Optimal valve closure operations for pressure suppression in fluid transport pipelines

Abstract

When a valve is suddenly closed in fluid transport pipelines, a pressure surge or shock is created along the pipeline due to the momentum change. This phenomenon, called hydraulic shock, can cause major damage to the pipelines. In this paper, we introduce a hyperbolic partial differential equation &#x0028 PDE &#x0029 system to describe the fluid flow in the pipeline and propose an optimal boundary control problem for pressure suppression during the valve closure. The boundary control in this system is related to the valve actuation located at the pipeline terminus through a valve closing model. To solve this optimal boundary control problem, we use the method of lines and orthogonal collocation to obtain a spatial-temporal discretization model based on the original pipeline transmission PDE system. Then, the optimal boundary control problem is reduced to a nonlinear programming &#x0028 NLP &#x0029 problem that can be solved using nonlinear optimization techniques such as sequential quadratic programming &#x0028 SQP &#x0029. Finally, we conclude the paper with simulation results demonstrating that the full parameterization &#x0028 FP &#x0029 method eliminates pressure shock effectively and costs less computation time compared with the control vector parameterization &#x0028 CVP &#x0029 method.