Environ. Sci. Technol. 1989, 23,442-450
Detailed Chemical Kinetic Modeling of Fuel-Rich C2HCI3/O2/Ar Flames Wen-Donq Chang and Selim M. Senkan"
Department of Chemical Engineering, Illinois Institute of Technology, Chicago, Illinois 606 16
A detailed chemical kinetic mechanism for the combustion of C2HC13under fuel-rich and slightly sooting conditions has been developed. This mechanism was used to calculate the stable species concentration profiles in atmospheric pressure, premixed, one-dimensional flat flames of C2HC13/02/Ar measured previously ( I ) . The agreement between the model and experimental data is generally reasonable. The major reaction pathways responsible for the formation and destruction of species have been identified via the calculation reaction rates and sensitivity analysis.
hensive mechanisms in the future. The present mechanism involves the participation of 53 species in 147 elementary reactions and accounts for the available experimental data with reasonable accuracy. Numerical Model For one-dimensional, premixed, laminar flat flames, the enthalpy and species balance equations can be shown to be given by the following: mcp dT/dx - d(kA dT/dx)/dx + N
N
ACpYiVic,i(dT/dx) Introduction The development of detailed (micro) chemical kinetic mechanisms describing the combustion of chlorinated hydrocarbons (CHC) quantitatively is important for a number of reasons. First, there is a growing need to better understand and control pollutant emissions into the environment from combustion systems burning these materials. For example, CHCs are associated with the formation of chlorinated aromatics, dibenzodioxins, and dibenzofurans in incinerators, some of which are extremely toxic (2,3). In addition, the formation of these pollutants is a consequence of rate limitations, as opposed to thermal equilibrium considerations (4). However, the underlying chemical kinetic mechanisms responsible for these observations are not fully understood yet ( 5 ) . Second, detailed chemical kinetic models constitute a rational starting point to evaluate the combustion behavior of complex hazardous mixtures. Consequently, these models will be of considerable use in the proper interpretation of large-scale incineration test burn data and in directing applied incineration research in the future. Third, the nanufacture of useful chemicals by the controlled combustion of CHCs also is a promising enterprise. This was shown recently by the development of a chlorine-catalyzed oxidative pyrolysis (CCOP) process to convert methane, the major component in natural gas and an important product in the anaerobic digestion of organic matter, into more valuable products such as ethylene, acetylene, and vinyl chloride (6). In recognizing these growing needs we have been developing such detailed chemical kinetic mechanisms describing the oxidation and pyrolysis of CHCs in a systematic way, starting with the most simple chlorinated hydrocarbons, such as CH3Cl and C2HC13,representing hydrogen-rich and chlorine-rich CHCs, respectively (7-10). Related research is also in progress elsewhere (11-13). In this communication, we report a detailed (micro) chemical kinetic mechanism for the high-temperature combustion of C2HCl, under fuel-rich conditions as a follow-up on our earlier work with fuel-lean flames (8). This mechanism was used to simulate the stable species mole fraction profiles measured in an atmospheric pressure, premixed, one-dimensional flat flame of C2HC13/ 02/Ar under slightly sooting conditions. In the current mechanism, we expanded the pool of reactive species considerably and proposed a simple path for the formation of c6c&to improve model predictions. These modifications broaden the range of applicability of the model significantly and should help develop even more compre442
Envlron. Scl. Technol., Vol. 23, No. 4, 1989
i=l
m dY,/dx
+ d(pAYiV,)/dx
+ ACwihiMi = 0.0 i=l
- AwiMi = 0.0
(i = 1, ...,N) where m = puA is the mass flow rate, p = P(MW)/(RT) is the mass density, P is the total pressure (1atm in this work), MW is the mean molecular weight, cp is the mean specific heat of the mixture, T i s the temperature, x is the distance along the flame which is equivalent to time, A is the cross-sectional area of the stream tube enclosing the flame, u is the fluid velocity, k is the thermal conductivity of the mixture, V,, is the diffusion velocity of the ith species, w, is the net molar rate of generation of species i as a consequence of competition between various elementary reactions in the mechanism presented in Table I below, Mi is the molecular weight, hiis the specific enthalpy, and Yi is the mass fraction of species i. Calculations were performed by using the SandiaFLAME code (14) running on a DEC VAX 11/750 computer, and by specifying the temperature profile along the flame zone, which was experimentally measured in prior studies ( I ) . Such a procedure makes it possible to account for heat losses from the flame in a reasonable manner. In addition, the specification of the temperature profile decouples