Analytical modeling of grout heat storage effects in thermal response tests: Toward faster and more reliable parameter estimation

Accurate estimation of subsurface thermal properties is essential for the efficient design of ground-source heat pump (GSHP) and underground thermal energy storage (UTES) systems. However, conventional analytical models for thermal response tests (TRTs), such as the infinite line-source (ILS) and infinite cylindrical-surface-source (ICSS) solutions, neglect grout heat storage, leading to systematic bias during early heating periods. This study develops an analytical composite cylindrical source (CCS) model that explicitly accounts for the volumetric heat capacity of the grout (defined generically herein to denote borehole filling materials, including silica–sand backfill). The closed-form formulation reproduces Laplace-transform finite-difference simulations within 0.1 ° C and demonstrates excellent agreement with a distributed TRT conducted on a 54 m borehole. The CCS model reduces the root-mean-square error from 0.163 ° C (ILS) to 0.116 ° C , resolves meter-scale stratification, and yields practically stable estimates of thermal conductivity and heat capacity using 48–50 h of data. A Bayesian uncertainty analysis reveals a ‘transition zone’ around 42 h, suggesting that tests should extend beyond this period to avoid false convergence, but need not extend to 72 h for engineering purposes. Sensitivity analysis indicates that grout heat capacity governs early-time temperature response, whereas ground conductivity dominates later stages. The results show that incorporating grout heat storage significantly improves TRT interpretation accuracy and allows test duration to be shortened without compromising reliability, offering a practical framework for field-scale thermal characterization in GSHP design.