Prediction of Air Emission Factors for Combustion Point Sources

Ind. Eng. Chem. Res. 1996, 35, 2007-2014

2007

GENERAL RESEARCH Prediction of Air Emission Factors for Combustion Point Sources John B. Phillips Engineering Development Institute, 7925-A North Oracle Road, Suite 155, Tucson, Arizona 85704

The state of California and the Environmental Protection Agency have developed AP-42 emission factors for prediction of atmospheric emissions from combustion of gasoline, diesel, fuel oil, and natural gas. This work develops a method to predict emission factors for the combustion of any substance, based on the kinetics of the combustion reaction. As part of the method to develop an emission factor for any individual substance, a dimensionless group is formulated which considers the ratio of the log-mean rate of combustion to the product of the space velocity through the combustion zone and the concentration differential between the precombustion and postcombustion states. This dimensionless group, which is referred to as Φ in this work, takes the value of approximately 530-780. The method provides emission factors which are in good agreement with those contained in the AP-42 documentation. Introduction The State of California and the United States Environmental Protection Agency (EPA) developed and distributed the AP-42 emission factors (U.S. Environmental Protection Agency, 1985) as a public resource in an effort to quantify emissions from industrial point sources such as boilers, furnaces, compressors, internal combustion engines, storage tanks, rail tank cars, tank trucks, service stations, motor vehicle tanks, barges, FCC units, cokers, and other industrial equipment items, as well as fugitive emissions. The general method of predicting emissions using the AP-42 emission factors is to multiply the appropriate emission factor by the throughput. In the case of emissions due to combustion sources, this gives emissions of particulate matter, sulfur dioxide, sulfur trioxide, carbon monoxide, nitrogen oxides, and volatile organic compounds (broken down into methane and nonmethane emissions). Emission factors generally are in units of mass of emitted substance per volume of fired material. When considering combustion sources, such as boilers and internal combustion engines, particular fuels require their own emission factors. The AP-42 emission factors address combustion of fuels such as fuel oil, natural gas, diesel, and gasoline. However, combustion of other substances is not addressed in the AP-42 documentation. This omission is significant because subsequent EPA regulations, including the benzene NESHAP (National Emission Standards for Hazardous Air Pollutants) regulation (U.S. Environmental Protection Agency, 1993) and the HON (Hazardous Organic NESHAP) Rule (U.S. Environmental Protection Agency, 1992), require limitations on emissions of hazardous or carcinogenic materials if combustion is used as a means of emission control. One concern is that incomplete combustion of a hazardous air pollutant (HAP) would result in significant emissions of uncombusted or partially-combusted species. Both the benzene NESHAP regulation and the HON Rule are designed to limit emissions of hazardous or carcinogenic substances into the atmosphere. The HON Rule defines a process vent as a gas stream which is S0888-5885(95)00388-5 CCC: $12.00

discharged continuously from an air oxidation process unit, reactor process unit, or distillation column within a SOCMI (synthetic organic chemical manufacturing industry) chemical manufacturing process. Vents are classified as group 1 or group 2 according to their TRE (total resource effectiveness) index. The TRE Index, which is calculated immediately prior to atmospheric discharge and after the last recovery device, is defined as follows:

TRE ) (EHAP)-1[a′ + b′(Qs) + c′(HT) + d′(ETOC)] (1) where TRE ) TRE Index value (dimensionless), EHAP ) emission rate of total organic HAP (kg/h), Qs ) vent stream flow rate (standard m3/min) at a standard temperature of 293.15 K, HT ) vent stream net heating value (MJ/m3), ETOC ) hourly emission rate of NMNE (nonmethane, nonethane) TOC (total organic compounds), a′,b′,c′,d′ ) coefficients defined for various flare and incinerator cases in the regulation (units defined in the regulation). EHAP, Qs, HT, and ETOC may be computed using standard conservative engineering methods, i.e., those which will yield the lowest possible TRE Index value. If the TRE Index is less than unity, then the vent stream is classified as group 1, and must conform to control requirements of 20 ppmv HAP in the effluent from the final control device, or 98% reduction in HAP levels brought about by the control system. If the TRE Index is greater than unity, no additional controls are required, but the TRE Index must be maintained above unity. The need to verify compliance with the HON Rule is typical of situations which require emission factors for a variety of substances. The HON Rule defines halogenated organic streams as those vent streams emanating “from a process vent or transfer operation determined to have a total concentration of halogen atoms (by volume) of 200 parts per million” or more. Halogenated streams which are brought into compliance with the 98% or 20 ppmv threshold through combustion must vent the emissions to an acid gas scrubber prior to atmospheric release. The scrubber must reduce the © 1996 American Chemical Society