the energy balance equation from the species balance equations, and this greatly enhances the rate of convergence of the numerical method. Thermochemical information, which includes heats of formation, entropies, and temperature-dependent specific heats, was acquired from the JANAF tables (15,16),NASA compilations (13,Baulch et al. (18),Pedley et al. (19),and Benson's work (20-22), whenever they were available. However, such data for some of the species in the mechanism have not been documented; consequently, they were estimated by semiempirical methods. Physical molecular properties, which include LennardJones parameters, dipole moments, polarizabilities etc., that are necessary to determine thermophysical properties, such as the gas-phase viscosities, conductivities, and species diffusion coefficients, were acquired from conventional sources (23-25),whenever available. In the absence of such data, they were again estimated by semiempirical methods (23-26). Reaction Mechanism An elementary reaction set describing the high-temperature fuel-rich combustion of C2HC13is pfesented in Table I together with the rate parameters for the forward reaction paths. Reverse reaction rates were then calculated from the considerations of the detailed balancing between
0013-936X/89/0923-0442$01.50/0
0 1989 American Chemical Society
the forward and reverse rates through the use of the equilibrium constant. Whenever possible we used recommended rate parameters based on recent evaluations of experimental rate data as well direct experimental measurements, and the sources of this information are indicated in the last column in Table I. In the absence of such data, we estimated rate parameters by analogy with similar hydrocarbon reactions, with corrections made for the highly electronegative chlorine atom (20). Although the resulting uncertainties in rate parameters for the latter reactions may be substantial, their impact on model predictions will be small unless they are important reactions in the mechanism. Important reactions identified by sensitivity and reaction path analyses subsequently must be isolated and studied with greatest scrutiny for the redetermination of their rate parameters (24). Sensitivity analysis will be discussed further below. The mechanism presented in Table I was constructed by systematically considering all plausible elementary reactions of C2HC13and 02,and their daughter species, consistent with the principles of physical organic chemistry, available experimental data, and thermochemistry and by eliminating those reactions that did not contribute to reaction rates and were determined to be unimportant by the sensitivity analysis. The C2HC13mechanism subsequently was combined with the chlorine-inhibited CO oxidation submechanism developed and tested previously (27). As is evident from Table I, the combustion kinetics of C2HC13are intimately related to the kinetics of combustion of many other C1 and C2 chlorohydrocarbons, as well as to some of the higher molecular weight CHCs. As a consequence of such intimate relationships, which are also seen in the combustion of regular hydrocarbons (28), the detailed chemical kinetics of combustion of simple chlorinated hydrocarbons must be understood sufficiently well before such mechanisms are proposed for the combustion of complex chlorinated hydrocarbons, e.g., chlorinated aromatics. The present mechanism of combustion of C2HC13differs considerably from the one published previously (8) because of a number of significant improvements. First, falloff corrections were made for all the major pressure-dependent elementary reactions, since a large temperature increase occurs along the flame, concomitant with a sharp decrease in gas-phase density. Consequently, reactions that may be a t their high-pressure limits in the preflame zone can exhibit considerable falloff behavior a t the high temperatures associated with the later stages of the flame (29). In this regard it is also important to recognize that the recombination of radicals or the addition of radicals to stable species with unsaturated bonds is responsible for molecular weight growth processes in flames. Since all these processes are inherently exothermic, the adduct formed initially contains an excess amount of energy corresponding to the exothermicity of the reaction and thus will be chemically activated. In the presence of falloff conditions, a number of endothermic reaction channels may become accessible to the chemically activated adduct, competing directly with collisional stabilization. Therefore, proper rate parameters for individual reaction channels must be determined by considering the composite behavior of chemical reaction and collisional stabilization processes (10). In the present study, all the major chemically activated recombination and addition processes were analyzed by using the bimolecular version of the quantum RRK (Rice-Rampsperger-Kassel), or QRRK method developed recently (30). Falloff corrections for regular unimolecular
Symbols: Experimental d a t a t i n e s : Model p r e d i c t i o n s
