Lean nox trap desulfation process

A process for desulfation of a NOx adsorber in a diesel internal combustion engine exhaust system is disclosed, which comprises: determining an amount of post fuel ( Q 2 ) required to reach a relatively rich target exhaust air fuel ratio (AFR rich ) on the basis of a measured air flow; determining a heating-contributing fuel value ( ·Q 2 ) required to reach or maintain a target desulfation temperature in said NOx adsorber by way of an exothermal reaction; calculating a target air flow (Air tgt ) corresponding to the air flow required for a substantially stoichiometric combustion of a torque-contributing main fuel quantity ( Q 1 ) together with said heating-contributing fuel value ( ·Q 2 ) ; and causing the engine to inject said post fuel amount ( Q 2 ) and said main fuel quantity ( Q 1 ) while controlling the air flow to meet said target air flow ( Air tgt ) .