Kinetic Mechanisms for Formation of Pollutants


Uncertainty Analysis of Detailed Kinetic Mechanisms for Formation of Pollutants

7.1 Introduction;

There wide application of detailed kinetic reaction mechanisms in multiple fields of application such as atmospheric chemistry, combustions systems, pyrolysis etc. These proposed reaction models have been verified or tested against experimental measurements. Usually, the both experimental result and simulation based results do not coincides perfectly. The level of agreements between the results can be estimated by measurements errors and uncertainty existing in the simulation results.

A discussed in the Chapter-4 and Chapter-8, the errors among the simulation data and experimental data of pollutants species exists in combustion chamber of IC engine. In Chapter-4, the uncertainty originating from the input operating parameters has been discussed and in current study, local uncertainty of kinetic parameters four proposed kinetic reaction mechanism has been discussed.

The contribution of errors individual elementary reaction of a reaction mechanism calculated by the variance analysis of estimated models for each species. In this analysis, for each reaction, the percentage contribution of error in the predicted profile of each pollutants species is calculated under the various simulation conditions.

The uncertainty factor due to Factor “A” of Arrhenius Rate Law is defined as;

(1)where is the recommended values of the rate coefficient of reaction j.

, are the lower and upper limits of rate coefficients. These minimum and maximum values of rate parameters corresponding to 2σ deviation from the recommended value on log scale, the uncertainty factor defined above can be converted to the variance of logarithm of rate coefficient using the relation . In the lack of detailed information and based on central limits thermo, normal distribution was assumed for the parameter lnk. Also assuming that, the reaction rate coefficients are not correlated, the variance of model output Yi is calculated by where, the subscript K means to an uncertainty originating form the kinetic parameters. σ2(lnkj)

The percentage contribution of error due to each reaction involved in the formation and consumption of pollutants is defined by the equation;

In this equation, and are defined further σk, is the variance coefficients due to Factor “A” which is the temperature coefficient of respectively.

7.2 Uncertainty Analysis of Detailed Mechanisms by Chemkin 4.1.1;

Chemkin 4.1.1 has built in simulation routine for local uncertainty analysis of input operating parameters (engine speed, equivalence ratio, initial inlet pressure, temperature of gas mixture etc), engine geometrical parameters (compression ratio, crank to connecting rod ratio, starting crank rotation angle etc) and kinetic parameters (temperature exponent, temperature coefficient, activation energy etc). The local uncertainty analysis has the great advantage that the origin of the uncertainty can be traced to the various input parameters.

IC engine code of Chemkin 4.1.1 was used for simulation. The sequential calculations with kinetic parameters (Factor A of Arrhenius Rate Law) for local sensitivity coefficients were made by modifying this code. These local sensitivities were converted to uncertainty using KINALC.

In present study, the contribution of reactions involved in the formation and consumption of pollutant species (NO, NO2, NH3 and CO) to the concentrations in the combustion chamber of IC engine with the specifications given in Table 4.1.the uncertainty analysis of proposed reactions mechanisms was carried out for fuel lean conditions and fuel rich conditions but the results shown in plots were obtained at stoichiometric condition (when fuel-to-air ratio, φ=1.0) and when engine was operating at 3000 rev/min, Tini=1500 °C and Pini=1.0 atm. The common reactions involved in the formation and consumption of the pollutants species are given in Table 4.13. According to this Table, there are about 17, 52, 12 and 14 reactions involved the CO, NO, NO2, and NH3 respectively.

The uncertainty analysis by Chemkin solver involved the;

* Approximation of output models in which the algebraic equations are developed for each out variables (Mole Fractions of pollutant species) to approximate for given values of the input variables.

* Error Analysis, it gives the results of error analysis on the approximate models. It includes a list of comparisons between the output values from the actual model and those from the approximations. The most important information is the relative sum-square-root error and the index of agreement. A small relative sum-square-root error (i.e. << 1.0) and a high index of agreement (i.e. close to 1.0) indicate high accuracy of the approximation. On the other hand, either a large relative sum-square-root error or a low index of agreement indicates poor accuracy of the approximation. The results are not given for this study.

* Variance analysis indicates the effect of variation (or uncertainty) in input variables on the variation (or uncertainty) in the model response of output variables. A high percentage contribution from an input means that there is a strong dependency of the output on the input. A low percentage contribution means that the input has little effect on the output.

