A Stochastic Optimization Model for a Ground Source Heat Pump System with Uncertainty Quantifications on Transient Geologic Variables

Abstract

In this study, a stochastic model for optimizing the design configurations of a ground source heat pump (GSHP) with the objective of cost minimization was developed. Firstly, the concept of reliability-based design optimization (RBDO) is introduced by demonstrating the simulation workflow including linearization of workspace, steps of design optimization, and formulated constraints that are applied as reliability criteria to ensure a turbulent flow within the ground heat exchanger and avoid extreme temperature variations over seasonal operation. Furthermore, to enhance the model's fidelity, uncertainties pertaining to the groundwater velocity and ground thermal conductivity were incorporated as random variables in the optimization process. The stochastic characteristics of groundwater velocity are particularly investigated by using its temporal value profiles, considering both amplitude at specific time instances and transient variations over time. The utilization of normal distributions effectively addressed these characteristics. The efficacy of this novel model was demonstrated in yielding the minimized total costs during a GSHP’s lifespan by concurrently addressing the uncertainties of the both design variables and geological parameters, ultimately reaching a state of convergence. The findings revealed that uncertainties related to geological factors can exert a significant influence on both the initial and operational costs of GSHP system. The optimized design variables, including borehole length, ground pipe radius, and working fluid flow rate, were provided at a confidence level of 85% across multiple predicted scenarios, ensuring the robustness and reliability of the GSHP system design.