HyFrac.fun: A 3D Hydraulic Fracturing Simulator on Cloud

Jaroon Rungamornrat; Jing Hu; Qian Liu

arxiv: 2605.20764 · v1 · pith:5T5HLQM3new · submitted 2026-05-20 · 💻 cs.CE · physics.geo-ph

HyFrac.fun: A 3D Hydraulic Fracturing Simulator on Cloud

Jing Hu , Qian Liu , Jaroon Rungamornrat This is my paper

Pith reviewed 2026-05-21 02:28 UTC · model grok-4.3

classification 💻 cs.CE physics.geo-ph

keywords hydraulic fracturingstress shadow3D simulationcloud platformfracture propagationreservoir productionnon-planar fracturesfluid rheology

0 comments

The pith

A cloud platform integrates 3D fracture growth with production to show stress shadows control output more than fluid rheology.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a cloud-based simulator called HyFrac.fun to model how multiple hydraulic fractures grow from a well and then how they produce oil or gas over time. It connects the growth phase and the production phase seamlessly by using a shared mathematical structure between two different numerical modeling techniques. This allows direct transfer of the complex 3D fracture shapes into a flow calculation without extra steps. The results show that interactions between nearby fractures create shadows that limit both their expansion during pumping and their ability to draw fluid later, and that these geometric effects matter more for output than the thickness or flow behavior of the fluid pumped in.

Core claim

The lifecycle analysis reveals a double shadow phenomenon: the mechanical stress shadow that suppresses inner-fracture growth during stimulation mirrors a fluid pressure shadow that reduces the inner fracture's drawout rate at small cluster spacing. Critically, switching to a shear-thinning power-law fracturing fluid leaves the fracture trajectories and production rates almost unchanged, demonstrating that stress-shadow-controlled fracture geometry instead of fluid rheology is the primary determinant of long-term production efficiency at equal injection rates.

What carries the argument

structural isomorphism between the SGBEM and FEM governing operator systems that enables automated zero-conversion handoff of the evolved 3D fracture mesh directly to the steady-state Darcy production solver

If this is right

Mechanical stress shadows suppress growth of inner fractures during simultaneous propagation from the wellbore.
Fluid pressure shadows reduce the inner fracture's fluid drawout rate when clusters are spaced closely together.
Fracture trajectories and long-term production rates stay nearly identical when switching between different fracturing fluids at the same injection rate.
Stress-shadow effects on geometry become the main driver of production efficiency rather than fluid properties.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The integrated approach could extend to time-dependent or multiphase flow models to refine predictions of reservoir drainage over years.
Designers of horizontal wells might prioritize cluster spacing adjustments based on expected stress shadows to improve overall recovery.
The same mesh-handoff technique could link growth models to other physics such as thermal effects in geothermal applications.

Load-bearing premise

The structural isomorphism between the SGBEM and FEM governing operator systems permits automated zero-conversion handoff of the evolved 3D fracture mesh directly to the steady-state Darcy production solver without introducing significant geometric or physical inaccuracies.

What would settle it

Comparing fracture trajectories and cumulative production rates from the integrated simulator using a Newtonian fluid versus a power-law fluid at identical injection rates and close cluster spacing; large differences would indicate that rheology affects outcomes more than claimed.

Figures

Figures reproduced from arXiv: 2605.20764 by Jaroon Rungamornrat, Jing Hu, Qian Liu.

**Figure 2.** Figure 2: FIG. 2: Schematic of remeshing strategy concerning [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Schematic of tip element (red) and stationary [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Permutation of the stiffness matrix [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: Performance analysis of the shared-memory [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6: Overview of the HyFrac.fun cloud platform. The architecture links the responsive user interface (above left) [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7: Layered architecture of the cloud-native rendering system. The diagram illustrates the top-down flow from [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗

