Mohr-Coulomb

The Mohr-Coulomb Criterion: A Cornerstone in Oil & Gas Engineering

The Mohr-Coulomb criterion is a fundamental concept in geotechnical and petroleum engineering, providing a framework for understanding the failure behavior of rocks and soils under stress. This criterion, named after Christian Otto Mohr and Charles Augustin de Coulomb, describes the relationship between shear stress and effective normal stress at which a material will fail.

In essence, the Mohr-Coulomb criterion establishes a failure envelope, a straight line on a plot of shear stress versus normal stress. This line represents the boundary between safe and failure states for a given material. The equation for this line is:

τ = c + σ'tan(φ)

Where:

• τ is the shear stress
• c is the cohesion, representing the material's resistance to shear failure when no normal stress is applied.
• σ' is the effective normal stress, which is the normal stress minus the pore pressure.
• φ is the angle of internal friction, representing the material's resistance to shearing due to interparticle friction.

Applications in Oil & Gas:

The Mohr-Coulomb criterion finds widespread use in various aspects of Oil & Gas operations:

• Drilling: Determining the mud weight required to prevent wellbore instability and optimize drilling operations.
• Wellbore stability: Assessing the risk of borehole collapse or fracturing based on the in-situ stresses and rock properties.
• Reservoir characterization: Understanding the strength and deformation behavior of reservoir rocks, which impacts hydrocarbon production.
• Fracturing: Predicting the pressure required to induce fractures in formations, vital for hydraulic fracturing techniques.
• Geomechanics: Modeling the mechanical behavior of subsurface formations under various conditions, crucial for reservoir simulation and well planning.

The Plot:

The Mohr-Coulomb failure envelope is typically plotted on a graph with shear stress (τ) on the y-axis and normal stress (σ') on the x-axis. The slope of the line is determined by the angle of internal friction (φ), while the intercept on the y-axis represents the cohesion (c).

Key Points:

• The Mohr-Coulomb criterion provides a simplified representation of material behavior and is more accurate for brittle materials like rocks.
• It does not account for strain hardening or other complex material behaviors.
• The values of cohesion (c) and angle of internal friction (φ) are material-specific and can vary significantly depending on factors like rock type, mineralogy, and pore pressure.
• While a powerful tool, the Mohr-Coulomb criterion requires careful calibration and validation with experimental data for reliable predictions in real-world scenarios.

Conclusion:

The Mohr-Coulomb criterion plays a crucial role in the Oil & Gas industry by providing a framework to understand and predict the behavior of rocks and soils under stress. By understanding the failure envelope defined by this criterion, engineers can optimize drilling, wellbore stability, and reservoir development strategies, ultimately leading to safer and more efficient operations.