Calculation of Equilibrium Composition of Automotive Exhaust Gases Rem0 del Grosso Esso Italiana Research Centre, Roma, Fiumicino, Italy
The equilibrium composition of automotive exhaust gases suggests the trend of the pollutant concentrations when varying chemical-physical parameters and indicates some insuperable barriers to decrease the emissions in certain conditions. The chemical equilibrium has been calculated by minimizing the total free energy with the assumption that the outlet components are known. Compositions at air-fuel ratio from 13.0 to 17.0, temperature from 600 to 1 500°K, and pressure from 1 to 60 atrn have been considered. In addition to already well-known conclusions these calculations show that NO can b e reduced even in an oxidizing atmosphere, that NHs formation can b e significant in a reducing catalytic reactor, and that CO is not uniquely determined b y the water-gas reaction but b y other reactions as well.
T h e drastic reductions of automotive exhaust emissions for CO, NO,, and unburned hydrocarbons (HC) that are going to be enforced in the United States before 1976 require a deeper knowledge of the chemical phenomena which take place both in the combustion chamber and in the thermal and catalytic afterburners used to minimize the emissions of noxious products. This report describes the influence of temperature, pressure, and air-fuel ratio on the equilbrium composition of exhaust gases. Certainly, the flow dynamics of exhaust gases never allow the air and fuel mixture to reach conditions close to those of equilibrium. Therefore we know a priori that the equilibrium composition cannot be compared, even in the order of magnitude, with the real composition of a n exhaust gas. Xevertheless, this study can suggest the trend of pollutant concentrations when varying the chemical-physical parameters, and furthermore it can indicate some insuperable thermodynamic barriers. This same approach has been taken by some other investigations (Vickland, et al., 1962; Gross, Biller, 1968), but always with the restrictive hypothesis that the equilibrium was controlled solely by certain basic reactions; for example, that the water-gas shift reaction is the only controlling factor for CO, C o n , HzO, and Hzequilibrium concentrations. I n this work, on the contrary, the equilibrium composition has been calculated by minimizing the total free energy of the system, and the only assumption was fixing the species of components in the exhaust gas a t equilibrium. This hypothesis is also restrictive, but it is not unduly so because of the large number of the components chosen and the experimental data on which the choice is based. Calculation of Equilibrium Composition
“Chemical Equilibrium” Program. T h e equilibrium configuration of every chemical system is wholly determined when the free-energy function G has a minimum. For a perfect gas mixture of k chemical components containing nt moles of the i t h component, G can be written as
with S nt(Ct
=
(ni, n?
+ In n,/n), C,
, n, =
, na) set (Go,
of mole numbers; g,
=
+ RT In P ) / R T ; Go, = molar
390 Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
standard free energy; P = total pressure, a t m ; and n = 2,- I , k n,. The chemical equilibrium is solved by finding the nonnegative set n , which minimizes, for fixed values bf T and P , the function G and satisfies, a t the same time, the mass balance equations
C a+,
a=l,L
=
b,(j
=
1,2
, m)
where rn = number of elements; a,, = atoms of t h e j element in the i compound; and b, = gram atoms of j element in the whole system. T o solve the set of differential equations arising from the minimum condition, numerical methods are described in the literature (Smith, llissen, 1968; Storey, Van Zaggeren, 1967; White, et al., 1958; Cruise, 1964). We used the Chemical Equilibrium Program, written in Fortran IV by the Rand Corporation for the IBM 360/65. The capability of this program is large; it can calculate the equilibrium of a chemical system with 169 components arranged in 25 phases for a given composition of the inlet mixture and a given value of G of any compound in any phase. Input Data. A typical commercial gasoline was chosen having a carbon-hydrogen ratio equal to 6.39 (mol/mol) and a stoichiometric air-fuel ratio ( A / F ) of 14.64 (kg/kg). The mass balance equations are determined if values have been given for the air-fuel ratio (the range considered lies between 13.0 and 17.0) and the base weight of fuel. Some of the equilibrated gas components have been taken from experimental analysis while the others are justified by chemical considerations. As far as unburned hydrocarbons are concerned, only those hydrocarbons (HC) with relatively large concentrations, representing together 75% of the total unburned, have been considered (Dishart, 1970). The reference state of the molar free energy of the components is that of the elements in the ideal gas state a t 1 a t m and a t 298OK. I n Table I the C, values a t 1 a t m for six temperatures are shown; all data have been taken from the literature except those marked with an asterisk which have been calculated from the formation enthalpy and specific heat through Van’t Hoff’s formula. I n the same table are also shown Ct values for various pressures a t 1300’K. The ideality of the gaseous mixture has been controlled by fugacity coefficients (Hougen, et al., 1959).
