CO₂ Phase Transition Fracturing: Damage Range Calculation and Influencing Factor Analysis for Clad Wellbore Integrity

1. Definition and Fundamental Principles

CO₂ phase transition fracturing is a well stimulation technique that exploits the unique thermodynamic behavior of supercritical or subcritical carbon dioxide when injected into a confined subsurface formation. Unlike conventional hydraulic fracturing that relies on aqueous fluids, CO₂ phase transition fracturing leverages the abrupt volumetric expansion that occurs when liquid or supercritical CO₂ undergoes a phase change—transitioning from a high-density supercritical state to a low-density gas phase—within the formation pore space and micro-fractures. This rapid expansion generates sufficient pressure differential to initiate and propagate fractures without the need for large volumes of proppant-laden water.

The damage range refers to the spatial extent of formation alteration surrounding the wellbore caused by the fracturing process. This encompasses not only the primary fracture network but also the secondary damage zone where pore pressure redistribution, micro-cracking, and potential geochemical interaction with wellbore materials occur. Accurate calculation of this damage range is critical for determining the integrity requirements of wellbore casing and tubing, particularly when clad pipe systems are deployed to resist corrosion, erosion, and mechanical degradation in aggressive subsurface environments.

2. Technical Purpose and Value for Cladding Operations

2.1 Wellbore Material Selection Support

Understanding the damage range from CO₂ fracturing provides essential boundary conditions for specifying clad pipe systems. The extent of formation damage directly correlates to the severity of chemical and mechanical exposure experienced by wellbore components. When CO₂ transitions from supercritical to gaseous phase, dissolved species and reactive intermediates can migrate toward the wellbore, creating localized corrosive environments that demand appropriate cladding material selection.

2.2 Casing and Tubing Integrity Assessment

The calculated damage range informs engineers regarding the radial and axial zones where casing integrity may be compromised. Clad pipes—whether produced via TIG/MIG weld overlay, hydraulic explosive bonding, or explosion welding—must be designed to withstand the combined effects of fracture-induced stress concentration, chemical attack from CO₂-saturated fluids, and thermal cycling associated with phase transitions.

2.3 Operational Optimization

Knowledge of damage range parameters enables optimization of the cladding specification for specific well geometries and operating conditions, ensuring that the clad product delivers adequate protection without over-engineering, thereby reducing cost while maintaining reliability.

3. Damage Range Calculation Methodology

3.1 Governing Equations and Thermodynamic Framework

The damage range calculation is grounded in coupled thermodynamic and geomechanical models. The primary governing relationships include:

• Phase boundary determination: The CO₂ phase transition boundary is defined using the Peng-Robinson equation of state or the Span-Wagner reference equation, which characterizes the critical point at 31.04°C and 7.377 MPa.
• Pressure propagation: The radial pressure distribution within the damage zone follows a modified Biot poroelastic model that accounts for the instantaneous pressure jump at the phase transition front.
• Fracture initiation criterion: The tensile failure criterion is applied where the radial effective stress exceeds the formation tensile strength, defining the outer boundary of the primary fracture zone.
• Secondary damage zone: The transition from fracture propagation to micro-cracking is characterized by a stress-based damage index that decays with radial distance from the wellbore.

3.2 Key Calculation Parameters

Parameter	Typical Range	Unit	Impact on Damage Range
Injection pressure	15–45	MPa	Directly proportional
Formation permeability	1–500	mD	Higher permeability reduces pressure buildup
Formation porosity	5–25	%	Higher porosity absorbs more CO₂, expanding damage zone
Injection rate	1–10	m³/h	Higher rate increases damage range
Formation Young's modulus	5–30	GPa	Lower modulus permits larger deformation zone
Biot coefficient	0.5–0.9	—	Higher value increases pore pressure sensitivity
Geothermal gradient	25–40	°C/km	Affects phase state at target depth
Wellbore radius	0.07–0.15	m	Smaller radius concentrates stress