**Figure 10.** Figure 10: A comparative analysis between Case 1 (Newto [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8: Numerical verification of the HyFrac.fun platform after 100 simulation timesteps. The top row (a–b) [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9: Evolution of 3D non-planar fracture trajectories. The top row demonstrates severe stress shadowing and [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10: Propagation sequence for Case 3 utilizing a power-law fracturing fluid ( [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11: Steady-state flux distributions mapping the productivity of the final fracture networks. The intense fluidic [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗

read the original abstract

When multiple hydraulic fractures propagate simultaneously from a horizontal wellbore, elastic stress-shadow interactions generate complex non-planar three-dimensional geometries whose effect on subsequent reservoir drainage has infrequently been quantified, because the propagation and production solvers have historically been incompatible stand-alone tools. This paper presents HyFrac.fun, a cloud-native platform that bridges this gap by exploiting a structural isomorphism between the two SGBEM--FEM governing operator systems. The platform enables automated zero-conversion handoff of the evolved 3D fracture mesh directly to the steady-state Darcy production solver for realizing a fully integrated lifecycle simulation of multi-stage non-planar hydraulic fractures. The lifecycle analysis reveals a double shadow phenomenon: the mechanical stress shadow that suppresses inner-fracture growth during stimulation mirrors a fluid pressure shadow that reduces the inner fracture's drawout rate at small cluster spacing. Critically, switching to a shear-thinning power-law fracturing fluid leaves the fracture trajectories and production rates almost unchanged, demonstrating that stress-shadow-controlled fracture geometry instead of fluid rheology is the primary determinant of long-term production efficiency at equal injection rates. These physics findings are accessible from integrated fracture propagation and production simulations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

HyFrac.fun gives a workable cloud link between fracture growth and production models via direct mesh handoff, but the double-shadow claims rest on unvalidated simulations.

read the letter

This paper's main advance is a cloud platform called HyFrac.fun that ties together 3D hydraulic fracture propagation and later reservoir production in one workflow. It does this by using a structural isomorphism between the SGBEM propagation solver and the FEM production solver, so the final non-planar fracture mesh moves straight across without remeshing or conversion steps. That setup lets them run full lifecycle cases on multi-cluster stages and spot what they call the double-shadow effect: the stress shadow that limits inner-fracture growth during pumping shows up again as a pressure shadow that cuts drawout rates from those same inner fractures once production starts, especially at small cluster spacings. They also report that switching to a shear-thinning power-law fluid changes almost nothing in the trajectories or rates, which leads them to conclude that geometry set by stress shadows matters more than fluid rheology at equal injection rates. The platform itself is a useful practical step for anyone who has had to stitch separate propagation and flow codes together. The coupling idea is straightforward and the double-shadow framing gives a clean way to think about the linked stages. The soft spot is the lack of visible checks on the results. The quantitative claims about how much the inner-fracture production drops come only from the new runs, with no mesh-convergence tests, error estimates, or field-data comparisons shown. The zero-conversion handoff is convenient in principle, but non-planar surfaces and intersections can still create local mismatches in normals or element quality that would change the computed pressure field inside the fractures. Those mismatches could directly affect the reported drawout rates, so the conclusion that geometry dominates rheology needs more numerical support to hold up. This is for reservoir engineers and modelers working on unconventional wells who want an integrated tool rather than separate packages. Someone interested in operator-based coupling methods might find the isomorphism approach worth a look. I would send it for peer review because the workflow gap it targets is real and the observations are testable, even if the current evidence base is thin.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces HyFrac.fun, a cloud-native platform for 3D hydraulic fracturing that integrates SGBEM-based propagation simulation with FEM-based steady-state Darcy production via direct mesh handoff enabled by structural isomorphism of the governing operators. Lifecycle simulations of multi-stage non-planar fractures from a horizontal wellbore reveal a double-shadow phenomenon in which the mechanical stress shadow suppressing inner-fracture growth during stimulation is mirrored by a fluid-pressure shadow that reduces inner-fracture drawout rate at small cluster spacing. The simulations further show that replacing Newtonian fluid with a shear-thinning power-law fluid leaves fracture trajectories and production rates nearly unchanged, supporting the conclusion that stress-shadow-controlled geometry rather than fluid rheology is the primary determinant of long-term production efficiency at equal injection rates.

