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This work presents a diagnosis algorithm that combines structural causal graphical model and nonlinear dynamic Principal Component Analysis (PCA) for nonlinear systems with coupled energies incorporate the chemical kinetics of an equilibrated reaction, heat and mass transport phenomena. Therein, a coupled Bond Graph (BG) model, as an integrated decision tool, is used for modeling purpose. A Signed Directed Graph (SDG) is then deduced. A fault detection step is later carried out by generating initial responses through causal paths between exogenous and measured variables. After that, the localization of the actual fault is performed based on a nonlinear PCA (NLPCA) and back/forward propagations on the SDG. Simulation results on a pilot reactor show that the physic-chemical defects such as matter leakage, thermal insulation, or appearance of secondary reaction or temperature runaway when a very exothermic reaction occurs, can be detected and isolated.