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An apparatus, system, and method are disclosed for determining a catalyst bed temperature. The method may include receiving a current fluid mass flow within an exhaust pipe and a total amount of unburned fuel available for catalytic combustion. The method may further include determining a plurality

An apparatus, system, and method are disclosed for determining a catalyst bed temperature. The method may include receiving a current fluid mass flow within an exhaust pipe and a total amount of unburned fuel available for catalytic combustion. The method may further include determining a plurality of fluid enthalpy values corresponding to various locations within the exhaust pipe. The method may continue with calculating an amount of fuel burned on an upstream catalyst based on the plurality of fluid enthalpy values, and determining an amount of fuel remaining that is available for combustion on a downstream catalyst. The method may determine a combustion efficiency of the downstream catalyst based on the temperature rise across the downstream catalyst, and an amount of heat generated within the downstream catalyst based on the combustion efficiency and the amount of fuel remaining that is available for combustion on the downstream catalyst. The method may conclude with determining a downstream catalyst bed temperature based on the net heat generation, the fluid mass flow through the downstream catalyst, and the thermal response of the downstream catalyst.

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What is claimed is: 1. An apparatus for determining a catalyst bed temperature, the apparatus comprising: an energy balance module configured to determine a first fluid enthalpy value of a fluid upstream of a first catalytic component; a fueling module configured to determine an amount of unburned

