An analytical solution to optimal heat pump integration

Heat pump integration has a large potential for reducing carbon emissions and operating costs of industrial processes. The Break-even COP method determines the maximum economically- or environmentally feasible heat pump temperature and the level of process heat electrification under specified economic conditions. However, this method fails to capture the optimal heat pump temperature and the possible emissions- and costs reduction in sensible heat processes. The present work introduces an analytical equation based on the Lorenz efficiency approach to determine the optimal heat pump sink temperature, maximizing the operating costs savings or the emission savings. Furthermore, it advances the break-even method to account for heat pumps with a temperature glide by applying a Lorenz efficiency approach. The method is applied to a spray-drier case study, showing a reduction on operation costs of 7.8 % and emissions by 11.9 % by a partial process electrification of 32 %. A parameter study is conducted, underscoring the importance of accurate predictions of the Lorenz efficiency factor and the electricity-to-fuel price and emissions ratios in heat pump integration studies.