2008

Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996

Figure 1. Three-stage emission control process suggested by the HON rule.

emissions of halogens and hydrogen halides by 99% or reduce the concentration of each individual hydrogen halide or halogen to 0.5 g/dscm or less. Thus, the portion of the HON rule which addresses treatment of halogenated vent streams raises three interesting design challenges. The first of these is to estimate the performance of an incinerator, and that is a principal focus of this work. The second is to design a heat exchanger which will cool the combustion products to a temperature at which aqueous scrubbing can be conducted. This step allows energy recovery as part of the pollution reduction process and was the subject of previous work (Phillips, 1994). The final design step, per the regulation, is to devise a scrubber which will remove at least 99% of the hydrogen halides which are produced by the combustion of an organic halogencontaining compound. This also is the subject of previous work (Bailey and Phillips, 1994) . Thus , a threestep procedure is suggested by the HON Rule: incineration followed by cooling and then scrubbing. The process is shown schematically for the combustion of vinyl chloride monomer (VCM), a halogenated hydrocarbon of particular concern in recent work (Figure 1). Estimating the performance of the incinerator requires an emission factor for whatever substance is being combusted, or an equivalent methodology. Hence the need for this work. Typically, operators of industrial facilities will use an emission factor approach if this allows continued operation of the facilities without fines or other regulatory burdens. However, if the use of emission factors to estimate emissions is found to result in emissions greater than the applicable regulatory threshold(s), then analytical testing usually is conducted to determine whether actual emissions are less than those which were predicted by the emission factors. Thus, the net effect is to allow facilities with worse than average emissions to report emissions typical for that process (i.e., an industry-wide mean), and facilities with better than average emissions can report actual emissions. In this sense the use of emission factors provides a great degree of latitude in reporting emissions from industrial processes (vide infra, A Note on Empirical Correlations). Previous work on the development of emission factors has concentrated on refinements to EPA methodology pertaining to combustion of hydrocarbon fuels (Frederick, 1978; U.S. Environmental Protection Agency, 1977; Himi et al., 1977; Gerold et al., 1980; Littman, et al., 1978; Cavagnaro, 1979; U.S. Environmental Protection Agency, 1980; U.S. Environmental Protection Agency, 1978; Ciszewski and Wojciechowski, 1982; Goklany and

