Pipe-line corrosion is of a major concern in the transportation of crude oil and natural gas. The corrosion is caused by the presence of water in contact with the walls. Following water-tests and/or shut-down, small amounts of water tend to accumulate at low sections along the pipe line. Flushing out of the water from the pipe by the oil flow is required to avoid damages in the pipeline. From a practical point of view, the minimal oil flow rate required for displacement and flush-out of the accumulated water by the oil flow has to be determined. Experimental study, mechanistic models and numerical simulations are used to investigate the characteristics of water displacement by oil flow in hilly terrain pipelines. Various mechanisms for the onset of water displacement from a lower (horizontal) section into an upward inclined section are considered and the associated minimal (critical) oil-flow rate for the water displacement is evaluated. For oil-flow rates exceeding the critical value, the possible patterns of water movement in the inclined pipe are examined.