Control-Oriented SCR Model

The main reactions to be considered in the SCR control-oriented model are reactions of Eqs. (14.4), (14.5), (14.6), (14.8), and (14.11). Reactions which are ignored are the slow SCR in Eq. (14.7), ammonia oxidation to NO in Eq. (14.9), ammonia oxidation to N2O in Eq. (14.10), and the AdBlue to ammonia reactions of Eqs. (14.1), (14.2), and (14.3). Because the fast SCR is comparably much faster and most NO2 can be converted by this process, the NOx after the upstream SCR catalyst is mostly NO. Consequently, the slow SCR in Eq. (14.7) is assumed to be a minor reaction. For ammonia oxidation, it has been reported that most of the SCR catalysts used on vehicles are 100 % selective toward N2 [14], 

The reaction rates of the processes being considered are modeled by Arrhenius equations. The reaction rate models are presented below  

To avoid partial differential equations in the control-oriented model, the SCR catalyst is assumed to be a continuous stirred tank reactor (CSTR), as shown in Fig. 14.1, for developing a 0-D model [12], Under this CSTR assumption, the states are considered homogenous within the catalyst. Based on the CSTR assumption and the mass conservation law, the dynamic equations of the considered states in a single SCR catalyst can be expressed below. 

Parameters of the model are strenuous to be calibrated due to the high number of parameters and the complexity of the chemical reactions. One way to calibrate the model effectively is to use the Genetic Algorithm (GA) to optimize the model parameters such that the model predictions best match with the calibration measurement data. GA has been known of optimizing complex and nonconvex equations. This feature makes it a good candidate to calibrate the SCR model. Detailed explanation of how to use GA to calibration the model and a cahbration example is available in [11]. 

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Hsieh M-F, Wang J (2011) Development and experimental studies of a control-oriented SCR model for a two-catalyst SCR system. Control Engineering Practice, 19(4) 409-422... 

Schar, C.M., Onder, C.H., Geering, H.P., et al. (2004) Control-Oriented Model of an SCR Catalytic Converter System, SAE Technical Paper Series 2004-01-0153. 

According to the SCR control-oriented model shown in Eq. (14.29), the key states of an SCR catalyst are SCR inlet NO(x) concentration, SCR inlet NH3 concentration, exhaust flow rate, SCR catalyst temperature, SCR-outlet NO concentration, SCR-outlet NH3 concentration, and SCR catalyst ammonia coverage ratio. Current vehicle onboard sensors are capable of measuring gas flow rate, temperature, NOx concentration, and NH3 concentration. However, the current production NOx sensors are cross-sensitive to NH3, which make the accurate measurement of SCR-outlet NOx concentration difficult. Without the information of SCR-outlet NOx concentration, closed-loop SCR control is difficult, and so is the diagnostics of SCR NOx reduction capability. Moreover, the catalyst ammonia coverage ratio ( NHa) is also hard to be directly measured. Ammonia coverage ratio is an inherent state in the SCR catalyst which directly affects the catalytic reactions. This state is... 

Schar CM et al (2004) Control-oriented model of an SCR catalytic converter system, 2004 SAE World Congress, SAE paper 2004-01-0153... 

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