Determination of Effective Fracturing Radius for CO₂ Phase-Change Induced Coal Seam Gas Drainage via Time-Source Separation Method

1. Definition and Fundamental Principles

1.1 CO₂ Phase-Change Fracturing Technology

CO₂ phase-change induced fracturing is an advanced in-situ coal seam pre-conditioning technique used to enhance gas drainage efficiency and reduce coal and gas outburst risks. The fundamental principle relies on the thermodynamic properties of carbon dioxide: when liquid CO₂ is injected into a coal seam at high pressure (typically 8–15 MPa), it remains in liquid phase due to the confining pressure of the surrounding coal matrix. Upon release or when the pressure exceeds the coal's tensile strength, the CO₂ undergoes a rapid phase transition from liquid to supercritical/gas phase, expanding by a factor of 300–500 times its original liquid volume. This abrupt volumetric expansion generates localized stress concentrations that exceed the tensile and shear strength of the coal body, thereby creating a network of fractures and micro-cracks radiating from the injection point.

The effectiveness of this fracturing process is quantified by the effective fracturing radius (R_eff), which defines the radial extent from the injection borehole within which the coal mass has been sufficiently fractured to permit enhanced gas flow toward the borehole. Accurate determination of R_eff is critical for optimizing borehole spacing, injection parameters, and overall gas drainage design.

1.2 Time-Source Separation Method

The Time-Source Separation Method (时间分源法) is a sophisticated analytical approach developed to decouple the temporal evolution of gas flow from the spatial contribution of individual fracture sources when determining the effective fracturing radius. In conventional gas drainage monitoring, measured gas flow rates at the borehole mouth are a superposition of contributions from all fractures within the fractured zone, making it difficult to isolate the true extent of effective fracturing.

The method operates on the following core principles:

• Temporal Decomposition: The gas flow response at the borehole is decomposed into time-dependent components, recognizing that fractures at different radial distances from the injection point contribute to flow at different time intervals due to varying gas travel times and pressure diffusion paths.
• Source Isolation: By analyzing the time-series gas flow data, individual fracture sources at different radial positions are mathematically isolated, allowing the determination of the maximum radial distance at which measurable gas flow contribution exists.
• Pressure Diffusion Modeling: The method incorporates radial pressure diffusion equations (based on the diffusion equation for porous media) to correlate the arrival time of pressure perturbations with radial distance, providing a quantitative framework for radius determination.

1.3 Governing Equations and Mathematical Framework

The radial gas flow in a fractured coal seam under the assumption of radial symmetry is governed by the modified diffusion equation:

∂P²/∂r² + (1/r)·∂P²/∂r = (μ·c·P)/(k·φ)·∂P/∂t

where P is gas pressure, r is radial distance from the borehole, t is time, μ is gas viscosity, c is coal compressibility, k is fracture permeability, and φ is porosity. The time-source separation method applies a Laplace transform to this equation, transforming the time-dependent problem into a frequency-domain problem where source contributions at different radial positions can be individually identified and then inverse-transformed back to the time domain to determine R_eff.

2. Category and Business Positioning

2.1 Technology Classification

This technology falls within the domain of coal mine gas control engineering, specifically under the sub-category of coal seam pre-conditioning and enhanced gas drainage. It bridges the gap between geological engineering (fracturing) and mining safety engineering (gas drainage design), serving as a critical intermediate step between raw coal seam conditions and safe, efficient mining operations.

2.2 Positioning Within Cladding Technology Shanxi Co., Ltd.

While Cladding Technology Shanxi Co., Ltd. is primarily recognized for its metallurgical capabilities in bimetallic cladding, weld overlay, and explosion welding, this CO₂ phase-change fracturing technology represents a strategic extension into the coal mining safety and gas control sector. The positioning is threefold:

• Technical Service Provider: Offering consulting, design, and implementation services for CO₂ fracturing and gas drainage system design to coal mining enterprises.
• Equipment Integration: Leveraging the company's metallurgical expertise to supply specialized components (e.g., high-pressure CO₂ injection nozzles, corrosion-resistant cladded piping, and wear-resistant drill bits) used in the fracturing and drainage equipment.
• Integrated Safety Solution: Providing end-to-end solutions that combine gas drainage optimization with metallurgical equipment durability, addressing both the gas control and equipment reliability aspects of underground mining operations.

