Temperature gradient correction of ammonia storage model

1. An exhaust gas treatment system for use with an internal combustion engine to treat exhaust gas containing NOx emissions, the exhaust gas treatment system comprising:

a selective catalytic reductant (SCR) device that stores a reductant that reacts with the NOx emissions;

a reductant supply system configured to inject the reductant according to a reductant load model; and

an electronic control module including a non-transitory memory having computer readable instructions stored thereon, and a computer processor configured to execute the computer readable instructions that perform operations of:

generating at least one temperature signal indicating an SCR temperature of the SCR device;

determining an actual amount of reductant that slips from the SCR device based on the at least one temperature signal and a rate of change of the SCR temperature;

determining a correction factor based on the actual amount of slipped reductant to modify the reductant load model, the correction factor based on a difference between the actual amount of slipped reductant and an amount of reductant stored on the SCR device, the amount of reductant stored on the SCR device is based on the reductant load model stored in the non-transitory memory, an age of the SCR device, and the correction factor;

calculating the age of SCR device based on a temperature realized by the SCR device over a time period to determine an age factor;

updating the load model based on the age factor to the determine the amount of reductant stored on the SCR device;

determining a desired load of the SCR device based on at least one driving condition; and

adjusting the reductant injected by the reductant supply system based on the updated load model and the correction factor to achieve the desired load.

2. The exhaust gas treatment system of claim 1 , wherein the amount of slipped reductant is based on an absolute temperature model of the SCR device indicative of the SCR temperature and a temperature gradient model of the SCR device that is indicative of the rate of change of the SCR temperature.

3. The exhaust gas treatment system of claim 2 , further comprising at least one of a temperature sensor that is in electrical communication with the electronic control module, and that measures the SCR temperature and a temperature model that estimates the SCR temperature, wherein the amount of reductant that is injected is adjusted in response to modifying the reductant load model with the correction factor.

4. The exhaust gas treatment system of claim 3 , wherein the correction factor is determined in response to a temperature change of the SCR device exceeding a threshold value.

5. An electronic control module including non-transitory memory that stores computer readable instructions, and a computer processor configured to execute the computer readable instructions, wherein

the non-transitory memory further stores a reductant load model indicating an amount of reductant to inject in response to one or more driving conditions, and an initial SCR age value indicating an initial age of a SCR device, and

wherein the computer process executes the computer readable instructions to perform the operations of:

generating a correction factor that controls operation of a reductant supply system;

controlling the reductant supply system to inject an amount of reductant based on the reductant load model;

determining an actual amount of reductant that slips from the SCR device based on at least one temperature signal and a rate of change of a SCR temperature of the SCR device;

determining the correction factor based on the actual amount of slipped reductant to modify the reductant load model;

determining an age factor and updating the age factor based on a temperature realized by the SCR device over a time period, wherein the amount of reductant stored on the SCR device is based on the reductant load model, the age of the SCR device, and the correction factor;

generating an age factor signal indicating the age factor that is applied to the determined amount of reductant indicated by the reductant load model to more precisely determine the amount of reductant stored on the SCR device;

determining a desired load of the SCR device based on at least one driving condition, and

controlling the reductant supply system to inject an amount of reductant based on the updated load model and the correction factor to achieve the desired load.

6. The electronic control module of claim 5 , wherein the amount of slipped reductant is determined based on an absolute temperature of the SCR device and a temperature gradient of the SCR device.

7. The electronic control module of claim 6 , wherein the amount of reductant injected is adjusted in response to modifying the reductant load model with the correction factor.

8. The electronic control module of claim 7 , wherein the correction factor is determined based on an actual amount of reductant stored on the SCR device and the amount of slipped reductant.

9. The electronic control module of claim 8 , wherein the correction factor is determined in response to a temperature change of the SCR device exceeding a threshold value.

10. A method of correcting a reductant load model that controls an amount of reductant injected in an exhaust treatment system of an internal combustion engine, the method comprising:

storing a reductant on an SCR device to reduce an amount of NOx emissions contained in exhaust gas flowing through the exhaust treatment system;

generating at least one temperature signal indicating a SCR temperature of the SCR device;

determining an actual amount of reductant that slips from the SCR device based on the at least one temperature signal and a rate of change of the SCR temperature;

calculating an age factor indicating an age of SCR device based on a temperature realized by the SCR device over a time period;

determining a correction factor based on the actual amount of reductant that slips from the SCR device;

determining an amount of reductant stored on the SCR device according to a reductant storage model, the age of the SCR device, and the correction factor;

modifying the reductant load model based on the correction factor and the age factor; and

determining a desired load of the SCR device based on at least one driving condition, and controlling the amount of reductant injected based on the modified reductant load model and the correction factor to achieve the desired load.

11. The method of claim 10 , wherein the amount of slipped reductant is based on an absolute temperature of the SCR device and a temperature gradient of the SCR device.

12. The method of claim 11 , further comprising adjusting the amount of reductant injected in response to modifying the reductant load model with the correction factor.

13. The method of claim 12 , wherein the determining an age factor further comprises updating the age factor over the time period.

14. The method of claim 13 , further comprising determining the correction factor in response to a temperature change of the SCR device exceeding a threshold value.