What is claimed is: 1. An apparatus for determining a catalyst bed temperature, the apparatus comprising: an energy balance module configured to determine a first fluid enthalpy value of a fluid upstream of a first catalytic component; a fueling module configured to determine an amount of unburned hydrocarbons in the fluid available for combustion on the first catalytic component; a catalyst combustion module configured to calculate a net heat generation within the first catalytic component based on the amount of unburned hydrocarbons in the fluid available for combustion on the first catalytic component and the first fluid enthalpy value, the catalyst combustion module being communicable in data receiving communication with the energy balance module and fueling module; a peak temperature module configured to determine a thermal driving force based on the net heat generation, the peak temperature module being communicable in data receiving communication with the catalyst combustion module; and a bed temperature module configured to calculate a current bed temperature of the first catalytic component based on the thermal driving force, a previous bed temperature of the first catalytic component, and a predicted time constant of the thermal response of the first catalytic component, the bed temperature module being communicable in data receiving communication with the peak temperature module. 2. The apparatus of claim 1, wherein the energy balance module is further configured to determine a second fluid enthalpy value upstream of a second catalytic component, and a third fluid enthalpy value downstream of the second catalytic component, and wherein the catalyst combustion module is further configured to calculate the net heat generation based on the second and third fluid enthalpy values, wherein the first catalytic component is disposed in the exhaust fluid conduit downstream of the second catalytic component. 3. The apparatus of claim 2, further comprising a catalyst efficiency module configured to determine a first catalyst fuel combustion efficiency based on a temperature rise across the first catalytic component, wherein the catalyst combustion module is further configured to calculate the net heat generation based on the first catalyst fuel combustion efficiency. 4. The apparatus of claim 3, wherein the catalyst efficiency module is further configured to determine the first catalyst fuel combustion efficiency based on a derivative of the temperature rise across the first catalytic component with respect to time. 5. The apparatus of claim 2, further comprising a catalyst efficiency module configured to determine a second catalyst fuel combustion efficiency based on the second and third fluid enthalpy values, and wherein the catalyst combustion module is further configured to calculate an intermediate amount of unburned hydrocarbons in the fluid downstream of the second catalytic component available for combustion on the first catalytic component based on the amount of unburned hydrocarbons in the fluid available for combustion on the first catalytic component and the second catalyst combustion efficiency, and to calculate the net heat generation based on the intermediate amount of unburned hydrocarbons in the fluid downstream of the second catalytic component available for combustion on the first catalytic component. 6. The apparatus of claim 5, wherein the catalyst efficiency module is further configured to determine a first catalyst fuel combustion efficiency based on the temperature rise across the first catalytic component, and wherein the catalyst combustion module is further configured to calculate the net heat generation based on the first catalyst fuel combustion efficiency. 7. The apparatus of claim 6, wherein the catalyst efficiency module is further configured to determine the first catalyst fuel combustion efficiency based on a derivative of the temperature rise across the first catalytic component with respect to time. 8. The apparatus of claim 5, wherein the catalyst efficiency module is further configured to determine the second catalyst combustion efficiency based on a second catalytic component ambient heat loss factor. 9. The apparatus of claim 4, wherein the first catalytic component comprises a NOx adsorption catalyst, and wherein the second catalytic component comprises a diesel oxidation catalyst. 10. The apparatus of claim 2, wherein the thermal driving force comprises a steady-state temperature, and wherein the bed temperature module is further configured to operate a first-order filter to calculate a current bed temperature based on the steady-state temperature, the previous bed temperature, and the filter time constant. 11. A method for determining a catalyst bed temperature, the method comprising: determining a first fluid enthalpy value upstream of a first catalyst, a second fluid enthalpy value upstream of a second catalyst, and a third fluid enthalpy value downstream of the second catalyst, wherein the first catalyst is disposed in the exhaust fluid conduit downstream of the second catalyst; determining an amount of unburned hydrocarbons in a fluid upstream of the second catalyst that is available for combustion on the first catalyst and second catalyst; determining a combustion efficiency for the second catalyst based on the second and third fluid enthalpy values; calculating an amount of unburned hydrocarbons in the fluid downstream of the second catalyst that is available for combustion on the first catalyst based on the amount of unburned hydrocarbons in a fluid upstream of the second catalyst that is available for combustion on the first catalyst and second catalyst and the combustion efficiency for the second catalyst and; calculating the net heat generation within the first catalyst based on the amount of unburned hydrocarbons in the fluid downstream of the second catalyst that is available for combustion on the first catalyst and the first fluid enthalpy value; determining a steady state temperature of the first catalyst bed based on the net heat generation; and calculating a first catalyst bed temperature based on the steady state temperature, a previous bed temperature, and a predicted time constant of the thermal response of the first catalyst. 12. The method of claim 11 wherein the amount of unburned hydrocarbons in a fluid upstream of the second catalyst that is available for combustion on the first catalyst and second catalyst comprises at least one member selected from the group consisting of an amount of unburned fuel provided by the engine in a very late post injection, and an amount of unburned fuel provided by a fuel doser in fluid communication with an exhaust pipe. 13. The method of claim 11, wherein determining a combustion efficiency for the second catalyst comprises interpreting an enthalpy rise across the second catalyst, determining a fuel quantity required to induce the enthalpy rise, and comparing the fuel quantity to the amount of unburned hydrocarbons in a fluid upstream of the second catalyst that is available for combustion on the first catalyst and second catalyst. 14. The method of claim 11, wherein calculating the net heat generation comprises determining a combustion efficiency for the first catalyst, wherein the combustion efficiency for the first catalyst comprises a function of the temperature rise across the first catalyst, and a derivative of the temperature rise across the first catalyst with respect to time. 15. An exhaust aftertreatment system for treating exhaust gas generated by an internal combustion engine, comprising: an exhaust fluid conduit configured to vent exhaust gas generated by an internal combustion engine; a first catalytic component configured to treat exhaust gas within the exhaust fluid conduit; a controller comprising: an energy balance module configured to determine a plurality of exhaust fluid enthalpy values each corresponding to one of a plurality of axial locations along the exhaust fluid conduit; a fueling module configured to determine an amount of unburned hydrocarbons in the exhaust fluid available for combustion on the first catalytic component; a catalyst combustion module configured to calculate a net heat generation within the first catalytic component based on the amount of unburned hydrocarbons in the exhaust fluid available for combustion on the first catalytic component and the plurality of exhaust fluid enthalpy values, the catalyst combustion module being communicable in data receiving communication with the energy balance module and fueling module; a peak temperature module configured to determine a thermal driving force based on the net heat generation, the peak temperature module being communicable in data receiving communication with the catalyst combustion module; and a bed temperature module configured to calculate a bed temperature of the first catalytic component based on the thermal driving force, a previous bed temperature of the first catalytic component, and a predicted time constant of the thermal response of the first catalytic component, the bed temperature module being communicable in data receiving communication with the peak temperature module. 16. The system of claim 15, further comprising a second catalytic component configured to treat the engine exhaust, wherein the energy balance module is further configured to determine a second fluid enthalpy value upstream of the second catalytic component, and a third fluid enthalpy value downstream of the second catalytic component, and wherein the catalyst combustion module is further configured to calculate the net heat generation based on the second and third fluid enthalpy values, wherein the first catalytic component is disposed in the exhaust fluid conduit downstream of the second catalytic component. 17. The apparatus of claim 16, further comprising a catalyst efficiency module configured to determine a first catalyst fuel combustion efficiency based on a temperature rise across the first catalytic component, wherein the catalyst combustion module is further configured to calculate the net heat generation based on the first catalyst fuel combustion efficiency. 18. The apparatus of claim 17, wherein the catalyst efficiency module is further configured to determine the first catalyst fuel combustion efficiency based on a derivative of the temperature rise across the first catalytic component with respect to time.