The class of isotherm lumped process systems with constant overall mass in each of its balance volumes is considered in this paper. It is shown that the convection and transfer mechanisms can be described by a mass action law chemical reaction network (MAL CRN) with only linear kinetics where the in- and outflow terms are represented using the zero complex. This gives rise to a convection and transfer reaction sub-graph that connects atomic complexes consisting of the components in the balance volumes of the system. The real chemical reactions in each of the balance volumes can be described by their own CRNs, where the chemical reaction sub-graphs may be disconnected from the convection and transfer reaction sub-graph when nonlinear reactions occur. In the case of chemical reactions with a finite number of steady state points, the underlying linear dynamical system enables us to construct a dynamically similar linear overall reaction graph for the whole process system. The resulting overall reaction graph can be used for structural stability analysis by applying its graph theoretical properties.