Author Comment on EGUSPHERE-2025-36

Dear Mohammad Sabah,

We sincerely appreciate your thorough and constructive review of our manuscript on UpsFrac. Your detailed comments will significantly improve the quality and impact of our work. We are committed to addressing all your concerns comprehensively. We have carefully considered all comments and already initiated several improvements. Below, we provide our initial response to each point and our planned revisions.

Response to General Comments

Comment 1: We appreciate the referee's recognition of UpsFrac as a "useful integrated workflow" and the constructive suggestion to better articulate our innovations. We agree that clearer positioning will strengthen the manuscript. UpsFrac represents the first open-source platform that bridges the gap between fractal theory and practical permeability upscaling of fractured porous rocks, addressing a critical need in fractured reservoir modeling. Specifically, our contributions include: (1) Unified handling of both deterministic and stochastic fractal fracture networks, enhancing modeling capabilities for complex geological systems. (2) Direct coupling between DFN generation and MBM upscaling without intermediate file conversions, eliminating data loss and reducing workflow execution time. (3) Accessibility through open-source implementation with extensible modular architecture, enabling researchers to easily incorporate new fracture modeling algorithms, upscaling methods, and flow solvers, fostering community-driven development.

Planned revision: 1. We will add the following positioning statement in the revised manuscript: "UpsFrac advances the state-of-the-art in fractured media modeling by providing the first integrated open-source solution that directly couples fractal DFN generation with flow-based permeability upscaling. This tool fills a critical gap between theoretical fractal geometry models and practical reservoir simulation needs. By automating the entire process from stochastic fracture realization to upscaled equivalent properties, UpsFrac enables Monte Carlo analyses, transforming our ability to quantify uncertainty in fractured porous rock modeling. The platform makes large-scale stochastic analysis accessible to the broader research community." 2. We will add a comprehensive comparison table in the Introduction to position UpsFrac against PorePy, DFN-Works, MRST, and OpenGeoSys, evaluating four key dimensions: (1) Programming Language and accessibility; (2) Fracture Modeling capabilities; (3) Flow Simulation methods; and (4) Permeability Upscaling techniques. This systematic comparison will demonstrate that UpsFrac uniquely provides an integrated workflow from fracture generation through permeability upscaling within a single framework, thereby eliminating data conversion overhead and enabling automated ensemble-based uncertainty quantification—a combination of capabilities currently unavailable in existing tools.

Comment 2: We fully agree with this excellent point. Grid refinement effects, fracture-matrix permeability contrast, and fracture orientation relative to grid alignment are indeed crucial factors affecting upscaling accuracy. We recognize that these parameters can significantly influence the computed equivalent permeability tensor and appreciate the reviewer highlighting this important aspect.

Planned revision: We will add a new subsection (Section 3.3: Numerical Accuracy and Sensitivity Analysis) to comprehensively evaluate UpsFrac's computational reliability. This section will present: (1) Grid convergence studies using systematic mesh refinement ; (2) Parametric analysis of fracture-matrix permeability contrast and its influence on upscaling accuracy; (3) Orientation-dependent error quantification for fractures at various angles relative to the computational grid. These systematic investigations will establish rigorous bounds on numerical accuracy and demonstrate UpsFrac's robustness across diverse fracture configurations.

Comment 3: We greatly appreciate this insightful comment. Indeed, most current DFM implementations, including ours, adopt the constant aperture assumption for individual fractures. This simplification stems from both the scarcity of high-resolution roughness measurements and computational constraints for geological field-scale simulation. We acknowledge that this assumption may limit accuracy when modeling realistic fracture-matrix systems. The UpsFrac framework's modular architecture is designed to accommodate future incorporation of variable aperture models.

Planned revision: We will expand Section 5 to include: (1) A thorough discussion of the constant aperture assumption's limitations based on literature review; (2) Quantitative error analysis comparing constant versus variable aperture models using synthetic test cases; (3) Clear implementation pathways for future variable aperture extensions, including data structure requirements and algorithmic modifications. This comprehensive analysis will establish error bounds for the current implementation and provide a roadmap for incorporating aperture variability in future releases.

Comment 4: We agree that while the current 2D implementation is well-suited for validation and pedagogy, 3D capability is essential for industrial applicability. We have previously demonstrated 3D upscaling (Chen et al., 2018, Hydrogeology Journal 26:1903-1916), but it has not yet been integrated into UpsFrac. Building on our existing DFN generation and simulation tooling (e.g., ADFNE and MRST), we expect the 3D integration to be technically straightforward, though it involves substantially higher computational demands and more complex fracture geometries.