T CEXPT.)
0044
/ H O
+
1300
4 "
0.3
//
Y
u
//
w z
3
1100 W
a x W
c 900
5
700
DISTRNCE RLONG FLRME (MMI Figure 1. Comparison of the experimental data with model predictions for C2HC13,O,, CO, C02, HCI, and C12, and the experimental temperature profile.
decomposition reactions similarly were made by the unimolecular quantum RRK method (31). In Table I, we report phenomenological rate parameters evaluated specifically at 1 atm by using a three-parameter rate coefficient of the form k = AT' exp(-E/RT). Second, the following two-channel process has been proposed for the oxidation of the C2Cl3 radical: C,CI,
+
02 z=
-
IcpC130~3*
-
+ COCl C2C120 + C I O COClp
since both C0C12 (phosgene) and C2C1,O (dichloroketene) were identified as products in the isolated studies of the C2C13+02reaction (32). Third, reaction mechanisms responsible for the formation and destruction of acyl chlorides, i.e., CHC12COCland CCl,COCl, and of C3Cl, and C4C&were developed, as all of these species were also noted to be present in fuel-rich flames of C2HC13( I ) . In addition, to improve model predictions, a simple irreversible reaction scheme, i.e., reactions 83 and 92,for the formation of C6C&(hexachlorobenzene)was proposed and incorporated into the mechanism.
Results and Discussion The precombustion composition of the atmospheric pressure, fuel-rich and slightly sooting flame investigated in this work was as follows: C2HC13,22.6%,02,33.1 9%,and Ar, 44.3%. This mixture corresponds to an equivalence ratio of 1.36, considering HC1 as the preferred combustion product. That is, H 2 0 does not form as a major equilibrium product in CHC combustion when the Cl/H ratio of the mixture is larger than unity (4). This was also verified experimentally both in fuel-rich ( I ) and in fuel-lean (7) flames. In the figures, calculated mole fraction profiles (indicated by lines) for various species are compared to those determined experimentally (indicated by symbols). The experimentally determined temperature profile along the flame, used in the calculations, is also presented in Figure 1. As evident from these figures, the agreement between the model and experimental data is generally reasonable, suggesting that the major features of the flame chemistry of C2HC13 have been described reasonably well by the model. The validity of the mechanism to predict the structure of trichloroethylene flames under fuel-lean conditions was also explored. The mechanism presented in Table I faithfully reproduced the species mole fraction Environ. Sci. Technol., Vol. 23, No. 4, 1989 443
Table I. Chemical Kinetic Mechanism for the Combustion of CzHC13" reactionb"
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
CzHCl3 P CzHClz + C1 CzHC13 + C1 s C2HCl4 CzHC13 ~2 CZC12 + HC1 (*) CzHCl3 ~i CzHCl+ Clz CzHC13 + C1 F! CpHClp + Cl2 CzHCl3 C1 P CzC13+ HC1 (**) CzHC13 + 0 P CHOCl + CClz CZHCl3 OH ~2 CHClzCOCl + H CZHCl3 + C10 ~t CHClzCOCl + C1 (*) CZHCl3 CC13 P CC14 + CzHClz CZHCl3 CHClz s CHC13 + CzHClz CzHC13 + CzHCl4 P CzHC16 + CpHClz CpCl4 + OH s CHClzCOCl+ C1 CpCl4 + 0 P COClp + CClz CzCl4 + C10 P CC13COCl+ C1 C2Cl4 C1 P CzC16 CzCl3 + Cl2 s CzCl4 + C1 (**) CzHCl6 P HCl + Czc14 CzHC16 P C1+ CzHCl4 CzHC16 + c 1 P HCl + Czc& CzHClb + C1 Clz + CzHCl4 CzCls Clz + CzCl4 CzC16 C1+ CzCl5 C2C16+ C1 ~1 Clz + C2C16 CzHClp + M s C2HCl+ C1+ M CZHClz + C1 CzClp + HCl C2HClp + C1 P CzHCl+ Clz CzHClz + 02 P CHOCl + COCl CzCl3 C1 s CzCl4 CzCl3 + C1 P CzClz + Clz CzCl3 + 02 s COClz + COCl (**) C2Cl3 02 s CzCl20 C10 (**) C2Clz0 + C1 s CO + CC13 (**) CZCl3 + 0 s CO + CC13 C2Cl3 C10 P CO t CC14 CzHCl4 02 P CHClzCOCl+ C10 CHClZCOCl+ C1 P CCl2COCl+ HCl (*) CHClzCOCl + C1 P CHClzCO + Clz CClzCOCl P CC13 + CO (*) CHClzCO CHClp + CO CzHC14+ C1 F! CHClz CC13 CzC16+ C1 P CC13 CCl, CzC16+ C1 s CzCl4 + Clp CzC16 Oz s CCl3C0Cl+ C10 CCl,COC1+ c1 S CCl3CO + Clz cc1,co P cc1, + co + 0 s ce1, + co o2s COCl COCl (**) + Clz P CZCl4 M s CzClz + C1+ M (*) + C10 ~1 CO CC13 + OH P CO + CHClz
Cz Kinetics 33.48d 32.56 26.03 35.98 13.50 12.30 13.00 11.50 11.00 11.50 12.40 11.00 12.75 13.00 11.00 35.42 12.40 33.22 29.34 12.30 13.00 35.21 36.13 13.80 14.90 15.86 5.72 11.0 33.65 17.72 11.50 11.50 13.00 13.0 12.00 11.0 13.00 14.00 12.00 13.50 20.79 27.23 27.10 12.00 14.00 13.50 13.85 11.00 36.42 14.90 11.0 12.00
53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
CHCl3 P CHC12 + C1 CHC13 + 0 P COClp + HCl CHC1, 0 ~t CC13 + OH CHC13 + C1 s CHClz + Cl2 CHC13 + C1 P CC13 HCl (*) CC14 P CCl, + C1 CC14 + 0 s CC13 + C10 CC13 + Oz P COClz + C10 (*) CC13 + 0 s COClz + C1 CC13 + Clz P CC14 + C1 (*) CC13 + CC13 P C2C16 CC13 + CC13 s CzCl4 + Cl2 Ccl3 + CHClz P C2HCl6 CC13 + CHC12 P CZCl4 + HCl CHClz + Oz CHOCl + C10 CHClz + 0 P CHOCl + C1 CClZ+ 0 2 P c10 + COCl CClz + C12 P CC13 + C1 CHOCl+ M P CO + H C l + M CHOCl + C1 s COCl + HCl
C1 Kinetics 27.40 11.00 12.46 14.00 12.84 35.87 10.40 13.00 14.00 12.40 36.15 26.35 34.22 20.37 13.00 14.00 13.00 12.70 17.00 13.30
1 2
444
log A
+ + +
+
*
*
*
+ + +
+
+
+
+
+
+ +
+
+
+
+
Environ. Scl. Technol., Vol. 23, No. 4, 1989
n
E
AHr(298 K)