Southerland, 1985), but the development of emission factors for combustion of other substances has received almost no attention. It should be noted that the fringes of this problem have been addressed by considering toxicological threshold exposure limits (Trzeszczynski and Kukula, 1978) and by examining emissions from incineration of hazardous wastes (Coyle and Potenta, 1983; Roessertj 1990). In particular, combustion efficiency has been measured for industrial furnaces (Mine et al., 1987), and the results have been found to be in good agreement with those predicted by the AP-42 emission factors. Additional laboratory data have been gathered on the combustion of indoor materials, such as paints, adhesives, waxes, and insecticides (Tichenor, 1987). Also, the combustion of toluene has been examined to determine emissions of particluate matter and uncombusted or partially-combusted materials (Van Dell, 1990). And in a study which is of more relevance to compliance with the HON Rule, the combustion of halogenated organics has been studied using an elegant Fourier-transform infrared (FTIR) set of experiments (Hall et al., 1991). The advantage of using FTIR measurements for the detection of halogenated species is that the Cl-Cl stretching region is far removed from spectral absorption bands for H2O and CO2. Laboratory data of the type contained in such studies can form the foundation for empirical means to determine emission factors for combustion of substances other than hydrocarbon fuels, in a manner similar to that employed in developing the AP-42 emission factors. Unfortunately, this approach requires separate experimental testing to be conducted for the combustion of each species requiring an emission factor. Clearly, a more general method is needed. It should be noted that the EPA has computerized some of their emission factor calculation procedures in an effort to improve user efficiency (U.S. Environmental Protection Agency, 1989). Yet, the central issue of the development of emission factors for the combustion of substances other than hydrocarbon fuels is an area which needs further attention. Thus, the focus of this work is the development of means to predict emissions of uncombusted fuel from combustion sources in which substances other than the select fuels listed in the AP-42 document are being combusted. A Note on Empirical Correlations Users of emission factors must remain mindful that an emission factor represents no more than an empirical correlation between a large number of similar equipment items currently in place and the average emissions from operating that type of equipment. Thus, the development of an emission factor does not imply that the emissions from any single equipment item, such as a boiler or an internal combustion engine, will be that which is calculated by using the emission factor, but rather that the emissions on average will be approximated by the use of an emission factor. Variations in emissions between individual combustion point sources are a function of residence time, turbulence, and combustion temperature. Thermodynamics of Combustion The adiabatic flame temperature of a substance can be found using the relation:

Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996 2009

Hin ) Hout

(2)

The standard enthalpies of any combustion reaction can be found from the sum of the products of the standard enthalpies of formation and the stoichiometric coefficients, i.e.,

∆H°RX )

∑(νi∆H°f,i)

(3)

For hydrocarbons, the combustion reaction is as follows:

CnH2n+2 + (1.5n + 0.5)O2 f nCO2 + (n + 1)H2O (4) The standard enthalpies of formation for reactants and products of hydrocarbon combustion can be found in the JANAF (Joint Army, Navy, Air Force) tables (i.e., Sandler, 1989). In the case of the combustion of butane, pentane, hexane, and heptane, which are analyzed in more detail in this work due to the volume of data available, the relevant date are contained in Table 1. (Note: In this work, n-butane, n-pentane, n-hexane, and n-heptane are simply referred to as butane, pentane, hexane, and heptane, respectively.) It should be noted that in the field, combustion is likely to be conducted with a slight excess of air, but the calculation based on no excess air represents a thermodynamic limit to the situation. Ideal gas heat capacity data used in the calculation of adiabatic flame temperatures were obtained (Reklaitis, 1983) in the form:

CP ) a + bT + cT2 + dT3 + eT4

(5)

Specifically, the ideal gas heat capacity data used for the calculations are contained in Table 2. These heat capacity data are not valid at temperatures above 1500 K (Reklaitis, 1983). Attempting to integrate the heat capacity from an assumed inlet temperature of 311 K to the adiabatic flame temperature, which is well above 1500 K for each combustable substance examined in this work, would lead to a physically unrealistic result due to the negative coefficient in the quartic term for nitrogen. Accordingly, to determine the adiabatic flame temperatures it was assumed that the heat capacity could be evaluated at an average temperature of between 1350 and 1500 K and that the resultant average heat capacity could be used, i.e.,

Tad ) Tin -

∆H° CP,av

(6)

The heat capacity pertains to the flue gas from the combustion process, i.e., the mole-weighted average of gases produced by the combustion of one mole of fuel. Results obtained are in Table 3. While combustion reactions usually are presumed to go to completion, when examining the emissions from a combustion point source it is illustrative to examine the maximum possible conversion of fuel which can be realized in a combustion process. The maximum conversion would occur at the point of chemical equilibrium. Accordingly, the adiabatic flame temperature, combined with the Gibbs free energy of combustion and enthalpy of combustion, can be used to determine the equilibrium constant at the adiabatic flame temperature. Standard Gibbs free energies of formation and combustion are contained in Table 4. Gibbs free energies of formation were obtained from the JANAF tables (i.e., Reklaitis, 1983), and the Gibbs free energies of reaction