The results of variance analysis are important in uncertainty analysis of kinetic mechanisms. The results of variance analysis of four proposed kinetic mechanism (discussed in Chapter-3 and Chapter-4) with normal distribution (assumed for the parameter lnk as discussed above) discussed in next section each reactions mechanisms developed to simulate combustion of natural gas in IC engine.

7.3 Results and Discussion;

In this section, the results of variance analysis of kinetic mechanisms is presented and percentage contribution of each reactions involved in the output concentrations of pollutant species is discussed.

The partial variances () of each individual reaction and their percentage to overall variances illustrate the share of uncertainty of parameter “j” to the uncertainty of output “i”. In this analysis, the reactions are identified which contribute the uncertainty in output concentrations of pollutant species in each proposed reaction mechanisms.


The uncertainty analysis of comprehensive reaction Mechanism-I are given in Table 7.1 and shown in Figure 7.1 for error analysis and variance analysis. The output value of Relative Sum-Square-Root Error (RSSRE) and Index of Agreement (IOA) indicate that approximate concentration (given by algebraic equation) model acceptable level of accuracy for CO, NO and NH3.

According to Figure 7.1, the main sources of uncertainty (above 10%) are the rate parameters of reaction H+NCO=NH+CO (60.81%) and NO+C=CO+N (14.38%) for CO concentrations in IC engine at equivalence ratio of =1.0. For specie NO, NO2, and NH3

Table 7.1 Error Analysis of Mechanism-I for Output Pollutants Species Concentrations

Pollutant Species

Relative Sum-Square-Root Error

Index of Agreement













Following reaction is major contributor to uncertainty in output concentrations (above 10%)

For Nitric Oxide (NO); only five reactions shows uncertainty contribution;

1. O2+NH=NO+OH (10.45%),

2. N+OH=>NO+H (21.32%),

3. NO2+NH=HNO+NO (14.28%),

4. NO2+M=NO+O+M (12.31%)

5. N+NCO=NO+CN (13.4%)

For Nitrogen dioxide (NO2); four reactions are main sources (10%) of uncertainty for NO2 formation given below

1. NO+N2O=N2+NO2 (23.35%)

2. NO2+NH=N2O+OH (12.34%)

3. NO2+NH2=N2O+H2O (35.76%)

4. NO2+CN=NCO+NO (17.56%)

For Ammonia (NH3); three reactions (above 10 %) are main contributor to uncertainty to NH3 concentrations given below

1. NH2+NH2=NH3+NH (65.29%)

2. NH2+NNH=N2+NH3 (11.31%)

3. NH2+HNO=NH3+NO (20.06%)


The uncertainty analysis of kinetic Mechanism-II (a low temperature mechanism) is shown in Figure 7.2 and error analysis of this detailed mechanism is given in Table 7.2. The results plotted in Figure 7.2 for pollutants species CO, NO, NO2 and NH3 shows that the major sources of uncertainty to the concentration of these species are the following reactions (The reaction showing the uncertainty above 10% are given below.);

For Carbon monoxide (CO);

1. NCO+M=N+CO+M (28.61%)

2. CO2+N=NO+CO (14.38%)

3. HNCO+M=NH+CO+M (28.37)

For Nitric Oxide (NO);

1. O2+NCO=NO+CO2 (11.56 %)

2. NH2+HNO=NH3+NO (17.25%)

3. NO2+M=NO+O+M (21.32%)

4. HNO+M=H+NO+M (30.18%)

For Nitrogen Dioxide (NO2)

1. NO2+NH2=N2O+H2O (34.34%)

2. NO2+CN=NCO+NO (10.91%)

3. NO2+M=NO+O+M (30.26%)

For Ammonia (NH3)

1. NH3+M=NH+H2+M (43.34%)

2. NH2+NH2=NH3+NH (15.32%)

3. HNCO+NH2=NH3+NCO (31.29%)

4. NH2+HNO=NH3+NO (10.05%)

Table 7.2 Error Analysis of Mechanism-II for Output Pollutants Species Concentrations

Pollutant Species

Relative Sum-Square-Root Error

Index of Agreement













The error analysis data given in Table 7.2 predict that the approximate models for the concentrations estimated using mechanism-II in IC engine are accurate one and did not coincide with the actual models as indicate the IOA data for each pollutant specie. This shows that Mechanism-II is unable to predict actual pollutants concentrations.