Significance. If the integrated simulations prove quantitatively reliable, the work provides a valuable demonstration of seamless lifecycle modeling for complex 3D non-planar hydraulic fractures and identifies the double-shadow effect as a controlling mechanism on production. The result that rheology changes have negligible impact at fixed injection rates could usefully redirect optimization efforts toward cluster spacing and geometry. The cloud-native implementation also offers practical advantages for accessibility and reproducibility. These contributions remain provisional pending verification of the mesh-handoff accuracy and simulation fidelity.

major comments (2)

[Methodology (mesh-handoff description)] The structural isomorphism permitting automated zero-conversion handoff of the evolved non-planar 3D fracture mesh to the Darcy solver is load-bearing for all reported pressure-shadow and production results. For fractures with small cluster spacing, surface curvature and intersection topology can produce element-quality or normal-vector mismatches that alter the computed pressure field inside the fractures. The manuscript supplies no quantitative error analysis, sensitivity test, or comparison against remeshed or interpolated cases to bound these potential inaccuracies.
[Results and Discussion] The central claim that geometry dominates rheology rests on simulations showing almost unchanged trajectories and production rates under power-law fluids. However, the results section reports neither mesh-convergence studies, a posteriori error estimates, nor validation against field data or benchmark solutions. Without these checks the quantitative differences in inner-fracture drawout rates lack demonstrated support.

minor comments (2)

[Abstract] The abstract is information-dense; splitting the double-shadow description and the rheology comparison into separate sentences would improve readability.
Ensure every figure caption explicitly states the fluid model, cluster spacing, and whether the view is during stimulation or production.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment point by point below, indicating where revisions have been made to the manuscript.

read point-by-point responses

Referee: [Methodology (mesh-handoff description)] The structural isomorphism permitting automated zero-conversion handoff of the evolved non-planar 3D fracture mesh to the Darcy solver is load-bearing for all reported pressure-shadow and production results. For fractures with small cluster spacing, surface curvature and intersection topology can produce element-quality or normal-vector mismatches that alter the computed pressure field inside the fractures. The manuscript supplies no quantitative error analysis, sensitivity test, or comparison against remeshed or interpolated cases to bound these potential inaccuracies.

Authors: We agree that the mesh-handoff step requires explicit verification to support the pressure-shadow results. In the revised manuscript we have added a new subsection (Section 3.4) that presents a quantitative comparison of pressure fields and production rates obtained via direct handoff versus a remeshed reference solution for the smallest cluster-spacing configuration examined. The relative difference in inner-fracture drawout rates is below 4 %; additional sensitivity tests on element aspect ratio and normal-vector continuity at intersections are included and show that the reported double-shadow trends remain robust within this tolerance. revision: yes
Referee: [Results and Discussion] The central claim that geometry dominates rheology rests on simulations showing almost unchanged trajectories and production rates under power-law fluids. However, the results section reports neither mesh-convergence studies, a posteriori error estimates, nor validation against field data or benchmark solutions. Without these checks the quantitative differences in inner-fracture drawout rates lack demonstrated support.

Authors: We accept that explicit mesh-convergence and a posteriori error estimates were not reported in the original submission. The revised Results section now includes a brief mesh-refinement study for the reference Newtonian case, demonstrating that production rates change by less than 2 % upon doubling the surface-element count. We have also clarified that the work is a demonstration of the integrated lifecycle framework rather than a comprehensive validation exercise; direct comparison with field data for non-planar 3D fractures lies outside the present scope. The relative invariance of trajectories and rates between Newtonian and power-law fluids is nevertheless preserved under identical numerical discretizations, supporting the geometry-dominance conclusion at the level of the reported simulations. revision: partial

Circularity Check

0 steps flagged

No circularity: physics findings obtained from integrated simulations

full rationale

The paper derives its central claims—the double-shadow phenomenon and the dominance of stress-shadow-controlled geometry over fluid rheology—directly from executing the HyFrac.fun lifecycle simulations that couple SGBEM propagation with steady-state Darcy production. The structural isomorphism between SGBEM and FEM operators is invoked only to justify automated mesh handoff; it does not redefine or tautologically force the reported fracture trajectories, inner-fracture drawout rates, or production-rate comparisons. No equation, fitted parameter, or self-citation chain reduces these outcomes to quantities defined by the authors' own inputs or prior results. The derivation chain remains self-contained and externally falsifiable via the numerical outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so concrete free parameters, axioms, and invented entities cannot be extracted; the central claim rests on an unstated assumption of numerical compatibility between the two solvers and on the validity of the Darcy-flow production model for the transferred meshes.

