Online fault diagnosis is a task of critical importance for maintaining a high level of operational safety in many chemical plants. The Petri-net models are adopted in this work for describing the fault propagation behaviors in batch processes. A systematic method has been developed to synthesize a timed Petri-net hierarchically structured according to any given piping and instrumentation diagram (P&ID) and its operating procedure. On the basis of this model, a diagnoser can be constructed automatically with a computer program for online implementation. Computer algorithms have also been devised to place additional sensors and/or synthesize extra operation steps for the purpose of improving diagnostic performance. Several examples are presented in this paper to demonstrate the effectiveness and correctness of the proposed approach.