Table 1. Standard Enthalpies of Formation and Reaction Pertaining to Combustion of Butane, Pentane, Hexane, and Heptane species

standard enthalpy of formation (kcal/mol)

standard enthalpy of combustion (kcal/mol)

butane pentane hexane heptane carbon dioxide water oxygen

-30.019 -35.00 -39.938 -44.861 -94.052 -57.7979 0 (by definition)

-635.179 -782.051 -928.959 -1075.886 NA NA NA

Table 2. Ideal Gas Heat Capacity Data Used in Adiabatic Flame Temperature Calculationsa a b c d e a

carbon dioxide

water

nitrogen

19.0223 7.96291 × 10-2 -7.37067 × 10-5 3.74572 × 10-8 -8.13304 × 10-12

34.0471 -9.65064 × 10-3 3.29983 × 10-5 -2.04467 × 10-8 4.30228 × 10-12

29.4119 -3.00681 × 10-3 5.45064 × 10-6 5.13186 × 10-9 -4.25308 × 10-12

CP [)] J/mol K; T [)] K.

Table 3. Calculated Adiabatic Flame Temperatures for Butane, Pentane, Hexane, and Heptane substance

temp, K

butane pentane hexane heptane

2439 2448 2452 2458

Table 4. Standard Gibbs Free Energies of Formation and Reaction Pertaining to Combustion of Butane, Pentane, Hexane, and Heptane

species

standard Gibbs free energy of formation (kcal/mol)

standard Gibbs free energy of combustion (kcal/mol)

butane pentane hexane heptane carbon dioxide water oxygen

-4.111 -1.96 -0.908 1.912 -94.26 -54.6351 0 (by definition)

-646.106 -797.151 -947.098 -1098.813 NA NA NA

Table 5. Equilibrium Constants at Standard Conditions for Combustion of Butane, Pentane, Hexane, and Heptane substance

equilibrium constant


7.666 × 10473 4.674 × 10584 4.442 × 10694 8.412 × 10805

were obtained by summing the products of the Gibbs free energies of formation and the stoichiometric coefficients, i.e.,

∆G°RX )

∑νi∆G°f,i

(7)

The equilibrium constant at standard conditions is found by the relation:

K° ) exp(-∆G°RX/RT°)

(8)

The equilibrium constants at standard condition can be found in Table 5. Using the Gibbs-Helmholtz equation in conjunction with the assumption that the enthalpies of reaction are not nearly as dependent on temperature as Gibbs free energies of reaction (Smith and Van Ness, 1975), the equilibrium constant at the adiabatic flame temperature

2010


Table 6. Emissions of Uncombusted Hydrocarbons at Chemical Equilibrium, and Emissions Predicted by the Use of the AP-42 Emission Factors substance

fraction emitted at equilibrium

fraction emitted predicted by AP-42 factors


1.131 × 10-9 5.673 × 10-10 3.666 × 10-10 2.114 × 10-10

3.431 × 10-5 2.674 × 10-5 2.314 × 10-5 1.99 × 10-5

can be found by the relation:

[

KTad ) exp

(

)]

-∆G°RX -∆H°RX 1 1 + RT° R Tad T°

(9)

For the combustion of a substance with a stoichiometric amount of air (or oxygen), knowledge of the equilibrium constant allows the calculation of the amount of fuel which remains uncombusted. Although combustion processes are actually multistep reaction sequences which cannot be described completely by a single equilibrium constant (Norrish and Foord, 1936; Butzert, 1964; Andrews and Bradley, 1972; Chelliah and Williams, 1990; Egolfolopoulos and Law, 1990), the step most germane to this work is the first step in the reaction sequence, i.e., the one in which the fuel is converted to a partially-combusted intermediate. Thus, the use of the equilibrium constant can be expected to give a reasonable determination of the amount of fuel which remains uncombusted (but not any intermediate combustion products which may be formed). Accordingly, the fraction of uncombusted butane, pentane, hexane, and heptane which may be expected is found in Table 6. In addition to the aforementioned method of determining thermodynamic parameters such as adiabatic flame temperature for common hydrocarbons, there are a number of sophisticated computer programs which have been developed for this purpose. Included among these are CHEMKIN (Sandia National Laboratories), StanJan (Stanford University), THERM (New Jersey Institute of Technology), PRO II (SimSci), and ChemCAD (Chemstations). Comparison to Emissions Predicted by the AP-42 Emission Factors Thus far, this work has focused on the maximum theoretical extent of combustion which may be realized. It is illustrative to compare the results in Table 6 to the emissions which are predicted by the AP-42 emission factors. The AP-42 document expresses emissions of hydrocarbons from the combustion of natural gas as mass of emissions per volume of fuel fired. Emissions of volatile organics are broken down into methane emissions and nonmethane emissions. The emission factor for combustion of natural gas in domestic and commercial boilers is 84 kg/106 m3 for nonmethane emissions and 43 kg/106 m3 for methane emissions. If it is assumed that the fuel enters the combustion unit at standard conditions and that emissions of volatile organics are in the form of uncombusted fuel, then the fraction of uncombusted fuel may be calculated. (Note: The emissions of byproducts of combustion, which may be at least as toxic as the fired material, are not considered in this work, but will be the subject of future studies.) The results are shown for comparison, also in Table 6. Since the AP-42 emission factors are based on actual emissions as determined by stack tests and

