Rheology-controlled hydraulic selection in fracture–matrix heat transport: Mechanisms and thermal signatures

Geological fractures exhibit heterogeneous aperture fields that localize flow along preferential pathways and produce nonuniform fluid–matrix contact times. Heat transport combines channelized advection with conductive matrix exchange. For non-Newtonian fluids this coupling is constitutive: shear thinning biases the aperture-to-flux mapping toward larger apertures, while yield stress suppresses flow below the mobilization threshold. Thermal-front advance, longitudinal spreading, and outlet breakthrough diagnose this selection. A stochastic semi-analytical model represents aperture classes as parallel pathways with constitutive fluxes and superposes their channel-scale advection–conduction solutions for a semi-infinite matrix. Matrix diffusion sets the late-time scalings of breakthrough curves and front moments, while aperture variability and rheology control their amplitudes and crossover. Rheology acts on spreading not only through the mean velocity but through high-order flux-weighted aperture moments that set the amplitude of persistent inter-channel variance, making longitudinal variance the most sensitive diagnostic. For monomial flux laws the reduced late-time amplitudes collapse onto a single similarity variable, so shear thinning acts as amplified effective aperture variability. Global sensitivity analysis attributes flux reweighting to shear thinning and hydraulic accessibility to yield stress. Two-dimensional simulations verify the construction for Newtonian and power-law flow; a connected rough-field comparison at low aperture variability recovers mean advance and outlet survival but overestimates variance, so Ellis and Herschel–Bulkley results remain independent-channel predictions. The model is an interpretable reference limit separating rheology-controlled hydraulic selection from matrix-controlled transport: it predicts the breakthrough signature of a rheologically selective thermal tracer during engineered injection, rather than guiding the choice of a long-term production fluid.