To reduce environmental risks and impacts from orphaned wells (abandoned oil and gas wells), it is essential to first locate and then plug these wells. Although some historical documents are available, they are often unstructured, not cleaned, and outdated. Additionally, they vary widely by state and type. Manual reading and digitizing this information from historical documents are not feasible, given the high number of wells. Here, we propose a new computational approach for rapidly and cost-effectively locating these wells. Specifically, we leverage the advanced capabilities of large language models (LLMs) to extract vital information including well location and depth from historical records of orphaned wells. In this paper, we present an information extraction workflow based on open-source Llama 2 models and test them on a dataset of 160 well documents. Our results show that the developed workflow achieves excellent accuracy in extracting location and depth from clean, PDF-based reports, with a 100% accuracy rate. However, it struggles with unstructured image-based well records, where accuracy drops to 70%. The workflow provides significant benefits over manual human digitization, including reduced labor and increased automation. In general, more detailed prompting leads to improved information extraction, and those LLMs with more parameters typically perform better. We provided a detailed discussion of the current challenges and the corresponding opportunities/approaches to address them. Additionally, a vast amount of geoscientific information is locked up in old documents, and this work demonstrates that recent breakthroughs in LLMs enable us to unlock this information more broadly.