quantitative analytical methods, the emissions predicted by the use of AP-42 emission factors may represent a good prediction of the actual emissions which may be observed if pure butane, pentane, hexane, or heptane were combusted. However, the fraction of fuel combusted decreases with increasing molecular weight, and this may be counter-intuitive. There are a number of reasons that could contribute to this phenomenon, but the most likely explanation is that the AP-42 emission factor data were determined predominantly for natural gas (i.e., methane) combustion and may be less accurate for analysis of combustion of higher hydrocarbons. This may point to the need for more complete and accurate emission factor data for combustion of higher hydrocarbons. It should be noted that the AP-42 emission factors have been applied conservatively (i.e., to give the maximum possible emissions) in this work. This is consistent with the intended application of the TRE Index, as specified in the HON Rule and other regulations, where it is stated that engineering judgements may be applied, but if they are applied they must be applied conservatively. Specifically, the calculation of emissions by the use of the AP-42 emission factors is conservative in the following respects: (1) The largest possible category of emission factors from the AP-42 document was employed. The emission factors for combustion of natural gas in utility or industrial boilers are lower than those for domestic and commercial boilers, which were employed herein. (2) It was assumed that the volatile organic compound emissions were entirely in the form of uncombusted fuel. In practice, it is expected that some emissions would be in the form of partially-combusted species. (3) Combustion of pure species was examined. In practice, a mixture of species usually will be combusted, so the emission of each species will be smaller. This is significant from a regulatory point of view, because maximum emissions of single species usually are regulated, as is the case in the HON Rule. Table 6 clearly indicates that the AP-42 model of a typical industrial combustion process does not proceed to the state of chemical equilibrium. This result, while intuitive, required verification. Accordingly, the kinetics of combustion need to be examined. Kinetics of Combustion Since Table 6 shows that combustion of natural gas in boilers does not yield an equilibrium state, examination of the kinetics of combustion is illustrative. The rate of combustion can be expressed as follows:

d[fuel] ) k[fuel]a[O2]b dt

(10)

k ) A exp(-Ea/RT)

(11)

r) where

The parameters a, b, A, and Ea have been determined experimentally for the combustion of butane, pentane, hexane, and heptane (Dryer, 1991) and are listed in Table 7. Dryer’s work is especially of interest because it yields good single-step kinetic expressions and parameters which model the complex multistep processes embodied in a combustion reaction (Westbrook and Dryer, 1981).

Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996 2011 Table 7. Parameters for the Kinetics of Combustion of Butane, Pentane, Hexane, and Heptane species

a

b

A (mol/L s)

Ea (cal/mol K)


0.15 0.25 0.25 0.25

1.6 1.5 1.5 1.5

7.4 × 1011 6.4 × 1011 5.7 × 1011 5.1 × 1011

30 000 30 000 30 000 30 000

Table 8. Parameters Pertaining to Hydrocarbon Combustion fuel butane pentane hexane heptane

V* [fuel]lm (s-1) (mol/cm3) 82.9 60.3 54.0 48.8

1.65 × 10-8 1.32 × 10-8 1.09 × 10-8 9.32 × 10-9

[O2]lm (mol/cm3) 1.075 × 10-7 1.054 × 10-7 1.039 × 10-7 1.026 × 10-7

rlm Φ (mol/cm3 s) (dimensionless) 7.324 × 10-4 4.935 × 10-4 4.143 × 10-4 3.543 × 10-4

534.2 620.4 701.3 778.2

Figure 2. Effect of molecular weight on space velocity.