Similarly, the uncertainty analysis mechanism-III are shown in Figure 7.3 and error analysis results are given in Table 7.3. The calculated Index of Agreement (IOA) for each of pollutant specie is very low which indicate that the estimated models for pollutant species do not exhibit the closer agreement between the estimated response and the actual model response of IC engine.

The percentage contribute each individual reactions involved in the pollutant species is calculated using IC engine code of Chemkin 4.1.1 under given simulation conditions. The reaction given below are those showing more that 10% share of contribution to the uncertainty output concentrations formed in combustion chamber of IC engine. According to this, only five reactions have more 10% share of contribution to uncertainty of predicted concentrations and similarly, 2, 3 and 2 reactions share more than 10% of over all uncertainty of output concentrations of NO, NO2 and NH3 respectively.

The error analysis results and other discrepancies discussed in Chapter-4 indicate low temperature mechanism (Mechanism-III) do not predict the accurate results in IC engine.

Table 7.3 Error Analysis of Mechanism-III for Output Pollutants Species Concentrations

Pollutant Species

Relative Sum-Square-Root Error

Index of Agreement













Main sources of uncertainty of CO predictions are;

1. CO2+N=NO+CO (11.34%)

2. NO+NCO=N2O+CO (15.06%)

3. HNCO+O=HNO+CO (12.67%)

4. HCCO+N=HCN+CO (13.44%)

5. NCO+M=N+CO+M (13.22%)

Main sources of uncertainty predicted NO concentrations are;

1. O2+NCO=NO+CO2 (16.4%)

2. N2O+C=CN+NO (11.32%)

Main sources of uncertainty predicted NO2 concentrations are;

1. NO2+NO2=NO+NO+O2 (23.7%)

2. NO2+O=NO+O2 (51.76%)

3. NO2+NH=N2O+OH (12.7%)

Main sources of uncertainty predicted NH3 concentrations are;

1. OH+NH2=>O+NH3 (26.3%)

2. NH2+HNO=NH3+NO (35.25%)


The results of uncertainty analysis of this mechanism are shown in Figure 7.4 and in Tale 7.5. According to the data of The approximate models for pollutant species shows the high accuracy as very low values of Relative Sum-Square-Root Error (RSSRE) and higher values (close to unity) of Index of Agreement (IOA) for each of pollutants under given simulation conditions. Theses error analysis results indicate that the predicted profiles of pollutant specie (for CO, NO, NO2 and NH3) give the accurate results as discussed in Chapter-4.

The variance analysis of formation of pollutants species are shown in Figure 7.4. The reaction NO+C=CO+N (81.8%) is main source of uncertainty in predated concentration of carbon monoxide (CO) under given simulation condition for IC engine. Similarly, the main source of uncertainty in NO concentrations are reactions O2+NCO=NO+CO2 (44.4%) and O+HNO=OH+NO (44.4%) and following reactions are major contributor to uncertainty of nitrogen dioxide (NO2); (only reaction with above 10%)

1. NO+N2O=N2+NO2 (13.45%)

2. NO2+H=NO+OH (22.34%)

3. NO2+O=NO+O2 (15.76%)

4. NO2+N=N2O+O (12.56%)

5. NO2+NH=HNO+NO (12.67%)

Four reactions given below are the main source of uncertainty (above 10%)

1. H+N2H3=NH+NH3 (45.29%)

2. OH+NH2=>O+NH3 (12.76%)

3. NH2+NH2=NH3+NH (15.27%)

4. NH2+HNO=NH3+NO (17.72%)

Table 7.4 Error Analysis of Mechanism-IV for Output Pollutants Species Concentrations

Pollutant Species

Relative Sum-Square-Root Error

Index of Agreement













7.4 Summary;

The variance analysis and error analysis of four kinetic reaction mechanisms were carried out. The approximate models showing the contribution of the variation input variables were determined for pollutants (CO, NO, NO2 & NH3) species formed in IC engine. The variance analysis identified the reactions which contribute the uncertainty in the output of the approximate models from the individual reactions involving the formation or consumption of pollutants. The error analysis produced very useful results. The error analysis of approximate models from Mechanism-IV predicts that this mechanism produces accurate results.

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