Optimizing Particle Transport and Drag Coefficient in Petroleum Pipelines Using a Sensitivity Based Pontryagin Approach

This study presents a sensitivity based optimal control framework for enhancing solid particle transport in petroleum pipelines. A nonlinear dynamic model is developed to describe particle velocity evolution under the effects of drag force, mixture density, particle size, and bounded flow disturbances. A control variable is introduced to regulate the effective mixture velocity and actively stabilize particle motion. Local sensitivity analysis identifies the drag coefficient, mixture density, and particle diameter as dominant parameters that reduce particle transport, with sensitivity indices of 0.82, 0.65, and 0.50, respectively. In contrast, mixture velocity and control input exhibit strong positive influence, with sensitivity indices of +0.85 and +0.95. An optimal control strategy is formulated using Pontryagins Maximum Principle and solved numerically using a forward backward sweep algorithm. Simulation results show that, with optimal control applied, the particle velocity converges smoothly to a stabilized value of 0.458 m/s, corresponding to 91.6% of the mixture velocity (0.5 m/s), with a relative deviation of less than 0.5% from the analytical steady state prediction.. Comparison with published CFD and multiphase flow studies confirms that the predicted velocity range and stabilization trends are consistent with reported particle transport behavior. The proposed approach provides an efficient tool for stabilizing particle motion and improving flow assurance in pipeline systems.