Supercharge, Invasion, and Mudcake Growth in Downhole Applications

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Mysterious «supercharge effects,» encountered in formation testing pressure transient analysis, and reservoir invasion, mudcake growth, dynamic filtration, stuck-pipe remediation, and so on, are often discussed in contrasting petrophysical versus drilling contexts. However, these effects are physically coupled and intricately related. The authors focus on a comprehensive formulation, provide solutions for different specialized limits, and develop applications that illustrate how the central ideas can be used in seemingly unrelated disciplines. This approach contributes to a firm understanding of logging and drilling principles. Fortran source code, furnished where applicable, is listed together with recently developed software applications and conveniently summarized throughout the book. In addition, common (incorrect) methods used in the industry are re-analyzed and replaced with more accurate models, which are then used to address challenging field objectives.
Sophisticated mathematics is explained in «down to earth» terms, but empirical validations, in this case through Catscan experiments, are used to «keep predictions honest.» Similarly, early-time, low mobility, permeability prediction models used in formation testing, several invented by one of the authors, are extended to handle supercharge effects in overbalanced drilling and near-well pressure deficits encountered in underbalanced drilling. These methods are also motivated by reality. For instance, overpressures of 2,000 psi and underpressures near 500 psi are routinely reported in field work, thus imparting a special significance to the methods reported in the book.
This new volume discusses old problems and modern challenges, formulates and develops advanced models applicable to both drilling and petrophysical objectives. The presentation focuses on central unifying physical models which are carefully formulated and mathematically solved. The wealth of applications examples and supporting software discussed provides readers with a unified focus behind daily work activities, emphasizing common features and themes rather than unrelated methods and work flows. This comprehensive book is «must» reading for every petroleum engineer.

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4 Chapter 4Figure 4.1a. Supercharge problem in formation testing.Figure 4.1b. Linear flow Catscans, thin dark mudcake at center of core and invas...Figure 4.1c. Stuck tool removal mechanism.Figure 4.2. Exact lineal invasion solution (Chin et al., 1986).Figure 4.3. Any surface f(x,y,z,t) = 0 in a reservoir.Figure 4.4. Lineal flow.Figure 4.5. Cylindrical radial flow.Figure 4.6. Spherical flow at the drillbit.Figure 4.7. Simple laboratory mudcake buildup.Figure 4.8. Simple linear flow of two dissimilar fluids.Figure 4.9. Three-layer lineal flow.Figure 4.10. Three-layer radial flow.Figure 4.11. Lineal flow.Figure 4.12. Radial flow test, 15 ppg mud, Δp = 150 psi.Figure 4.13. Radial mudcake growth on filter paper.Figure 4.14. Radial versus lineal mudcake theory.Figure 4.15. Radial invasion without mudcake.Figure 4.16. Numerical results, forward invasion simulation.Figure 4.17. Numerical results, inverse invasion simulation.Figure 4.18. Numerical results, forward invasion simulation.Figure 4.19. Numerical results, inverse invasion simulation.

5 Chapter 5Figure 5.1. Finite difference discretizations.Figure 5.2. Tridiagonal equation solver.Figure 5.3a. Fortran source code (Example 5-1).Figure 5.3b. Numerical results (Example 5-1).Figure 5.3c. Numerical results (Example 5-1).Figure 5.4a. Fortran source code (Example 5-2).Figure 5.4b. Numerical results (Example 5-2).Figure 5.4c. Numerical results (Example 5-2).Figure 5.5a. Numerical results (Example 5-3).Figure 5.5b. Numerical results (Example 5-3).Figure 5.6a. Fortran source code (Example 5-4).Figure 5.6b. Numerical results (Example 5-4).Figure 5.7. Gas displacement by liquid.Figure 5.8a. Fortran source code (Example 5-6).Figure 5.8b. Numerical results (Example 5-6).Figure 5.8c. Numerical results (Example 5-6).Figure 5.9a. Three-layer lineal flow problem.Figure 5.9b. Fortran source code (Example 5-7).Figure 5.9c. Numerical results (Example 5-7).Figure 5.10. Pressure in lineal core.Figure 5.11. Diffusive front motion.Figure 5.12a. A diffusing lineal flow.Figure 5.12b. An “un-diffusing” lineal flow.Figure 5.13a. A diffusing radial flow.Figure 5.13b. An “undiffusing” radial flow.Figure 5.14. Nonlinear saturation solver.Figure 5.15a. Zero mud filtrate influx.Figure 5.15b. Very slow constant injection rate.Figure 5.15c. Q = 1, constant rate, high inertia flow.Figure 5.15d. Q = 2, constant rate, high inertia flow.Figure 5.15e. Q = 3, constant rate, high inertia flow.Figure 5.16. Mudcake-dominated invasion.Figure 5.17a. High filtration rate mudcake model (α = 1).Figure 5.17b. Very high filtration rate mudcake model (α = 5).Figure 5.17c. Very slow filtration rate model (α = 0.001).Figure 5.18. “Un-shocking” a steep gradient.Figure 5.19a. Forward shock formation.Figure 5.19b. Backward shock migration.Figure 5.20. Implicit pressure – implicit saturation solver.Figure 5.21a. Early time saturation and pressure.Figure 5.21b. Intermediate time saturation and pressure.Figure 5.21c. Late time saturation and pressure.Figure 5.22. Two-layer mudcake-rock, immiscible flow model.Figure 5.23a. Early time solution.Figure 5.23b. Intermediate time solution.Figure 5.23c. Late time solution.Figure 5.24a. Early time solution.Figure 5.24b. Intermediate time solution.Figure 5.24c. Late time solution.Figure 5.25a. COSL formation testing software platform.Figure 5.25b. COSL formation testing software platform.Figure 5.25c. COSL formation testing software platform.Figure 5.25d. COSL formation testing software platform.Figure 5.25e. COSL formation testing software platform.

Guide

1 Cover

2 Table of Contents

3 Title Page

4 Copyright

5 Preface

6 Acknowledgements

7 Begin Reading

8 Cumulative References

9 Index

10 About the Authors

11 Also of Interest

12 End User License Agreement

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