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, shear thinning biases the aperture-to-flux mapping toward larger apertures, while yield stress suppresses flow below the mobilization threshold. 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 affects spreading through high-order flux-weighted aperture moments that determine persistent inter-channel variance. 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 provides an interpretable reference limit separating rheology-controlled hydraulic selection from matrix-controlled transport.