Fracture Propagation Analysis of Limited-Entry Perforation in Horizontal Multi-Cluster Fracturing Considering Thermal Effects

Technical Summary: Fracture Propagation Analysis of Limited-Entry Perforation in Horizontal Multi-Cluster Fracturing Considering Thermal Effects

Problem Statement
The development of deep shale gas reservoirs, particularly in regions like the Wufeng-Longmaxi formation in southern Sichuan, relies heavily on long-stage multi-cluster hydraulic fracturing. However, this process faces significant challenges regarding the non-equilibrium propagation of multiple fractures. While the mechanisms of stress shadows and heterogeneous in-situ stress are understood, the specific impact of thermal effects remains unclear. Deep formations often exhibit high temperatures (exceeding 90°C), whereas injected fracturing fluids are significantly cooler. This temperature differential induces thermal stress and alters fluid properties (viscosity and filtration), potentially exacerbating the competitive extension of fracture clusters and leading to unbalanced stimulation. Previous studies have addressed thermal effects on single fractures or static systems but have not sufficiently clarified the competition laws of multi-cluster fractures under these coupled thermal-hydro-mechanical conditions.

Methodology
To address this gap, the authors developed a numerical model for non-planar fracture propagation in multi-stage, multi-cluster fracturing that incorporates thermal effects. The model integrates the following components:

• Fluid Flow: Governed by mass conservation and pressure balance in the wellbore, and Poiseuille's law within fractures. The model accounts for temperature-sensitive dynamic filtration using an exponential viscosity-temperature relationship.
• Heat Transfer: Based on the KDR model, the study calculates temperature fields in the fracture fluid, fracture walls, and formation rock. It assumes mutual independence of temperature distributions between adjacent fractures due to cluster spacing exceeding the near-fracture thermal variation zone.
• Solid Deformation: The Displacement Discontinuity Method (DDM) is employed to model rock elasticity and stress distribution, including thermal stress calculations based on rock thermal expansion coefficients.
• Fracture Propagation: The F-criterion, applicable to mixed-mode propagation, is used to determine fracture extension.
• Numerical Solution: A fully coupled implicit approach solves the thermo-hydro-mechanical (THM) system. The finite volume method discretizes fluid and energy equations within fractures, while a box-type grid and Crank-Nicolson scheme handle formation heat exchange.

The model was validated against analytical solutions for viscosity-dominated KGD fracture propagation (with and without thermal stress) and compared with existing numerical results for dual-fracture synchronous propagation.

Key Results
Simulations based on a deep shale gas well in southeastern Sichuan (formation temperature ~115.6°C) yielded the following findings:

• Impact of Temperature on Propagation: Thermal effects intensify the non-equilibrium extension of multi-cluster fractures. As formation temperature increases from 60°C to 180°C, the dimensionless length variation coefficient ($L_{cv}$) rises from 0.28 to 0.61, and the standard deviation of the transient inflow ratio ($Q_{sd}$) increases from 6.82% to 12.29%.
• Mechanism of Change: Higher formation temperatures reduce fluid viscosity, increasing fluid loss and shortening fracture lengths. Simultaneously, enhanced heat exchange creates rapid temperature drops near fractures, generating tensile thermal stress that increases fracture width. This increased width amplifies stress shadow effects, further hindering balanced fluid intake.
• Threshold for Thermal Effects: The study indicates that thermal effects are negligible for formations below 60°C (shallow depths). However, when underground temperatures exceed 90°C, thermal effects become a critical factor in fracture design.
• Perforation Optimization:
  • Limited-Entry Strategy: Reducing the number of perforations increases perforation friction, which can counteract non-uniform propagation caused by stress heterogeneity, stress shadows, and thermal effects.
  • Friction Requirements: To achieve balanced propagation, perforation friction must be maintained between 3.3 MPa and 7.5 MPa. Without thermal effects, 1.6 MPa friction allows initiation against an additional 1 MPa of compressive stress, but 3.3 MPa is required for balance. With thermal effects, even higher friction is necessary.
  • Optimal Perforation Count: The optimal number of perforations decreases as Young's modulus increases and increases with pumping rate. For instance, under uniform stress with thermal effects at 12 m³/min, the optimal count drops from 10 to 8 as Young's modulus rises from 25 to 45 GPa.
• Mitigation via Pumping Rate: Increasing the pumping rate can relatively weaken the negative impact of thermal effects on balanced fluid intake, helping to stabilize the optimal perforation count across varying rock stiffness.

Significance and Claims
The paper claims that its research provides a more comprehensive reference for the design of deep shale fracturing operations. By establishing a validated THM coupling model, the study clarifies that thermal effects significantly alter the competitive propagation of multi-cluster fractures in high-temperature environments. The authors assert that ignoring these effects in deep reservoirs (T > 90°C) can lead to suboptimal stimulation designs. The study offers specific engineering guidance, demonstrating that optimizing perforation numbers and managing pumping rates are effective strategies to mitigate thermal-induced non-uniformity, thereby improving the efficiency of deep shale gas development.