System for determining sulfur storage of aftertreatment devices

An exhaust gas treatment system for an internal combustion engine that determines a total amount of sulfur stored on at least one aftertreatment device, comprising:

• a control module monitoring operation of the internal combustion engine for an amount of fuel consumed and an amount of oil consumed by the internal combustion engine, the control module comprising:
• a sulfur adsorption module determining a rate of sulfur adsorption in the at least one aftertreatment device, the sulfur adsorption module receiving a sulfur exposure from fuel value and a sulfur exposure from oil value as inputs, wherein the rate of sulfur adsorption is based on the amount of fuel consumed, the amount of oil consumed, the sulfur exposure from fuel value, and the sulfur exposure from oil value;
• a sulfur desorption module that calculates a rate of sulfur desorption by the at least one aftertreatment device based on an exhaust temperature value and one of an exhaust mass flow of the internal combustion engine and an exhaust gas space velocity value;
• and
• a total sulfur storage module in communication with the sulfur adsorption module and the sulfur desorption module, the total sulfur storage module determining the total amount of sulfur stored based on the rate of sulfur adsorption and the rate of sulfur desorption.