Hydraulic fracturing analysis in fluid-saturated porous medium.

Area of Science:

• Geomechanics
• Computational mechanics
• Porous media physics

Background:

• Fluid-driven crack propagation is crucial in geomechanics.
• Simulating hydraulic fracturing requires robust numerical methods.
• Accurate modeling of porous media behavior under fluid pressure is challenging.

Purpose of the Study:

• To develop and validate a numerical method for fluid-driven crack propagation in porous media.
• To introduce a specialized fluid pressure degree of freedom for crack simulation.
• To enhance the accuracy and efficiency of hydraulic fracturing models.

Main Methods:

• Utilizing cohesive interface elements to represent crack behavior.
• Employing Powell-Sabin B-splines for domain geometry and field variable interpolation.
• Introducing a separate fluid pressure degree of freedom within the crack.
• Developing a new least-square mapping methodology for state vector transfer during remeshing, incorporating energy balance and mass conservation constraints.

Main Results:

• Achieved smooth stress and pressure gradients across the domain due to B-spline continuity.
• Enabled direct assessment of fracture criteria at the crack tip and ensured local mass conservation.
• Demonstrated straightforward crack insertion and remeshing capabilities using triangular elements.
• Validated the accuracy of the model for free crack propagation through numerical examples, including a plate with notches.

Conclusions:

• The proposed method accurately simulates fluid-driven crack propagation in porous media.
• The use of Powell-Sabin B-splines and cohesive elements offers a robust framework for hydraulic fracturing.
• The novel remeshing technique ensures accurate state vector mapping, crucial for complex crack propagation simulations.