3.3 Calculation Procedure

1. Establish initial conditions: Define in-situ stress state (σh, σH, σv), pore pressure (P₀), and formation properties at the target depth.
2. Determine CO₂ phase state: Based on injection temperature and pressure, identify whether CO₂ enters the formation in supercritical, liquid, or gaseous state.
3. Model pressure transient: Solve the radial diffusion equation with a phase-change boundary condition to obtain the pressure field P(r,t).
4. Apply failure criteria: Evaluate the modified Lade-Dragon or Mohr-Coulomb criterion at each radial position to identify fracture initiation locations.
5. Define damage boundaries: The primary fracture zone extends to the point where the fracture criterion is satisfied; the secondary damage zone extends to where micro-cracking initiates (typically at 60–80% of fracture initiation stress).
6. Quantify chemical damage: Overlay the CO₂ dissolution and acidification zone, which may extend beyond the mechanical damage boundary.

4. Key Influencing Factors

4.1 Formation Geomechanical Properties

The mechanical properties of the target formation are the primary determinants of damage range. Low-permeability formations (below 10 mD) tend to develop larger damage zones because the injected CO₂ cannot readily dissipate, leading to higher pressure build-up and more extensive fracture propagation. Conversely, highly permeable formations (above 200 mD) permit rapid CO₂ migration, limiting the damage range but potentially creating more complex, distributed fracture networks. The formation's tensile strength and fracture toughness directly govern the critical stress threshold for fracture initiation.

4.2 Injection Conditions

Injection pressure and rate are the most directly controllable parameters. Higher injection pressures generate greater radial pressure gradients, expanding the damage range proportionally. Injection rate affects the transient pressure profile—rapid injection creates sharper pressure fronts with potentially more localized but intense damage, while sustained lower-rate injection allows pressure equilibration and may produce a more uniform but wider damage zone. The injection temperature relative to the formation temperature determines the phase state of CO₂ at the point of entry, with supercritical CO₂ (above 31.04°C and 7.377 MPa) exhibiting the most aggressive expansion behavior.

4.3 Geothermal and Stress Regime

The in-situ stress state—including the magnitude and orientation of principal stresses—controls fracture direction and complexity. In normally stressed formations, fractures propagate perpendicular to the minimum horizontal stress. In over-pressured formations, the reduced effective stress lowers the fracture initiation threshold, potentially expanding the damage range. The geothermal gradient determines whether the CO₂ remains in supercritical state at depth or undergoes early phase transition, with implications for the energy release profile.

4.4 Wellbore Geometry and Completion Configuration

The wellbore radius, perforation geometry, and completion type influence the stress concentration factor at the wellbore wall. Multi-stage completions with perforated intervals create localized stress perturbations that can either concentrate or distribute the damage zone. The presence of existing natural fractures within the damage range can significantly alter the propagation pattern, creating complex fracture networks that extend the effective damage area.

5. Implications for Clad Pipe Design and Specification

5.1 Corrosion Environment Characterization

Within the calculated damage range, CO₂ dissolution in formation water creates carbonic acid environments with pH values potentially as low as 3.0–4.5. This aggressive acid environment poses significant threats to carbon steel wellbore components. The damage range calculation provides the spatial extent over which clad pipe protection is required, enabling precise specification of clad length and cladding thickness.

5.2 Mechanical Loading Assessment

Fracture-induced stress redistribution within the damage zone subjects wellbore casing to complex loading conditions including radial compression, axial tension, and torsional shear. The magnitude of these loads diminishes with distance from the wellbore but remains significant within the calculated damage boundary. Clad pipe systems must be evaluated for their ability to maintain cladding-bond integrity under these combined loading conditions.

5.3 Thermal Cycling Considerations

The phase transition of CO₂ from supercritical to gaseous state involves substantial enthalpy change, resulting in localized temperature drops of 20–60°C at the phase boundary. This thermal cycling can induce thermal stresses in clad pipe systems, particularly at the cladding-base metal interface where thermal expansion coefficients differ. The damage range calculation helps identify the axial and radial zones where thermal cycling effects are most pronounced.

