Converter
3.3 Process Model of the TWC
3.3.3 Simulation and Model Calibration
The goal of this investigation was to keep the reaction scheme as slim as pos- sible. Therefore, the water adsorption and dissociation was considered more on a phenomenological level. It is described by reaction (3.26). Hence, water is adsorbed on the ceria and dissociated to adsorbed hydrogen on the noble metal and oxygen on the ceria, if vacant sites are available both on the noble metal and on the ceria. Under lean operation, the occupancy on the surfaces by oxy- gen inhibits the adsorption of water. Additionally, hydrogen from the water dissociation is immediately oxidised because of the abundance of oxygen. Un- der rich operation, water adsorption is inhibited, if the noble metal surface is coked, i. e., covered with hydrocarbons. It will be shown that this very sim- ple approach suffices to describe the rather complex behaviour of the H2, CO, and HC concentrations during a lean–rich step. The same mechanism, which inhibits the water-gas shift reaction will be shown to also hinder the NO dissoci- ation. It is clear that this is a purely phenomenological approach, but hopefully it provides some inspiration for more detailed reaction schemes.
The Role of Sulfur
Basically, sulfur plays an important role in the deactivation of the TWC, espe- cially during rich operation, see e. g. [29]. It occurs in the exhaust mainly as SO2and is assumed to inhibit the water-gas shift and the steam-reforming reac- tions, especially on Pd and ceria [70]. Additionally, it has been found to hinder even NO reduction under rich operation [29]. Exactly these phenomena are fo- cused on here and can be reproduced by the TWC model (see Figures3.7–3.9).
For all experiments presented in this thesis, a fuel with a rather low sulfur con- tent (17 wtppm) was used. Therefore, sulfur was neglected. However, there is no contradiction of this thesis with the cited work, since it is still possible that sulfur promotes the mechanisms presented here. This means that the TWC is deactivated by stored carbonaceous species, but the storage mechanism itself can be enhanced by the presence of sulfur. In fact, it has been observed in [10]
that SO2promotes the coking of the TWC, when alkanes are present.
vantages of an implicit method (stability) with the advantages of an explicit method (no iteration). A two dimensional extrapolation method is applied to calculate solutions of higher order and to estimate separate errors of the state variables in time and space. Based on these error estimations, an equilibration of the errors is achieved through inserting gridpoints in regions of high errors and cancelling gridpoints in regions of small errors (local regridding). Finally, such a combination of spatial grid, time step and extrapolation order, promises an optimised performance of the method for a user specified tolerance.
In order to facilitate the use of this package, a MatlabTMGUI was developed.
This GUI allows an efficient parametrisation of both the model and the solver, and a convenient and flexible handling of the input and the output data. Since the GUI runs under MatlabTM, powerful graphical tools are accessible directly from the GUI.
For the model parameters describing the TWC geometry, physically reason- able values were chosen. They are presented in Appendix B.2. As for the kinetic parameters and the storage capacities, a different approach was taken.
Since the model uses rather global kinetics, parameters could not be obtained from the literature. Therefore, they were calculated using an optimisation rou- tine which minimises the error between measured and simulated transients of the gas concentrations during steps between lean and rich inlet exhaust gas mix- tures. For this purpose, the model and the solver had to be simplified, since one simulation of 100 s takes approximately 10-60 minutes with the PDEXPACK2. The longitudinal axis was divided into five cells. Then, an implicit Rosenbrock algorithm of 4th order was applied to solve the set of ordinary differential equa- tions, see [83]. The calculation demand for this model is considerably reduced as compared to the original model.
The simplified model was used for an automated adjustment to measured concentration transients by means of a non-linear leastsquares algorithm [64].
The reference measurements consisted of low-frequencyλexcitations at steady- state engine operating points. Thereby,λwas switched between 0.97 and 1.03 every30 s. In order to keep the calculation burden manageable, only three oper- ating points and three ageing levels of the TWC were considered for the param- eter fitting procedure. The resulting reaction constants were fitted according to the Arrhenius-Ansatz (pre-exponential factorAand activation energyE).
