Digital twin development of a full-scale industrial heat pump

Industrial heat pumps (HPs) are a sustainable alternative to fossil-fueled boilers for process heat generation, particularly when powered by green electricity. However, their wider adoption is hindered by a limited understanding of HP performance under diverse operating conditions. Traditional methods for studying HP performance, such as high-fidelity numerical simulations or experimental testing, are often costly and impractical. To address this, we propose a digital-twin framework that unites machine learning, specifically Gaussian Process Regression (GPR), to efficiently model an industrial HP for energy recovery from (industrial) waste heat using experimental data. This approach is novel, as few data-driven models have been developed for designing industrial HPs employed for this purpose, thereby contributing to achieving a sustainable processing industry. This digital twin was developed for a 1 MWth industrial HP, using n-Pentane as the working medium and recovering waste heat from hot water to produce steam for industrial processes, and trained by experimental data collected from 55 steady-state operating points in a state-of-the-art test facility. The digital twin accurately predicts both relevant process variables (e.g. outlet pressures and temperatures) for each HP component and key performance indicators, including the Coefficient of Performance (COP) and heating duty, with prediction errors within 7% as a function of process parameters such as flow properties of the hot-water source, compressor rotational speed, and steam pressure. The digital twin is furthermore applied for an economic and environmental analysis, demonstrating a payback period of 3.8–4.2 years and reductions in CO2 emission of 250–1000 tons annually compared to a propane-fueled boiler. The HP achieved a COP equal to 44% of the Carnot COP based on condenser/evaporator saturation temperatures and enabled significant energy savings, exceeding 3000 MWh annually when operated at steam pressures of 1.9–2.4 bar. This study hereby demonstrates the potential of data-driven models to enhance the design and operation of industrial HPs and thus provides an efficient and scalable framework for developing and advancing sustainable energy systems in industry. © 2025 The Authors