Control oriented model for LNT regeneration
A method of determining an amount of nitrogen oxides (NOx) stored in a NOx trap of an engine exhaust assembly may include determining a mass flow rate of NOx into the NOx trap, determining an efficiency of storing of the NOx within the trap, and calculating the amount of NOx stored in the NOx trap based on the determined mass flow rate and the determined efficiency. The method may further include determining a mass flow rate of a reductant entering the NOx trap, determining a relationship between the determined reductant mass flow rate and the NOx removed from the NOx trap, and calculating the amount of NOx removed from the NOx trap based on the determined mass flow rate and the determined relationship. The calculated amount of NOx stored may be adjusted by subsequent amounts of calculated NOx stored and subsequent amounts of NOx removed from the NOx trap.
1. A method of determining an amount of NOx stored in a NOx trap of an engine exhaust assembly for an engine, said method comprising:
determining a mass flow rate of a reductant entering the NOx trap;
determining a relationship between the determined reductant mass flow rate and an amount of NOx removed from the NOx trap;
calculating the amount of NOx removed from the NOx trap based on the determined reductant mass flow rate and the determined relationship; and
altering at least one operating parameter of the engine based on the calculated amount of NOx removed from the NOx trap.
2. The method of claim 1 , wherein said calculating includes determining a product of the determined reductant mass flow rate and the determined relationship.
3. The method of claim 2 , wherein the determining the mass flow rate and the determining the relationship between the determined reductant mass flow rate and the NOx removed from the NOx trap are performed at a predetermined time step, the calculating including integrating the product over the time step.
4. The method of claim 1 , wherein the determining the mass flow rate includes determining a mass flow rate of exhaust from the engine entering the NOx trap and determining an operating air-fuel ratio.
5. The method of claim 4 , wherein the determining of the mass flow rate of the reductant entering the NOx trap includes determining a ratio (λ) between the operating air-fuel ratio and a stoichiometric air-fuel ratio.
6. The method of claim 5 , wherein the determining of the mass flow rate of the reductant entering the NOx trap includes determining the product of (1/λ−1) and the mass flow rate of exhaust from the engine entering the NOx trap.
7. The method of claim 1 , wherein the determining the relationship includes referencing a predetermined empirically based ratio between the reductant and the NOx removed from the NOx trap.
8. The method of claim 7 , wherein the determination of the empirically based ratio includes operating an engine at a lean condition, measuring a NOx accumulation during the lean condition, operating the engine at a rich condition after the lean condition, and integrating the determined mass flow rate of the reductant during the rich condition until an inflection point is detected in a reductant mass measured downstream of the NOx trap.
9. The method of claim 8 , wherein the determination of the empirically based ratio includes determining a space velocity and temperature associated with the NOx trap during the operation of the engine at the rich condition.
10. The method of claim 8 , further comprising determining the average mass of reductant per unit mass of NOx removed during the rich condition.
11. The method of claim 1 , wherein the determining the mass flow rate and the determining the relationship are performed during a rich condition of the engine.
12. The method of claim 11 , further comprising determining a mass of NOx stored in the NOx trap during a lean condition of the engine.
13. The method of claim 12 , wherein the calculating includes subtracting the amount of NOx removed from a previously determined amount of NOx stored.