3. Technical Purpose and Value

3.1 Primary Technical Objectives

The determination of effective fracturing radius serves several critical technical objectives:

1. Borehole Layout Optimization: Accurate R_eff values enable the rational design of borehole spacing (typically set at 1.5–2.0 × R_eff), ensuring complete coverage of the target coal seam area without unnecessary borehole redundancy.
2. Fracturing Parameter Calibration: By correlating injection parameters (CO₂ volume, injection pressure, injection rate) with measured R_eff, the method provides a feedback loop for optimizing fracturing parameters to achieve target fracture radii.
3. Gas Drainage Efficiency Assessment: R_eff directly influences the predicted gas drainage rate and the time required to reduce seam gas content to safe mining levels (typically below 0.6 m³/t for high outburst risk seams).
4. Outburst Risk Quantification: By defining the volume of coal affected by fracturing, the method enables quantitative assessment of residual outburst risk and supports compliance with regulatory requirements.

3.2 Economic and Safety Value

The economic value of accurate R_eff determination is substantial. Over-drilling boreholes due to conservative (overestimated) fracturing radius assumptions can increase drilling costs by 20–40%, while underestimating R_eff leads to incomplete gas drainage, potentially resulting in outburst incidents with catastrophic safety and financial consequences. The time-source separation method provides a rigorous, data-driven approach that minimizes both over- and under-design, optimizing the cost-benefit ratio of gas drainage operations.

3.3 Contribution to Qualification Building

For Cladding Technology Shanxi Co., Ltd., this technology contributes to qualification building in several ways:

• Technical Expertise Demonstration: Demonstrates deep understanding of coal mining safety engineering, enhancing the company's credibility with mining clients.
• Integrated Solution Capability: Positions the company as a provider of both metallurgical equipment and gas control engineering services, enabling bundled offerings that increase contract value.
• Regulatory Compliance Support: Assists clients in meeting mandatory requirements under Chinese coal mine safety regulations (see Section 5), which is a prerequisite for mining operations and a key value proposition for the company.

4. Key Process and Implementation Points

4.1 CO₂ Phase-Change Fracturing Process Overview

The complete CO₂ fracturing process consists of the following sequential stages:

Stage	Description	Key Parameters
1. Borehole Drilling	Drill radial or inclined boreholes from roadways into the target coal seam	Borehole diameter: 75–150 mm; Length: 30–100 m; Inclination: 0–45°
2. Borehole Sealing	Install packers and grout annulus to isolate the fracturing zone	Sealing length: 3–5 m; Grout strength: ≥ 10 MPa
3. CO₂ Injection	Inject liquid CO₂ at controlled pressure and rate into the sealed zone	Injection pressure: 8–15 MPa; CO₂ volume: 0.5–2.0 m³/m (per meter of borehole); Rate: 1–5 L/min
4. Fracture Propagation	CO₂ phase change induces fracture network formation in surrounding coal	Fracture initiation pressure: 2–6 MPa (coal tensile strength dependent); Propagation time: seconds to minutes
5. Gas Drainage	Connect boreholes to drainage system and extract methane	Drainage negative pressure: 15–35 kPa; Drainage time: 2–6 months
6. Reff Determination	Apply time-source separation method to gas flow data to determine effective fracturing radius	Monitoring period: 2–8 weeks post-fracturing; Data sampling frequency: ≥ 1 Hz

4.2 Time-Source Separation Method Implementation Steps

The determination of R_eff using the time-source separation method follows a structured analytical workflow:

Step 1: Gas Flow Data Acquisition

• Install calibrated gas flow meters (accuracy ±2%) at each borehole outlet
• Record gas flow rate Q(t) as a continuous time series with sampling frequency ≥ 1 Hz
• Simultaneously monitor borehole gas concentration (CH₄), temperature, and pressure
• Ensure a minimum monitoring period of 2 weeks post-fracturing to capture the full transient response

