Port-Hamiltonian formulations of the elastic foam-bed reactor model

In this paper, we develop a port-Hamiltonian formulation for the elastic foam-bed reactor. We begin by deriving the mass and momentum balance equations for the gas, liquid and solid phases. Based on these equations, we construct a dissipative Hamiltonian representation and the corresponding port-Hamiltonian formulation to capture the system’s energy-conserving and dissipative dynamics. The framework is further extended to incorporate a time-dependent moving boundary induced by a piston, resulting in a port-Hamiltonian system defined on a dynamic spatial domain.