It is assumed that combustion occurs at a total pressure of 1.0 atm and at the adiabatic flame temperature of each species. As stated previously (vide supra), this work considers the combustion of substances with theoretical air. Thus, certain aspects of this work must be taken as a limiting case, instead of an actual physical result. In the field, combustion typically is conducted with excess air, and at temperatures below the adiabatic flame temperature. In particular, it is recognized that tempartures can vary within the combustion zone due to quenching at the walls, imperfect mixing, radiation losses, and related factors. By integrating the rate equation for the combustion of each of these species, it is possible to determine a residence time, and therefore a space velocity, related to the flow of combustable mixtures through the combustion zone. The space velocity for combustion of each species examined is shown in Table 8. Dimensional Analysis of Combustion It is illustrative to consider the average concentration of fuel and oxygen during the combustion process. If we define a log-mean concentration as

Clm ) Cf + [(Ci - Cf)/ln(Ci/Cf)]

(12)

where Clm ) log-mean concentration, Ci ) initial concentration, and Cf ) final concentration, then we also are led to the concept of a log-mean reaction rate, where

rlm ) rlm(Clm) ) k[fuel]lma[O2]lmb

(13)

A log-mean concentration would be of little physical significance over small concentration differences. Specifically, for changes less than 60% between inlet and exit values, the log-mean will be greater than the inlet value. However, just as the concept has proven useful when applied to large temperature differences, it also can provide a more accessible analysis to large changes in concentration. It is expected that combustion reactions will go nearly to completion, so the change in concentration will be well in excess of 60%. By considering the space velocity, the log-mean concentration of the consumed species, and the logmean reaction rate during the combustion process, a dimensionless parameter is suggested, which will be referred to as Φ in this work. Thus, we may state

Φ ) (rlm/Clm)/V*

(14)

where V* is the space velocity, and rlm and Clm are the

Figure 3. Semi-log plot of Φ vs molecular weight.

log-mean reaction rate and log-mean concentration, as defined above. (Under many circumstances the space velocity is simply the inverse of the residence time.) The physical significance of the parameter Φ is that it represents the ratio of a reaction rate normalized by reactant concentration (i.e., rlm/clm) to the flow rate of materials passing through the reaction locus (V*). This dimensionless group recently has been referred to by others as the Phillips number (Mysore, 1996; Kuttruff, 1996). Specifically, the concentration of the combusted species (i.e., hydrocarbon) is used in the denominator of the Φ calculation. The space velocity, log-mean reaction rate, log-mean concentrations, and values of Φ for combustion of butane, pentane, hexane, and heptane are listed in Table 8. The space velocity is observed to decrease monotonically as the molecular weight increases. This trend is highlighted in Figure 2. The significance of this relationship will be seen in the method to predict emission factors which is developed in this work (vide infra). Examination of Table 8 leads to two refinements on the concept of a dimensionless group to describe the combustion process. First, the parameter Φ appears to be proportional to some power of the molecular weight of the combusted substance (Figure 3). Moreover, the log-mean concentration used in the denominator of the expression for Φ is only that for the hydrocarbon species and does not take into account the change in oxygen concentration. If a weighted average log-mean concentration is defined as

Clm′ )

a[fuel]lm + b[O2]lm a+b

and we define a new dimensionless group, Φ′, as

(15)

