NOVELTY - The method involves partially regenerating a set of catalyst particles by exposing a solid phase product and the catalyst particles to a first oxidizing condition to produce an oxidized solid phase and a partially-regenerated catalyst. The partially-regenerated catalyst and a non-oxidized portion of the solid phase product are cooled. The partially-regenerated catalyst is regenerated by exposing the non-oxidized portion of the solid phase product and the partially-regenerated catalyst to a second oxidizing condition to produce a regenerated catalyst.    USE - Method for facilitating a catalytic pyrolysis of a carbonaceous material i.e. biomass feedstock (claimed), using a multi-stage regenerator.    ADVANTAGE - The method enables providing an improved biomass pyrolysis reactor system that includes a regenerator that is able to combust coke on the catalyst and biochar without overheating the catalyst such that the regenerator is provided in multiple stages with inter-stage cooling so as to maintain temperature of the catalyst below a desired maximum level, thus preventing likelihood of damage to the pyrolysis catalyst during regeneration process. The method enables restricting regeneration heat transmitted to fresh feed through the regenerated catalyst and reducing potential for thermal damage to the catalyst, while simultaneously affording an opportunity to reduce carbon level on regenerated catalyst to very low percentage so as to enhance catalyst activity, thus protecting the catalyst from severe conditions.    DETAILED DESCRIPTION - The solid phase product comprises biochar. The partially-regenerated catalyst is a pyrolysis catalyst. An INDEPENDENT CLAIM is also included for a system for facilitating catalytic pyrolysis of a carbonaceous material.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of a system for catalytic pyrolysis of biomass.    Hopper or feed bin (218)    Reactor feed chamber (222)    Solid heat transfer medium inlet (231)    Outlet (238)    Separator (246)    Condenser (254)