Planned revision: We will outline concrete acceleration strategies and a development roadmap in Section 5 covering: (i) generalizing DFN generation from 2D line fractures to 3D triangulated fracture surfaces with realistic size, orientation, and aperture distributions; (ii) extending the multiple boundary method (MBM) to 3D with robust treatment of fracture intersections; and (iii) mitigating the substantially higher computational cost through algorithmic accelerations, including adaptive/octree meshing, domain decomposition with parallel CPU/GPU solvers, and graph-based pruning of disconnected subnetworks.

Comment 5: We thank the reviewer for this valuable suggestion and acknowledge that computational performance and scalability analysis was indeed missing from our original manuscript. We fully agree that these metrics are critical for assessing the practical utility of any numerical method intended for field-scale applications.

Planned revision: We will add a section reporting performance for a field-scale case, including the number of fractures and grid cells and hardware specifications. We will present wall-clock runtime and peak memory usage for key stages (DFN generation/meshing, MBM assembly, linear solves) and provide a comparison with the open-source DFM simulator such as OpenGeoSys (OGS) using identical inputs and hardware. Results will be summarized in tables and scaling plots to highlight UpsFrac's efficiency; where gaps exist, we will identify bottlenecks and outline remedies. This analysis will also underscore the computational advantages of the upscaling approach.

Comment 6: We thank the reviewer for this valuable suggestion regarding validation of heterogeneous matrix-fracture systems. We agree that, to better reflect practical upscaling use cases, the manuscript should include broader validation that explicitly incorporates heterogeneity and matrix-fracture coupling at field scale.

Planned revision: We will add a validation case (Section 4.2) based on a field-scale example that (i) benchmarks against known analytical solutions for equivalent permeability in heterogeneous fracture-matrix systems, (ii) compares upscaled permeability from our method with full-domain DFM and/or EDFM simulations, and (iii) demonstrates that the upscaled properties accurately reproduce domain-scale flow behavior. This new Section 4.2 will also include dedicated performance analysis (runtime and memory statistics) to jointly address Comments 5 and 6.

Comment 7: We thank the reviewer for this valuable suggestion regarding uncertainty quantification. We agree that demonstrating ensemble-based uncertainty quantification is essential, especially given the inherent uncertainty in subsurface observations due to data sparsity and noise. UpsFrac supports Monte Carlo workflows by generating stochastic DFNs and performing batch upscaling to quantify variability in effective properties.

Planned revision: We will add an ensemble uncertainty quantification subsection in Section 4.3 featuring 50–100 stochastic DFN realizations of the discrete-fracture case. We will report statistics of the upscaled permeability tensor components (Kxx, Kyy, Kxy), including means, variances, and empirical distributions; assess convergence of ensemble statistics; and document computational requirements for ensemble runs (wall-clock time and memory). This example will directly address the reviewer's request to substantiate the abstract's ensemble claim and discuss statistical convergence.

Comment 8: We thank the reviewer for this valuable suggestion regarding algorithm reproducibility. We agree that the current algorithm description lacks sufficient detail and intuitive presentation, and that the functions of key scripts are not adequately summarized. This indeed affects the understanding and usability of the software algorithm.

Planned revision: We will enhance algorithm reproducibility through three complementary additions: (1) Revise Figure 2 as a comprehensive flowchart that maps each workflow step to its corresponding script name, including key input/output parameters for each processing stage; (2) add a Code Implementation section in Section 2, featuring a detailed table on "Core Scripts and their Functions in the UpsFrac Framework" that summarizes the purpose and computational role of each major script (e.g., SubDivideToGrid.m, CalcuKeq.m); and (3) provide comprehensive pseudocode for the core upscaling algorithm in Appendix A, enabling readers to understand the computational logic and reproduce the methodology independently.

Comment 9: We thank the reviewer for pointing out the language issues and acknowledge that grammatical errors and misspellings indeed distract from the technical content. We apologize for these oversights and agree that thorough language editing is essential for clear scientific communication.

Planned revision: We will conduct comprehensive language editing throughout the revised manuscript and address all technical corrections: (1) explicitly state "2D MATLAB-based implementation" in the abstract; (2) recreate Figure 2 workflow using vector graphics to ensure clear, crisp fonts; (3) add appropriate colorbar units (log10(K) [m²]) to Figures 7 and 8 permeability maps; (4) include normalized scale indicators for Figure 9 ellipses with clarification of axis normalization; and (5) unify reference formatting to abbreviated journal names throughout. Additionally, we will ensure thorough proofreading to eliminate grammatical errors and enhance overall readability.

