Industrial automation in the energy sector requires AI systems that can operate autonomously regardless of network availability, a requirement that cloud-centric architectures cannot meet. This paper evaluates the application of Device-First Continuum AI (DFC-AI) to critical energy sector operations. DFC-AI, a specialized architecture within the Hybrid Edge Cloud paradigm, implements intelligent agents using a microservices architecture that originates at end devices and extends across the computational continuum. Through comprehensive simulations of energy sector scenarios including drone inspections, sensor networks, and worker safety systems, we demonstrate that DFC-AI maintains full operational capability during network outages while cloud and gateway-based systems experience complete or partial failure. Our analysis reveals that zero-configuration GPU discovery and heterogeneous device clustering are particularly well-suited for energy sector deployments, where specialized nodes can handle intensive AI workloads for entire fleets of inspection drones or sensor networks. The evaluation shows that DFC-AI achieves significant latency reduction and energy savings compared to cloud architectures. Additionally, we find that gateway based edge solutions can paradoxically cost more than cloud solutions for certain energy sector workloads due to infrastructure overhead, while DFC-AI can consistently provide cost savings by leveraging enterprise-owned devices. These findings, validated through rigorous statistical analysis, establish that DFC-AI addresses the unique challenges of energy sector operations, ensuring intelligent agents remain available and functional in remote oil fields, offshore platforms, and other challenging environments characteristic of the industry.