Exhaust after-treatment system and exhaust aftertreatment process

Exhaust gas aftertreatment system (2) for an internal combustion engine (1) with a downstream of an internal combustion engine (1) arranged particle separator (3) in the form of a granulataltigen moving bed reactor or fluidized bed reactor for removing soot and ash particles from the exhaust gas, wherein in the particle separator (3) to be cleaned Exhaust gas can be supplied to the particle separator (3) via at least one exhaust gas feed line (4), wherein the exhaust gas purified from the particle separator (3) can be discharged from the particle separator (3) via at least one exhaust gas outlet (5), wherein granules pass the particle separator (3) via at least one granulate inlet (6) can be supplied, wherein granules from the particle separator (3) at least one granulate outlet (7) can be discharged, the exhaust gas in the particle separator (3) flows around the granules and this carbon black and ash particles adhere to the granules and / or bound to the granules and / or react with the granules, and wherein the granules together with the Ru - and ash particles and / or the reaction products thereof from the particle separator (3) by the or each granule outlet (7) can be discharged; and with the particle separator (3) associated with separating device (8) for separating together with the granules from the Partikelabscheider (3) separated soot and ash particles and / or reaction products thereof from the granules and at least partially return of the soot and Ash particles and / or granules separated from reaction products thereof in the particle separator (3) via at least one of the granule feeds (6).