In the modern petroleum development and production process, a context-aware and self-adaptive environment is required to satisfy the dynamic changes of the well site operations. With the ubiquitous computing technology, a framework of high-confidence petroleum extraction software system is proposed to capture the system reconfiguration to fit special applications. As a sanity check, a bigraph model with a set of bigraphical reactive rules is used to discuss the structure and the dynamic behaviors of the framework. Finally, an example, with partly implementing the model, is briefly described to confirm the feasibility of the framework models.