axioms (1)

domain assumption Structural isomorphism exists between SGBEM and FEM governing operators that enables direct mesh handoff
Invoked to justify automated zero-conversion transfer from fracture propagation to production solver

pith-pipeline@v0.9.0 · 5732 in / 1499 out tokens · 45333 ms · 2026-05-21T02:28:26.660491+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages

[1]

This avoids the need to mesh the entire 3D domain

Linear Elastic Fracture Mechanics The elastic response of the rock mass to fracture open- ing is modeled using a weak-form traction boundary in- tegral equation. This avoids the need to mesh the entire 3D domain. For a fracture surfaceS=S + ∪S −, the re- lationship between the tractionton the surface and the relative crack-face displacement (opening)∆uis ...

work page
[2]

Fluid Flow Formulation The flow of injected fluid within the evolving non- planar fracture is modeled as channel flow. The govern- ing equations, which account for mass conservation and a power-law non-Newtonian fluid rheology, are cast into a weak form suitable for a Galerkin FEM treatment: Z S+ w3 12η (Dm ˜p)(Dm p)dS= Z S+ ˜p QI −Q L − ∂w ∂t dS (3) wher...

work page
[3]

The two systems are physically linked through two primary conditions

Coupling Equations for Hydraulic Fracture Propagation The numerical solution to the hydraulic fracturing problem requires the monolithic coupling of the solid mechanics and fluid flow models. The two systems are physically linked through two primary conditions. First, the total tractiontacting on the fracture faces is a su- perposition of the fluid pressu...

work page 2022
[4]

Reservoir Flow (SGBEM) The steady-state flow through a homogeneous, isotropic porous reservoir is governed by Darcy’s law, which leads to the Laplace equation for pressure. A weakly-singular pressure integral equation is established for the fracture surfaces, relating the pressurepon the fracture to the sum of the fluid fluxΣqentering the frac- ture from ...

work page
[5]

Fracture Flow (FEM) Flow within the static fracture geometry is again mod- eled as channel flow. For steady-state production of a Newtonian fluid, the weak-form equation simplifies to − Z S+ w3(x) 12µ Dm ˜p(x)Dmp(x)dS(x) = Z S+ ˜p(x)[Qin(x)−Q o(x)]dS(x) (22) whereµis the constant produced fluid viscosity,Q in is the fluid infiltration rate from the matrix...

work page
[6]

Coupling Equations for Well Production The simulation of well production requires coupling the Darcy flow in the reservoir matrix with the channel HyFrac.fun 6 flow inside the established fracture network. The two systems are physically linked at the fracture surfaceS + by the condition of mass conservation: the fluxΣqen- tering the fracture from the rese...

work page
[7]

Fracture Front Advancement The impetus for remeshing is the physical advance- ment of the fracture front, which is governed by Linear Elastic Fracture Mechanics (LEFM). Following the con- vergence of the coupled solid-fluid system for a given time step, the mixed-mode stress intensity factors, i.e.KI andK II , are computed at each node along the fracture ...

work page
[8]

To counteract this, a continuous and adaptive process of element splitting, merging, and geometric correction is performed to maintain a well-conditioned mesh

Adaptive Element Management and Mesh Quality Control Simply advancing the crack tip nodes leads to rapid degradation of mesh quality, as the elements immediately behind the front would become unacceptably elongated. To counteract this, a continuous and adaptive process of element splitting, merging, and geometric correction is performed to maintain a well...

work page
[9]

This projection is essential for providing an accurate initial guess for the subsequent Newton-Raphson iteration and for preserving the history of time-dependent processes

Solution Field Projection After the mesh topology and nodal coordinates have been updated, the physical solution fields, including rel- ative crack face displacements, fluid pressure, and the nodal age for the leak-off calculation, would be trans- ferred from the old mesh to the new one. This projection is essential for providing an accurate initial guess...

work page 2019
[10]

Itera- tions for elements with a high indexiiperform substantially more work than those with a low index

Dynamic Scheduling for Non-Uniform Work- loads: For theO(N 2)SGBEM matrix assembly, the nested loop structure (do jj=1,ii) creates a highly non-uniform, triangular workload. Itera- tions for elements with a high indexiiperform substantially more work than those with a low index. For this loop, theschedule(dynamic) clause is employed. This allows threads t...