Timeline and Further Discussion

We are already working on the sensitivity analyses and validation (Comments 2, 5 and 6) and expect to share preliminary results. The ensemble analysis (Comment 7) is computationally intensive but should be complete within the discussion period.

Thank you again for your valuable feedback. We believe these revisions will substantially strengthen UpsFrac's contribution to the fracture modeling community. We welcome any additional suggestions from the referee and the community.

Best regards,

Tao

Author Comment on EGUSPHERE-2025-36

Dear Reviewer,

We sincerely appreciate your thorough and constructive review of our manuscript. Your detailed feedback will significantly improve the clarity and scientific contribution of our work. We agree with your assessment that the manuscript requires major revision, and we are committed to addressing all your concerns comprehensively. Below, we provide our point-by-point response and planned revisions.

Response to Major Comments

Comment 1: We fully agree that much of the manuscript reads like a user manual rather than a scientific contribution. Your specific examples clearly illustrate this issue, and we really appreciate the constructive suggestions.

Planned revision: We will comprehensively address this issue through the following actions: (1) check and revise the manuscript to emphasize scientific contributions over implementation details, moving file names, script references, and format specifications to supplementary documentation on GitHub; (2) revise Section 2 to focus on the mathematical formulation and algorithmic aspects rather than implementation details; (3) comprehensively compare the innovation with existing approaches or tools.

Comment 2: We acknowledge the numerous language issues and apologize for these oversights that detract from the technical content. We greatly appreciate your valuable suggestions.

Planned revision: We will address language issues for better understanding and clarity through: (1) checking and correcting grammatical errors; (2) proper handling of abbreviations by introducing them once and using consistently throughout, removing unnecessary repetitions; (3) clarification or removal of ambiguous terms such as "engineering structures" in line 27, and proper definition of "MFU" in line 17; (4) correction of all typographical errors; (5) verification and correction of the DOI in line 310 to ensure proper citation.

Comment 3: We thank the reviewer for this excellent point that requires clarification. We need to better demonstrate what UpsFrac offers beyond existing tools like MRST and clarify the novelty of our work.

Planned revision: We will clarify our scientific contributions through: (1) adding a detailed comparison showing the differences between UpsFrac and MRST's upscaling capabilities, highlighting the specific advantages of our approach; (2) focusing on our true innovations such as the integrated workflow for uncertainty quantification; (3) reorganizing the introduction to clearly distinguish between standard features and our actual scientific contributions.

Comment 4: We thank the reviewer for this constructive comment. We agree that the validation section requires more detailed explanation and simulations to improve clarity and reproducibility.

Planned revision: We will completely revise the validation section to ensure clarity and reproducibility: (1) provide a clear description of the simulation setup, including: single fracture dimensions and position within the matrix domain, matrix dimensions, and specified boundary conditions; (2) present the exact analytical solution equation for calculating equivalent permeability and explain the underlying assumptions of the comparison (e.g., steady-state flow, incompressible fluid, homogeneous matrix properties); (3) conduct sensitivity analyses for different fracture angles and grid sizes to further validate our method.

Comment 5: We thank the reviewer for this valuable suggestion and acknowledge that computational performance analysis was indeed missing from our original manuscript. We fully agree that these metrics are critical for assessing the practical utility for field-scale applications.

Planned revision: We will add a section reporting performance of the upscaling method, including: (1) Detailed performance metrics for field-scale fracture networks; (2) Wall-clock runtime and memory usage for key stages; (3) Comparison with open-source DFM simulators such as OpenGeoSys (OGS) using identical inputs and hardware; (4) Hardware specifications used for benchmarking (CPU model, RAM, OS); (5) Results summarized in tables or plots to highlight UpsFrac's efficiency and identify bottlenecks where improvements are needed.

Timeline and Further Discussion

We are already working on several key improvements: (1) manuscript restructuring and language improvements to address clarity concerns and highlight our novel contributions (Comments 1, 2 and 3); (2) sensitivity analyses and validation studies (Comment 4); (3) performance benchmarking for field-scale applications (Comment 5). We expect to complete most of these modifications within two weeks.

Thank you again for your valuable feedback. We believe these revisions will substantially strengthen UpsFrac's contribution to the fracture modeling community. We welcome any additional suggestions from the referee and the community.

Best regards,

Tao