A method and apparatus for alkylating an alkylation substrate with an alkylating agent in the presence of solid catalyst particles in a transport reactor is disclosed. Solid catalyst particles in the transport reactor effluent recirculate to the inlet of the transport reactor through one or more conduits. The rate through each conduit is regulated by fluid-controlled valves that use the alkylation substrate as the regulating fluid. This method and apparatus help ensure uniform or symmetric flow of catalyst from the effluent of the transport reactor to the bottom of the transport reactor. This method and apparatus also help ensure uniform or symmetric flow of alkylation substrate to the bottom of the transport reactor with minimal bypassing by the alkylating agent around of the transport reactor. This invention finds use in the production of motor fuels by the alkylation of liquid hydrocarbons in the presence of solid catalyst particles.