Many interesting problems in the oil and gas industry face the challenge of responding to disturbances from afar. Typically, the disturbance occurs at the inlet of a pipeline or the bottom of an oil well, while sensing and actuation equipment is installed at the outlet, only, kilometers away from the disturbance. The present paper develops an output feedback control law for such cases, based on modelling the transport phenomenon as a 2 2 linear partial differential equation (PDE) of hyperbolic type and the disturbance as a finite-dimensional linear system affecting the left boundary of the PDE. Sensing and actuation are co-located at the right boundary of the PDE. The design provides a separation principle, allowing a disturbance attenuating full-state feedback control law to be combined with an observer. The results are applied to a relevant problem from the oil and gas industry and demonstrated in simulations.