Table I. Free Energy Function C
= G/RF T = 1300'K
P = 1 atm Components
Methane Ethylene Acetylene Propylene %-Butane Isopentane Benzene Toluene Ethylbenzene o-Xylene m-Xylene p-Xylene Isobutylene H2
600'K
800'K
1000'K
-22. '3954 -23 5485 -24.6167 -0,8603 -8 7798 - 14,0371
+28.6260 +14 0896 +4.9890 - 5.4127 -14 2800 -20.5282 -25.0349 -31 6699 - 36.8577 -27.2356 -35 1622 -41.4188 +7.6746 - 5 9765 - 14.9956 +2,OO84 -12 1560 -22,0527 +O. 3487 -15 5118 -26.7160 -0.9453 -16 2597 -27.1241 - 1,7874 -16 9558 -27,7230 -0.9822 -16 1541 -26.9188 -8.6618 -18 4906 -25.4456 -8.5881 -11 1127 - 12.8100 - 58.0501 -48 2193 -45.5740 Ha0 co -40.1826 -36 8487 -35 0429 -92.9424 -77 2383 - 68.1277 COa -13.1175 -16 7916 -19,2011 0 2 - 12.2778 -15 7225 - 17,9812 Nz +3.9251 KO -4 1688 -9.2239 KO2 -4.1530 -11 0936 -15.5453 +8.8290 Nz03* - 3 8236 -11.9236 +3.1293 -8 0517 -15.4265 N20r* - 1.4309 -11 9086 -20.6439 NzOs* +3.6090 NzO* - 5 8937 -11.9328 NH3* -15.9142 -18 8271 -20.9158 Formaldehyde* - 37.0264 -35 8594 - 35.6414 Acetaldehyde* - 50.8549 -51 4055 - 52.5944 a Reference state: pure elements at 1 atm, 298.16'K.
1200'K
1300'K
1500'K
-25.6225 -26.0999 -27.0157 - 17.9271 - 19.5395 -22.3147 - 1.3464 -3.8661 -7.9600 -25.2028 -27.1869 - 30.6524 - 39.6217 -43.2648 -46.8225 -46.8379 -49.2349 - 53.5150 -21.8520 -24.7597 -29.8256 - 29.7662 -32.9672 - 38.7205 -35.4435 - 39.4435 -45.8266 -35.6150 - 39.2698 - 36.1443 - 39.7784 -35.3366 -38,9702 - 31.2565 - 33.1954 - 14.0618 - 14.5805 -42.7237 -41 ,6775 - 33.9726 - 33.6008 - 62.2718 -60.0879 - 20.9473 -21 ,6628 - 19.6218 -20.2874 -12.7314 - 14.1216 - 18.7095 - 19.9879 - 18.0893 - 19.9880 -20.8214 - 23.0290
20 atm
40 atm
60 otrn
-23.1038 -22.4111 -22,0056 - 16.5438 - 15.8507 -15.4451 -0,8704 -0.1773 0,2281 -24.1912 -23.4981 -23.0924
+
-45.7565 - 46.2044 -45.4100
-37,2972 - 15.4666 -40.0737 - 33.0694 - 50 6848
-11.5848 - 10.8917 - 10.4862 - 38.6818 - 37,9887 - 31.5832 - 30.6051 -29.9120 -29.5065 - 57.0922 - 56.3991 - 55,9936 -22.8802 - 18,6671 - 17,9440 - 17.5685 -21.4212 - 17.2917 -16.5974 - 16.1931 - 16,4089 -11.1259 - 10.4328 - 10.9273 -22.1397 - 16.9907 - 16.2976 -15.8921 -23.8556 - 26.8520 -20.0333 - 19,3402 - 18.9347 -26,9678 -29,5225 - 33.8604 - 16.1918 -17.9024 -20.7494 - 14.9067 - 14.2136 - 13.8081 -22,5621 - 23.2883 - 24,5878 -20.2926 -19.5995 - 19.1936 - 35.8810 -36.1038 - 36.6833 - 30.3651 - 54,5562 -51.3158 - 51,5605 - 50.8674 - 50.4616
Results and Comments
Preliminary Remarks. All components t h a t were assumed to be present in the outlet gas are reported in Table I. However, some of them are not present in the results because their mole fractions are smaller than Atomic 0, S , H, and HO were not included because a t the temperatures of interest (600-1500°K) their effect was believed negligible. Figures 1-4 show the equilibrium concentrations at atmospheric pressure. The influence of the pressure a t 1300°K for some values of air-fuel ratio is reported in Figures 5 and 6. Figure 7 shows the plot of the equilibrium constants us. temperature, a t atmospheric pressure, of some reactions involved in the equilibrium (Le., the equilibrium concentrations of the components satisfy the reaction constant values for each temperature, whatever is the value of A / F ) . Only the compositions a t atmospheric pressure have been thoroughly studied, because the effect of pressure, although noticeable enough in the range 1-20 atm, is negligible in comparison with the influence of other parameters. At constant temperature, all the curves have a point of inflection around the stoichiometric value of A/F ratio. Increasing A I F , the larger available quantity of Oz causes a n increase of all the oxidized compounds (except CO and organic oxides which are less stable when the combustion increases). Unburned hydrocarbons and NH3 are correspondingly decreased. Increasing the temperature a t constant A / F value, the equilibrium concentrations of CO, NO,, and CHzO become larger and larger while the concentrations of unburned H C gradually decrease. N&, Ha, and COz show a n anomalous behavior; below the stoichiometric A / F value a n increase of temperature causes a n increase in the concentration of KH3