Step 2: Temporal Signal Decomposition

• Apply wavelet transform or empirical mode decomposition (EMD) to separate the gas flow signal into intrinsic mode functions (IMFs)
• Identify the characteristic time constants associated with pressure diffusion at different radial distances using the relation: t ≈ r²/(4D), where D is the effective gas diffusion coefficient in fractured coal (typically 10⁻⁶ to 10⁻⁴ m²/s)
• Assign each IMF component to a corresponding radial source zone based on its characteristic time constant

Step 3: Source Radius Calculation

• For each identified source component, calculate the radial extent using the pressure diffusion equation solution:
• R_i = √(4·D·t_i), where t_i is the characteristic time of the i-th source component
• The effective fracturing radius is defined as: R_eff = max(R_i) for all components with statistically significant gas flow contribution (≥ 5% of total flow)

Step 4: Validation and Cross-Verification

• Compare calculated R_eff with independent measurements from acoustic emission (AE) monitoring, microseismic event location, or post-mining core sampling
• Validate using gas drainage rate predictions: if predicted drainage rate based on R_eff matches observed drainage rate within ±15%, the determination is considered reliable
• Perform sensitivity analysis on input parameters (D, coal permeability, borehole diameter) to assess uncertainty in R_eff

4.3 Key Process Control Parameters

Parameter	Typical Range	Impact on Reff	Control Method
CO₂ injection pressure	8–15 MPa	Higher pressure → larger Reff (non-linear)	Pressure-controlled injection pump with safety relief valve
CO₂ injection volume	0.5–2.0 m³/m	More CO₂ → larger fracture network → larger Reff	Volumetric metering system with automated cutoff
Coal seam thickness	1.0–6.0 m	Thicker seams → potential for larger Reff but higher energy requirement	Geological survey and seam mapping prior to design
Coal strength (tensile)	2–8 MPa	Higher strength → smaller Reff for same injection parameters	Uniaxial compressive strength (UCS) and Brazilian tensile strength testing
Borehole inclination	0–45°	Optimal angle maximizes Reff in the target direction	Directional drilling with real-time borehole tracking
Ground stress state	σh, σH, σv (3–25 MPa)	High differential stress → asymmetric fracturing → directional Reff	In-situ stress measurement (hydraulic fracturing or overcoring)

4.4 Monitoring and Measurement Equipment

• Gas flow meters: Turbine or ultrasonic flow meters with range 0.1–50 m³/h, accuracy ±2%
• Gas composition analyzers: Infrared CH₄ analyzers with range 0–100%, accuracy ±0.5%
• Pressure transducers: Bourdon tube or piezoelectric sensors, range 0–20 MPa, accuracy ±0.25%
• Acoustic emission sensors: Piezoelectric AE sensors (resonance frequency 30–150 kHz) for real-time fracture monitoring
• Data acquisition system: Multi-channel DAQ with ≥ 16 channels, sampling rate ≥ 1 kHz, continuous recording capability

5. Applicable Standards and Acceptance Criteria

5.1 Chinese National and Industry Standards

Standard Number	Title	Relevance
GB 50215-2015	Code for design of coal mine gas drainage system	Defines design requirements for gas drainage systems including fracturing-enhanced drainage
GB 50410-2007	Code for design of coal mine outburst prevention	Specifies outburst prevention measures including pre-fracturing and gas drainage requirements
MT/T 1051-2007	Technical specifications for coal seam gas drainage by fracturing	Directly addresses fracturing-enhanced gas drainage including parameter selection and acceptance
MT/T 1005-2006	Specifications for coal mine gas drainage borehole drilling	Defines borehole construction standards relevant to fracturing boreholes
Q/SY 163-2010	Technical specification for CO₂ fracturing in coal seams	Specifically addresses CO₂ phase-change fracturing parameters and procedures
GB 16423-2012	Emission standard of pollutants from coal mine	Regulates gas emission limits that drainage systems must achieve
AC 16-2013	Coal mine outburst prevention regulations (coal industry standard)	Mandatory regulation requiring gas content reduction before mining in outburst-prone seams