The parameters were obtained in three iterations. In the first iteration, all parameters were identified. In the second iteration, the sticking probabilities s, and in the third iteration additionally the storage capacitiesLN M andLCer
were fixed.
2All Simulations were performed on a PC with a Pentium IV processor (3.2 GHz) running under Windows XP.
10−4 10−2 100
Des 1
104 105
Des 2
104 106
Des 3
104 106
Des 4
10−1 100 101
Des 5
104 105
Reac 1
108 109
Reac 2
103 104 105
Reac 3
106 107 108
Reac 4a
10−3 10−2 10−1
Reac 4b
105 106 107
Reac 5
1.1 1.2 10−1
100 101
1/Texh [1/1000K]
Reac 6
1.1 1.2 102
103
1/Texh [1/1000K]
Reac 7
1.1 1.2 102
103 104
1/Texh [1/1000K]
Reac 8
1.1 1.2 101
102 103
1/Texh [1/1000K]
Reac 9
Figure 3.4: Kinetic parameters obtained from the calibration. Des 1 – Des 5 denote the kinetic parameters according to (3.13) of the desorption reactions (3.15)–(3.19). Reac 1 – Reac 9 denote the kinetic parameters according to (3.14) and (3.30) of the reactions (3.20) – (3.29). The dots mark the value obtained by the optimisation, the lines are fitted according to the Arrhenius Ansatz using a least-squares algorithm.
An example of the desorption and reaction parameters is presented in Fig- ure3.4. The three operating points, where the model was calibrated are de- picted in Table3.2. The TWCs used for the procedure were considerably aged (at1100◦C), moderately aged (at900◦C) and fresh, see also Section2.5. The storage capacities of the noble metal (LN M) and the ceria (LCer) obtained from the calibration are shown in Figure3.5. Actually, the total storage capac- ity is dependent on both the specific capacityLN MorLCerand on the catalyst
Table 3.2: Operating points for the calibration of the TWC model.
Nr neng[rpm] load [%] Texh[K] m˙exh[g/s]
1 1500 30 775 7.5
2 1750 35 830 10.4
3 2000 40 875 13.8
The exhaust gas mass flow corresponds only to one exhaust gas line here.
surface Acat. Ageing might in fact influence both parameters. Presumably, thermal ageing leads to a reduction ofAcat, whereas poisoning affectsLN M
andLCer. However,Acathas been assumed to remain constant here, whereas LN M andLCerhave been assumed to be subject to ageing.
TWC 1 TWC 2 TWC 3
1.4 1.6 1.8 2 2.2 2.4x 10−4
L NM [mol/m2 ]
TWC 1 TWC 2 TWC 3
1 2 3 4 5 6x 10−3
L Cer [mol/m2 ]
Figure 3.5: Storage capacitiesLN MandLCerof the differently aged TWCs. TWC 1 denotes the considerably aged (at1100◦C) converter. TWC 2 is moderately aged (at 900◦C), and TWC 3 is fresh.
0 2000 4000
NO [ppm]
1000 2000 3000
HC [ppm C 1]
0 2 4
CO [%]
11 12 13
CO 2 [%]
0 1 2x 104
H 2 [ppm]
0 2 4x 104
O 2 [ppm]
0.9 1 1.1
12 13 14
λ [−]
H 2O [%]
0.9 1 1.1
70 72 74
λ [−]
N 2 [%]
775 K 830 K 875 K
Figure 3.6: Measured raw exhaust gas concentrations dependent onλat different engine operating points corresponding to the exhaust gas temperature depicted in the legend.
The inlet concentrations were obtained from steady-state measurements. The concentrations are dependent on the air-to-fuel ratioλand on the engine oper- ating point, i. e., the exhaust gas temperature. They are shown in Figure3.6.
The instantaneous inlet concentration of each species was calculated by inter- polation using theλvalue from the sensor and the exhaust gas temperature.
All parameters obtained from the calibration procedure are presented in Ap- pendixB.2.