Nonlinear seepage–heat transfer mechanism and prediction model for buried tubes under multi-factor coupling

Significant potential exists for enhancing the heat extraction efficiency of ground heat exchangers under groundwater seepage conditions, but existing design models generally oversimplify the seepage–heat transfer coupling process and fail to capture the nonlinear enhancement effects under high seepage velocities and partial seepage zones. To address this gap, a modified predictive model for the heat extraction enhancement factor is proposed to characterize the nonlinear seepage–heat transfer coupling mechanism, providing a refined theoretical tool for performance evaluation in hydrogeologically complex environments. Theoretical derivation is first used to build the basic model framework; small-scale laboratory experiments verify the seepage-conduction coupling mechanism and numerical solving method, and full-size numerical simulations are then adopted to quantitatively analyze the nonlinear influences of seepage velocity, seepage zone ratio, U-tube length and diameter. The initial linear model based on a modified Peclet number is revised through the incorporation of a quadratic term for seepage velocity and exponential terms for seepage zone proportion and tube diameter. Orthogonal numerical experiments are conducted to determine the model coefficients, resulting in a quantitative multivariate prediction formula with high accuracy. The study demonstrates that groundwater seepage markedly improves heat extraction via convection–dispersion synergy, while the enhancement factor exhibits nonlinear saturation trends with increasing seepage velocity and seepage zone proportion. This work quantifies the nonlinear coupling mechanisms between seepage and geometric parameters, and develops a multi-factor prediction model that improves upon conventional linear formulations. The established model offers a reliable reference for the optimized design of ground heat exchangers systems under seepage conditions, thereby supporting the efficient and sustainable utilization of shallow geothermal energy.