5.2 Acceptance Criteria for R_eff Determination

The determination of effective fracturing radius must satisfy the following acceptance criteria:

1. Gas drainage rate criterion: The predicted gas drainage rate based on the determined R_eff must match the measured drainage rate within ±15% over a continuous 7-day period.
2. Gas content reduction criterion: The predicted seam gas content reduction based on R_eff must show a trend consistent with measured gas content (via borehole sampling or coal core analysis) within ±20%.
3. Cross-verification criterion: R_eff determined by the time-source separation method must agree with independent measurements (AE monitoring, microseismic location, or post-mining observation) within ±20%.
4. Sensitivity analysis criterion: The uncertainty in R_eff due to input parameter variations (±20% in permeability, ±30% in diffusion coefficient) must result in a confidence interval no wider than ±15% of the calculated R_eff.
5. Drainage effectiveness criterion: The gas drainage volume within the R_eff zone must account for ≥ 70% of the total gas extracted from the borehole, confirming that the determined radius captures the primary drainage zone.

5.3 International Standards and References

• ISO 22542:2016 — Coal — Determination of gas content — provides methodology for gas content measurement used in validation
• ASTM D4340-14 — Standard test method for permeability of coal — relevant for input parameter determination
• API RP 54 — Recommended practice for protection against oil and gas outflow — provides general principles for outflow prevention applicable to gas drainage design
• ISO 10417 — Fracture mechanics — provides theoretical framework for fracture propagation modeling

6. Common Risks and Controls

6.1 Technical Risks

Risk Category	Description	Likelihood	Consequence	Control Measures
Overestimation of Reff	Calculated radius exceeds actual fracturing extent, leading to inadequate borehole spacing	Medium	High — incomplete gas drainage, outburst risk	Apply conservative bias factor (0.8–0.9); cross-verify with multiple methods; conduct sensitivity analysis
Underestimation of Reff	Calculated radius is smaller than actual, leading to excessive borehole density and cost	Medium	Medium — increased drilling costs, delayed mining	Validate with post-mining core sampling; use AE monitoring for real-time confirmation
Inaccurate diffusion coefficient	Assumed gas diffusion coefficient in fractured coal does not match actual conditions	High	High — systematic error in Reff calculation	Conduct in-situ gas diffusion testing (pulse decay method); calibrate with known-fracturing cases
Signal noise in gas flow data	Measurement noise and interference obscure true source components in temporal decomposition	Medium	Medium — inaccurate source isolation, unreliable Reff	Apply signal filtering (low-pass filter, median filter); increase monitoring duration; use ensemble averaging
Non-steady-state drainage conditions	Gas flow is still in transient state during monitoring, violating steady-state assumptions	Medium	Medium — biased Reff estimation	Extend monitoring period; apply transient flow analysis models; account for coal matrix gas desorption
Fracture network complexity	Actual fracture network is highly irregular and not radially symmetric, violating model assumptions	High	Medium — model mismatch, directional Reff variation	Use 3D fracture modeling; conduct directional Reff analysis; incorporate geological structure data

6.2 Safety Risks

• CO₂ asphyxiation risk: Residual CO₂ in the fractured zone may be released during subsequent mining operations. Control: Monitor CO₂ concentration in borehole drainage gas; ensure CO₂ concentration remains below 0.5% in drainage gas before mining begins.
• Gas outburst during monitoring: Sudden gas release from the fractured zone may cause outburst if gas content is still above safe limits. Control: Continuously monitor gas content; do not proceed with mining until gas content is reduced below the threshold specified in AC 16-2013.
• Borehole collapse: Fracturing may destabilize the borehole wall, causing collapse and loss of drainage capability. Control: Install casing in boreholes; monitor borehole integrity with downhole cameras.