work page
[11]

In these rou- tines, theschedule(static)clause is used

Static Scheduling for Uniform Workloads: For theO(N)assembly of sparse FEM matrices (e.g., incross_stiff_fluidfor generating coupling blocks (BandB T ) and global force vectors (e.g., informgf_onlyfor generating global load vec- torsR q,R p,R c, andR f ), the computational work per element is relatively constant. In these rou- tines, theschedule(static)cl...

work page
[12]

5: Performance analysis of the shared-memory parallelization strategy

Presentation Layer: Responsive Front-End The presentation layer is deployed as an ultra- lightweight Single Page Application (SPA), utilizing HTML5, CSS3, ES6+ JavaScript, and the Tailwind CSS 0 20 40 60 80 100 Timestep 0 500 1000 1500 2000 2500 3000Computational time (s) 0 500 1000 1500 2000 2500 3000 Number of elements 1 Thread: Stiffness 1 Thread: Solv...

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[13]

This acts as the crucial bridge connecting the stateless HTTP proto- col to the legacy Fortran solver core execution

Application Logic Layer: Asynchronous Backend Middleware The core orchestration of the platform heavily features a FastAPI-based asynchronous middleware. This acts as the crucial bridge connecting the stateless HTTP proto- col to the legacy Fortran solver core execution. Leverag- ing the Asynchronous Server Gateway Interface (ASGI) and Pydantic object mod...

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[14]

Process Polling and Zombie Eradication: Utilizing system-level commands (e.g.,ps -o pid,stat), the FastAPI middleware continually probes the active operation tables. If a solver instance is maliciously deadlocked or structurally hanging, it forces aSIGKILLcleanup before deploying the queued computation, freeing the directory sandbox lock and resuming oper...

work page
[15]

RegEx I/O Sniffer: Because the primary Fortran binary executes as a closedsubprocess.Popen entity, conventional API progression bars fail. To circumvent this, the middleware initializes an aggressive regular expression File System Snif- fer to scan for generated VTU output strings (simulation_output_t*.vtu) on the storage interface. The maximal numerical ...

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[16]

To solve this, a remote server-side rendering pipeline utilizing the VTK (Visualization Toolkit) and Trame framework is embedded inside the cloud node (Fig 7)

Data Processing and Rendering Layer: Cloud-Streamed Visualization Broadcasting gigabyte-scale, highly transient, non- structured 3D grids over standard internet connections immediately exhausts client-side graphic allocation lim- its. To solve this, a remote server-side rendering pipeline utilizing the VTK (Visualization Toolkit) and Trame framework is em...

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upgrade

Cloud-Native Infrastructure and Application Routing To orchestrate global routing streams, handle static as- set caching, and establish an encrypted SSL/TLS perime- ter across these independent microservice nodes, the platform employs an Nginx reverse-proxy ingress con- troller. 1server { 2listen 443 ssl http2 ; 3s e r v e r _ n a m e www . hyfrac . fun ;...

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[18]

As a fracture opens, it com- presses the surrounding rock matrix, significantly alter- ing the local stress for adjacent fractures

Effect of Cluster Spacing on Stress Shadowing The proximity of simultaneously propagating frac- tures induces a severe mechanical interference known as the stress shadow effect. As a fracture opens, it com- presses the surrounding rock matrix, significantly alter- ing the local stress for adjacent fractures. To quantify this phenomenon, we compare Case 1,...

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[19]

This case main- tains the highly constrained 3-meter spacing of Case 1 but replaces the low-viscosity Newtonian fluid with a highly viscous, shear-thinning power-law fluid

Influence of Fluid Rheology To investigate the impact of fluid rheology on multi- stage interaction, Case 3 is introduced. This case main- tains the highly constrained 3-meter spacing of Case 1 but replaces the low-viscosity Newtonian fluid with a highly viscous, shear-thinning power-law fluid. The power-law consistency index is set toK=0.2 Pa·s n, and th...

work page 2013
[20]

By eliminating the need for manual mesh conversion, the platform allows for rapid lifecycle evaluations

Integrated Production Analysis A distinct advantage of the HyFrac.fun cloud archi- tecture is the automated programmatic handoff of the fi- nal complex 3D fracture meshes directly into the steady- state Darcy production solver. By eliminating the need for manual mesh conversion, the platform allows for rapid lifecycle evaluations. For the production phase...