ref
-5.88 -6.52 -3.83 -7.06
88.3 55.2 61.6 83.5 20.0 5.0 2.0 -0.9 2.0 8.0 5.0 8.0 2.4 5.0 5.0 5.3 3.0 68.1 72.0 3.3 16.6 63.2 74.4 18.3 28.0 1.9
76.6 -22.5 19.5 52.4 17.2 -7.3 -43.2 -15.4 -54.0 5.8 -3.0 7.8 -38.6 -54.3 -51.9 -17.8 -15.5 9.1 68.8 -8.7 9.4 26.8 68.5 9.0 35.2 -57.2 -24.3 -91.0 -75.0 -32.7 -100.4 -38.9 -17.4 -111.4 -116.4 -42.3 -3.1 17.5 5.4 12.8 8.9 -1.0 -41.7 -44.9 15.5 8.6 -70.9 -49.2 -42.3 26.8 -72.4 -51.8
35,37 37,39 35,37 35,37 40 41 40 42 42,43 40 40 40 42 40 42,43 37, 38 40 37, 38 37, 38 37 37 37,44 37,44 44 41 37, 40 34, 40 40 35,37 37, 40 32 32 40 40 40 43,45 40 46,47 46,47 46,47 37,40 37,40 37,40 43,45 40 46,47 40 40 35,37 41 40 40
79.7 -110.5 -6.7 20.2 -7.8 70.8 5.0 -47.7 -102.8 -11.4 -67.5 -40.7 -77.8 -68.7 -41.8 -96.9 -37.1 -7.8 -8.3 -15.4
37,40 40 18 48 48 37,40 18 49 40 44 37,44 37, 40 37, 38 37, 40 40 40 40 40 50 50, 51
0 0 0 0 0 0 0 0 0 0 0
-7.71 0 -5.79 -4.14 0 0 -6.53 -6.48 0 0
-0.97 1.65 0 -7.21 -1.66 0 0 0 0 0 0 0 0 0 0
-1.75 -4.01-4.73 0 0 0 0 0
-7.17 0 0 0 -4.02 0 0 0 0
-6.52 0 0 0 0
-7.48 -4.43 -6.79 -2.45 0 0 0 0 0 0
1.1
5.0 5.7 5.1 5.0 5.0 0 0 0 5.0 5.0 17.6 5.0 13.5 16.5 12.1 8.9 12.0 17.6 8.0 0
5.0 40.9 28.0 0 0 79.7 4.0 5.0 21.0 3.3 75.4 2.3 28.0 0
6.0 6.7 9.0 6.0 6.4 28.0 0
1.0 3.0 40.0 3.0
Table I (Continued) reactionbVc
log A Kinetics 11.50 12.70 13.50 11.76 12.00 13.00 13.00 11.50 11.80 12.30 10.00 12.70 13.30 11.26 13.00 12.00 11.70 13.00 11.70 10.00
n
E
AH,(298 K)
5.3 5.0 20.0 5.3 5.0 22.0 18.6 4.3 4.2 4.0 0 20.0 3.0 4.1 18.0 5.0 3.0 16.0 1.0
-32.6
ref
c3-c6
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112
113 114 115 116 117 118
119 120 121 122
123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145
CO + 0 + M s COZ + M CO OH s COP + H co + 0 2 s coz + 0 (*) CO + HOP F! COz OH Hz + 02 it OH + OH OH + Hz s HzO + H H + 02 s OH + 0 0 + H2 F! OH + H H + 02 + M e HOz+ M OH + HOz s HzO + 0 2 H + HOZ s OH + OH 0 + HOz it Oz+ OH OH + OH + 0 HzO H + H + M s Hz+ M H + H + Hz H ~ Hz P H + H + HzO it Hz + HzO H + H + COZ e Hz + COZ H t OH + M s H20 + M H + O + M it O H + M H + HOz e Hz 02 c10 + co e coz c1 (*) COCl + M it CO + C1 + M (**) COCl + H it CO + HC1 COCl OH + CO + HOCl COCl + 0 S co + c10 COCl + 0 i- coz + c1 COCl + oz S coz+ c10 COCl + CL S co + Clz (*) Clz + M F? C1+ C1+ M H C l + M s H C1+ M HCl + H s Hz C1 H + Clz s HCl + C1 0 + HCl it OH + C1 OH + HCl s C1+ HzO 0 + ClZF? c10 + c 1 0 + c10 e c 1 + oz C1+ HOz it HCl + 0 2 C1+ HOZ s OH + C10 C10 + Hz e HOCl + H H + HOCl e HCl + OH C1 + HOCl ii HCl + C10 C1 + HOCl ~t Clz + OH 0 HOCl e OH + C10 OH + HOCl e HzO + C10 HOCl + M ii OH + C1+ M ClOO + co F! coz+ c10 ClOO + M ii C1 + Oz M c 1 + ClOO e ClZ+ oz c 1 + ClOO ii c10 + c10 0 + ClOO ii c10 + o2 COClp + M i- COCl + C1+ M COClz + M s CO + Clz + M COClZ + c 1 S COCl ClZ (**)
+
+
+
+
+
+
+ +
+
+
+
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
CO and Hz Kinetics 13.72 0 1.5 6.64 13.20 0 14.18 0 13.23 0 1.6 8.00 17.08 -0.91 7.18 2.0 17.85 -0.8 0 13.30 14.20 0 13.30 0 1.14 9.18 -1.0 18.00 16.96 -0.6 -1.25 19.78 20.74 -2.0 22.20 -2.0 16.79 -0.6 13.40 0 11.78 0 14.30 0 14.00 0 14.00 0 14.00 0 13.00 0 10.90 0 13.10 0.5 13.37 0 13.44 0 12.90 0 13.93 0 13.50 0 12.35 0 13.10 0 13.76 0 12.90 0 13.80 0 13.00 0 13.00 0 13.00 0 13.10 0 13.70 0 12.26 0 18.00 0 14.00 0 15.00 0 13.90 0 12.70 0 13.50 0 16.00 0 16.00 0 13.50 0.5
0
-4.5 -0.7 41.0 23.6 48.1 3.3 16.5 7.6 0
0 1.0 0 0 0 0 0
0 0 0 0.7 7.4 6.5 0
0 0 0 3.3 0.5 47.0 81.8 3.4 1.2 6.7 1.0 2.8 0.4 0 1.7 13.5 1.0 2.0 6.0 1.5 3.0 56.0 20.0 7.0 0.5 0.5 0.5 76.0 50.0 20.0
-12.2
19.5 -22.6 -17.4 21.8 17.5 -27.3 -40.7 -39.4 -19.6 17.7 -12.2 -32.7 16.6 -22.5 -23.9 14.9 -15.4 0.9 -128.0 -23.6 -7.2 -58.1 18.3 -15.3 16.4 1.9 -53.5 -68.1 -34.5 -51.0 -17.1 -106.3 -106.3 -106.3 -106.3 -121.6 -104.5 -52.8 -62.2 7.1 -98.4 -50.5 -58.7 -120.9 -65.9 -52.4 59.5 105.5 -0.8 -46.0 1.0 -16.1 -6.4 -55.0 -52.0 4.1 10.2 -47.9 -9.3 -1.9 -8.3 -25.4 57.6 -66.4 6.6 -52.9 -4.2 -59.2 78.0 25.6 18.5
40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 52 52 53 52 52 52 52 52 52 52 52 52 52 54 54 54 54 54 54 52 55 56, 57 40 40 40 40 58 48 18 18 18 18 18 18 18 18 21 21
40 40 21 21 55 55 21
40 59 55 55 40 40 40 48
Environ. Sci. Technol., Vol. 23, No. 4, 1989 445
Table I (Continued) reactionb" COC12 + OH s COCl + HOC1 COC12 H e COCl + HCl
146 147
+
log A
n
E
AHr(298 K)
ref
12.00 13.00
0 0
10.0 2.0
20.4 -27.5
40 40
O k = A P exp(-E/RT), in cm, kcal, s, and mole units. *Chaperon efficiencies of third-body M: O2= 0.35, HzO = 6.5, COz = 1.47, CO = 0.74, H2= 1.0, N2 = 0.44. c * * , most sensitive reactions; *, second most sensitive reactions. dSignificant figures are for consistency, not to indicate an established accuracy of these parameters.
" " " " " 1
1.o
0.0
.......,,.
m
I...
'. ..
0 4
X r7
$0.5
Vj
(I)
U
L w
\
0
-
u
0
\
u >
w
r l . O H
-1
-
p1.0 u
>
H
w,
I - . .
H v)
z
W
vr2.0
-
51.5 H
-3.SfO' 0.5
I
1.o I
I
1.5 I
I
2.0
I
2.5 I
1
'
3.0
D I S T R N C E RLONG FLRME CMMJ Figure 2. Sensitivity coefficlent profiles of the most sensitive 10 reactions with respect to C,HCI,. Numbers correspond to reactions in Table I.