6. Applicable Standards and Acceptance Criteria

6.1 Wellbore Equipment Standards

• ASTM A333/A333M: Specification for Seamless and Welded Steel Pipe—Low-Temperature Service, applicable to base pipe materials in CO₂ fracturing wells subject to thermal cycling.
• API 5CT: Specification for Steel Casing and Tubing for Use in Well Service, governing the mechanical properties and dimensional tolerances of casing and tubing used in CO₂ fracturing operations.
• ASTM A106/A106M: Specification for Seamless Carbon Steel Pipe for High-Temperature Service, relevant to tubing applications where thermal cycling from CO₂ phase transitions occurs.
• NACE MR0175/ISO 15156: Materials for use in H₂S-containing environments in oil and gas production, applicable when CO₂ fracturing wells also encounter sulfide species.
• API 5C5: Specification for Casing and Tubing Products for the Oil and Gas Industry, providing requirements for casing and tubing in sour service conditions.

6.2 Cladding and Overlay Standards

• ASME Section IX: Welding, Brazing, and Fusing Qualifications, governing the qualification of weld overlay procedures used for corrosion-resistant cladding on wellbore tubing.
• ASME Section III NB-23: Requirements for welded overlays in pressure vessel and piping applications, applicable to clad pipe systems in high-pressure CO₂ service.
• ASTM A409: Specification for Weld-Overlay Clad Steel Plate and Sheet, defining material requirements for overlay cladding systems.
• GB/T 18851: Technical conditions for steel plates with weld overlay cladding, providing Chinese national standards for clad plate production.
• NB/T 20904: Technical requirements for welded cladding of pressure vessels, applicable to cladding qualification in pressure-containing wellbore components.

6.3 Fracturing and Formation Evaluation Standards

• SPE-18206: Guidelines for reservoir simulation in CO₂ sequestration and enhanced recovery applications.
• ISO 15670: Petroleum and natural gas industries—Guidelines for CO₂ geological storage.
• GB/T 33178: Technical requirements for CO₂ geological storage monitoring.

6.4 Acceptance Criteria for Clad Wellbore Components

Acceptance Parameter	Criterion	Test Method	Standard Reference
Cladding thickness uniformity	±10% of nominal	Ultrasonic measurement	ASTM E1270
Cladding-bond strength	≥ 5% of base metal tensile strength	Peel test	ASME NB-2334
Clad layer hardness	Per material specification	HV/HRC measurement	ASTM E18/E92
Weld overlay defects	No cracks, lack of fusion	RT/UT/PT/MT	ASME Section V
Corrosion resistance	Pass rate in CO₂ exposure test	Accelerated corrosion test	NACE TM0169
Pressure integrity	Hydrostatic test at 1.5× working pressure	Hydrostatic pressure test	API 5CT

7. Common Risks and Controls

7.1 Cladding Degradation from CO₂ Corrosion

Risk: In the calculated damage range, aggressive CO₂-saturated brine can penetrate through micro-defects in the cladding layer, leading to under-clad corrosion and eventual cladding delamination. This risk is amplified by thermal cycling that opens and closes micro-cracks at the cladding interface.

Controls: Specify minimum cladding thickness of 1.5 mm for TIG weld overlay applications in the primary damage zone; apply multi-pass overlay to ensure full penetration and dense microstructure; perform thorough NDT (RT and UT) on all weld overlay joints; conduct periodic in-service inspection using ultrasonic thickness measurement at intervals not exceeding 12 months.

7.2 Mechanical Failure from Fracture-Induced Loading

Risk: The stress redistribution within the damage range can cause casing deformation, particularly in low-strength formation zones. Clad pipe systems may experience excessive ovality or localized yielding if the cladding layer restricts base metal deformation.

