Whereas, the semantic grid is considered as the uniting concept of semantic web and grid computing, and the ontology technology provide an efficient data retrieval methodology in widely distributed semantic grid resources over the Internet. As the number of semantic grid resources increase, e.g., ontology servers, the amount of data increases and managing job workflows is becoming increasingly complex. This paper proposed a validation framework for sub-ontology extraction workflows in our proposed semantic grid computing environment. We considered two ontology optimization schemes and design its workflow models using Petri Net. The workflow for each model is described and validated. Preliminary results justify the feasibilities of our proposed validation framework of the aforementioned models which can be used as building blocks to model large and efficient sub-ontology extraction workflows in a semantic grid.