Mohr-Coulomb

Test Your Knowledge

Quiz: The Mohr-Coulomb Criterion

Instructions: Choose the best answer for each question.

1. What does the Mohr-Coulomb criterion describe?

a) The relationship between stress and strain in a material b) The temperature at which a material will melt c) The relationship between shear stress and effective normal stress at failure d) The rate of deformation of a material under load

2. Which of the following is NOT a factor influencing the Mohr-Coulomb failure envelope?

a) Cohesion b) Angle of internal friction c) Poisson's ratio d) Effective normal stress

3. In the Mohr-Coulomb equation (τ = c + σ'tan(φ)), what does "c" represent?

a) Shear stress b) Effective normal stress c) Angle of internal friction d) Cohesion

4. How is the Mohr-Coulomb criterion used in drilling operations?

a) To determine the optimal drilling fluid density b) To calculate the rate of penetration c) To predict the formation temperature d) To estimate the drilling cost

5. What is a key limitation of the Mohr-Coulomb criterion?

a) It is only applicable to ductile materials b) It does not account for strain hardening c) It is too complex to apply in practical scenarios d) It is not accurate for predicting fracture initiation

Exercise: Applying the Mohr-Coulomb Criterion

Scenario: You are working on a drilling project where the reservoir rock has a cohesion (c) of 20 MPa and an angle of internal friction (φ) of 30 degrees. The pore pressure at the drilling depth is 10 MPa.

Task:

1. Calculate the effective normal stress (σ') at a depth of 2,000 meters, assuming a density of the overburden rock of 2.5 g/cm³.
2. Use the Mohr-Coulomb equation to determine the shear stress (τ) at failure for this effective normal stress.

Note:
- Assume gravitational acceleration (g) = 9.81 m/s² - Convert units as needed.

Techniques

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

This expanded document delves deeper into the Mohr-Coulomb criterion, breaking down its application in oil and gas engineering across several key aspects.

Chapter 1: Techniques for Determining Mohr-Coulomb Parameters

Determining the cohesion (c) and angle of internal friction (φ) is crucial for applying the Mohr-Coulomb criterion effectively. Several techniques are employed to obtain these parameters, each with its own advantages and limitations:

• Direct Shear Tests: This is a common laboratory test where a soil or rock sample is subjected to a normal stress and a shear stress until failure. The shear stress at failure, along with the applied normal stress, is used to plot points on the Mohr-Coulomb failure envelope. Multiple tests at different normal stresses are needed to define the envelope. Limitations include sample disturbance and difficulty in representing in-situ stress conditions.

• Triaxial Tests: These tests subject a cylindrical sample to confining pressure (lateral stress) and axial stress. The axial stress at failure, along with the confining pressure, allows for the determination of c and φ. Triaxial tests are considered more representative of in-situ conditions than direct shear tests, but are more complex and expensive. Different types of triaxial tests (consolidated undrained, consolidated drained, etc.) provide information under various drainage conditions.

• In-situ Tests: Methods like the Pressuremeter Test and the Borehole Shear Test provide in-situ measurements of soil or rock strength parameters. These tests offer advantages in terms of representing the actual conditions in the subsurface, but are more expensive and may be less suitable for all geological formations.

• Empirical Correlations: In cases where laboratory or in-situ testing is limited, empirical correlations based on rock type, mineralogy, and other geological parameters can be used to estimate c and φ. However, these correlations should be used with caution and validated against available data whenever possible.

The accuracy of the Mohr-Coulomb parameters is heavily reliant on the quality of the testing and the representative nature of the samples. Careful sample preparation and selection, coupled with rigorous testing procedures, are vital for obtaining reliable results.

