Valve Stroking to Control Water Hammer Transients Using Dynamic Programming

Abstract

Fluid transients in a pipeline caused by valve operation can be minimized by operating the valve in an optimally prescribed manner, in a given time of closure (t c > 2L /a ). Dynamic programming is used to select the operation of the valve (i.e., set the valve-operating policy) over the time period t c so that the pressure rise at the valve (the objective function) is minimized. Constraints on the valve closure policy may also be specified, e.g., monotonic valve closure. Application of this method to a simple pipeline with a reservoir at one end and a valve at the other end shows that the pressure rise at the valve is lower than when the valve is closed linearly with time. The benefits of dynamic programming are shown to be greatest when the time of closure t c is small. The method has also been applied to valve opening, so that the pressure drop at the valve is a minimum.