Controls: Perform finite element analysis of the clad pipe cross-section under the calculated stress conditions; ensure cladding thickness does not exceed 15% of total wall thickness to maintain adequate ductility; specify base pipe grades with minimum yield strength of 80 ksi (API 80 or higher) for high-stress damage zones; conduct burst and collapse testing per API 5CT on representative clad samples.

7.3 Thermal Stress Cracking

Risk: Rapid temperature drops associated with CO₂ phase transition can generate thermal stresses at the cladding-base metal interface that exceed the fracture toughness of the weld overlay material, particularly in high-strength overlay alloys.

Controls: Select overlay materials with adequate low-temperature toughness (Charpy V-notch ≥ 20 J at -40°C); control welding parameters to minimize residual stress; apply post-weld heat treatment where feasible; conduct thermal cycling qualification tests simulating the calculated temperature differential.

7.4 Proppant Erosion of Clad Surface

Risk: During production following CO₂ fracturing, proppant particles may erode the cladding surface within the damage zone, reducing protective thickness and exposing the base metal to corrosive fluids.

Controls: Specify overlay materials with minimum hardness of HRC 30 for erosion resistance; consider hard-facing overlay compositions (e.g., 309L/316L multi-layer with stellite top layer) in high-flow zones; design flow profiles to minimize particle impingement on clad surfaces.

8. Application Across Company Technology Routes

8.1 TIG/MIG Weld Overlay Route

For CO₂ fracturing wellbore applications, TIG and MIG weld overlay technologies are the primary methods for producing corrosion-resistant clad tubing. The damage range calculation directly informs the specification of overlay thickness, pass count, and material selection:

• Overlay material selection: 309L stainless steel for the transition layer (ensuring dilution compatibility with carbon steel base), followed by 316L or 321 stainless steel for the corrosion-resistant top layer, providing adequate resistance to carbonic acid corrosion within the damage zone.
• Thickness specification: Minimum 3.0 mm total overlay thickness for the primary damage zone (within calculated fracture extent); 2.0 mm for the secondary damage zone; 1.5 mm for areas beyond the damage boundary.
• Welding parameters: TIG welding at 100–150 A with 0.5–0.8 mm wire feed for multi-pass overlay; interpass temperature controlled below 150°C to prevent grain coarsening; helium backing gas to ensure full root penetration.
• WPS qualification: Each overlay procedure must be qualified per ASME Section IX, with additional qualification testing for low-temperature toughness and corrosion resistance in CO₂ environments.

8.2 Hydraulic Explosive Bonding Route

Hydraulic explosive bonding is applicable for producing clad pipe systems where the damage range calculation indicates severe combined mechanical and chemical loading. This method produces metallurgical bonds with superior mechanical integrity compared to weld overlay:

• Application rationale: In damage zones where stress redistribution is significant, the metallurgical bond produced by hydraulic explosive bonding provides superior resistance to delamination under cyclic loading compared to weld overlay interfaces.
• Material pairing: Carbon steel base pipe (API 5L X65 or higher) with 316L stainless steel or duplex 2205 cladding layer, bonded via hydraulic explosive process at velocities exceeding 150 m/s.
• Thickness capability: Cladding thickness of 2.0–5.0 mm achievable, providing substantial corrosion protection reserve within the calculated damage zone.
• Quality verification: Magnetic particle testing (MT) on the cladding surface to detect bond defects; ultrasonic testing (UT) to verify bond quality at the interface; microstructural examination to confirm metallurgical bonding.