2012


Φ′ ) (rlm/Clm′)/V*

(16)

then the results obtained are found in Table 9. While dividing the dimensionless group Φ by the molecular weight improves the correlation, the relation Φ/MW0.69 gives an almost exact correlation. However, it should be noted that there is no physical significance to the molecular weight raised to the 0.69 power, so it is not considered to be anything more than an empirical correlation that the data fit this relation (vide infra, Introduction and Note on Empirical Correlations). Moreover, it is apparent that the parameter Φ′ provides a satisfactory correlation of the data, and there is a certain physical significance present in each term comprising Φ′ which is absent in a molecular weight raised to an unusual power. In any event, either line of thought suggests a satisfactory method of predicting emission factors solely on the basis of kinetic data. Before continuing with the subject of air emissions, it should be noted parenthetically that the development of a dimensionless group for the design and analysis of reacting systems represents new ground that is being broken in this treatise. Previous work on the dimensional analysis of reacting systems has produced the trivial dimensionless group k0τ for describing first-order systems, and the Damkohler number, which considers heat effects in reacting systems (Zlokarnik, 1991). In contrast, this work provides a dimensionless group which can be used to analyze a much broader range of reacting systems. The dimensionless groups Φ and Φ′ presented herein can be applied to reactions of any order. Details of the application of Φ (or Φ′) for the design and analysis of a broader spectrum of reacting systems are beyond the scope of this work but will be the subject of a future paper. However, it can be stated at this juncture that the dimensional analysis of reacting systems represents virgin territory, and the parameter Φ is expected to be of significant benefit in designing a broad spectrum of industrial processes involving chemical reactions. Examples might include slurry bed reactor design, catalytic cracker design, and biological waste treatment unit design. Procedure for Determining Emission Factors As stated above, the results obtained herein suggest a procedure for predicting emission factors based only on kinetic data for the combustion reaction of a given species. The steps are as follows: (1) Select a space velocity from Figure 2, based on the molecular weight of the combusted species, i.e.,

V* ) V*(MW)

(17)

Alternatively, the space velocity-molecular weight data in Table 8 may be curve-fitted using a cubic spline or equivalent numerical method, and an analytical result thereby obtained. (2) Express the oxygen concentration as a multiple of the combusted species concentration, in a manner consistent with the stoichiometry of the combustion reaction, i.e.,

for

A + xO2 f products [O2] ) x[A]

(3) Substitute into the relation

(18)

Table 9. Dimensionless Group Refinements fuel

MW

Φ/MW0.69

Φ′


58 72 86 100

32.4 32.4 32.4 32.4

88.6 88.6 84.6 81.3

Φ/MW0.69 ) 34.2

(19)

Φ′ ) 80

(20)

or

(Note: While the values of Φ′ range from the low 80’s to the high 80’s in Table 9, choosing a slightly smaller value will yield a more conservative calculation, i.e., one in which the maximum expected emissions will be predicted.) (4) Solve for Clm. This step requires kinetic data for the combustion of the substance at hand, if the system is to be reduced to that of one equation and one unknown, since

Φ ) Φ(rlm,Clm,V*) ) Φ(k,Clm,V*)

(21)

Since the initial concentration is known, this allows calculation of the final concentration. (5) Convert units to determine an emission factor in units of kg/106 m3. While emission factors for substances other than those discussed in this work are not generally known, the use of this procedure for the combustion of n-octane was able to reproduce the emission factor published in the AP-42 document to three significant figures. Discussion This work provides a means to determine emission factors for the combustion of substances other than the hydrocarbon fuels covered in the AP-42 documentation. Previous work on emission of uncombusted substances from industrial point sources containing a combustion process has relied on the assumption that emission factors for nonhydrocarbon substances are nearly the same as those for hydrocarbons. While this work provides a method which does not rely on such an assumption, it should be noted that knowledge of kinetic data pertaining to the combustion of the substance in question must be known. Fortunately, kinetic data of this nature are more readily attainable than emission factors for combustion of a wide variety of substances. Another point which merits further attention is the assumption that adiabatic flame temperatures can be determined by using a heat capacity calculated at a mean temperature. While this does not produce a result which is as rigorous as an integration-based method, errors associated with the use of a mean heat capacity should be minor. Heat capacity data which are valid over a wider range of temperatures would ameliorate this situation. Potentially more significant is the assumption that the Gibbs-Helmholtz equation (in its form contained in eq 9) can be used over a temperature differential as large as that contained in this methodology. This may or may not yield errors which are significant. And while knowledge of enthalpies of formation at a range of conditions which are at variance with standard conditions would allow more precision in the application of the Gibbs-Helmholtz equation, the degree of accuracy which may be gained by the acquisition of such data

