Equation graph representations are proposed for generic diffusion-convection-reaction systems described by parabolic partial differential equations. A measure of structural input-output closeness is proposed, and its relationship with the equation graph representation is established. A graph-based algorithm to obtain network decompositions for distributed control is extended to networks that have diffusion-convection-reaction systems, and the effectiveness of the decomposition is demonstrated through a case study on a prototypical reaction-separation plant. (C) 2019 Elsevier Ltd. All rights reserved.