profiles reported in fuel-lean C2HC13 flames reported earlier (7). As noted previously, sensitivity analysis is an important element in detailed chemical kinetic modeling for the identification of the rank order of significance of reactions in the mechanism in effecting model predictions. For this, normalized first-order sensitivity gradients (Sij) were calculated along the flame by using the following definition: where Ci is the molar concentration for species i, and A j is the preexponential factor for the j t h reaction at a particular location in the flame. This definition is particularly useful because influential reactions can be identified even without the explicit presence of a particular species in that reaction. It must be noted that because of the reversible nature of the elementary reactions, the signs of the Sjjs calculated according to the above equation do not necessarily reflect the direction of the reaction. This is especially the case for reactions in which the forward and revese rates are nearly balanced. Therefore, a detailed analysis based on the rates of individual reactions along the flame must also be performed. In Table I, reactions determined to be most important by the sensitivity and reaction rate analyses have been identified by the symbol "**". Reactions that were significant, but less important than the above group have been identified by the symbol "*". A representative set of Sij profiles for C2HC13are presented in Figure 2. Before discussing the details of the reaction mechanism, a number of issues must be noted. First, as discussed in our previous work ( I ) , the experimental data within -0.5 mm from the burner surface should be considered unreliable because probe-burner interactions are likely to disturb the flame structure. Second, as also noted in our previous communication, carbon and chlorine balances in 446
Envlron. Sci. Technol., Vol. 23, No. 4, 1989
wi
V
} I
I
I
L
I
1.0 1.5 D I S T R N C E RLDNG FLRME IMMJ 0.5
2.0
Flgure 3. Rate profiles for four reactions having the highest net rates involving C2HC13. Numbers correspond to reactions in Table I.
the experiments were about 80% and 85%, respectively, suggesting that the formation of chlorinated high molecular weight species was significant ( I ) . This was confirmed by the visual observation of the formation of yellow carbonaceous deposits, the analysis of which revealed the presence of highly chlorinated aromatics, primarily c&& (hexachlorobenzene) ( I ) . Therefore, in order to simplify the analysis of the experimental data and to better assess the validity of model predictions we assumed that all the unaccounted chlorine can be represented by C6C16. This will be discussed further below. Third, flame simulations reported here utilize experimentally determined temperature profiles measured by thermocouples, which are subject to considerable uncertainties. For example, because of imperfect corrections for radiation caused in part by soot coating of the thermocouple wires, the temperature of the gas phase cannot be determined precisely. Consequently, part of the discrepancies that exist between model predictions and the data are directly attributable to these issues. After the determination of species mole fraction profiles, the net rates of individual elementary reactions in the mechanism were also calculated along the flame zone. From the considerations of these net rates the following conclusions can be reached concerning the formation and destruction of various species in the fuel-rich flames of C2HC13. C2HClP As seen in Figure 1,calculated mole fractions for C2HC13are in reasonable agreement with those determined experimentally. In particular, the shape of the experimental mole fraction profile and the relative location at which the destruction of C2HC13was complete has been reproduced very well by the model. The sensitivity gradient profiles for the most influencial reactions affecting the concentration profile of C2HC13are presented in Figure 2, to illustrate the utility of Sijs in identifying the rank order of the reactions in the mechanism.
In Figure 3, rate profiles for five reactions involving C2HC13that have the highest rates are presented. As evident from these profiles, the major reaction pathway for C2HC13 in the flame was by C1 radical attack, Le., C2HC13 C1 F? C2C13 HCl (6), where the number in parentheses indicates the reaction number in Table I. Reaction 6 also is the major route for the formation of HC1 in this flame. In the earlier, i.e., cooler, parts of this fuel-rich flame, addition of C2C13 and C10 radicals to C2HC13is also important. In contrast, in fuel-lean flames, C2C13would have been consumed rapidly by its reaction with 02,i.e., C2C13 O2 s C0C12 + COCl (31). The addition of C2C13to C2HC13results in the formation of C4C& via the sequence C2HC13 C2C13 e C4HC1G (89) and C4HC16 O2 9 C4C16+ H02 (88). The addition of C10 to C2HC13produces CHC12COCl by C2HC13+ C10 e CHC12COC1+ Cl(9). Both C4C16and CHC1,COCl form in significant levels in fuel-rich flames of C2HC13,and this will be discussed further below. At the higher temperatures associated with the later zones of the flame, unimolecular decomposition of C2HCl3 also becomes an important reaction path. 02.For O2 the agreement between the model and the experiment is exceptionally good, as seen in Figure 1. From the calculation of reaction rates, the major reactions responsible for the consumption of O2 were identified to be C2C13+ O2 G C0C12 COCl(31), C2Cl3 + 0 2 e C2C120 + C10 (32) and C2C12+ O2 G COCl + COCl(48). The first of these reactions is also important in fuel-lean flames of C2HC13(8). It is important to note that because of the hydrogen-lean nature of this flame, the H + O2 s OH + 0 (99) reaction contributes very little to the consumption of 0 2 . CO and C 0 2 . As seen in Figure 1,the model predicts the experimental CO mole fraction profile reasonably well. The slight underprediction of CO early in the flame zone, although possibly a manifestation of the deficiency of the mechanism, is also likely to be due to probe-burner interactions discussed earlier (1).Based on the reaction rate analysis, CO forms as a consequence of the unimolecular decomposition of COC1, Le., COCl + M F! CO + C1+ M (114), in which COCl forms via C2C13+ O2 C0C12 + COCl (31) and C2C12 O2 e COCl + COCl (48). The major reaction responsible for the consumption of CO was CO C10 e C 0 2 C1 (113), which was also the primary reaction path for the formation of C02. Again, because of the hydrogen-lean nature of this mixture, the concentration of OH is low, thus the CO OH + C 0 2 + H (94) reaction, which is the major reaction pathway for CO oxidation in normal hydrocarbon systems, contributes very little to the formation of C 0 2 in C2HC13flames (27). HCl and Clz. As evident from Figure 1, model predictions for HC1 and C12 are in good agreement with the data. As noted above, HC1 forms primarily as a consequence of C1 radical attack on C2HC13,i.e., C2HC1, + C1 a C2C13+ HCl(6); thus its early appearance in the flame zone is expected (see Figure 1). In addition, HC1 forms by the reaction C4HC15+ C1 s c4c15 + HC1(85), in which C4HC15forms by the decomposition of the adduct in reaction C2C13+ C2HC13* C4HC16(89). According to the mechanism, major reaction pathways responsible for the formation of C12 are COC1, + C1 s COCl + C12 (145) and COCl C1 * CO C12 (120). On the other hand, consumption of C12 occurs via C&13 + C1, e C&l4 + C1 (17). Since C2C13 forms very early in the flame zone, i.e., by C1 attack on C2HC13,it prevents the buildup of Cl2 in the system; thus, the C12 mole fraction profile exhibits an induction period (see Figure 1).