Ind. Eng. Chem. Res., Vol. 35, No. 6, 1996 2013

remains debatable. Moreover, determination of enthalpies of formation at a wide range of temperature and pressure conditions for a broad spectrum of combustible substances represents an immense task. It appears unlikely that such data will be forthcoming in the near future. Therefore, dependence on the relative constancy of enthalpies of formation (Smith and Van Ness, 1975) may represent not only the most accurate available method but also the only accurate approach to the problem of predicting Gibbs free energies of reaction at elevated temperatures. The concept of space velocity requires additional attention. In this context, it is interpreted as meaning the portion of a boiler or incinerator where the combustion reaction takes place, i.e., the flame. It should not be confused with the space velocity of a fuel-oxygen mixture and/or flue gases through a plenum. In determining space velocities by the use of Figure 2, it should be noted that only hydrocarbon species were used to correlate space velocity with molecular weight. As emission factor data for the combustion of other substances, i.e., those containing heteroatoms, become available, the space velocity correlation may need to be modified. In any event, the use of Figure 2 should provide much better than an order of magnitude estimate of the space velocity. If an additional safety margin is desired, then an appropriate engineering judgement can be applied to the situation. Conclusions This work has developed a method to determine atmospheric emission factors for industrial point sources containing a combustion reaction. The method can be applied to the combustion of substances other than the fuels which are the subject of the EPA’s AP-42 document. Kinetic parameters, including the rate constant (or, equivalently, the energy of activation and the Arrhenius pre-exponential term) and the reaction orders, are required to implement the method presented herein. The procedure for determining emission factors uses a novel dimensionless group, which was formulated as part of this work. This dimensionless group, referred to as Φ in this work, makes use of a log-mean concentration and a log-mean reaction rate which is a function of the log-mean concentration. In addition to having utility in determining emission factors for combustion reactions, the parameter Φ appears to be applicable to the analysis and design of a wide variety of reacting systems. Notation A ) Arrhenius pre-exponential term a ) combusted species reaction order b ) oxygen reaction order a′, b′, c′, d′ ) coefficients for calculation of TRE Index a, b, c, d, e ) coefficients for calculating heat capacity Cf ) final concentration Ci ) initial concentration Clm ) log-mean concentration Clm′ ) weighted average log-mean concentration CP ) constant pressure heat capacity CPav ) constant pressure heat capacity at average conditions Ea ) energy of activation EHAP ) hourly emission rate of total organic HAP ETOC ) hourly emission rate of NMNE TOC

∆G°f,i ) Gibbs free energy of formation of species i at standard conditions ∆G°RX ) Gibbs free energy of reaction (combustion) at standard conditions HT ) vent stream net heating value ∆H°f,i ) enthalpy of formation of species i at standard conditions ∆H°RX ) enthalpy of reaction (combustion) at standard conditions KTad ) equilibrium constant at the adiabatic flame temperature K° ) equilibrium constant at standard conditions k ) rate constant k0 ) first-order rate constant MW ) molecular weight of combusted species Qs ) vent stream flow rate R ) ideal gas constant r ) rate of reaction rlm ) log-mean reaction rate T ) absolute temperature Tad ) adiabatic flame temperature Tin ) inlet temperature T° ) standard temperature TRE ) total resource effectiveness index V* ) space velocity x ) ratio of stoichiometric coefficients νi ) stoichiometric coefficient of species i τ ) residence time Φ ) dimensionless parameter for the analysis and design of reacting systems Φ′ ) modified dimensionless parameter for the analysis and design of reacting systems

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Received for review June 21, 1995 Accepted February 26, 1996X IE950388K

X Abstract published in Advance ACS Abstracts, May 1, 1996.

Prediction of Air Emission Factors for Combustion Point Sources

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