ing flame rarely has much excess air, and if it does this again militates against the high flame temperature that is the ideal requirement. It is not always appreciated that withou t excess air, ignition of the solid starts at the periphery of the flame zone since the center is devoid of oxygen. When the ignition flame is swithced off, this peripheral flame on the solid may be too distribu ted for best maintenance and may extinguish. This is particuarly probable if the center of the zone has been devolatilized but has still not reached the ignition temperature of the resultant char.

A far better method of ignition would be by hot air, particularly for the solid. The obvious difficulty with such a device would be the design of an effective, high­temperature (and low cost) heat exchanger. If continuous operation is required then the temperature may be too limited, but if the ignition time is fairly short a refractory regnerator working on a single cycle might be more ef­fective.

However, the general problem of incinerator capacity and smoke elimination centers on maintaining and pos­sibly increasing the flame temperature. It may be that satisfactory methods will be developed to achieve this. In the meantime, the central problem has now been iden­tified, and the analysis given here shows how moisture can be taken into account if the basic kinetics of the dry material can be established. This simplifies the overall problem considerably. As a first approximation it will

be quite satisfactory to work with dry materials, and it also justifies further the decision already made on other grounds to restrict the initial materials under investiga­tion to simple cellulosic materials such as wood and paper. Otherwise, it is now clear that a prime problem for investigation is the kinetics of smoke formation and combustion.

CONCLUSIONS

From the above analysis of the heat and mass balance on an incinerator it is concluded that:

1) The reduction in incinerator capacity when burning waste of high moisture is directly due to the reduced re­activity of the reactants (mostly smoke, volatiles, and similar gaseous combustibles) .

2) The presence of moisture reduces the flame tem­perature, and the reaction rate then drops substantially because the activation energy of the reaction is high, in excess of 20 kcal.

3) The influence of other factors directly introduced by the moisture such as dilution, decreased stay time, etc, is evidently negligible.

4) The reduction in reactivity leads to a reduced capacity because the burning time increases and, unless the stay time is increased to match this, combustion will be completed outside the combustion chamber . Since the stay time is increased by cutting back the air, the firing rate of the waste has to be reduced also to main­tain the same fuel! air ratio.

S) The activation energy obtained for the overall re­action, of 22 kcal, is typical of the carbon-oxygen re­action when the particles are so small that boundary layer diffusion is very rapid. It should seem then that smoke burn-up is the limiting factor to increasing in-

• •

cmerator capaclty. 6) Increase of incinerator capacity is therefore best

achieved by increasing the flame temperature. This can be achieved directly by reducing the excess air if the overfire air mixing can be improved. This is the objec­tive of one current research program.

(7] The effect of auxiliary fuel seems to be somewhat similar. It maintains the flame temperature in the presence

100

of high moisture and thus maintains burn-out within a reasonable time.

[ 8 ] For the future, however, the problems to be solved center, first, on maintenance of the combustion in the fuel bed, and, second, on increasing the rate of burn­up of the gases, volatiles and smoke in the overfue volume of the incinerator. These are the two problems being given principal attention in current research programs.

ACKNOWLEDGMENT

This paper has been prepared as part of a research pro­gram on Incinerator Emissions, sponsored by the Depart­ment of Health, Education, and Welfare (Public Health Service) under Grant Number SR01AP00397-03 whose financial support is gratefully acknowledged.

REFERENCES

( 1 ] Essenhigh, R. H., Colliery Engineering, Vol. 38, 1961,

p. 534; Vol. 39, 1962, pp. 23, 6 5, 103.

[ 2 ] Thring, M. W., Science of Flames and Furnaces, 2nd ed.,

J ohn Wiley, N . Y., 1 962.

[ 3 ] MacLellan, D. E., "Thermal Efficiency of Industrial

Furnaces: A Study of the Effect of Firing Rate and Output,"

M. S. Thesis, Department of Fuel Science, The Pennsylvania State

University, September, 1 965.

[ 4] Beer, J . M. , and Essenhigh, R. H., Nature, Vol. 187, 1 960,

p. 1 106.

Beer, J . M., Lee, K . B., Marsden, C., and Thring, M. W., ,

Fifth J ournees Internationales de I'Institut Francais des Combus-

tibles et de l'Energie Paris, 19=23 May, 1964.

[ 5 ] Lee, K. B. , Thring, M. W., and Beer, J . M., Combustion

and Flame, Vol. 6, 1962, p. 137.

[ 6 ] Essenhigh, R. H., "Dominant Mechanisms in the Com­

bustion of Coal," accepted for publication by ASME.

[ 7 ] Thring, M. W., and Reber, J . , "The Effect of Output on

the Thermal Efficiency of Heating Appliances," J. Inst. Fuel,

1945.

[ 8 ] Crouse, L. F . , and Waid, D. E., "Incineration of Industrial

Fumes by Direct Gas Flame," presented at 1967 Technical Meet­

ing of the Central States Section of the Combustion Institute,

Cleveland, Ohio, 1 967.