A Reduced-Order Model for Tank–Pump–Valve Systems

Dynamic modeling of tank–pump–valve systems is fundamental to the analysis and control of oil and gas midstream pipeline facilities. However, high-fidelity models often involve significant complexity due to nonlinear pressure dynamics and distributed effects. Motivated by the above, this work presents a reduced-order nonlinear state-space model that captures the dynamics of tank-pump-valve systems for model-based control design and real-time implementation.

The model is derived based on mass balance principles for tank inventory, coupled with first-order actuator dynamics for both pump and valve. The pump behavior is represented by a smooth nonlinear formulation that allows for continuous ramp-up and ramp-down, avoiding discontinuities associated with on/off switching of single-speed pumps. This formulation is based on experimental observation of sigmoidal behaviors during pump ramp-up conditions, as reported by [Li et. al., 2011]. While the valve is modeled as a dynamic actuator regulating outlet flow as a function of the pump outflow. The model also includes pump system and operation curves, allowing model simulations of identical pumps operating in parallel.

The resulting state-space model therefore preserves key physical interactions, including flow coupling and actuator constraints, while significantly reducing model complexity found in traditional hydraulic formulations. Simulation studies demonstrate the quantitative model validation against transient behavior under varying operating conditions reported by [Li et. al., 2011]. The reduced-order model structure also allows for direct application of classical and advanced control design approaches. Practical applications to existing tank-pump-valve systems are also presented and discussed.