Experimental investigation into the influence of rock mechanical properties and etching patterns on acid fracture conductivity in the ilam carbonate formation

Acid fracturing represents a primary stimulation technique for unlocking commercial hydrocarbon productivity in tight carbonate reservoirs, yet predicting post-treatment fracture conductivity under closure stress remains challenging due to the coupled effects of dissolution geometry and rock mechanical deformation. In this study, we present an experimental methodology that decouples mechanical closure from stochastic dissolution kinetics by machining deterministic, idealized channel geometries onto standardized split core plugs (18.4 cm length × 4.75 cm width) of Cretaceous Ilam formation limestone from southwest Iran. Using an API RP-61 compliant high-pressure conductivity cell, tests were conducted across systematic variations in channel depth (0.6-1.6 mm), width (1.4-2.48 mm), and multiplicity (1–3 channels) under closure stresses spanning 1,321 to 5,283 psi (9.1–36.4 MPa). Two distinct mechanical facies were evaluated: compliant Ilam 1 (Young’s modulus E = 19.7 GPa, UCS = 50.0 MPa) and stiff Ilam 2 (E = 39.63 GPa, UCS = 78.8 MPa). Our results demonstrate that channel depth is the governing geometric control, providing 6- to 9-fold greater retained conductivity per unit volume of dissolved rock than channel widening or multiplicity. Classical linear superposition and parallel-plate cubic formulations fail systematically under closure due to sidewall compliance and inter-channel pillar stress concentrations. Notably, in multi-channel systems subjected to stresses exceeding 3,500 psi, stiffer rock undergoes accelerated conductivity loss via brittle pillar crushing, whereas compliant rock exhibits ductile stress redistribution that preserves conduit patency. Regularized third-degree polynomials accurately model this multi-stage closure behavior (R 2 > 0.98), providing physically grounded inputs for reservoir stimulation design.