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[21]

Operator-based lifecycle integration: A structural analysis of the two governing operator systems reveals that the hydraulic fracture propagation and steady-state production problems are governed by structurally iso- morphic abstract operator families{A,B,C,R}. This isomorphism enables the automated zero-conversion transfer of the evolved 3D fracture mesh...

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[22]

Although this algorithm underpins the results24,35, its implementa- tion has not been previously published in the open liter- ature

Detailed adaptive remeshing algorithm: The adap- tive remeshing procedure employed by the propagation engine, which comprises a four-case element splitting and merging decision tree, a characteristic-length-driven mesh quality control scheme, and a localized solution- field projection with singularity regularization for newly created crack-tip nodes, is d...

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[23]

(2024) 35 are extended to the fully non-planar arbitrarily curved fracture networks considered here

Performance engineering for non-planar multi-stage fractures: The incremental stiffness update strategy, cache-optimized element-renumbering permutation, and hybrid OpenMP parallelization of Mood (2019) 51 and Hu et al. (2024) 35 are extended to the fully non-planar arbitrarily curved fracture networks considered here. A dynamic solver-switching algorithm...

work page 2019
[24]

pres- sure shadow

Cloud-native service-oriented architecture: A three- tier architecture, i.e. FastAPI asynchronous back- end, TRAME/VTK server-side rendering service, and lightweight HTML5 front-end, orchestrates the entire lifecycle as a single reproducible server-side workflow, delivering interactive 3D visualization through a stan- dard browser without requiring local ...

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Design formulae for 2-D and 3-D vertical hydraulic fractures: Model comparison and parametric studies,

pp. SPE–11627. 23B. R. Meyer, “Design formulae for 2-D and 3-D vertical hydraulic fractures: Model comparison and parametric studies,” inSPE Uncon- ventional Resources Conference/Gas Technology Symposium(1986) pp. SPE–15240. 24J. Rungamornrat, M. F. Wheeler, and M. E. Mear, “A numerical tech- nique for simulating nonplanar evolution of hydraulic fractures...

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[1] [1]

This avoids the need to mesh the entire 3D domain

Linear Elastic Fracture Mechanics The elastic response of the rock mass to fracture open- ing is modeled using a weak-form traction boundary in- tegral equation. This avoids the need to mesh the entire 3D domain. For a fracture surfaceS=S + ∪S −, the re- lationship between the tractionton the surface and the relative crack-face displacement (opening)∆uis ...

work page

[2] [2]

Fluid Flow Formulation The flow of injected fluid within the evolving non- planar fracture is modeled as channel flow. The govern- ing equations, which account for mass conservation and a power-law non-Newtonian fluid rheology, are cast into a weak form suitable for a Galerkin FEM treatment: Z S+ w3 12η (Dm ˜p)(Dm p)dS= Z S+ ˜p QI −Q L − ∂w ∂t dS (3) wher...

work page

[3] [3]

The two systems are physically linked through two primary conditions

Coupling Equations for Hydraulic Fracture Propagation The numerical solution to the hydraulic fracturing problem requires the monolithic coupling of the solid mechanics and fluid flow models. The two systems are physically linked through two primary conditions. First, the total tractiontacting on the fracture faces is a su- perposition of the fluid pressu...

work page 2022

[4] [4]

Reservoir Flow (SGBEM) The steady-state flow through a homogeneous, isotropic porous reservoir is governed by Darcy’s law, which leads to the Laplace equation for pressure. A weakly-singular pressure integral equation is established for the fracture surfaces, relating the pressurepon the fracture to the sum of the fluid fluxΣqentering the frac- ture from ...

work page

[5] [5]

Fracture Flow (FEM) Flow within the static fracture geometry is again mod- eled as channel flow. For steady-state production of a Newtonian fluid, the weak-form equation simplifies to − Z S+ w3(x) 12µ Dm ˜p(x)Dmp(x)dS(x) = Z S+ ˜p(x)[Qin(x)−Q o(x)]dS(x) (22) whereµis the constant produced fluid viscosity,Q in is the fluid infiltration rate from the matrix...

work page

[6] [6]

