Simultaneous transport of two-component solution in flows in tubes and channels, coupled via a matrix wall reaction coefficient, is considered. Expressions for long-time effective axial matrix solute properties are derived in the particular case of a channel formed by two parallel plates. These matrix coefficients include effective axial solute reactivity, velocity and diffusivity. These coefficients are systematically investigated both analytically and numerically for a two-component species, having different molecular diffusivities and moving in a plane Poiseuille how between two parallel walls, on which surfaces they undergo coupled surface reactions. It is shown that for small coupling reactivity coefficient the species initially behave like uncoupled constituents, the dispersive transport of which can be studied via single-species solution scheme. At large times the species transport becomes coupled and all constituents are characterized by the same nonmatrix transport properties. These properties constitute leading modes of the corresponding matrix coefficients, governing the species transport for earlier times. Physically, in this situation the effective properties of both constituents are controlled by the (microscale) molecular diffusivity of the slowest component.