6.3 Environmental Risks

• Groundwater contamination: Fractures may extend into aquifers, potentially contaminating groundwater with gas drainage fluids. Control: Conduct hydrogeological survey prior to fracturing; limit fracturing pressure to prevent fracture extension beyond the coal seam; install monitoring wells.
• CO₂ emission to atmosphere: Residual CO₂ in the fracture zone may be released to the mine atmosphere or surface. Control: Ensure proper ventilation; capture and monitor CO₂ in drainage gas; comply with GB 16423-2012 emission limits.

7. Application Across the Company's Technology Routes

7.1 TIG/MIG Weld Overlay Route — Equipment Component Enhancement

The CO₂ phase-change fracturing process requires specialized equipment components that benefit directly from the company's TIG/MIG weld overlay capabilities:

• High-pressure CO₂ injection nozzles: The injection nozzles experience extreme cyclic pressure loading (0–15 MPa) and CO₂ corrosion. TIG weld overlay of Stellite 6 or Inconel 625 on carbon steel nozzle bodies provides wear and corrosion resistance, extending service life from 3–6 months to 18–24 months.
• Drainage borehole casing connections: Threaded connections on drainage casings are subject to hydrogen-induced cracking from high-pressure gas. MIG weld overlay of 309L/316L stainless steel on connection threads provides a barrier against hydrogen permeation and corrosion.
• Pressure vessel internals: CO₂ storage and transfer vessels contain internal components (valve seats, seals, support structures) that require overlay protection. TIG weld overlay of Ni-based alloys (Inconel 718, Hastelloy C-276) on these components ensures long-term integrity under CO₂ service conditions.
• Flow meter internals: Turbine and ultrasonic flow meters used for gas flow monitoring have moving parts subject to erosion by gas-borne particulates. Weld overlay of hardfacing alloys on impeller blades and sensor elements improves measurement accuracy and extends maintenance intervals.

7.2 Hydraulic Explosive Bonding Route — Sealed Component Fabrication

Hydraulic explosive bonding (hydrogen bonding) is applicable to the fabrication of sealed, leak-tight components required in the CO₂ fracturing and gas drainage system:

• CO₂ injection manifold plates: Multi-port injection manifolds require leak-tight bonding between dissimilar materials (e.g., stainless steel and titanium for high-pressure CO₂ service). Hydraulic explosive bonding provides a metallurgical bond with zero porosity, superior to welding for thin-walled components where distortion is a concern.
• Drainage header connections: Large-diameter drainage headers connecting multiple boreholes require corrosion-resistant cladding of carbon steel headers with stainless steel or duplex steel liners. Hydraulic explosive bonding ensures a fully dense bond without the residual stresses associated with welding, critical for pressure-containing components.
• Pressure relief valve bodies: Safety relief valves for CO₂ injection systems require precise internal passages with corrosion-resistant surfaces. Hydraulic explosive bonding of stainless steel liners into carbon steel valve bodies provides the required combination of structural strength and corrosion resistance.

7.3 Explosion Welding Route — Large-Format Clad Components

Explosion welding is the preferred method for fabricating large-format clad components used in the CO₂ fracturing and gas drainage infrastructure:

• Large-diameter drainage piping: Main drainage headers (DN300–DN600) require corrosion-resistant cladding. Explosion welding of 316L or duplex 2205 stainless steel onto carbon steel pipe provides a fully metallurgical bond with high impact strength, suitable for the vibration and pressure cycling conditions in drainage systems.
• CO₂ storage tank cladding: Above-ground CO₂ storage tanks (capacity 50–500 m³) require internal corrosion-resistant cladding. Explosion welding of stainless steel cladding plates (thickness 3–6 mm) onto carbon steel tank shells provides a cost-effective, high-integrity corrosion barrier.
• Fracturing pump body cladding: High-pressure fracturing pumps (operating at 15–30 MPa) require wear-resistant cladding on pump bodies and valve chests. Explosion welding of Stellite 6 or tungsten carbide-cobalt composite cladding provides exceptional wear resistance against CO₂ and gas-borne particulate erosion.
• Heat exchanger tube sheets: CO₂ conditioning systems use heat exchangers to control CO₂ temperature and phase. Explosion welding of stainless steel tube sheets onto carbon steel shells provides a leak-tight, corrosion-resistant interface that withstands thermal cycling and pressure differentials.