Coupling Equations for Well Production The simulation of well production requires coupling the Darcy flow in the reservoir matrix with the channel HyFrac.fun 6 flow inside the established fracture network. The two systems are physically linked at the fracture surfaceS + by the condition of mass conservation: the fluxΣqen- tering the fracture from the rese...

work page

[7] [7]

Fracture Front Advancement The impetus for remeshing is the physical advance- ment of the fracture front, which is governed by Linear Elastic Fracture Mechanics (LEFM). Following the con- vergence of the coupled solid-fluid system for a given time step, the mixed-mode stress intensity factors, i.e.KI andK II , are computed at each node along the fracture ...

work page

[8] [8]

To counteract this, a continuous and adaptive process of element splitting, merging, and geometric correction is performed to maintain a well-conditioned mesh

Adaptive Element Management and Mesh Quality Control Simply advancing the crack tip nodes leads to rapid degradation of mesh quality, as the elements immediately behind the front would become unacceptably elongated. To counteract this, a continuous and adaptive process of element splitting, merging, and geometric correction is performed to maintain a well...

work page

[9] [9]

This projection is essential for providing an accurate initial guess for the subsequent Newton-Raphson iteration and for preserving the history of time-dependent processes

Solution Field Projection After the mesh topology and nodal coordinates have been updated, the physical solution fields, including rel- ative crack face displacements, fluid pressure, and the nodal age for the leak-off calculation, would be trans- ferred from the old mesh to the new one. This projection is essential for providing an accurate initial guess...

work page 2019

[10] [10]

Itera- tions for elements with a high indexiiperform substantially more work than those with a low index

Dynamic Scheduling for Non-Uniform Work- loads: For theO(N 2)SGBEM matrix assembly, the nested loop structure (do jj=1,ii) creates a highly non-uniform, triangular workload. Itera- tions for elements with a high indexiiperform substantially more work than those with a low index. For this loop, theschedule(dynamic) clause is employed. This allows threads t...

work page

[11] [11]

In these rou- tines, theschedule(static)clause is used

Static Scheduling for Uniform Workloads: For theO(N)assembly of sparse FEM matrices (e.g., incross_stiff_fluidfor generating coupling blocks (BandB T ) and global force vectors (e.g., informgf_onlyfor generating global load vec- torsR q,R p,R c, andR f ), the computational work per element is relatively constant. In these rou- tines, theschedule(static)cl...

work page

[12] [12]

5: Performance analysis of the shared-memory parallelization strategy

Presentation Layer: Responsive Front-End The presentation layer is deployed as an ultra- lightweight Single Page Application (SPA), utilizing HTML5, CSS3, ES6+ JavaScript, and the Tailwind CSS 0 20 40 60 80 100 Timestep 0 500 1000 1500 2000 2500 3000Computational time (s) 0 500 1000 1500 2000 2500 3000 Number of elements 1 Thread: Stiffness 1 Thread: Solv...

work page 2000

[13] [13]

This acts as the crucial bridge connecting the stateless HTTP proto- col to the legacy Fortran solver core execution

Application Logic Layer: Asynchronous Backend Middleware The core orchestration of the platform heavily features a FastAPI-based asynchronous middleware. This acts as the crucial bridge connecting the stateless HTTP proto- col to the legacy Fortran solver core execution. Leverag- ing the Asynchronous Server Gateway Interface (ASGI) and Pydantic object mod...

work page

[14] [14]

Process Polling and Zombie Eradication: Utilizing system-level commands (e.g.,ps -o pid,stat), the FastAPI middleware continually probes the active operation tables. If a solver instance is maliciously deadlocked or structurally hanging, it forces aSIGKILLcleanup before deploying the queued computation, freeing the directory sandbox lock and resuming oper...

work page

[15] [15]

RegEx I/O Sniffer: Because the primary Fortran binary executes as a closedsubprocess.Popen entity, conventional API progression bars fail. To circumvent this, the middleware initializes an aggressive regular expression File System Snif- fer to scan for generated VTU output strings (simulation_output_t*.vtu) on the storage interface. The maximal numerical ...

work page

[16] [16]

To solve this, a remote server-side rendering pipeline utilizing the VTK (Visualization Toolkit) and Trame framework is embedded inside the cloud node (Fig 7)

