A fully coupled transient wellbore–fracture model for analyzing fracture stability during tripping out deep gas reservoirs

Technical Summary: A Fully Coupled Transient Wellbore–Fracture Model for Analyzing Fracture Stability During Tripping Out Deep Gas Reservoirs

Problem Statement
Lost circulation induced by the swab effect during tripping-out operations represents a critical risk in drilling fractured gas reservoirs, particularly in deep formations where pressure windows are narrow. As the drill string moves upward, it induces a transient reduction in bottomhole pressure (swab pressure). In fractured formations, this pressure drop increases the effective stress on fracture walls, promoting fracture closure and potentially triggering fluid loss. While existing research has advanced transient wellbore pressure modeling and fracture mechanics separately, a unified framework capturing the bidirectional feedback between wellbore pressure transients and dynamic fracture deformation has been lacking. Current approaches often treat fractures as static boundaries or use sequential coupling, failing to account for the real-time interplay where fracture deformation alters flow capacity, which in turn modifies pressure propagation.

Methodology
The authors developed a fully coupled, transient numerical model integrating wellbore hydraulics with fracture fluid flow and elastic deformation. The physical system is idealized as a vertical fracture intersecting a wellbore, where the upward movement of the drill string reduces wellbore pressure, inducing elastic closure of the fracture.

• Governing Equations: The model couples the wellbore mass balance equation (accounting for fluid compressibility and piston displacement) with the fracture fluid flow equation (governed by the cubic law for laminar flow between parallel plates) and the fracture deformation constitutive model (relating width to effective stress via fracture normal stiffness).
• Coupling Mechanism: The system is solved via a fully implicit numerical scheme. At the wellbore–fracture interface, the model enforces pressure continuity and mass flux continuity. The flow rate from the fracture acts as a source/sink term in the wellbore mass balance, while the wellbore pressure serves as the boundary condition for fracture pressure diffusion.
• Numerical Solution: A fully implicit (backward) Euler scheme is employed for temporal discretization to ensure stability. The resulting nonlinear system of equations is solved iteratively using the Newton–Raphson method. The Jacobian matrix is constructed analytically to handle the strong coupling between pressure and fracture width.
• Validation: The model was validated against field data from a deep shale gas well (Well Gao-X) in the Sichuan Basin, targeting the Dengying Formation. The simulation results showed good agreement with measured bottomhole pressures, with relative errors ranging from 5.7% to 6.5%.

Key Contributions and Results
The study provides a quantitative basis for understanding how operational parameters and intrinsic formation properties interact to influence fracture stability.

1. Dominance of Tripping Speed: Parametric analysis identifies tripping speed as the primary operational control variable. Increasing speed from 0.3 m/s to 1.5 m/s causes a wellbore pressure drop of 7.6 MPa, resulting in a 78% reduction in fracture width (from 0.36 mm to 0.08 mm). A critical speed threshold of approximately 1.4 m/s was identified, beyond which fracture closure accelerates markedly.
2. Depth-Dependent Sensitivity: The risk of fracture closure is strongly depth-dependent. At a constant speed of 0.3 m/s, the closure amplitude at 5200 m depth is 3.2 times greater than at 1200 m. This is attributed to higher initial hydrostatic pressure and greater attenuation of pressure waves over longer propagation paths in deeper sections.
3. Drill String Design Impact: The drill pipe annular ratio (ratio of drill string outer diameter to wellbore inner diameter) significantly intensifies the "piston effect." Increasing this ratio from 0.65 to 0.68 reduces fracture width by 18%. In contrast, the annular ratio of the Bottom Hole Assembly (BHA) has a marginal effect.
4. Role of Fluid Viscosity: Drilling fluid viscosity plays a minor, secondary role. Increasing viscosity from 0.025 to 0.035 Pa·s results in only a 5.6% reduction in fracture width, indicating that viscosity optimization alone is insufficient for mitigating lost circulation risks compared to speed and annular design control.
5. Intrinsic Formation Property: Fracture normal stiffness is identified as the governing intrinsic property. Doubling the stiffness from 50 to 100 GPa/m increases fracture width by 19% under the same pressure drop. This explains why different formations exhibit divergent stability responses under identical drilling operations.

Significance and Engineering Implications
The paper claims that its primary contribution lies not in inventing new physical equations, but in the successful integration of established wellbore and fracture mechanics into a fully coupled, transient framework. This approach captures bidirectional feedback mechanisms that previous decoupled or sequentially coupled models neglect.

The study translates these mechanistic insights into specific engineering guidelines for deep gas reservoirs:

• Depth-Specific Protocols: Implement segmented tripping strategies with reduced speed limits (e.g., ≤0.3 m/s for depths >4000 m, and ≤0.2 m/s for depths >5000 m) when approaching fractured intervals.
• Design Optimization: Prioritize optimizing the drill pipe annular ratio (targeting ≤0.65) to minimize the piston effect, rather than relying solely on fluid viscosity adjustments.
• Pre-Drill Characterization: Incorporate fracture normal stiffness estimation (via DFIT, acoustic logs, or core data) into geomechanical assessments to predict formation-specific stability risks.
• Risk Management: The proposed framework supports a shift from empirical, one-size-fits-all practices to predictive, formation-specific risk management, enabling more reliable assessment of lost circulation potential in complex gas well operations.

The authors acknowledge limitations, including the assumption of Newtonian fluids and isolated planar fractures, noting that future work should address non-Newtonian rheology, complex fracture networks, thermal effects, and multiphase flow to further refine the model for deep gas reservoir applications.