Chapter 2: Models Utilizing the Mohr-Coulomb Criterion

The Mohr-Coulomb criterion forms the basis for numerous models used in oil and gas engineering:

• Wellbore Stability Analysis: Models incorporating the Mohr-Coulomb criterion are used to predict the risk of wellbore collapse or fracturing. These models consider in-situ stresses, pore pressure, and rock properties to determine the effective stresses acting on the wellbore wall. The Mohr-Coulomb failure criterion then determines whether failure is likely to occur. Software packages commonly employ finite element methods to solve these complex stress-strain problems.

• Hydraulic Fracturing Simulations: Predicting the propagation of fractures during hydraulic fracturing requires understanding the rock's strength and fracture toughness. The Mohr-Coulomb criterion helps define the stress state at which fractures initiate and propagate. Complex models accounting for fluid flow, fracture mechanics, and the rock's mechanical properties are employed.

• Reservoir Simulation: Geomechanical models coupled with reservoir simulation can predict changes in reservoir stress and pore pressure during production or injection. These models incorporate the Mohr-Coulomb criterion to determine the potential for compaction, subsidence, or fault reactivation. This is particularly important for assessing the long-term integrity of the reservoir and surrounding formations.

• Slope Stability Analysis: In surface operations, the Mohr-Coulomb criterion is used to analyze the stability of cuttings piles, embankments, and other earth structures.

Chapter 3: Software for Mohr-Coulomb Analysis

Several software packages are available to perform Mohr-Coulomb analyses:

• ABAQUS: A comprehensive finite element analysis (FEA) software capable of simulating complex geomechanical problems, incorporating the Mohr-Coulomb criterion.

• ANSYS: Similar to ABAQUS, ANSYS provides advanced FEA capabilities for modeling geomechanical behavior.

• Rocscience Software (RS2, Slide, Dips): This suite of software is specifically designed for geotechnical and rock mechanics analyses, including wellbore stability and slope stability. They often include built-in functionality for the Mohr-Coulomb criterion.

• COMSOL Multiphysics: A powerful multiphysics simulation software, COMSOL allows coupling geomechanical models with fluid flow and other relevant physics, enabling sophisticated reservoir simulation and wellbore stability studies.

These software packages often require expertise in numerical modeling and geomechanics for effective use.

Chapter 4: Best Practices for Applying the Mohr-Coulomb Criterion

• Appropriate Material Characterization: Careful selection and testing of representative rock samples are crucial for obtaining accurate values of cohesion and angle of internal friction.

• Accurate Stress State Determination: Determining the in-situ stress state requires thorough geological and geophysical data.

• Consider Pore Pressure Effects: Pore pressure significantly influences effective stress and therefore the likelihood of failure. Accurate pore pressure prediction is crucial.

• Model Validation: Comparing model predictions with field data (e.g., drilling data, wellbore stability observations) is essential for validating the model and ensuring its reliability.

• Understanding Limitations: The Mohr-Coulomb criterion is a simplified model. It is important to understand its limitations and avoid applying it to scenarios where more sophisticated constitutive models may be necessary (e.g., situations involving significant plastic deformation).

• Sensitivity Analysis: Conduct sensitivity analyses to assess the impact of uncertainties in input parameters on the model predictions.

Chapter 5: Case Studies of Mohr-Coulomb Applications in Oil & Gas

This chapter would include specific examples of how the Mohr-Coulomb criterion has been applied to real-world oil and gas projects. These could include:

• Case Study 1: Analysis of wellbore instability during drilling, including the determination of optimal mud weight based on Mohr-Coulomb analysis. The case study would detail the data collected, the model used, and the results obtained.

• Case Study 2: Prediction of fracture initiation pressure during hydraulic fracturing, showcasing the application of Mohr-Coulomb failure criterion within a larger fracture propagation model.

• Case Study 3: Assessment of reservoir compaction and subsidence using a coupled geomechanical-reservoir simulation model, where the Mohr-Coulomb criterion defines the failure behavior of the reservoir rock.

Each case study would highlight the challenges faced, the methodologies employed, and the lessons learned. These real-world examples would demonstrate the practical significance of the Mohr-Coulomb criterion in the oil and gas industry.