+
Symbols: E x p e r i m e n t a l d a t a L i n e s : Model p r e d i c t i o n s
t
+
+
+
+
+
*
+
+
+
+
+
+
OISTRNCE RLONG FLRME CMMI Figure 4. Comparison of the experimental data with model predictions for COCI,, C,Cl,, C,CI,, and CCI,.
C0Cl2. Phosgene (COCl2)is an important intermediate in C2HC13combustion, both under fuel-rich and fuel-lean conditions (7), and model predictions are in reasonable agreement with the experimental data (see Figure 4). C0C12forms early in the flame, primarily as a consequence of reaction C2C13 O2 s C0C12 + COCl (31), and to a lesser extent by CC13 O2 s COCl2 + C10 (60). The destruction of C0C12 occurs essentially due to C1 radical attack, i.e., C0C12 C1 e COCl C12 (145), which also is one of the major pathways responsible for the formation of C1, and CO. C2C14. C2C14also is an important chlorocarbon intermediate in both fuel-lean and fuel-rich flames of C2HC13, and the mechanism predicts its behavior along the flame zone reasonably well (see Figure 4). The reaction C2Cl3 + C12 s C2C14 C1 (17) is mainly responsible for the formation of C2C14,with minor contributions from C2C15 s C2C14 C1(-16) where C2C15forms by C2HC15+ C1 e C2C15 HCl(20). The destruction of C2C14occurs essentially by the reversal of its major formation reaction, Le., C2C14 C1 e C2C13+ C12 (-17), later in the flame. Additionally C&14 reacts via C2C13+ C&14 e C4Cl, (86), which also represents the major path for the formation of C4Cls. C2C12. As first noted by Chang et al. (7) C2C12forms in substantial quantities in flames of C2HC13under both fuel-lean and fuel-rich conditions. As seen in Figure 4, considerable discrepancy exists between model predictions and the experimental data for C2C12. This, however, is not surprising in view of uncertainties that exist both in the experiments and in the mechanism. First, uncertainties in the experimental data are substantial because C2C12 mole fraction profiles were determined by using the method of ionization cross sections (33),since calibration gas mixtures containing C2C12are not commercially available (1). Consequently, the experimental C2C12mole 'fractions would be expected to be accurate only within a factor of
+
+
+
+
+
+ +
+
2.
Second, although reactions between chloroacetylenes and oxygen are well-known to be fast (34),the elementary reactions of C2C12are virtually unknown. Thus, reactions of C2C12presented in Table I correspond to plausible steps in the absence of other evidence. The rate parameters for these reactions were estimated by the transition-state theory (20). According to the mechanism, the formation of CzC12is due to the decomposition of C4C16,C2C13,and Environ. Sci. Technol., Vol. 23, No. 4, 1989 447
10-1
I
-
I
I
I
I
I
I
Symbols: E x p e r i m e n t a l d a t a L i n e s : Model p r e d i c t i o n s
CHClsCOCl
3
6.0 I
I
I
1
I
I
I
I
I
I
1
I
Symbols: E x p e r i m e n t a l d a t a L i n e s : Model p r e d i c t i o n s
DISTRNCE ALONG FLRME CMMI Flgure 6. Comparison of the experimental data with model predictions fOi c2cls, c&I,, and c,cIs, and the experimentally derived c&i, profile (see text).
C2HC13 in an approximate order of importance, i.e., C4C16 @ CzCl3 + Czcl2 (-81), CZCl3 M $ C2C12 C1+ M (50), and CzHCl3 F? C2C12+ HCl(3). C2C12destruction is then proposed to occur via the complex process C2C12+ O2 8 COCl + COCl(48), which is likely to be a nonelementary reaction. The rate parameters for reaction 48 were determined, in part, by the use of experimental data since it is one of the most sensitive reactions in the mechanism. CC4. Carbon tetrachloride also forms in substantial quantities in fuel-rich flames of C2HC1,, and as shown in Figure 4, model predictions are in reasonable agreement with this experimental observation. In the proposed mechanism, major reaction sequences responsible for the formation of CC14 are C2C13 O2 z=? C2Cl2O C10 (32), C2Cl2O+ C1 * CC13 CO (33) followed by the chlorination of the CC13 radical by CCl, Clz z=? CCl, + C1 (62) and CCl, + C2HC1, s CC14 C2HC12(lo), and directly by the reaction C2C13 + C10 CC14 + CO (35). Minor routes for CCl, formation also exist, and they include CCl,COCl+ C1 F? CC1,CO + C12 (45) followed by CC13C0 + CCl, + CO (46), and CHC1, C1 + CC13 + HC1(57), again followed by the chlorination of CCl,. The reactions responsible for the formation of CC1,COCl and CHC1, are discussed below. CHC12COCland CC1,COCl. For dichloroacetyl chloride (CHC1,COCl) and trichloroacetyl chloride (CCl&OCl), some discrepancies exist between the model predictions and the experiment (Figure 5). The model correctly predicts the relative ordering and the peak locations in CHClzCOCland CC1,COCl profiles. However, the absolute mole fractions for these species have been underpredicted by a factor of 2. In this case, the major uncertainty is likely to be in the reaction mechanism, as the experimental data have been estimated to be accurate within *20% (I). At present, the reactions of acyl chlorides in flames are poorly understood, thus the reactions presented in Table I represent plausible steps. According to the proposed mechanism, the major reaction paths responsible for the formation of acyl chlorides are due to C10 addition to C2HC13and C2C14,Le., C2HC1, C10 s CHCl,COCl+ Cl(9) and C2C14 + C10 e CC13COCl C1 (15). They are destroyed by the following sequence of reactions: CHC12COC1+ C1 G CHClzCO + Clz (38)and CC1,COCl C1 F', CC1,CO + C12 (451, followed by CHC12C0 s CHClz + CO (40) and CC1,CO e CC13 + CO (46), respectively. These reactions also constitute
+
+
+
+
+
+
+
+
+
+
+
448
Environ. Sci. Technol., Vol. 23, No. 4, 1989
