In this paper we suggest some alternative representations of the Continuous Stirred Tank Reactor (CSTR) in terms of port-controlled Hamiltonian (PCH) and contact systems, elaborating on some recent work on this subject. In a first instance we suggest a PCH formulation of the CSTR in the isothermal case, generated by a Hamiltonian being a reaction invariant with a Poisson structure matrix defined by the stoichiometric coefficients of the reaction or reaction network. In a second instance we include the energy balance equation and suggest a pseudo port Hamiltonian formulation with Hamiltonian function being either the internal energy or the entropy. In a third instance we consider the lift of the latter formulation on the whole Thermodynamic Phase Space and discuss two alternative formulations differing outside the Legendre submanifold associated with the thermodynamic properties of the CSTR.