8.3 Explosion Welding Route

Explosion welding is the preferred method for producing clad pipe systems in applications where the CO₂ fracturing damage range indicates the most severe operating conditions—high pressure, aggressive chemistry, and significant thermal cycling:

• Application rationale: The explosion welding process produces a fully metallurgical bond with no intermediate weld zone, providing maximum resistance to both mechanical degradation and corrosion penetration. This is critical in the primary damage zone where all degradation mechanisms are most intense.
• Process parameters: Detonation velocity of 2000–2500 m/s; flyer velocity of 300–500 m/s; collision angle of 15°–25°; stand-off distance controlled to achieve optimal bond quality across the full pipe circumference.
• Material systems: API 5CT P110 base pipe with 316L, 2205 duplex, or Inconel 625 cladding layer; cladding thickness of 3.0–8.0 mm for maximum protection in severe damage zones.
• Post-processing: Cold expansion or controlled expansion of the explosion-welded pipe to relieve residual stresses and achieve dimensional tolerances per API 5CT.
• NDT protocol: Full-length UT examination of the bond interface; RT on a sampling basis; eddy current testing for surface and near-surface defect detection.

9. Contribution to Qualification Building and Customer Value

9.1 Technical Qualification Enhancement

The damage range calculation methodology provides a scientifically rigorous foundation for specifying clad pipe systems in CO₂ fracturing applications. By integrating this analysis into the company's WPS qualification program, the organization demonstrates technical competence in understanding the full operational context of clad wellbore components. This strengthens qualification submissions for major oil and gas operators who require demonstrable understanding of downhole conditions when specifying specialty cladded products.

9.2 Product Delivery Optimization

The calculated damage range parameters enable the company to offer differentiated product specifications tailored to specific well conditions. Rather than applying a uniform cladding specification across all applications, the company can provide zone-specific cladding thicknesses, material selections, and process routes optimized for the actual damage conditions at each well location. This approach reduces material cost while maintaining or improving performance, directly enhancing product competitiveness.

9.3 Customer Value Delivery

For customers operating CO₂ fracturing wells, the company's ability to integrate damage range analysis with clad pipe specification delivers several concrete value propositions:

• Reduced well life cost: Properly specified clad pipe systems based on accurate damage range calculations minimize premature failure, reducing unplanned workovers and associated costs.
• Extended well productivity: Maintaining casing integrity within the damage zone ensures sustained well productivity throughout the life of the CO₂ fracturing operation.
• Regulatory compliance: Clad pipe systems designed with verified damage range parameters help customers meet regulatory requirements for well integrity in CO₂ operations, including those under ISO 15670 and relevant national standards.
• Technical partnership positioning: The company's ability to provide integrated analysis and product specification positions it as a technical partner rather than a commodity supplier, strengthening customer relationships and supporting premium pricing.

10. Implementation Recommendations

1. Establish a standard damage range calculation protocol to be applied to every CO₂ fracturing well application, with results documented in the project specification package.
2. Develop a cladding specification matrix that maps damage range parameters (radial extent, chemical aggressiveness, thermal cycling severity) to specific cladding technology routes, materials, and thicknesses.
3. Qualify representative clad pipe specimens under simulated CO₂ fracturing damage zone conditions, including corrosion testing in CO₂-saturated brine at elevated temperature and pressure, thermal cycling testing, and combined loading tests.
4. Integrate damage range analysis into the company's NDT planning, ensuring that inspection protocols are tailored to the specific degradation mechanisms expected within the calculated damage zone.
5. Document all qualification results in accordance with ASME Section IX, API 5CT, and applicable national standards (GB/NB) to build a comprehensive qualification database for CO₂ fracturing applications.

11. Conclusion

The calculation of CO₂ phase transition fracturing damage range and the systematic analysis of its influencing factors represent a critical technical capability that bridges formation engineering with wellbore materials engineering. For Cladding Technology Shanxi Co., Ltd., this knowledge base enables the precise specification and manufacture of clad pipe systems that meet the demanding requirements of CO₂ fracturing wellbore applications. By integrating damage range analysis with the company's three core technology routes—TIG/MIG weld overlay, hydraulic explosive bonding, and explosion welding—the organization can deliver optimized, qualified, and cost-effective clad products that extend well life, reduce operational risk, and provide measurable value to customers operating in CO₂ fracturing environments. The resulting qualification documentation, supported by rigorous testing against recognized international and national standards, establishes a defensible technical position in the specialty cladding market for unconventional well stimulation applications.