An easy-to-use analytical model for standing column wells operating with bleed

Accurate assessment of subsurface heat transport is vital for the design of standing column well systems. When bleed is utilized, the mathematical problem is governed by coupled heat transfer and groundwater flow within a radially convergent flow field, making the development of models challenging. While numerical models exist to simulate these transient processes, the absence of simple and accessible analytical solutions limits their broader application. This study addresses this gap by developing a novel easy-to-use analytical model to accurately represent the heat advection–diffusion problem in standing column wells operating with bleed. The proposed model combines the well-known infinite line source model with an innovative scaling function, inspired from the field of solute transport, through a simple convolution product. Notably, the developed model depends on only three dimensionless parameters: dimensionless advection time, Péclet number, and bleed ratio. Rigorous validation against two distinct sets of reference numerical solutions demonstrated the model’s efficiency, accuracy, and reliability across a broad spectrum of nine physical parameters. Key results include relative root mean square errors on the order of 10 −3 across 200 reference solutions, confirming the model’s robustness. These findings highlight the model’s potential to significantly advance both research and practical applications in the design and optimization of standing column wells. • An analytical model is proposed for standing column wells operating with bleed. • The model is easy to implement and takes the form of a simple convolution product. • The model is validated by comparison with 200 reference solutions. • The model is robust across various dimensionless parameters, including Péclet. • The model is fast, aiding in system performance optimization.