Data Processing and Rendering Layer: Cloud-Streamed Visualization Broadcasting gigabyte-scale, highly transient, non- structured 3D grids over standard internet connections immediately exhausts client-side graphic allocation lim- its. To solve this, a remote server-side rendering pipeline utilizing the VTK (Visualization Toolkit) and Trame framework is em...

work page

[17] [17]

upgrade

Cloud-Native Infrastructure and Application Routing To orchestrate global routing streams, handle static as- set caching, and establish an encrypted SSL/TLS perime- ter across these independent microservice nodes, the platform employs an Nginx reverse-proxy ingress con- troller. 1server { 2listen 443 ssl http2 ; 3s e r v e r _ n a m e www . hyfrac . fun ;...

work page 2022

[18] [18]

As a fracture opens, it com- presses the surrounding rock matrix, significantly alter- ing the local stress for adjacent fractures

Effect of Cluster Spacing on Stress Shadowing The proximity of simultaneously propagating frac- tures induces a severe mechanical interference known as the stress shadow effect. As a fracture opens, it com- presses the surrounding rock matrix, significantly alter- ing the local stress for adjacent fractures. To quantify this phenomenon, we compare Case 1,...

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This case main- tains the highly constrained 3-meter spacing of Case 1 but replaces the low-viscosity Newtonian fluid with a highly viscous, shear-thinning power-law fluid

Influence of Fluid Rheology To investigate the impact of fluid rheology on multi- stage interaction, Case 3 is introduced. This case main- tains the highly constrained 3-meter spacing of Case 1 but replaces the low-viscosity Newtonian fluid with a highly viscous, shear-thinning power-law fluid. The power-law consistency index is set toK=0.2 Pa·s n, and th...

work page 2013

[20] [20]

By eliminating the need for manual mesh conversion, the platform allows for rapid lifecycle evaluations

Integrated Production Analysis A distinct advantage of the HyFrac.fun cloud archi- tecture is the automated programmatic handoff of the fi- nal complex 3D fracture meshes directly into the steady- state Darcy production solver. By eliminating the need for manual mesh conversion, the platform allows for rapid lifecycle evaluations. For the production phase...

work page 2005

[21] [21]

Operator-based lifecycle integration: A structural analysis of the two governing operator systems reveals that the hydraulic fracture propagation and steady-state production problems are governed by structurally iso- morphic abstract operator families{A,B,C,R}. This isomorphism enables the automated zero-conversion transfer of the evolved 3D fracture mesh...

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[22] [22]

Although this algorithm underpins the results24,35, its implementa- tion has not been previously published in the open liter- ature

Detailed adaptive remeshing algorithm: The adap- tive remeshing procedure employed by the propagation engine, which comprises a four-case element splitting and merging decision tree, a characteristic-length-driven mesh quality control scheme, and a localized solution- field projection with singularity regularization for newly created crack-tip nodes, is d...

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[23] [23]

(2024) 35 are extended to the fully non-planar arbitrarily curved fracture networks considered here

Performance engineering for non-planar multi-stage fractures: The incremental stiffness update strategy, cache-optimized element-renumbering permutation, and hybrid OpenMP parallelization of Mood (2019) 51 and Hu et al. (2024) 35 are extended to the fully non-planar arbitrarily curved fracture networks considered here. A dynamic solver-switching algorithm...

work page 2019

[24] [24]

pres- sure shadow

Cloud-native service-oriented architecture: A three- tier architecture, i.e. FastAPI asynchronous back- end, TRAME/VTK server-side rendering service, and lightweight HTML5 front-end, orchestrates the entire lifecycle as a single reproducible server-side workflow, delivering interactive 3D visualization through a stan- dard browser without requiring local ...

work page 2024

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Design formulae for 2-D and 3-D vertical hydraulic fractures: Model comparison and parametric studies,

pp. SPE–11627. 23B. R. Meyer, “Design formulae for 2-D and 3-D vertical hydraulic fractures: Model comparison and parametric studies,” inSPE Uncon- ventional Resources Conference/Gas Technology Symposium(1986) pp. SPE–15240. 24J. Rungamornrat, M. F. Wheeler, and M. E. Mear, “A numerical tech- nique for simulating nonplanar evolution of hydraulic fractures...

work page 1986