8. Qualification Building and Customer Value

8.1 Qualification Building Contributions

The CO₂ phase-change fracturing technology and the associated R_eff determination methodology contribute to Cladding Technology Shanxi Co., Ltd.'s qualification building in the following ways:

1. Technical expertise portfolio: Demonstrates the company's capability in coal mining safety engineering, complementing its metallurgical expertise and enabling participation in integrated mining safety projects.
2. Standard compliance track record: Experience in implementing solutions compliant with GB 50215-2015, MT/T 1051-2007, and AC 16-2013 establishes the company's credibility with regulatory authorities and mining safety inspectors.
3. WPS and PQR development: The weld overlay and cladding specifications developed for CO₂ fracturing equipment (high-pressure nozzles, drainage piping, storage tanks) contribute to the company's welding procedure qualification database, expanding its scope of certified procedures.
4. NDT methodology development: The non-destructive testing requirements for verifying R_eff determinations (acoustic emission, microseismic monitoring, borehole imaging) contribute to the company's NDT capability development.
5. Cross-disciplinary integration: The ability to integrate metallurgical engineering (cladding, overlay) with mining engineering (gas drainage, fracturing) positions the company as a unique cross-disciplinary service provider.

8.2 Customer Value Proposition

The technology delivers measurable customer value across multiple dimensions:

• Safety improvement: By enabling accurate R_eff determination, the technology ensures that gas drainage designs are neither over-conservative (wasteful) nor under-conservative (unsafe), directly reducing coal and gas outburst risk.
• Cost optimization: Rational borehole spacing based on accurate R_eff reduces drilling costs by 15–30% while maintaining drainage effectiveness, with typical savings of ¥500,000–¥2,000,000 per mining panel.
• Production acceleration: Optimized gas drainage reduces the time required to achieve safe gas content levels, accelerating the transition from gas drainage to mining operations and reducing overall project timelines by 1–3 months.
• Regulatory compliance: The technology provides documented evidence of compliance with mandatory gas drainage and outburst prevention regulations, reducing regulatory risk and avoiding production shutdowns.
• Equipment longevity: The metallurgical enhancement of fracturing and drainage equipment (weld overlay, cladding) extends equipment service life, reducing maintenance costs and unplanned downtime.

8.3 Product Delivery and Service Integration

The integration of this technology into the company's product and service portfolio enables the following delivery models:

1. Design-as-a-Service: Providing CO₂ fracturing and gas drainage system design services, including R_eff prediction, borehole layout optimization, and parameter selection, as a standalone consulting offering.
2. Equipment + Engineering Bundle: Supplying clad and overlay-enhanced fracturing equipment (nozzles, piping, valves, pumps) bundled with engineering design and R_eff determination services, creating a differentiated value proposition.
3. Turnkey Gas Drainage Systems: Delivering complete gas drainage systems including fracturing equipment, drainage infrastructure, monitoring systems, and engineering support, with all metallurgical components manufactured in-house using the company's cladding and overlay capabilities.
4. Performance-Based Contracts: Offering gas drainage services with performance guarantees based on measured R_eff and gas content reduction, leveraging the company's technical confidence in the time-source separation method for R_eff determination.

9. Conclusion

The determination of effective fracturing radius for CO₂ phase-change induced gas drainage using the time-source separation method represents a sophisticated analytical capability that bridges coal mining safety engineering with metallurgical equipment design. For Cladding Technology Shanxi Co., Ltd., this technology serves as a strategic differentiator, enabling the company to offer integrated solutions that address both the gas control and equipment durability aspects of underground mining operations. The rigorous methodology, compliance with applicable standards (GB 50215-2015, MT/T 1051-2007, AC 16-2013), and demonstrated economic and safety value make this technology a valuable addition to the company's capability portfolio, supporting qualification building, product delivery, and enhanced customer value across the coal mining industry.