Computational Solid Mechanics for Oil Well Perforator Design

The following sections are included:

• Dedication
• Preface
• About the Author
• Contents

In the oil industry, a method of completing a well is to first run the casing pipe through the oil sand formation, set it below the producing horizon, and then cement it in place as shown in Fig. 1.1. Then the casing is perforated to allow the oil or gas to flow into the wellbore. Perforating is accomplished with a gun pipe equipped with shaped charges. Figure 1.1 shows the application of a typically one shaped charge per 2.54 cm in the pipe length direction. Any two-neighboring shaped charges are separated with an angle of 60, 90 or 120 degree in the azimuthal direction. The gun, a circular container that fits inside the casing, has electrically fired cartridges that discharge small high-velocity jets. These jets penetrate the casing wall, the outside cement, and the oil sand. By doing this, channels are opened up through which the oil or gas can flow into the production pipe.

The following sections are included:

• Introduction
• The Governing Equations
• Calculation of Stress Deviators at tⁿ⁺¹
• Correction of Stresses for Rigid Body Rotation During Δt
• Calculation of Pⁿ⁺¹ and ∊ⁿ⁺¹
• Calculation of Longitudinal Sound Speed
• Artificial Viscosity Used in the Two-Dimensional Lagrangian Code
• Bibliography

The following sections are included:

• Introduction
• General Description of Physical Formulation
  • The Conservation Equation for a Stress-Supporting Medium
  • Equation of State
  • Spall
• Computational Scheme
  • General Discussion
  • Summary of Calculation Procedure
  • Lagrangian Phase
  • Stress Calculation in the Plastic Regime of Flow
  • Particle Transport and Remapping
  • Computation for Spall
  • Time Step Control
  • The Logic for the Calculation Procedure
• Truncation Error Analysis
  • Mass
  • Radial Momentum
  • Axial Momentum
  • Internal Energy
  • Deviatoric Stresses
• Equivalent Plastic Strain
• FCT Applied to Second-Order PIC
  • Introduction
  • Modified Mass Transport
  • The Modified FCT Analysis
• Bibliography

The following sections are included:

• Introduction to the Equation of State
• The Mie - Grüneisen EOS and the Simple u_s, u_p Model
• The Osborne Model
• The Tillotson Equation of State
• Introduction to the Constitutive Relationship
• Quadratic Model
• Steinberg–Guinan Model
• Steinberg’s New Model
  • Program EOSGY
• High Explosive
  • Introduction
  • JWL Equation of State
  • Small Variation of JWL EOS
  • Computer Code for Two-Dimensional Programmed Burn
  • Computer Code HEDET3 for Three-Dimensional Programmed Burn
• Derivation of the Hugoniot Relations
  • Introduction
  • Conservation of Mass
  • Conservation of Momentum
  • Conservation of Energy
• The Shock-Change Equations
  • Introduction
  • The Shock-Change Equation
  • Summary of the Shock-Change Equation
• The Theoretical Spall Strength
• Bibliography

The following sections are included:

• Introduction
• Perforator B
• Perforator E
• Perforator G
• Perforator L
• Perforator M
• Perforator N
• Perforator P
• The Penetrating Characteristic of the Penetrators
  • Introduction
  • Copper Liner of a Diameter 3.5 cm
  • Perforators Described in Figs. 6 and 11 of the File EULE2D-Fig
  • Perforators Described in Figs. 16, 26 and 31 of the File EULE2D-Fig
  • Special Design of 4.3 cm Charge Diameter Shaped Charge
• Program Curve
• Plotting Programs Using MATLAB
• The Exact Dimensions of Explosive Formed Projectile and Shaped Charge
  • Copper Explosive Formed Projectile
  • Bi-conical Copper Liner Shaped Charge
  • Small Charge Diameter Conical Shaped Charge
  • Small Charge Diameter Shaped Charge with Wave Shaper
  • Non-axisymmetric Tantalum EFP Warhead
  • Copper Hemi-spherical Liner with Energetic Explosive
• Computer Programs
• Bibliography

The following sections are included:

• Introduction
• Definition of Variable and Notation
• The Governing Equation
• Equation of State
• Calculation Procedures and Finite Differences
• Two-Dimensional Lagrangian Method for Radiation Diffusion Problems
  • Introduction
  • Finite Difference Approximation for the Radiation Diffusion Equation
  • Monte Carlo Method
  • Monte Carlo Procedure
• Bibliography

The following sections are included:

• Introduction
• The REZONE Model
  • Zone and Point Model
  • The Mass Model
  • Sub-zone Definition
• A Brief Description of the Rezone Method
  • The REZONE Code
  • The Displacement Pass
  • The Expansion Pass
  • The Vertex Pass
  • The Midpoint Pass
  • The Point 8 Pass
  • The Velocity Adjustment Pass
  • The Averaging Pass
• Testing for a Rezone
  • Philosophy
  • Test Details — General Case
  • Tests on Boundaries
  • Additions to the Tests
  • Limitations on the Testing
  • Changes in Test Values
  • General Remarks
• The Displacement Pass
  • Displacement Cases for the Interior Points
  • Displacement on Boundary Points
  • The Displacement Method
  • Limitations on the Displacement Calculations
  • Remarks
• Expansion Pass
  • Introduction
  • Sub-mesh Storage
• Rezone Method — General Case
  • Preparation — Definition of the System
  • Find Orientation of the System
  • The Rezone Process
  • The Rezone Cases
  • Mapping Other Quantities
  • Intersection Calculation
• Rezone Method — Boundary Cases
  • Constant R, Constant Z, and Slide Angle
  • Free Surface Case
  • Center of Mass Case
• The Vertex, Midpoint, Point 8, and Velocity Passes
  • Possible Cases
  • The Vertex Pass
  • The Midpoint Pass
  • The Point 8 Pass
  • The Velocity Adjustment Pass
• The Averaging Pass
  • Point Quantities
  • Zone Quantities
• Completing the Rezone
  • New Velocities
  • New Zone Mass
  • New Pressure
  • New q Terms (Artificial Viscosity)
  • Clear Flags
• Summary
• Final Remarks
• Examples
• Directed Kinetic Energy
• Bibliography

The following sections are included:

• Introduction
• Standard Methods
• Group-Collapse Coarse Mesh Re-balance
• Whole System Group-wise Re-balance
• Variable Convergence Precision and Iteration Strategies
• Test Problem and Results
• Subcritical Searches
• Implementation of α Re-balance Acceleration
• Conclusion
• Bibliography

The supplementary materials for this book is available from the website of World Scientific Publishing. The download process is described in Section A.1 below. The supplementary materials are computer programs written in Fortran for the calculation of high explosive burn time and burn distance, shear modulus and yield strength for many materials, as well as the MATLAB plotting programs for many perforators.

The following section is included:

• Index