A system, method, and software for triggering regeneration of an adsorber connected with a flow of exhaust from an engine. An exhaust sulfur flow rate module estimates a sulfur accumulation rate associated with an adsorber as a function of a flow of fuel. A sulfur removal rate module estimates a sulfur removal rate associated with the adsorber. An accumulated sulfur loading module includes a counter the value of which is increased as a function of the sulfur accumulation rate and decreased as a function of the sulfur removal rate. A combustion manager module controls an engine to regenerate the adsorber once the counter reaches an upper threshold value.