Dynamic Optimization and Optimal Control of Hydrogen Blending Operations in Natural Gas Networks

We present a dynamic model for the optimal control problem (OCP) of hydrogen blending into natural gas pipeline networks subject to inequality constraints. The dynamic model is derived using the first principles partial differential equations (PDEs) for the transport of heterogeneous gas mixtures through long distance pipes. Hydrogen concentration is tracked together with the pressure and mass flow dynamics within the pipelines, as well as mixing and compatibility conditions at nodes, actuation by compressors, and injection of hydrogen or natural gas into the system or withdrawal of the mixture from the network. We implement a lumped parameter approximation to reduce the full PDE model to a differential algebraic equation (DAE) system that can be easily discretized and solved using nonlinear optimization or programming (NLP) solvers. We examine a temporal discretization that is advantageous for time-periodic boundary conditions, parameters, and inequality constraint bound values. The method is applied to solve case studies for a single pipe and a multi-pipe network with time-varying parameters in order to explore how mixing of heterogeneous gases affects pipeline transient optimization.