Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction

Injection of cold fluids through/into deep formations may cause significant cooling, thermal stress, and possible fracturing. In this study, the fracturing low-permeability under one-dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture length , aperture spacing time effective confining stress were derived. Solution single derived analytically, while solution multiple fractures constant (or dynamic) obtained displacement discontinuity method (and stability analysis). For fracture, increases nonlinearly then transitions to scaling law indicating that late-time linearly square root cooling time. constantly spaced fractures, deviates from single-fracture at later for larger showing slower propagation inter-fracture interaction. dynamically arrest induced by interaction determined analysis; fully transient provides evolution length, spacing, aperture, pattern; similar law, shows effect both arrest. The provide fast predictions all reservoir conditions (single) model parameter . Application geothermal site demonstrates reach 0.67, 6.25, 78.00 m in 0.49, 2.30, 13.00 0.43, 2.09, 12.19 mm 1, 100 10,000 days.