I
and H Zand a decrease for COZ;on the opposite side of stoichiometric, the situation is reversed. We will consider now the influence of chemical-physical parameters on the formation and reduction of the single pollutants. Nitrogen Oxides. I n the whole range of A / F and T explored in the present study, nitrogen monoxide shows the highest concentrations. The highly oxidized nitrogen compounds, such as N203, Nz04, and N205, are always negligible, while NzO and SOz have average concentrations which are less than those of S O by a factor of loa. From data of YO concentration in Figures 3-6 it is seen that nitrogen oxides are insensitive to pressure variations, but increases with temperature and air-fuel ratio. The actual S O concentration found in automotive evhausts is much higher than that calculated for the equilibrium a t exhaust gas temperature. It is well known that this is a kinetics effect; the NO formed during combustion (up to 2500°K) is "frozen" when the temperature suddenly drops. An extrapolation of the data in Figures 1-4 indicates that a temperature of about 2000°K is enough to give the necessary NO concentration. This extrapolation might not be entirely valid because of the presence of dissociated 0, S , H, and OH. I n the range of temperature considered, these species were found not to influence the equilibrium concentration of the other components. However, the validity of this extrapolation seems to be confirmed b y Vickland's data (Vickland, et al., 1962). If the equilibrium concentration values are considered from the K O elimination point of view, as would be the case with thermal or catalytic afterburners, it is clear that reducing mixtures and low temperatures give the highest decrease in NO content. However, even looking a t the most drastic Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
391
1. 1000K"
Figure
Effect of air-fuel ratio at P =
1
atm and
r =
Figure 3. Effect of temperature at P = ratio = 13.5
800
1100
TFMPtRAIURI
Figure 2. Effect of air-fuel ratio at P = 1 atm and
r =
1 atm and air-fuel
1400
[%I
1300°K
Figure 4. Effect of temperature at P = 1 atm and air-fuel ratio = 15.0
limitations on S O emissions, good results could be achieved also in oxidizing mixtures. For a typical 3500-4000 lb American car, the average concentration of NO in the exhaust should be about 108 ppm to meet the United States' 197.6 standards (0.4 g/mile). The data in Figures 1-4 show that this concentration could be met by using a catalytic oxidizing reactor, which is expected to operate a t an A / F above the stoichiometric value and a tmiperature of about 800°K (Lunt,
et a/., 1972), or a thermal reactor, again above the stoichiometric value a t 1200-1300°K (Lang, 1971), even though for the latter device the KO equilibrium concentration is border line. The same considerations arise when studying the effect of temperature on the reactions involving NO elimination. Both the reduction with Hf or CO (reducing atmosphere) and the decomposition into Kl and O2 (oxidizing atmosphere) are
392
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
n
1
"
ti'-
"I
/
ON;
20
rb
IO
PREISURE [ A T M I
Figure 5. Effect of pressure at T = 1300°K and air-fuel ratio = 13.5
highly favored a t the low temperatures of exhaust gas (less than 800' in the exhaust manifold), Ammonia. N H , formation is favored b y reducing atmosphere, high pressures, and low temperatures if A / F is less than stoichiometric or high temperatures if A / F is greater than stoichiometric. It is strictly dependent on the availability of hydrogen; the S H 3 anomalous trend vs. temperature becomes evident if considered in connection with HP concentrations. At the usual average temperatures of a reciprocating engine combustion chamber, even with very rich mixtures, the NH3 equilibrium concentrations are only a few ppm; such values have been measured also in real exhaust gases. The presence of NH3 might be a problem when a CO and HC catalytic converter is downstream from a highly efficient reducing catalytic device for meeting United States' 1976 NO limits (Lunt, et al., 1972). At the usual working temperatures (ca. i O O o ) and A / F values (
