The Industrial Internet of Things (IIoT) presents numerous requirements, such as reliability, energy efficiency, and real-time performance, among others. Digital Twins technology addresses these needs by enabling the simulation, monitoring, and optimization of such systems. Specifically, Network Digital Twins (NDTs) have recently attracted significant attention from both the industrial and academic networking communities. Numerous research efforts focus on the challenge of network modeling in this context, as simulation tools can increase cost and computational complexity. In this paper, we explore the integration of the formal modeling technique, Petri-nets, within the context of NDTs to model the IIoT, enabling data-driven Petri-nets. We present an architecture based on open-source tools as a framework to encourage researchers to investigate this research direction. Furthermore, we validate the proposed architecture through a case study involving a small-scale network modeled with Timed Petri-Nets. The results demonstrate the model’s effectiveness in executing what-if scenarios based on the network’s operational parameters to predict the Packet Delivery Ratio and enable real-time fault detection. Lastly, we conduct a study on the IIoT observability by the NDT to address the challenge of virtual–real systems mapping in such a context.