pathways that subsequently lead to the formation of CHC1, and CCl, by the chlorination of the CHC12 and CCl,, respectively. C2C16, C3C16, and C4C16. Calculated mole fraction profiles for these species are compared to those determined experimentally in Figure 6. As seen from this figure, although the model predictions are not unreasonable, major discrepancies remain. Specifically, the second maximum in the mole percent profile for C2C16was not reproduced at all by the present model, and this appears to be a manifestation of the deficiency of the mechanism. According to the model, the earlier formation of C2C16is mainly due to CCl, recombination, i.e., CCl, + CC13 e C2G16(63), as opposed to the chlorination of C2C14,since equilibrium limitations do not favor the reaction C1+ C2C4 $ CZCl6(16) in the forward direction in the flame. The destruction of C2C16occurs via its unimolecular decomposition back to CCl, and by C-C1 bond fission, i.e., C2C16 s CCl, + CCl, (-63) and C2C16s C2C16 C1(23), and by complex molecular elimination process, CzC16s C2C14+ C12 (22). Since falloff conditions were present for C2Cl6 in this flame, the proper rate parameters for each of these channels were determined by considering the following composite reaction/collisional stabilization process:
+
cc13 + cc13
-
tcpctel*
-
CpclS
cpc14
+
Clp
cpc15
+
CI
I The increase in the C2C16mole fraction for the second time would likely to be caused by the fragmentation of higher molecular weight chlorohydrocarbons, which form early in the flame zone. We are presently exploring this feature of the CzC16profile by considering a broader reaction mechanism and will communicate the results of this work in a later paper. For C3C&,the model predictions are in reasonable accord with the experimental data (Figure 6). 'The formation of C3C16starts by the addition of CCl, to CzHC13, CzC14, or c2cl2,i.e., Cc1, + C2HC13F', C&C& (76), cc13 + czc4 C3Cl, (80), and CCl, + C2C12e C,Cl, (73), all of which are chemically activated processes, followed by C3HC16 * C,HCl, + C1 (78), C3C17s C3C16+ C1 (79), and C3C&+ C12 ~ r ?C3C16+ C1 (-75). The destruction of C&16 occurs primarily through C1 radical attack, i.e., C3C&+ C 1 2 C3Cl, + Cl2 (75).
10-2
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Clz (92) leading to the formation of c&&. Since the rate parameters for reactions leading to the formation of c&16 are not known, they were determined from the experimental data in the following manner: First, all of the unaccounted chlorine, i.e., chlorine atoms that cannot be accounted for by the measurement of gas-phase species, was assumed to be associated with c&.&( I ) . On the basis of this assumption, the mole percent c6c16 can then be calculated to be of the order 0.9% in the gas phase in the flame for most of the reaction zone (see Figure 6). This value, together with the experimentally measured concentrations of other gas-phase species leads to a figure of -2% for the amount of carbon unaccounted for in the system. Second, the rate parameters for the irreversible reactions leading to the formation of c&& were adjusted such that the c&& profile predicted by the model matched the values determined from the experimental data as described above. The resulting rate parameters for these reactions were well within the limits expected for these types of elementary reactions, as shown in Table I (20). This approach also had the very positive effect of improving the agreement between the model predictions and the experiment for all the gaseous species for which direct experimental measurements were available. Before the implementation of this corrective procedure, the discrepancy between the model and the experiment was considerably greater.
b;;.:?.. yCHC1: 0 0
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I
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Symbols: Experimental data Lines: Model predictions
,';
1.5
-
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-
I 2.0
2.5
Conclusions Detailed chemical kinetic modeling of the combustion of C2HC13,in conjunction with the available experimental data on fuel-rich flames of C2HC13/02/Ar suggests that major features of these flames can be described reasonably well. From reaction path and sensitivity analyses, principal reaction channels responsible for the destruction of trichloroethylene and oxygen, and for the formation and destruction of stable intermediates, have been identified. Although model predictions were generally satisfactory, several discrepancies still remain between the model and the experiment that require further investigations. On the experimental side, there exists a need to better quantify high molecular weight species in flames, especially those that exist in small concentrations. In addition, direct measurements of C2C12would help considerably in evaluating the quantitative validity of the model. The mechanism also needs further refinement, especially with regard to the reactions of chlorocarbon radicals with O2 and the elementary reactions of C2C12,as well as reactions responsible for molecular weight growth and decay processes. The mechanistic explanation of the dual maxima of the mole fraction profile for C2C16also appears to be related to these issues. Although the validity of the model was demonstrated by simulating the species mole fraction profiles in flames (both fuel-rich and fuel-lean), the mechanism should also be applicable under nonflame conditions, e.g., in a flow reactor, in the postflame zone in an incinerator, and in shock tubes with little or no modification. Furthermore, because of the comprehensive nature of this mechanism, it would be of considerable use to describe the combustion of C2HC13 in chlorine-rich CHC mixtures and to develop even more comprehensive chemical reaction mechanisms describing the combustion of complex chlorinated hydrocarbons in the future. Registry No. C2HC1,, 79-01-6; CO, 630-08-0; COS, 124-38-9; HCl, 7647-01-0; Cl2, 7782-50-5; COC12, 75-44-5; C2C14, 127-18-4; C2Clz,7572-29-4; CCld, 56-23-5; CHCl&OC1,79-36-7; CCl&!OCl, 76-02-8; C,Cls, 67-72-1; C3Cl6, 1888-71-7; C,C&, 87-68-3; CHCl,, Environ. Sci. Technol., Vol. 23, No. 4, 1989 449
67-66-3; C2HCl6, 76-01-7; CSHCls, 69102-77-8; C&&, 118-74-1.
