Influence of Grain-Scale Heterogeneity on Hydraulic Fracturing: A Study Based on a Hydro-Mechanical Phase-Field Model
, Jinquan Xing 2,3, Jialun Niu 2,3, Zhaosen Wang 1,2 and Wenkang Yu 1,2
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors1. The manuscript is purely numerical in nature; the authors formulate conclusions that are directly related to real fracture mechanisms in crystalline rocks. In the absence of any experimental validation, these conclusions should be regarded solely as hypotheses derived from the adopted modeling framework. In its current form, it is not possible to determine whether the observed effects reflect physical behavior or are artifacts of the underlying modeling assumptions.
2. Grain-scale heterogeneity is represented using an algorithmically generated, model microstructure. The manuscript does not demonstrate that the adopted grain geometry or mineral distribution is representative of real crystalline rocks. The lack of microstructural characterization based on experimental data (SEM, CT) significantly limits the applicability of the results to real geological materials.
3. All grains of a given mineral are assigned constant and homogeneous mechanical properties. In reality, minerals exhibit significant local variability and crystallographic anisotropy, which may strongly influence fracture initiation and propagation. The absence of parameter variability or orientation-dependent behavior constitutes a major methodological simplification that should be discussed in the context of the reliability of the obtained results.
4. Grain boundaries are treated as uniform, mechanically weakened zones with constant properties. In natural rocks, grain boundaries can differ substantially in terms of energy, cohesion, and susceptibility to cracking, which may affect the balance between intergranular and transgranular fracture modes.
5. Model validation is limited to comparison with a previous numerical benchmark. No reference is made to experimental data related to pressure evolution, critical pressure values, or fracture morphology. The lack of experimental validation significantly limits the quantitative credibility of the presented results.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsSynchronization of Text and Graphics, must review the claim that peak pressure is similar at 0 and 10 MPa (14.31 vs 14.21 MPa). Figures 5 and 9 show much wider variations reaching up to 18 MPa. It is necessary to recalculate these averages or explain the statistical deviations
Clarification of the Role of Axial Stress, the conclusion that axial stress is should be qualified. The results themselves show that axial stress fundamentally changes the fracture mechanism from intergranular to transgranular in specific zones.
Inclusion of Experimental Comparison it is suggested to include at least one direct comparison with laboratory results, such as CT images or acoustic emissions, to validate that the fracture trajectories observed in the Voronoi model match real rock specimens.
Justification of Properties provide a stronger justification for the specific volume fractions chosen (25% quartz, 30% albite, etc.) and how these represent a generic crystalline rock.
Energy Quantification mentions that behavior follows energy minimization, but does not present energy balance graphs. It is suggested to add figures tracking the evolution of elastic free energy and dissipated fracture energy to support theoretical claims
Process Zone Analysis since a phase-field model is used, it would be valuable to discuss how the length scale parameter affects fracture width and if this is physically representative of the grain size.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsI have no further comments and accept the manuscript in its current form.
