Enhancing ground source heat pump system design optimization: A stochastic model incorporating transient geological factors and decision variables

In this study, a cost minimization model of a ground source heat pump (GSHP) was performed to obtain its best design configurations based on system reliability. To implement a high-fidelity optimization, the uncertainties of decision parameters and geological parameters' distributions were considered. The GSHP's lifespan costs were functionalized based on an analytical borehole heat transfer model. Multiple constraints were established to serve as reliability goals to ensure a turbulent ground pipe flow without extreme temperature variations. The ground thermal conductivity, groundwater velocity, and unit price of electricity were considered as three random variables. Their dynamic characteristics were incorporated by assigning different increasing rates to the average magnitudes of them. Additionally, their transient fluctuations were accommodated by integrating probabilistic uncertainties into the optimization process, all of which followed normal distributions. The results demonstrated that the time-dependent characteristics of these uncertain variables could significantly affect the system investment of GSHP by reducing the total costs by 20.7% and 21.1% when the increasing rates of groundwater velocity and ground thermal conductivity reach 5% and 4% respectively. The study also provided optimized design variables under an 85% confidence level in various predicted scenarios, considering a wide range of dynamic geological parameters and energy costs.