Literature Cited Chang, W. D.; Senkan, S. M. Twenty-Second Symposium (International)on Combustion;The Combustion Institute: Pittsburgh, PA, in press. Junk, G. A.; Ford, C. S. Chemosphere 1980,9, 187. Oberg, T.; Aittola, J.-P.; Bergstrom, J. G. T. Chemosphere 1985, 14, 215. Yang, M.; Karra, S. B.; Senkan, S. M. Hazard. Waste Hazard. Mater. 1987, 4(1), 55. Schaub, W. M.; Tsang, W. Environ. Sei. Technol. 1983,17, 721. Senkan, S. M. U.S. Patent 4,714,796, 1987. Chang, W. D.; Karra, S. B.; Senkan, S. M. Environ. Sci. Technol. 1986,20, 1243. Chang, W. D.; Karra, S. B.; Senkan, S. M. Combust. Sei. Technol. 1986, 49, 107. Karra, S. B.; Senkan, S. M. Combust. Sei. Technol. 1987, 54, 333. Karra, S. B.; Senkan, S. M. Ind. Eng. Chem. Res. 1988,27, 447. Miller, D. L.; Senser, D. W.; Cundy, V. A.; Matula, R. A. Hazard. Waste 1984, 1, 1. Senser, D. W.; Cundy, V. A.; Morse, J. S. Combust. Sci. Technol. 1986, 51, 209. Senser, D. W.; Cundy, V. A. Chem. Eng. Commun. 1986, 40, 153. Kee, R. J.; Grcar, J. F.; Smooke, M. D.; Miller, J. A. Sandia National Laboratories Report, SAND85-8240, 1985. JANAF Thermochemical Tables. U.S. NBS Publication, Stull, D. R., and H. Prophet, H. Eds.; NSRDS-NBS 37, 1971. JANAF Thermochemical Tables. Chase, M. W. et al., Eds.
J. Phys. Chem. Ref. Data
1974, 1975, 1978, 1982, 1985,2,
4, 7, 11, 14. Bahn, G. S. NASA Report CR-2178, 1973. Baulch, D. L.; Duxbury, J.; Grant, S. J.; Montague, D. C. J. Phys. Chem. Ref. Data 1981, 10, Suppl. No. 1. Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds;Chapman and Hall: London, 1986. Benson, S. W. Thermochemical Kinetics;John Wiley: New York, 1976. Shum, G. S.; Benson, S. W. Int. J. Chem. Kinet. 1983,15, 341. Weissman, M.; Benson, S. W. Int. J. Chem. Kinet. 1984, 16, 307. Hirschfelder, J. 0.;Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids;John Wiley: New York, 1954. Svehla, R. A. NASA Technical Report R-132, 1962. Reid, R. C.; Prausnizt, J. M.; Sherwood, T. K. Properties of Gases and Liquids, 3rd ed.; McGraw Hill: New York, 1977. Kee, R. J.; Warnatz, J.; Miller, J. A. Sandia National Laboratories Report, SAND83-8209, 1983. Chang, W. D.; Karra, S. B.; Senkan, S. M. Combust.Flame 1987, 69, 113. Westbrook, C. K.; Dryer, F. L. Prog. Energy Combust. Sei. 1984, 10, 1. Golden, D. M.; Larson, C. W. Twentieth Symposium (International) on Combustion;T h e Combustion Institute: Pittsburgh, PA, 1984; p 585.
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(30) Dean, A. M. J. Phys. Chem. 1985,89,4600. (31) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; John-Wiley: New York, 1972. (32) Russel, J.; Senkan, S. M.; Seetula, J.; Gutman, D. J. Phys. Chem., in press. (33) Biordi, J. C. Prog. Energy Combust. Sei. 1977, 3, 151. (34) Smirnov, K. M.; Tomilov, A. D.; Shchekotikhin, A. I. Russ. Chem. Rev. (Engl. Transl.) 1967, 36, 326. (35) Zabel, V. F. Ber. Bunsenges. Phys. Chem. 1974, 78, 232. (36) Caballero, J. F.; Wittig, C. J . Chem. Phys. 1983, 78, 15. (37) Predicted by Quantum RRK method (ref 30 and 31). (38) Benson, S. W.; Weissman, M. Int. J . Chem. Kinet. 1982, 14,1287. (39) Ayscough, P. B.; Dainton, F. S. Trans. Faraday Soc. 1962, 58, 318; 1966, 62, 1838. (40) Estimated by this work. (41) Thomas, P. J. Current Topics in Mass Spectrometry and Chemical Kinetics; Heyden & Sons: London, 1982. (42) Chang, J. S.; Kaufman, F. J. Chem. Phys. 1977,66,4989. (43) Miller, W. T., Jr.; Dittman, A. L. J . Am. Chem. Soc. 1956, 78, 2793. (44) Weissman, M.; Benson, S. W. Int. J. Chem. Kinet. 1980, 12, 403. (45) Bertrand, L.; Franklin, J. A.; Goldfinger, P.; Huybrechts, G. J. Phys. Chem. 1968, 72, 3926. (46) Bock, H.; Hirabayashi, T.; Mohmand, S.; Solouki, B. Angew. Chem., Int. Ed. Engl. 1977, 16, 105. (47) Capey, W. D.; Majer, J. R.; Robb, J. C. J. Chem. SOC.B 1968, 447. (48) Kondratiev, V. N. COM-72-10014, National Bureau of Standards, Washington, DC, 1972. (49) Steacie, E. W. R. Atomic and Free Radical Reactions, 2nd ed.; Reinhold: New York, 1954; Vol. 2. (50) Spence, J. W.; Hanst, P. L.; Gay, B. W., Jr. J. Air Pollut. Control Assoc. 1976, 26, 994. (51) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. Int. J . Chem. Kinet. 1980,12,1001. (52) Warnatz, J. Combustion Chemistry; Gardiner, W. C., Jr., Ed.; Springer-Verlag: New York, 1984. (53) Brabbs, T. A.; Belles, F. E.; Brokaw, R. S. Thirteenth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1971; p 129. (54) Dixon-Lewis, G. Philos. Trans.R. Soc. London, A 1979,292, 45. (55) DeMore, W. B.; Molina, M. J.; Watson, R. T.; Golden, D. M.; Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R. Chemical Kinetics and Photochemical Data for Use in Stratospheric Modeling; Evaluation No. 6, J P L Publication 85-37, 1985. (56) Burns, W. G.; Dainton, F. S. Trans. Faraday Soc. 1952,48, 39. (57) Clark, T. C.; Clyne, M. A. A.; Stedman, D. H. Trans. Faraday SOC.1966, 62, 3354. (58) Trotman-Dickenson, A. F. Gas Kinetics; Butterworths: London, 1955. (59) Watson, R. T. J. Phys. Chem. Ref. Data. 1977, 6, 871.
Received for review April 28,1988. Accepted November 16,1988. This research was supported, in part, by funds from the U.S. EnvironmentalProtection Agency, Grant No. R81%&-01-0, and the Illinois Institute of Technology,Industrial Waste Elimination Research Center, Project No. 8705.
